1 1 0 https://doi.org/ Performance of a modular ton-scale pixel-readout liquid
argon time projection chamber Performance of a modular ton-scale pixel-readout
liquid argon time projection chamber A. Abed Abud1, B. Abi2, R. Acciarri3, M.
A. Acero4, M. R. Adames5, G. Adamov6, M. Adamowski3, D. Adams7, M. Adinolfi8,
C. Adriano9, A. Aduszkiewicz10, J. Aguilar11, B. Aimard12, F. Akbar13, K.
Allison14, S. Alonso Monsalve1,15, M. Alrashed16, A. Alton17, R. Alvarez18, T.
Alves19, H. Amar20, P. Amedo21,20, J. Anderson22, D. A. Andrade23, C.
Andreopoulos24, M. Andreotti25,26, M. P. Andrews3, F. Andrianala27, S.
Andringa28, N. Anfimov29, A. Ankowski30, M. Antoniassi5, M. Antonova20, A.
Antoshkin29, A. Aranda-Fernandez31, L. Arellano32, E. Arrieta Diaz33, M. A.
Arroyave3, J. Asaadi34, A. Ashkenazi35, D. Asner7, L. Asquith36, E. Atkin19,
D. Auguste37, A. Aurisano38, V. Aushev39, D. Autiero40, F. Azfar2, A. Back41,
H. Back42, J. J. Back43, I. Bagaturia6, L. Bagby3, N. Balashov29, S.
Balasubramanian3, P. Baldi44, W. Baldini25, J. Baldonedo45, B. Baller3, B.
Bambah46, R. Banerjee47, F. Barao28,48, G. Barenboim20, P. Barham Alzás1, G.
J. Barker43, W. Barkhouse49, G. Barr2, J. Barranco Monarca50, A. Barros5, N.
Barros28,51, D. Barrow2, J. L. Barrow52, A. Basharina-Freshville53, A.
Bashyal22, V. Basque3, C. Batchelor54, L. Bathe-Peters2, J.B.R. Battat55, F.
Battisti2, F. Bay56, M. C. Q. Bazetto9, J. L. L. Bazo Alba57, J. F. Beacom58,
E. Bechetoille40, B. Behera59, E. Belchior60, G. Bell61, L. Bellantoni3, G.
Bellettini62,63, V. Bellini64,65, O. Beltramello1, N. Benekos1, C. Benitez
Montiel20,66, D. Benjamin7, F. Bento Neves28, J. Berger67, S. Berkman68, J.
Bernal66, P. Bernardini69,70, A. Bersani71, S. Bertolucci72,73, M.
Betancourt3, A. Betancur Rodríguez74, A. Bevan75, Y. Bezawada76, A. T.
Bezerra77, T. J. Bezerra36, A. Bhat78, V. Bhatnagar79, J. Bhatt53, M.
Bhattacharjee80, M. Bhattacharya3, S. Bhuller8, B. Bhuyan80, S. Biagi81, J.
Bian44, K. Biery3, B. Bilki82,83, M. Bishai7, A. Bitadze32, A. Blake84, F. D.
Blaszczyk3, G. C. Blazey85, E. Blucher78, J. Bogenschuetz34, J. Boissevain86,
S. Bolognesi87, T. Bolton16, L. Bomben88,89, M. Bonesini88,90, C. Bonilla-
Diaz91, F. Bonini7, A. Booth75, F. Boran41, S. Bordoni1, R. Borges Merlo9, A.
Borkum36, N. Bostan83, J. Bracinik92, D. Braga3, B. Brahma93, D. Brailsford84,
F. Bramati88, A. Branca88, A. Brandt34, J. Bremer1, C. Brew94, S. J. Brice3,
V. Brio64, C. Brizzolari88,90, C. Bromberg68, J. Brooke8, A. Bross3, G.
Brunetti88,90, M. Brunetti43, N. Buchanan67, H. Budd13, J. Buergi95, D.
Burgardt96, S. Butchart36, G. Caceres V.76, I. Cagnoli72,73, T. Cai47, R.
Calabrese25,26, J. Calcutt97, M. Calin98, L. Calivers95, E. Calvo18, A.
Caminata71, A. F. Camino99, W. Campanelli28, A. Campani71,100, A. Campos
Benitez101, N. Canci102, J. Capó20, I. Caracas103, D. Caratelli104, D.
Carber67, J. M. Carceller1, G. Carini7, B. Carlus40, M. F. Carneiro7, P.
Carniti88, I. Caro Terrazas67, H. Carranza34, N. Carrara76, L. Carroll16, T.
Carroll105, A. Carter106, E. Casarejos45, D. Casazza25, J. F. Castaño
Forero107, F. A. Castaño108, A. Castillo109, C. Castromonte110, E. Catano-
Mur111, C. Cattadori88, F. Cavalier37, F. Cavanna3, S. Centro112, G. Cerati3,
C. Cerna113, A. Cervelli72, A. Cervera Villanueva20, K. Chakraborty114, S.
Chakraborty115, M. Chalifour1, A. Chappell43, N. Charitonidis1, A.
Chatterjee114, H. Chen7, M. Chen44, W. C. Chen116, Y. Chen30, Z. Chen-
Wishart106, D. Cherdack10, C. Chi117, R. Chirco23, N. Chitirasreemadam62,63,
K. Cho118, S. Choate85, D. Chokheli6, P. S. Chong119, B. Chowdhury22, D.
Christian3, A. Chukanov29, M. Chung120, E. Church42, M. F. Cicala53, M.
Cicerchia112, V. Cicero72,73, R. Ciolini62, P. Clarke54, G. Cline11, T. E.
Coan121, A. G. Cocco102, J. A. B. Coelho122, A. Cohen122, J. Collazo45, J.
Collot123, E. Conley124, J. M. Conrad52, M. Convery30, S. Copello71, P.
Cova125,126, C. Cox106, L. Cremaldi127, L. Cremonesi75, J. I. Crespo-Anadón18,
M. Crisler3, E. Cristaldo88,66, J. Crnkovic3, G. Crone53, R. Cross43, A.
Cudd14, C. Cuesta18, Y. Cui128, F. Curciarello129, D. Cussans8, J. Dai123, O.
Dalager44, R. Dallavalle122, W. Dallaway116, H. da Motta130, Z. A. Dar111, R.
Darby36, L. Da Silva Peres131, Q. David40, G. S. Davies127, S. Davini71, J.
Dawson122, R. De Aguiar9, P. De Almeida9, P. Debbins83, I. De Bonis12, M. P.
Decowski132,133, A. de Gouvêa134, P. C. De Holanda9, I. L. De Icaza Astiz36,
P. De Jong132,133, P. Del Amo Sanchez12, A. De la Torre18, G. De Lauretis40,
A. Delbart87, D. Delepine50, M. Delgado88,90, A. Dell’Acqua1, G. Delle
Monache129, N. Delmonte125,126, P. De Lurgio22, R. Demario68, G. De Matteis69,
J. R. T. de Mello Neto131, D. M. DeMuth135, S. Dennis136, C. Densham94, P.
Denton7, G. W. Deptuch7, A. De Roeck1, V. De Romeri20, J. P. Detje136, J.
Devine1, R. Dharmapalan137, M. Dias138, A. Diaz139, J. S. Díaz41, F. Díaz57,
F. Di Capua102,140, A. Di Domenico141,142, S. Di Domizio71,100, S. Di Falco62,
L. Di Giulio1, P. Ding3, L. Di Noto71,100, E. Diociaiuti129, C. Distefano81,
R. Diurba95, M. Diwan7, Z. Djurcic22, D. Doering30, S. Dolan1, F. Dolek101, M.
J. Dolinski143, D. Domenici129, L. Domine30, S. Donati62,63, Y. Donon1, S.
Doran144, D. Douglas30, T.A. Doyle145, A. Dragone30, F. Drielsma30, L.
Duarte138, D. Duchesneau12, K. Duffy2,3, K. Dugas44, P. Dunne19, B. Dutta146,
H. Duyang147, D. A. Dwyer11, A. S. Dyshkant85, S. Dytman99, M. Eads85, A.
Earle36, S. Edayath144, D. Edmunds68, J. Eisch3, P. Englezos148, A.
Ereditato78, T. Erjavec76, C. O. Escobar3, J. J. Evans32, E. Ewart41, A. C.
Ezeribe149, K. Fahey3, L. Fajt1, A. Falcone88,90, M. Fani’86, C. Farnese150,
S. Farrell151, Y. Farzan152, D. Fedoseev29, J. Felix50, Y. Feng144, E.
Fernandez-Martinez153, G. Ferry37, L. Fields154, P. Filip155, A. Filkins156,
F. Filthaut132,157, R. Fine86, G. Fiorillo102,140, M. Fiorini25,26, S.
Fogarty67, W. Foreman23, J. Fowler124, J. Franc158, K. Francis85, D. Franco78,
J. Franklin159, J. Freeman3, J. Fried7, A. Friedland30, S. Fuess3, I. K.
Furic59, K. Furman75, A. P. Furmanski160, R. Gaba79, A. Gabrielli72,73, A. M.
Gago57, F. Galizzi88, H. Gallagher161, A. Gallas37, N. Gallice7, V. Galymov40,
E. Gamberini1, T. Gamble149, F. Ganacim5, R. Gandhi162, S. Ganguly3, F.
Gao104, S. Gao7, D. Garcia-Gamez163, M. Á. García-Peris20, F. Gardim77, S.
Gardiner3, D. Gastler164, A. Gauch95, J. Gauvreau165, P. Gauzzi141,142, S.
Gazzana129, G. Ge117, N. Geffroy12, B. Gelli9, S. Gent166, L. Gerlach7, Z.
Ghorbani-Moghaddam71, T. Giammaria25,26, D. Gibin112,150, I. Gil-Botella18, S.
Gilligan97, A. Gioiosa62, S. Giovannella129, C. Girerd40, A. K. Giri93, C.
Giugliano25, V. Giusti62, D. Gnani11, O. Gogota39, S. Gollapinni86, K.
Gollwitzer3, R. A. Gomes167, L. V. Gomez Bermeo109, L. S. Gomez Fajardo109, F.
Gonnella92, D. Gonzalez-Diaz21, M. Gonzalez-Lopez153, M. C. Goodman22, S.
Goswami114, C. Gotti88, J. Goudeau60, E. Goudzovski92, C. Grace11, E.
Gramellini32, R. Gran168, E. Granados50, P. Granger122, C. Grant164, D. R.
Gratieri169,9, G. Grauso102, P. Green2, S. Greenberg170,11, J. Greer8, W. C.
Griffith36, F. T. Groetschla1, K. Grzelak171, L. Gu84, W. Gu7, V. Guarino22,
M. Guarise25,26, R. Guenette32, E. Guerard37, M. Guerzoni72, D. Guffanti88,90,
A. Guglielmi150, B. Guo147, Y. Guo145, A. Gupta30, V. Gupta132,133, G.
Gurung34, D. Gutierrez172, P. Guzowski32, M. M. Guzzo9, S. Gwon173, A.
Habig168, H. Hadavand34, L. Haegel40, R. Haenni95, L. Hagaman174, A. Hahn3, J.
Haiston175, J. Hakenmueller124, T. Hamernik3, P. Hamilton19, J. Hancock92, F.
Happacher129, D. A. Harris47,3, J. Hartnell36, T. Hartnett94, J. Harton67, T.
Hasegawa176, C. Hasnip2, R. Hatcher3, K. Hayrapetyan75, J. Hays75, E.
Hazen164, M. He10, A. Heavey3, K. M. Heeger174, J. Heise177, S. Henry13, M. A.
Hernandez Morquecho23, K. Herner3, V. Hewes38, A. Higuera151, C.
Hilgenberg160, S. J. Hillier92, A. Himmel3, E. Hinkle78, L.R. Hirsch5, J.
Ho178, J. Hoff3, A. Holin94, T. Holvey2, E. Hoppe42, S. Horiuchi101, G. A.
Horton-Smith16, M. Hostert160, T. Houdy37, B. Howard3, R. Howell13, I.
Hristova94, M. S. Hronek3, J. Huang76, R.G. Huang11, Z. Hulcher30, M.
Ibrahim179, G. Iles19, N. Ilic116, A. M. Iliescu129, R. Illingworth3, G.
Ingratta72,73, A. Ioannisian180, B. Irwin160, L. Isenhower181, M. Ismerio
Oliveira131, R. Itay30, C.M. Jackson42, V. Jain182, E. James3, W. Jang34, B.
Jargowsky44, D. Jena3, I. Jentz105, X. Ji7, C. Jiang183, J. Jiang145, L.
Jiang101, A. Jipa98, F. R. Joaquim28,48, W. Johnson175, C. Jollet113, B.
Jones34, R. Jones149, D. José Fernández21, N. Jovancevic184, M. Judah99, C. K.
Jung145, T. Junk3, Y. Jwa30,117, M. Kabirnezhad19, A. C. Kaboth106,94, I.
Kadenko39, I. Kakorin29, A. Kalitkina29, D. Kalra117, M. Kandemir185, D. M.
Kaplan23, G. Karagiorgi117, G. Karaman83, A. Karcher11, Y. Karyotakis12, S.
Kasai186, S. P. Kasetti60, L. Kashur67, I. Katsioulas92, A. Kauther85, N.
Kazaryan180, L. Ke7, E. Kearns164, P.T. Keener119, K.J. Kelly1, E. Kemp9, O.
Kemularia6, Y. Kermaidic37, W. Ketchum3, S. H. Kettell7, M. Khabibullin187, N.
Khan19, A. Khotjantsev187, A. Khvedelidze6, D. Kim146, J. Kim13, B. King3, B.
Kirby117, M. Kirby7, A. Kish3, J. Klein119, J. Kleykamp127, A. Klustova19, T.
Kobilarcik3, L. Koch103, K. Koehler105, L. W. Koerner10, D. H. Koh30, L.
Kolupaeva29, D. Korablev29, M. Kordosky111, T. Kosc123, U. Kose1, V. A.
Kostelecký41, K. Kothekar8, I. Kotler143, M. Kovalcuk155, V. Kozhukalov29, W.
Krah132, R. Kralik36, M. Kramer11, L. Kreczko8, F. Krennrich144, I. Kreslo95,
T. Kroupova119, S. Kubota32, M. Kubu1, Y. Kudenko187, V. A. Kudryavtsev149, G.
Kufatty188, S. Kuhlmann22, S. Kulagin187, J. Kumar137, P. Kumar149, S.
Kumaran44, P. Kunze12, J. Kunzmann95, R. Kuravi11, N. Kurita30, C. Kuruppu147,
V. Kus158, T. Kutter60, J. Kvasnicka155, T. Labree85, T. Lackey3, A.
Lambert11, B. J. Land119, C. E. Lane143, N. Lane32, K. Lang189, T.
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Lasorak19, D. Last119, A. Laudrain103, A. Laundrie105, G. Laurenti72, E.
Lavaut37, A. Lawrence11, P. Laycock7, I. Lazanu98, M. Lazzaroni125,190, T.
Le161, S. Leardini21, J. Learned137, T. LeCompte30, C. Lee3, V. Legin39, G.
Lehmann Miotto1, R. Lehnert41, M. A. Leigui de Oliveira191, M. Leitner11, D.
Leon Silverio175, L. M. Lepin188,32, J.-Y Li54, S. W. Li76, Y. Li7, H. Liao16,
C. S. Lin11, D. Lindebaum8, S. Linden7, R. A. Lineros91, J. Ling192, A.
Lister105, B. R. Littlejohn23, H. Liu7, J. Liu44, Y. Liu78, S. Lockwitz3, M.
Lokajicek155, I. Lomidze6, K. Long19, T. V. Lopes77, J.Lopez108, I. López de
Rego18, N. López-March20, T. Lord43, J. M. LoSecco154, W. C. Louis86, A.
Lozano Sanchez143, X.-G. Lu43, K.B. Luk193,170, B. Lunday119, X. Luo104, E.
Luppi25,26, J. Maalmi37, D. MacFarlane30, A. A. Machado9, P. Machado3, C. T.
Macias41, J. R. Macier3, M. MacMahon53, A. Maddalena194, A. Madera1, P.
Madigan170,11, S. Magill22, C. Magueur37, K. Mahn68, A. Maio28,51, A.
Major124, K. Majumdar24, M. Man116, R. C. Mandujano44, J. Maneira28,51, S.
Manly13, A. Mann161, K. Manolopoulos94, M. Manrique Plata41, S. Manthey
Corchado18, V. N. Manyam7, M. Marchan3, A. Marchionni3, W. Marciano7, D.
Marfatia137, C. Mariani101, J. Maricic137, F. Marinho195, A. D. Marino14, T.
Markiewicz30, F. Das Chagas Marques9, C. Marquet113, D. Marsden32, M.
Marshak160, C. M. Marshall13, J. Marshall43, L. Martina69, J. Martín-Albo20,
N. Martinez16, D.A. Martinez Caicedo 175, F. Martínez López75, P. Martínez
Miravé20, S. Martynenko7, V. Mascagna88, C. Massari88, A. Mastbaum148, F.
Matichard11, S. Matsuno137, G. Matteucci102,140, J. Matthews60, C. Mauger119,
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McAskill55, N. McConkey53, K. S. McFarland13, C. McGrew145, A. McNab32, L.
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Messier41, S. Metallo160, J. Metcalf161,52, W. Metcalf60, M. Mewes41, H.
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L. Morescalchi62, D. Moretti88, R. Moretti88, C. Morris10, C. Mossey3, M.
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J. Pasternak19, C. Patrick54,53, L. Patrizii72, R. B. Patterson139, T.
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Segreto9, A. Selyunin29, C. R. Senise138, J. Sensenig119, M. H. Shaevitz117,
P. Shanahan3, P. Sharma79, R. Kumar208, K. Shaw36, T. Shaw3, K. Shchablo40, J.
Shen119, C. Shepherd-Themistocleous94, A. Sheshukov29, W. Shi145, S. Shin209,
S. Shivakoti96, I. Shoemaker101, D. Shooltz68, R. Shrock145, B. Siddi25, M.
Siden67, J. Silber11, L. Simard37, J. Sinclair30, G. Sinev175, Jaydip
Singh202, J. Singh202, L. Singh210, P. Singh75, V. Singh210, S. Singh
Chauhan79, R. Sipos1, C. Sironneau122, G. Sirri72, K. Siyeon173, K.
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Ifft165, M. Soares Nunes3, H. Sobel44, M. Soderberg156, S. Sokolov29, C. J.
Solano Salinas211,110, S. Söldner-Rembold32, S.R. Soleti11, N. Solomey96, V.
Solovov28, W. E. Sondheim86, M. Sorel20, A. Sotnikov29, J. Soto-Oton20, A.
Sousa38, K. Soustruznik212, F. Spinella62, J. Spitz213, N. J. C. Spooner149,
K. Spurgeon156, D. Stalder66, M. Stancari3, L. Stanco150,112, J. Steenis76, R.
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B. Stillwell78, J. Stock175, F. Stocker1, T. Stokes60, M. Strait160, T.
Strauss3, L. Strigari146, A. Stuart31, J. G. Suarez74, J. Subash92, A.
Surdo69, L. Suter3, C. M. Sutera64,65, K. Sutton139, Y. Suvorov102,140, R.
Svoboda76, S. K. Swain214, B. Szczerbinska215, A. M. Szelc54, A. Sztuc53, A.
Taffara62, N. Talukdar147, J. Tamara107, H. A. Tanaka30, S. Tang7, N.
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J. Tena Vidal35, P. Tennessen11,56, M. Tenti72, K. Terao30, F. Terranova88,90,
G. Testera71, T. Thakore38, A. Thea94, A. Thiebault37, S. Thomas156, A.
Thompson146, C. Thorn7, S. C. Timm3, E. Tiras185,83, V. Tishchenko7, N.
Todorović184, L. Tomassetti25,26, A. Tonazzo122, D. Torbunov7, M. Torti88, M.
Tortola20, F. Tortorici64,65, N. Tosi72, D. Totani104, M. Toups3, C.
Touramanis24, D. Tran10, R. Travaglini72, J. Trevor139, E. Triller68, S.
Trilov8, J. Truchon105, D. Truncali141,142, W. H. Trzaska218, Y. Tsai44, Y.-T.
Tsai30, Z. Tsamalaidze6, K. V. Tsang30, N. Tsverava6, S. Z. Tu183, S.
Tufanli1, C. Tunnell151, J. Turner159, M. Tuzi20, J. Tyler16, E. Tyley149, M.
Tzanov60, M. A. Uchida136, J. Ureña González20, J. Urheim41, T. Usher30, H.
Utaegbulam13, S. Uzunyan85, M. R. Vagins219,44, P. Vahle111, S. Valder36, G.
A. Valdiviesso77, E. Valencia50, R. Valentim138, Z. Vallari139, E. Vallazza88,
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S. Westerdale128, M. Wetstein144, K. Whalen94, J. Whilhelmi174, A. White34, A.
White174, L. H. Whitehead136, D. Whittington156, M. J. Wilking160, A.
Wilkinson53, C. Wilkinson11, F. Wilson94, R. J. Wilson67, P. Winter22, W.
Wisniewski30, J. Wolcott161, J. Wolfs13, T. Wongjirad161, A. Wood10, K.
Wood11, E. Worcester7, M. Worcester7, M. Wospakrik3, K. Wresilo136, C. Wret13,
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Xiotidis19, B. Yaeggy38, N. Yahlali20, E. Yandel104, K. Yang2, T. Yang3, A.
Yankelevich44, N. Yershov187, K. Yonehara3, T. Young49, B. Yu7, H. Yu7, J.
Yu34, Y. Yu23, W. Yuan54, R. Zaki47, J. Zalesak155, L. Zambelli12, B.
Zamorano163, A. Zani125, O. Zapata108, L. Zazueta156, G. P. Zeller3, J.
Zennamo3, K. Zeug105, C. Zhang7, S. Zhang41, M. Zhao7, E. Zhivun7, E. D.
Zimmerman14, S. Zucchelli72,73, J. Zuklin155, V. Zutshi85, R. Zwaska3, and On
behalf of the DUNE Collaboration yes In memory of our colleague, Dr. Davide
Salvatore Porzio, who is no longer with us.

###### Abstract

The Module-0 Demonstrator is a single-phase 600 kg liquid argon time
projection chamber operated as a prototype for the DUNE liquid argon near
detector. Based on the ArgonCube design concept, Module-0 features a novel
80k-channel pixelated charge readout and advanced high-coverage photon
detection system. In this paper, we present an analysis of an eight-day data
set consisting of 25 million cosmic ray events collected in the spring of
2021. We use this sample to demonstrate the imaging performance of the charge
and light readout systems as well as the signal correlations between the two.
We also report argon purity and detector uniformity measurements, and provide
comparisons to detector simulations.

##  1 Introduction

Charge readout in liquid argon time projection chambers (LArTPCs) has
traditionally been accomplished via a set of projective wire planes, as
successfully demonstrated e.g. in the ICARUS Amerio et al. (2004), ArgoNeuT
Anderson et al. (2012), MicroBooNE Acciarri et al. (2017) and ProtoDUNE-SP Abi
et al. (2020); Abud et al. (2022) experiments, and as planned for the first
large detector module of the DUNE experiment currently in preparation at the
Sanford Underground Research Facility (SURF) underground laboratory in South
Dakota Abi et al. (2020). However, this approach leads to inherent ambiguities
in the 3D reconstruction of charge information that present serious challenges
for LArTPC-based near detectors, where a high rate of neutrino interactions
and an associated high-intensity muon flux cannot be avoided. In particular,
3D reconstruction becomes limited by overlap of charge clusters in one or more
projections, and the unique association of deposited charge to single
interactions becomes intractable.

To overcome event pile-up, a novel approach has been proposed and is being
developed for the LArTPC of the Near Detector (ND) complex of the DUNE
experiment, close to the neutrino source at Fermilab. This technology
implements three main innovations compared to traditional wire-based LArTPCs:
a pixelated charge readout enabling true 3D reconstruction, a high-performance
light readout system providing fast and efficient detection of scintillation
light, and segmentation into optically isolated regions. By achieving a low
signal occupancy in both readout systems, the segmentation enables efficient
reconstruction and unambiguous matching of charge and light signals.

This paper describes the first tonne-scale prototype of this technology,
referred to as Module-0, and its performance as evaluated with a large cosmic
ray data set acquired over a period of several days at the University of Bern.
Section 2 provides an overview of the detector, as well as of its charge and
light readout systems. Section 3 discusses the performance of the charge
readout system in detail, and Section 4 does the same for the light readout
system. Section 5 then reviews several analyses performed with reconstructed
tracks from the cosmic ray data set collected during the Module-0 that allow
to assess the performance of the fully-integrated system. Important metrics
for successful operation are addressed, such as electron lifetime, electric
field uniformity, and the ability to match charge and light signals, among
others. Section 6 offers some concluding thoughts.

##  2 The Module-0 Demonstrator

###  2.1 Detector Description

The Module-0 demonstrator is the first fully integrated, tonne-scale prototype
of the DUNE Liquid Argon Near Detector (ND-LAr) design. That detector will
consist of a $7\times 5$ array of $1\times 1\times 3$ m3 detector modules DUNE
Collaboration (2021) based on the ArgonCube detector concept Asaadi et al.
(2020), each housing two 50 cm–drift TPC volumes with 24.9% optical detector
coverage of the interior area. Module-0 has dimensions of
$0.7~{}\mathrm{m}\times 0.7~{}\mathrm{m}\times 1.4~{}\mathrm{m}$, and brings
together the innovative features of LArPix Dwyer et al. (2018); Russell et al.
(2022) pixelated 3D charge readout, advanced ArCLight Auger et al. (2018) and
Light Collection Module (LCM) Anfimov et al. (2020) optical detectors, and
field shaping provided by a low-profile resistive shell Berner et al. (2019).
This integrated prototype also tests the charge and light system control
interfaces, data acquisition, triggering, and timing. Module-0 is the first of
four functionally-identical modules that together will comprise an upcoming
$2\times 2$ ND-LAr prototype, known as ProtoDUNE-ND. Following construction
and initial tests with cosmic ray event samples, this larger detector will be
deployed underground in the NuMI neutrino beam at Fermilab Adamson et al.
(2016) to demonstrate the physics performance of the technology in a similar
neutrino beam environment to the DUNE ND. The work presented here describes
the analysis of a data set of cosmic ray events obtained with the Module-0
detector, installed in a liquid argon cryostat at the Laboratory for High-
Energy Physics of the University of Bern. Over a period of eight days, the
detector collected a sample of approximately 25 million self-triggered cosmic
ray–induced events along with sets of diagnostic and calibration data. The
data collection period included an array of characterization tests and data
collection with changes to detector trigger conditions, thresholds, and with
the TPC drift field as high as 1 kV/cm. For a brief second running period, the
cryostat was emptied and refilled following a series of gas purges rather than
complete evacuation, to assess the purity impact; this is discussed further in
Section 5.1. A gallery of events of different types is shown in Fig. 1. These
images illustrate the rich 3D raw data from the pixelated charge readout
system, the imaging capabilities for complex event topologies, and the low
noise levels.

Figure 1:  Gallery of four representative cosmic ray-induced events collected
with Module-0, as recorded in the raw event data, with collected charge
converted to units of thousands of electrons. In all cases, the central plane
in grey denotes the cathode, and the color scale denotes the collected charge.
(a) shows a stopping muon and the subsequent Michel electron decay, (b)
denotes an electromagnetic (EM) shower, (c) is a multi-prong shower, and (d)
is “neutrino-like” in that the vertex of this interaction appears to be inside
the active volume.

A schematic showing an exploded view of Module-0 with annotations of the key
components is provided in Fig. 2, and a photograph of the interior of the
Module-0 detector as seen from the bottom prior to final assembly in Fig. 3.
The module is divided into two identical TPC drift regions sharing a central
high-voltage cathode that provides the drift electric field. Opposite the
cathode at a distance of 30 cm are the anode planes, pixelated with charge-
sensitive gold-plated pads where drifting ionization electrons are collected.
The sides of the module are covered with photon detectors — alternating
ArCLight and LCM tiles. The TPC drift region is surrounded by a resistive
field shell made of carbon-loaded Kapton films. This low-profile field cage
provides field shaping to ensure a uniform electric field throughout the TPC
volumes.

Figure 2: Schematic of the $0.7~{}\mathrm{m}\times 0.7~{}\mathrm{m}\times
1.4~{}\mathrm{m}$ Module-0 detector with annotations of the key components.
Figure 3: Photograph of the Module-0 detector interior as seen from the
bottom, with annotations of the key components.

###  2.2 The Charge Readout System

The charge readout is accomplished using a two-dimensional array of charge-
sensitive pads on the two anode planes parallel to the cathode. While pixel-
based charge readout has already been implemented in gaseous TPCs, LArTPCs
have additional challenges due to restrictions on power dissipation. A proof
of principle for pixelated charge readout in a single-phase LArTPC is
described in Ref. Asaadi et al. (2020), where a test device was exposed to
cosmic ray muons. Readout electronics were also developed Asaadi et al.
(2018); Dwyer et al. (2018) and successfully applied in a pixel-readout
LArTPC. Each of the anode planes on opposite sides of the central cathode is
comprised of a $2\times 4$ array of anode tiles. Each tile is a large-area
printed circuit board (PCB) containing a $70\times 70$ grid of 4,900 charge-
sensitive pixel pads with a 4.43 mm pitch. On the back of each PCB is a
$10\times 10$ grid of custom low-power, low-noise cryogenic-compatible
LArPix-v2 application-specific integrated circuits (ASICs) Russell et al.
(2022), as shown in Fig. 4. Each ASIC is a mixed-signal chip consisting of 64
analog front-end amplifiers, 64 analog-to-digital converters, and a shared
digital core that manages configuration and data I/O. Each pixel channel
functions as an independent self-triggering detector with nearly 100$\%$
uptime, and is only unresponsive to charge for 100 ns while the frontend
resets. The LArPix ASIC leverages the sparsity of LArTPC signals. The chip is
in a quiescent mode when not self-triggering on ionization activity higher
than $\mathcal{O}(100)$ keV. Thus, it avoids digitization and readout of
mostly-quiescent data. At liquid argon temperatures, the rate of accumulation
of spurious charge (leakage current) is about 500 electrons/second. Each
channel periodically resets to discard spurious charge that has collected at
the input. In total, Module-0 comprises 78,400 instrumented LArTPC pixels.

Figure 4:  Front (left) and back (right) of a TPC anode tile. The front
contains 4,900 charge-sensitive pixels with 4.43 mm pitch that face the
cathode, and the back contains a $10\times 10$ array of LArPix ASICs. The
dimensions are $31~{}\mathrm{cm}\times 32~{}\mathrm{cm}$, with the extra
centimeter providing space for the light system attachment points. Figure 5:
The Pixel Array Controller and Network card (PACMAN), which controls the data
acquisition and power for the charge readout system.

Power and data I/O is provided to each tile by a single 34-pin twisted-pair
ribbon cable. These cables are connected at the cryostat flange to a custom
feedthrough PCB mounted on the cryostat lid. Data acquisition is controlled by
the Pixel Array Controller and Network (PACMAN) card (Fig. 5), which provides
filtered power and noise-isolated data I/O to eight tiles. Two PACMAN
controllers are mounted in metal enclosures attached to the outer surface of
each feedthrough. During Module-0 operation, the PACMAN controller received a
pulse-per-second timing signal for data synchronization between charge readout
and light readout systems, and external trigger signals from the light readout
system were embedded as markers into the charge readout data stream. Data are
carried over a standard copper ethernet cable connected at each PACMAN to a
network switch. Subsequently, data are transferred to and from the DAQ system
via an optical fiber connection.

For the LArTPC ionization charge measurement, LArPix ASICs mainly operate in
self-trigger mode, where a trigger is initiated on a per-channel basis when a
channel-level charge threshold is exceeded. In this mode of operation LArPix
incurs negligible dead time and produces only modest data volumes, due to the
sparsity of ionization signals in 3D, even for high-energy events. Serial data
packets stream out of the system continuously via the PACMAN boards and are
processed offline for analysis. A programmable channel-level threshold is set
using internal digital to analog converters (DACs), which are tuned so that
the spurious (i.e. noise-related) trigger rate is less than 2 Hz for each
channel. For Module-0, channel thresholds were operated in two regimes: low
and high threshold (see Fig. 6). Low threshold (${\sim 5.8}$ ke-/pixel or
${\sim\frac{1}{4}}$ MIP/pixel) operation optimized charge signal sensitivity
at the expense of incurring additional triggers due to e.g. digital pickup,
whereas high threshold (${\sim 10.7}$ ke-/pixel or ${\sim\frac{1}{2}}$
MIP/pixel) operation benefited from improved trigger stability at the expense
of charge sensitivity. Updated revisions of the LArPix ASIC include additional
pickup mitigation that will allow channel thresholds to be lowered further.
Also, a slight rising trend in event rate can be seen over some of the
different periods, most likely due to the emergence during data taking of
pixels with a high data rate. It is believed that this small effect, which has
no impact on the physics performance, can be mitigated by improving the
procedure used to set the thresholds.

Figure 6:  Run event rate and cumulative events as a function of time with
respect to charge readout operating condition.

ASICs within an anode tile are routed out to the DAQ through a configurable
“hydra” network, wherein each ASIC has the ability to pass data packets to and
from any adjacent neighbor. The scheme allows for system robustness in the
event that an ASIC along the signal path becomes nonfunctional, though none of
the 1600 ASICs failed during Module-0 operation. A few-millisecond delay is
incurred for data packets produced deeper in the network to reach the PACMAN
controller relative to data packets produced closer to it. This is accounted
for during hit digitization: each data packet carries a timestamp at creation
when the hit signal is digitized, and when packets reach the PACMAN
controller, a receipt timestamp is also assigned. Time ordering and filtering
on packet trigger type is performed offline. In order to monitor the integrity
of the data in near–real time, a dedicated nearline monitoring system was
developed and operated during the Module-0 run. An automated analysis was
performed on each run’s raw data once the run ended and provided metrics
including system trigger rates, trigger timing and offsets, channel occupancy
and trigger rates, and data corruption checks. Cosmic rays produced a self-
trigger rate of ${\sim 0.25}$ Hz per pixel. This resulted in a total pixel hit
rate of ${\sim 20}$ kHz for the entire Module-0 detector, yielding a modest
data rate of 2.5 Mb/s.

###  2.3 The Light Readout System

The Light Readout System (LRS) provides fast timing information using the
prompt ${\sim 128}$ nm scintillation light induced by charged particles in
LAr. The detection of scintillation photons provides absolute reference for
event timing ($t_{0}$) and, when operated in an intense neutrino beam, will
allow for unambiguous association of charge signals from the specific neutrino
interactions of interest (i.e. pile-up mitigation). The LRS uses a novel
dielectric light detection technique capable of being placed inside the field-
shaping structure to increase light yield and localization of light signals.
The LRS consists of two functionally-similar silicon photomultiplier
(SiPM)-based detectors for efficient collection of single UV photons with
large surface coverage: the Light Collection Module (LCM) and the ArCLight
module. The full LRS system includes these modules together with the ancillary
readout, front-end electronics, DAQ (ADCs, synchronization, and trigger),
feedthrough flanges, SiPM power supply subsystem, and slow controls, as well
as cabling and interconnection between different elements. LCM and ArCLight
modules share the same basic operation principle. The vacuum ultraviolet (VUV)
scintillation light produced by LAr is shifted from 128 nm to visible light by
a wavelength shifter (WLS). Tetraphenyl butadiene (TPB) coated on the surface
of the light collection systems provides an efficient WLS, and the emission
spectrum of TPB is quite broad with a peak intensity of around 425 nm (violet
light). Part of the light emitted at the surface of the light detection system
eventually enters the bulk structure of the detector and is shifted to green
light by a dopant (coumarin) in a bulk material, which also acts as a light
trap (see Fig. 7).

Figure 7:  Detection principle of the two types of modules comprising the LRS:
a segment of an ArCLight tile (top) and a single LCM optical fiber (bottom).
The wave-like lines indicate example photon trajectories, where the white
points indicate interactions. Drawings are not to scale.

The ArCLight module has been developed by Bern University Auger et al. (2018)
and uses the ARAPUCA Machado and Segreto (2016) principle of light trapping.
The general concept, illustrated in Fig. 7 (top), is that violet light enters
a bulk WLS volume and is re-emitted as green light, and the volume has a
coating reflective to green light on all sides except on the SiPM photosensor
window. A dichroic filter transparent to the violet light and reflective for
the green is used on the WLS (tetraphenyl butadiene, TPB) side. The overall
module dimensions are 300 mm $\times$ 300 mm $\times$ 10 mm. A photograph of
an ArCLight module is shown in Fig. 8 (left).

The LCM prototype is a frame cantilevered by a PVC plate that holds 25 WLS
fibers bent into a bundle whose both ends are readout by a SiPM light sensor.
Fibers are grouped and held by spacer bars with holes fixed on the PVC plate
by means of polycarbonate screws to provide matching of thermal contraction.
The PVC plate with the WLS fibers is coated with TPB, which re-emits the
absorbed VUV light to the violet (${\sim 425}$ nm). This light is then shifted
inside multi-cladding $\varnothing$=1.2 mm Kuraray Y-11 fibers to green
(${\sim 510}$ nm), and hence is trapped by total internal reflection guiding
it to the SiPM readout at the fiber end, as depicted in Fig. 7 (bottom). For
each group of LCMs, the center module uses bis-MSB as a WLS rather than TPB to
evaluate this alternative option; the photon detection efficiency performance
is discussed in Section 4 and the relative performance can be observed in Fig.
26. The LCM dimensions are 100 mm $\times~{}$300 mm $\times$ 10 mm. Fig. 8
(right) shows three LCMs.

Figure 8:  An ArCLight tile (left) and three LCM tiles (right), as assembled
within the Module-0 structure.

In order to digitize analog signals from SiPMs, a 100 MHz, 10-bit, 64-channel
(differential signals, full range $\pm 1.6$ V) ADC prototype module in VME
standard produced at the Joint Institute for Nuclear Research (JINR) was used
(see Fig. 9 left). This ADC module streams UDP/TCP data packets via M-link
MStream protocol using a 10 Gbps optical link. The ADC boards have the
capability to be synchronized via a White Rabbit system Serrano et al. (2009).
This was not available for Module-0 run, for which timing synchronization
between the charge light systems was provided by a dedicated system shown in
Fig. 9 (right). To merge data between light and charge systems, a trigger
signal generated by the LRS is written out to the charge readout data stream.
This trigger signal is also fed to the analog input of both ADCs to allow for
precise time matching between ADC boards for further LRS data analysis.
Additionally, a pulse-per-second from a stable GPS source was used for both
detection systems to provide accurate synchronization. For the LRS, the pulse-
per-second signal was fed to the analog input of each ADC. During the Module-0
run, the LRS operated in a self-triggered mode with adjustable threshold
settings. The thresholds for the LCMs are approximately 30 photoelectrons, as
discussed in Section 4.

Figure 9:  LRS data acquisition components: JINR ADC board (left),
synchronization and trigger scheme (right).

##  3 Charge Readout Performance

###  3.1 System Overview

Module-0 operation represents the first demonstration of the LArPix-v2
pixelated charge readout system in a tonne-scale LArTPC. Continuous
acquisition and imaging of self-triggered cosmic ray data were successfully
exercised, demonstrating the excellent performance of this technology. This
section presents an array of studies of the charge readout system performance,
including: pixel channel signal baselines and time stability, charge response
as a function of track position and angle relative to the pixel plane,
response uniformity across the instrumented area, ADC saturation, and overall
calorimetric measurement performance.

In parallel to this successful series of technological achievements, this
first large-scale integrated test highlighted areas for continued improvement
in future iterations of the module design. This includes improved anode tile
grounding and optimization of the pixel pad geometry. In the former case,
enhancements to the grounding scheme will enable improved system-wide per-
channel charge threshold sensitivity and system trigger stability,
specifically allowing readout of the pixels on the edge of neighboring tiles,
and mitigating the effects of triggering induced by system synchronization
signals observed in the Module-0 data. In the latter case, modifications to
the pixel pad geometry will further minimize far-field current induction in
the pixels, reducing the sensitivity of the readout system to drifting charge
that is far from the anode plane. Additional improvements to the ASIC-related
noise budget are planned for the next-generation LArPix design. Of the total
78,400 instrumented pixel channels in Module-0, 92.2% were enabled for LArTPC
operation. The channels were disabled mainly due to limitations noted above —
grounding near tile edges (4.2%), elevated noise levels due to signal pickup
(3.1%), high noise or leakage current (0.5%) — and their locations are
illustrated in Fig. 10. As noted above, no ASICs failed during Module-0
operations.

###  3.2 Noise and Stability

Periodic diagnostics (pedestal) runs were taken to monitor the stability of
the charge readout system. These diagnostic runs entailed issuing a periodic
trigger on a per-channel basis in a round-robin fashion among channels on a
single ASIC. In this way, sub-threshold charge was digitized to monitor
channel pedestal and the AC noise stability in time, with the ADC value
returned by each digitization reflecting the sum of the quiescent pedestal
voltage of the front-end amplifier and the integrated charge. The
distributions of ADC values collected during pedestal runs were in agreement
with the design expectations, with a median value of $\sim 78$ counts per
channel, and pedestal voltage varied by approximately 30 mV between channels.
To determine the integrated charge, a correction for this pedestal value must
be applied. We computed the channel-by-channel pedestal ADC value by using the
truncated mean around the peak of the ADC value distribution of each channel.
The signal amplitude in mV was inferred based on the internal reference DAC
values and the ASIC analog voltage, and a global gain value of 245 e-/mV was
then used to convert the signal amplitude to charge.

Additionally, the stability of the charge readout over time was verified using
cosmic ray data samples, by measuring the most probable value (MPV) and the
full width at half maximum (FWHM) of the $dQ/dx$ distribution of minimum
ionising particle (MIP) tracks for each data run, as shown in Fig. 11. To make
these track-based measurements, 3D hits registered by the charge system are
clustered together using the DBSCAN algorithm Ester et al. (1996). A principal
component analysis of hits within each cluster then provides three-dimensional
segments that we define as reconstructed tracks. The charge $dQ$ corresponds
to the sum of the hits associated to the reconstructed track and the 3D
reconstructed track length $dx$. The $dQ/dx$ distribution is then fitted with
a Gaussian-convolved Moyal distribution Moyal (1955), which is used to extract
the MPV and the FWHM. Total system noise contributes $\sim 950$ e- equivalent
noise charge (ENC) to each pixel hit, as assessed using periodic forced
triggering of pixel channels in the absence of actual signals (Fig. 12). To
put this metric in context, the intrinsic energy loss fluctuations associated
with the charge from a 4 GeV MIP would be $\sim 1800$ e- in ND-LAr’s 3.7 mm
pixel pitch. Therefore, the charge resolution is smaller than the intrinsic
physical fluctuations for particle kinematics relevant to ND-LAr.

Figure 10:  Self-trigger active pixel channels (in blue) and inactive channels
(in black). In these coordinates, $x$ is horizontal and $y$ is vertical, both
parallel to the anode plane, and $z$ is the drift direction, perpendicular to
the anode plane, completing a right-handed system. The origin is the center of
the module. Figure 11:  Most probable value (black circles) and full width at
half maximum (white circles) of the $dQ/dx$ distribution for each data run.
The system shows a good charge readout stability during data taking periods,
both for high threshold (yellow bands) and low threshold (purple bands) runs.
Figure 12:  LArPix channel noise in units of electron charge signal, as
observed using periodic forced triggers. The total system noise is $\sim
950~{}\mathrm{e}^{-}$, compared to a signal amplitude of $\sim
1800~{}\mathrm{e}^{-}$ for a 4 GeV MIP track in ND-LAr’s 3.7 mm pixel pitch.

Examining the corresponding charge in each pixel that has triggered (Fig. 13),
we identify a sharp rising edge corresponding to the self-trigger threshold at
approximately $5.8\times 10^{3}$ electrons (low threshold) and $11\times
10^{3}$ electrons (high threshold). Above the self-trigger threshold, a peak
at roughly $24\times 10^{3}$ electrons corresponds to the typical charge
deposited by a MIP crossing the full pixel pitch of 4.43 mm. Of note are the
markedly different charge distributions of the high– and low-threshold data.
We find that for the low-threshold data, the average number of triggers per
single channel for MIP energy deposition is substantially larger than for the
high-threshold data, with mean values of 1.53 and 1.14 respectively. These
numbers are well-reproduced by the Monte Carlo simulation (MC) described in
Section 5, with values of 1.52 and 1.12 respectively for a similar set of
reconstructed MIP tracks. Summing the charge of all digitizations on each
specific channel for a given event increases the similarity between the low-
threshold data with the high-threshold data (Fig. 14). This is indicative of a
“pre-triggering” effect, in which a channel is triggered by the induced signal
generated by the drifting charge in advance of the charge signal arrival at
the anode plane, thus motivating the reduction of far-field effects discussed
above.

Figure 13:  Self-trigger charge distribution for MIP tracks measured in
thousands of electrons (ke-); 50% of the rising edge are shown as indicators
of the charge readout self-trigger thresholds. The low- and high-threshold
curves are obtained from runs with the same 20 minute exposure. Each entry is
normalized by hit charge over fitted track length. The MC simulation shown in
comparison is described in Section 5. Figure 14:  Total event charge per
channel for MIP tracks measured in thousands of electrons (ke-). The MC
simulation shown in comparison is described in Section 5.

Figure 15:  Comparisons of response variation in the radial distance from the
pixel center to the point of closest approach of the track projected onto the
anode plane ($r$, top), the track inclination relative to the anode plane
(polar angle $\theta$, middle), and the orientation angle of the track
projected onto the anode plane (azimuthal angle $\phi$, bottom). The MC shown
in comparison is described in Section 5.

###  3.3 Pixel Charge Response

To study the individual pixel charge response, we examine the variation in
response based on the track inclination relative to the anode plane (polar
angle $\theta$), the orientation angle of the track projected onto the anode
plane (azimuthal angle $\phi$), and the radial distance from the pixel center
to the point of closest approach of the track projected onto the anode plane
($r$). Fig. 15 shows the distribution of these three quantities, normalized by
the total track length. Generally, the $\theta$ and $\phi$ distributions are
comparable between data and simulations. The $r$ distribution shows
significantly more triggers to peripheral tracks than simulated events. An
overall normalization difference between high- and low-threshold data reflects
the decreased sensitivity to tracks that clip the corners of the pixel.

A similar finding resulted from studying the distance between the MIP
ionization axis and the center of the pixel. This ionization axis can be
inferred by performing a Hough transform algorithm (HTA) on the $x$, $y$, and
estimated $z$ dimensions of the hit cloud. A projection of the HTA line onto
the pixel plane provides the minimum array of pixels along the axis that could
have recorded some charge. This line is then divided into 0.1 mm segments
longitudinally. Each individual segment’s center then falls into a specific
pixel, which is used to determine the distance between the segment center and
the pixel center in $x$ and $y$. The segments are split into three categories:
(1) all segments as mentioned above independent of the recorded charge on that
particular pixel, (2) those that fell into a pixel which did give a response,
and (3) those in pixels that did not trigger. Prior to this categorization,
all segments contained by pixels known to be inactive are excluded. In Fig.
16, the ratios of the number of segments in the latter two categories to the
first one are shown. The four corners are over-represented for pixels that did
not give a response but had the main ionization line crossing their pad. This
quantifies the sensitivity of individual pixels to tracks clipping the
corners. This difference in sensitivity is characterized by only a 3% drop
from pixel center to pixel edge where the minimum response is 85.5%.

Figure 16: Relative rate of pixel response as a function of the distance
between Hough line segments and segment containing pixel’s center for pixels
on gaps, i.e. no charge response (left), and on tracks, i.e. with charge
response (right) to the total.

Figure 17:  Self-trigger charge distribution for MIP tracks with different
track orientations with respect to the pixel, normalized to number of
triggered channels per reconstructed track length. Low-threshold data are
used. The MC simulation shown in comparison in the second column is described
in Section 5.

Figure 18:  Same as Fig. 17 but for high threshold data.

Figs. 17 and 18 show the charge distribution with respect to the track
orientation for low- and high-threshold data, respectively. Overall, similar
features appear in each panel: a prominent peak corresponding to the charge
deposited by a MIP across a single pixel width. In the $r$ distribution, a
secondary distribution of low-charge hits is present, corresponding to tracks
that clip the corners of the pixel. This feature is also present in the $\phi$
distribution as an increase in the spread of the charge as $\phi\to\pi/4$. The
$\theta$ distribution shows a characteristic increase in the charge as
$\theta\to 0$, which corresponds to tracks perpendicular to the anode plane,
where each pixel can see a contribution from a relatively long track length. A
flattening of the observed charge near $\theta=0.8$ is a threshold effect and
is not present in the low-threshold data. To test the responsiveness of
individual pixels and identify potentially malfunctioning channels beyond
those known to be inactive, a MIP response map of the entire pixel plane was
constructed. This map is the ratio of recorded over expected hits, and
identifies regions on the pixel plane which are less responsive than others.
Both components start off with the same principle of performing an HTA on the
$x$, $y$, and inferred $z$ dimensions of the hit cloud to obtain the MIP’s
central ionization axis in 3D. This axis is then projected onto the pixel
plane to result in a 2D line. Next, all hits within 8 mm of the line are
selected and the maximum track width is set equal to the most distant point
within this radius. To then obtain the first map, all pixels that recorded
hits within a radius equal to the maximum track width of the projected line
receive an entry. To construct the second map, all existing pixels within that
same radius receive an entry. If a pixel is unresponsive, it will not show up
in the first but will appear in the second, leading to a low ratio in that
specific area. Selection cuts place requirements on the straightness of tracks
relative to the fit Hough lines as well as the consistency with a roughly
constant energy deposition profile, to ensure that the events analyzed consist
primarily of MIP-like tracks. Fig. 19 shows the resulting MIP response maps
for both anode planes.

Figure 19: MIP response maps for anode plane 1 (left) and anode plane 2
(right), showing the fraction of triggered hits on each pixel relative to the
expected number based on reconstructed track trajectories.

###  3.4 Saturation

An additional consideration is saturation in the LArPix-v2 ASIC’s 8-bit
successive-approximation ADC, which is expected to occur when the charge on a
given channel exceeds 200 ke- within a 2.6 $\mu$s time window. A scan for
events including saturated packets was performed over eight hours of cosmic
ray data acquired at high gain and low threshold. Packets within 1 s of a time
synchronization pulse were found to include additional noise and saturation
effects, and were excluded. After accounting for this, a small fraction
($2.9\times 10^{-6}$) of events with matching charge and light information
contained a saturated ADC measurement. These events were manually inspected,
and the saturation was clearly uncorrelated in space and time with the
physical interactions, but rather they leaked into the event due to their
proximity with a sync pulse. With low thresholds, $<0.002$% of triggers
resulted in ADC saturation, again driven by the pulse-per-second sync signal;
channels 35-37 on all chips, which are located physically adjacent to the sync
pulse pin, saturated most often and together accounted for 15% of these
saturated packets. The ADC count distribution for events with deposited energy
between 2 and 10 GeV is shown in Fig. 20. These energies are of interest as
they are representative of neutrino interactions at ND-LAr, and the
distribution falls well within the dynamic range of the ADC.

Figure 20: Per-pixel ADC value distribution for cosmic ray events between 2
and 10 GeV. All signals are well within the ADC dynamic range of 0–256 counts.

###  3.5 Calorimetric Response

Finally, the calorimetric response of Module-0 charge readout was also
studied. Figs. 21 and 22 show the variation of the $dQ/dx$ for segments of
different lengths relative to the track orientation, defined by the azimuth
angle $\phi$ and the $\theta$ angle between the track and a vector normal to
the anode plane. The reconstructed tracks used for this analysis come from the
low threshold runs (see Section 1). Events with more than 20 reconstructed
tracks were excluded, since they often correspond to large showers or non-
cosmic triggers. Tracks were required to be longer than 10 cm and to have at
least 20 associated hits. They were then subdivided into segments of variable
length from 10 to 400 mm and the distributions were fit with a Gaussian-
convolved Moyal function. The MPV shows a slight dependence on $\cos\theta$,
with tracks that impinge perpendicularly to the anode plane tending to have a
larger amount of deposited charge per unit length. These data provide insight
into subtle effects in the pixel charge response, such as those related to
induction effects and electric field uniformity, and enable a data-driven
calibration.

Figure 21: $dQ/dx$ measured for segments of different lengths as a function of
the orientation relative to the anode planes. A value of $\cos\theta=0$
corresponds to segments parallel to the anode plane. The distributions in each
bin have been fitted with a Gaussian-convolved Moyal function. The red points
correspond to the most probable value of the fitted distribution and the
dashed rectangles correspond to the full width at half maximum. The dashed
black line represents the average MPV. Figure 22: $dQ/dx$ measured for
segments of different lengths as a function of the azimuthal angle
$\phi=\mathrm{atan2}(y,x)$, where $y$ and $x$ are the components of the
segment along the anode plane axes. The distributions in each bin are fitted
with a Gaussian-convolved Moyal function. The red points correspond to the
most probable value of the fitted distribution and the dashed rectangles
correspond to the FWHM. The dashed black line represents the average MPV.

##  4 Light Readout Performance

###  4.1 Overview

The Module-0 detector also provided a large-scale, fully integrated test of
the light readout system, enabling a detailed performance characterization of
the ArCLight and LCM modules, readout, DAQ, triggering, and timing with a
large set of events. Using cosmic ray data and dedicated diagnostic runs under
a variety of detector configurations, a suite of tests was performed to assess
the charge spectrum, inter– and intra-event timing accuracy, and photon
detection efficiency. The subsequent matching of events between the charge and
light system is considered in Section 5.3.

###  4.2 Calibration

Before collecting cosmic data, a SiPM gain calibration was performed using an
LED source, where the bias voltage for each SiPM channel was adjusted to
obtain a uniform gain distribution across the channels, as shown in Fig. 23.
The amplification factors for the variable gain amplifiers used in the SiPM
readout chain were also tuned, and set to maximum (31 dB) except for LCM
channels (21 dB) during cosmic ray data taking, to adjust signals to the input
dynamic range of the ADC. LCMs were used to provide an external trigger to the
charge readout system, with an effective threshold of about 30 photoelectrons
(p.e.). The trigger message, written into the continuous self-triggered data
stream of the charge readout system, provides a precise timestamped flag for
identifying coincidences between charge and light readout.

Figure 23:  Typical charge spectrum obtained during SiPM gain calibration
(left); SiPM gain distribution (right).

###  4.3 Time Resolution

Events induced by cosmic muons traversing the TPC volume were used to extract
the time resolution of the light detectors. The time measurement proceeds as
follows: each waveform is oversampled through a Fourier transform to increase
the number of points on the rising edge, enabling a good linear fit of it.
Then, a linear fit to the baseline is performed, and the crossing point of the
rising edge of the signal with the baseline is calculated, providing a robust
single-channel event time. This process is illustrated in Fig. 24 (left). The
extracted time resolution for a pair of neighboring LCM channels is shown in
Fig. 24 (right) as a function of the signal amplitude. This quantity is
obtained by taking the standard deviation of the time difference recorded
between the two channels over multiple events without any time-of-flight
corrections. For large signals, this resolution approaches $\sim 2$ ns. An
example application of the excellent timing resolution for the LCMs is the
identification of Michel electrons from stopping muon decays, where the
relative timing between the muon and electron signals is dominated by the mean
lifetime of the muon, $\tau\sim 2.2~{}\mu$s. Two examples of signals from a
stopping muon and a delayed Michel electron detected by the LCM are shown in
Fig. 25. Since the muon decay time is variable but follows a well-understood
exponential distribution, such events may be used, for example, to study event
pile-up in neutrino interactions.

Figure 24:  Oversampled signal using Fourier transformation. Red lines show
the linear approximations of the rising edge and the baseline (left). The time
resolution between two LCMs (LCM-011, LCM-017) as a function of the signal
response (right).

Figure 25:  Two examples showing signals of the stopping muon and delayed
Michel electron detected by the LCM. The waveforms were digitized at 10 ns
intervals.

###  4.4 Efficiency

To assess the efficiency of the LRS, the scintillation light induced by tracks
reconstructed from the TPC charge readout data is used. In particular, cosmic
muon tracks crossing the entire detector vertically are considered. In a 3D
simulation, the charge of a track is discretized to single points with a
$1\text{\,}\mathrm{mm}$ resolution along the track, assuming an infinitely
thin true trajectory. For each point in this voxelized event, the solid angle
to the light detector in the detector module is then calculated. Next,
assuming isotropic scintillation light emission, the solid angle can be used
to compute the geometrical acceptance of the light for each detector tile. The
number of photons hitting the detector surface is estimated by multiplying the
geometrical acceptance by the number of emitted photons per unit track length
and integrating over the full track length. Here, the number of emitted
photons per unit track length has been calculated for the nominal electric
field intensity of $0.5\text{\,}\mathrm{kV}\text{\,}{\mathrm{cm}}^{-1}$ Baller
. Rayleigh scattering, a small effect over the relevant distance scales, is
neglected in this calculation.

The photon detection efficiency (PDE) of the light detection system can be
estimated by comparing the measured number of p.e. and the estimated number of
photons hitting the detector surface, as obtained from the simulation
described above. Since the waveforms obtained with the light detectors have
been integrated using a limited gate length, the actual scintillation light
might be underestimated. This was corrected by multiplying the number of
reconstructed photons by an integration gate acceptance factor, which is
calculated based on the detector response and the scintillation timing
characteristics. Fig. 26 shows the measured PDE for all ArCLight and LCM
modules used in the Module-0 detector. The LCM shows an average PDE of 0.6%,
which enables a light trigger for events depositing MeV-scale energies, with
an accurate scintillation amplitude and energy reconstruction. The PDE of the
ArCLight modules is about a factor of $10\text{\,}$ lower than the
corresponding value obtained with the LCMs, which allows for a larger dynamic
range. The ArCLight technology additionally enables a high position
sensitivity, which can be used to accurately triangulate the origin of the
scintillation light emission point Auger et al. (2018). For the LCM it can be
observed that tiles placed at the top (see Fig. 26 (right), LCM groups 4–6,
10–12, 16–18, and 22–24) of the TPC show a systematically lower PDE with
respect to tiles placed in the middle of the TPC. This can be explained by an
anisotropy of light collection of LCM with respect to the angle of incoming
photons, driven by structural non-uniformity of fibers and spaces. The absence
of non-uniform effects in the ArCLight tiles due to reflections on the TPC
structure or Rayleigh scattering, meanwhile, further indicates that these
effects are negligible within the experimental uncertainties. In Module-0, a
Hamamatsu MPPC S13360-6025 Hamamatsu  is used. By replacing the SiPM for
future modules with the MPPC S13360-6050 with higher efficiency, the overall
PDE would improve by a factor of 1.6 to yield a LCM efficiency of about 1%.

Figure 26:  Absolute PDE for each ArCLight (left) and LCM (right) tile
(arbitrary numbering). ArCLight tile 7 was disabled during Module-0 data
taking. The LCM tiles are placed in sets of 3 to cover the same area as one
ArCLight tile.

##  5 Measurements with Cosmic Ray Data Samples

The following sections discuss the analyses performed using reconstructed
tracks from the large cosmic ray data set collected during the Module-0 run.
As discussed in Section 1, the Module-0 detector incorporates several novel
technologies for the first time in a LArTPC of this scale. These studies
assess the performance of the fully-integrated system, including the LArPix
charge readout with a very large channel count, the high-coverage hybrid LCM
and ArCLight photon detection systems, and their matching; the capability to
achieve the necessary levels of LAr purity for physics measurements without
prior evacuation of the cryostat; and the degree of drift field uniformity
achievable with the low-profile resistive shell field cage. Detailed studies
of each of these key detector parameters demonstrate excellent performance of
the integrated system relative to the requirements in view of the operation
for the DUNE ND-LAr.

In support of these studies, a sample of cosmic rays has been simulated using
CORSIKA Heck et al. (1998), a program for detailed simulation of extended air
showers. The passage of the particles through matter has been simulated using
a Geant4-based Monte Carlo Agostinelli et al. (2003). The detector simulation
has been performed with larnd-sim Soleti et al. (2021); Abed Abud et al.
(2023), a set of highly-parallelized GPU algorithms for the simulation of
pixelated LArTPCs. A track-fitting algorithm is applied to provide an estimate
of the particle track angle and location. First, a 3D point cloud is
reconstructed using the unique channel index to determine the position
transverse to the anode and the drift time. DBSCAN ($k=5$, $\epsilon=2.5$ cm)
Ester et al. (1996) is used to find the hit clusters. The cluster radius
($\epsilon$) was tuned using the $k=5$th-neighbor distance of 3D points from a
typical run. Each cluster is then passed through a RANSAC line fit Fischler
and Bolles (1981) with an outlier radius of $\rho=8$ mm and 100 random
samples. This provides a set of highly-collinear points which constitute the
reconstructed track.

###  5.1 Electron lifetime

The amount of charge collected by the readout system depends heavily on the
electron lifetime, $\tau$, in the argon of the TPC volume. The electron
lifetime parameterizes (in units of time) how much charge is lost due to
attachment to electronegative impurities in the argon, such as oxygen or
water, during the drift of the deposited ionization charge toward the anode.
The charge measured at the anode, $Q$, is given by

$Q=e^{-t/{\tau}}\cdot R\cdot Q_{0},$ (1)

where $Q_{0}$ is the amount of the primary ionization charge deposited by a
particle in the liquid argon, $R$ is the recombination factor that describes
the fraction of charge that survives prompt recombination of the ionization
with argon ions prior to drift, and $t$ is the drift time from the point of
original charge deposition to detection in the anode plane. Measuring signals
originating across the entire TPC via the charge readout system requires a
sufficient electron lifetime in the detector. For the DUNE ND-LAr detector
this requirement is $>$0.5\text{\,}\mathrm{m}\mathrm{s}$$ at a drift electric
field of $500\text{\,}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$; this
relatively low value compared to other large LArTPC detectors Abi et al.
(2020); Adams et al. (2020); Bettini et al. (1991) is due to the relatively
short maximum drift length of DUNE ND-LAr ($\sim 50$ cm) and allows ND-LAr to
meet the charge attenuation performance of the far detector, which specifies a
3 ms lifetime in a detector with a 3.5 m drift length at a 500 V/cm drift
field Abi et al. (2020). A measurement of the electron lifetime with Module-0
has been carried out to confirm that the materials used in the detector, which
will be similar to those of DUNE ND-LAr, are compatible with the argon purity
requirement. Additionally, tracking this parameter as a function of time is
necessary to provide a calibration of charge scale for other measurements
carried out using the Module-0 charge data.

As seen in Eq. 1, charge measurements at the anode depend both on the electron
lifetime and the recombination factor. However, by measuring $Q$ as a function
of the drift time for a collection of cosmic muon tracks that span the entire
drift distance, the dependence on $R$, which is independent of drift time, can
be ignored as an overall normalization factor. Additionally, a more fitting
quantity to use in this study is $dQ/dx$, the measured charge per unit length
along the cosmic muon track, given the dependence of the amount of charge seen
by a single pixel channel on the orientation of each track. The electron
lifetime for each Module-0 data run at a drift electric field of
$500\text{\,}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$ is measured by applying
an exponential fit to the mean $dQ/dx$ of muon track segments as a function of
drift time to the anode, assuming a uniform $dQ/dx$. A sample of anode-
cathode-crossing tracks is used for this measurement; these tracks span the
entire drift distance and the absolute drift time associated with each part of
the track is known for this track sample. The electron lifetime values
measured in Module-0 were consistently above 2 ms for the duration of the run,
thus satisfying the $\tau>0.5$ ms requirement. This trend continued in the
second run (Run 2) of Module-0, where cryogenic operations differed from those
in Run 1. Run 1 achieved LAr purity through cryostat evacuation before
cooldown and LAr filling, while Run 2 made use of a piston purge procedure
(repeatedly purging the volume with clean gas), as this is the anticipated
approach for the full-scale cryostat of ND-LAr. A recirculation system with
filtration was operational during both runs. Results are shown in Fig. 28.

Figure 27: Measured $dQ/dx$ versus drift time for ionization associated with
anode-cathode-crossing muon tracks (left); mean $dQ/dx$ versus drift time,
along with exponential fit, for the same track sample (right).

Figure 28: Extracted electron lifetime as a function of time during Module-0
Run 1 (top) and Run 2 (bottom), with the average uniformly exceeding 2 ms in
both cases.

###  5.2 Electric field uniformity

The magnitude of electric field distortions due to space charge effects for
Module-0 are expected to be much smaller than other, larger LArTPC detectors
running near the surface, such as MicroBooNE Abratenko et al. (2020) and
ProtoDUNE-SP Abi et al. (2020). This is due to the relatively small maximum
drift length of $\sim 30\text{\,}\mathrm{c}\mathrm{m}$ of Module-0, compared
to $\sim 2.5\text{\,}\mathrm{m}$ for MicroBooNE and $\sim
3.6\text{\,}\mathrm{m}$ for ProtoDUNE-SP. Even for a maximum drift length of
$\sim 50\text{\,}\mathrm{c}\mathrm{m}$ that is anticipated for DUNE ND-LAr,
the impact from space charge effects is expected to be negligible; the fact
that ND-LAr will operate $65\text{\,}\mathrm{m}$ underground will reduce this
effect further due to the smaller flux of cosmic muons. However, it is
possible that electric field inhomogeneities arise in the Module-0 detector
from other sources. In particular, it is important to determine whether or not
the field cage design causes significant distortions of the electric field,
which can alter the trajectories ionization electrons take while drifting to
the anode plane. Such distortions could lead to incorrect reconstruction of
the true position of original energy depositions in the detector due to
primary particles ionizing the argon, consequently impacting their trajectory
and energy reconstruction. Furthermore, associated modification to the
electric field intensity throughout the detector can lead to significant
impact on the amount of electron-ion recombination experienced by ionization
electrons, leading to bias in reconstructed particle energy scale or
degradation of reconstructed particle energy resolution. The use of the novel
resistive field cage technology in Module-0, as is anticipated for DUNE ND-
LAr, provides an important opportunity to study the impact on electric field
homogeneity.

Following the methodology developed by the MicroBooNE experiment for analysis
of space charge effects Abratenko et al. (2020), electric field distortions
are probed using end points of through-going cosmic muon tracks in Module-0
data. Tracks passing through an anode plane and another face of the detector
that is not the other anode plane are selected for this study, providing a
known absolute drift time associated with each part of the track via
subtracting the time associated with the anode side of the track. The track
end point associated with the non-anode side of the anode-crossing track is
then probed by measuring the transverse (i.e., perpendicular to the drift
direction) displacement from the edge of the TPC active volume, as measured
from the $y$ value (TPC top and bottom) or $x$ value (TPC front and back
sides, perpendicular to the drift direction) of the pixel channels at the edge
of the detector. The average transverse displacement is recorded as a function
of the two directions within the TPC face for all four non-anode faces of the
Module-0 TPC. If there are no electric field distortions in the detector,
there would be no inward migration of ionization electrons during drift,
leading to zero transverse displacement of ionization charge with respect to
the TPC face for this sample of through-going muon tracks (contamination from
stopping muons is expected to be less than 1%). The result of the average
transverse displacement measurement is shown for the TPC top and bottom in
Fig. 29 and for the TPC front and back in Fig. 30. A few features not
associated with electric field distortions in the detector should be pointed
out. First, there are gaps in coverage near the anode planes ($z$ values of
roughly $\pm$30\text{\,}\mathrm{c}\mathrm{m}$$) due to a requirement in the
track selection that the non-anode side of the track is at least
$5\text{\,}\mathrm{c}\mathrm{m}$ away from both anode planes, and near the
pixel plane edges (edges of the TPC face) due to a requirement that the non-
anode side of the track is not located within $1\text{\,}\mathrm{c}\mathrm{m}$
($2\text{\,}\mathrm{c}\mathrm{m}$) of these features. These selection criteria
were introduced to minimize contamination of the sample from poorly-
reconstructed muon tracks. Some residual contamination is seen near the edges
of the pixel planes, where the measured average transverse spatial offset is
artificially large due to edge channels of the pixel planes being turned off
for data-taking, leading to the ends of tracks being clipped off near the
edges of pixel planes. Second, the two horizontal bands in the bottom right
corner of the right side of Fig. 30 are associated with a known grounding
issue of an ArCLight unit in this part of the detector. The vertical gap in
the right panel of Fig. 29 is due to inactive channels in this region of the
anode plane (see Fig. 10).

Figure 29: Average spatial offsets measured at the top (left) and bottom
(right) of the Module-0 detector. These offsets in cm are measured with
respect to the location of the pixel channels at the edge of the detector.

Figure 30: Average spatial offsets measured at the front (left) and back
(right) of the Module-0 detector. These offsets in cm are measured with
respect to the location of the pixel channels at the edge of the detector.

After accounting for these two artifacts, non-negligible transverse spatial
offsets are observed near the cathode (central horizontal lines in Fig. 29,
central vertical lines in Fig. 30), roughly $1\text{\,}\mathrm{c}\mathrm{m}$
on average but as large as $2.5\text{\,}\mathrm{c}\mathrm{m}$ in some places
in the TPC. After adding an additional $\sim 1\text{\,}\mathrm{c}\mathrm{m}$
to these measurements to account for the separation between the edge pixel
channels and the field cage (or light detectors in the case of the front and
back of the TPC), the average (maximum) transverse spatial offset experienced
by drifting ionization charge originating near the cathode is roughly
$2\text{\,}\mathrm{c}\mathrm{m}$ ($3.5\text{\,}\mathrm{c}\mathrm{m}$).
Ascribing this transverse drift to an additional electric field component
strictly in the direction transverse to the TPC faces, the average (maximum)
transverse electric field magnitude leading to this amount of inward drift of
ionization charge is roughly
$30\text{\,}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$
($60\text{\,}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$). The associated
average (maximum) impact to the electric field magnitude in the detector is
0.2% (0.7%). This is below the conservative physics requirement of $1$%
maximum allowed deviation of the electric field magnitude within $95$% of the
detector volume, indicating that the design of the field cage is adequate for
the physics goals of DUNE ND-LAr. It is worth pointing out that this physics
requirement for electric field distortions corresponds to after detector
calibrations have been carried out, while the measurements presented here have
no calibration applied. It is thus expected that the calibrated electric field
map would be even more homogeneous at DUNE ND-LAr. An additional study is
carried out to determine if the small electric field distortions in the
Module-0 detector vary substantially over time. A substantial time dependence
of the electric field distortions may complicate efforts to obtain a
calibrated electric field map in the DUNE ND-LAr detector using cosmic muons,
neutrino-induced muons, or dedicated calibration hardware. Average transverse
spatial offsets were measured at four different places on each side of the
Module-0 cathode as a function of time, spanning two full days of data-taking.
The results of the study are shown in Fig. 31. No substantial time dependence
of transverse spatial offsets is observed
($<$0.2\text{\,}\mathrm{c}\mathrm{m}$$), indicating that calibration of the
underlying electric field distortions is achievable by averaging measured
spatial offsets over at least a few days of data-taking. A study of electric
field stability over longer periods of time is planned in future prototyping
of the DUNE ND-LAr detector concept.

Figure 31: Time dependence of spatial offsets in the $-z$ (top) and $+z$
(bottom) drift volumes. These offsets are measured with respect to the
location of the pixel channels at the edge of the detector.

###  5.3 Charge-light matching

Efficient matching between signals in the charge and light readout systems is
essential, as this enables the use of light to disambiguate pile-up of
separate neutrino interactions within a single beam spill. The unique
association between charge and light signals is a nontrivial problem in a
large-volume LArTPC, especially in an environment with a high rate of neutrino
event pile-up, such as DUNE ND-LAr. This motivates the modular design, where
the full active volume is composed of an array of optically-isolated TPC
volumes, each with high coverage of optical detectors with fast timing and
good spatial resolution. Charge-light matching in Module-0 has been
accomplished via association of precision GPS-synchronized timestamps in the
two systems. Here, two performance metrics are considered: the efficiency of
matching for a selection of tracks as a function of the allowed coincidence
time window and the resolution in terms of the offset between the two systems’
timestamps. Fig. 32 shows the matching efficiency for varying definitions of
the allowed time window for coincidence formation, for a selection of anode-
cathode-crossing muon tracks. The overwhelming majority of these are single
tracks, as the probability of having another event in the same $\sim$200 $\mu
s$ window is very small. For conservative matching parameters, an efficiency
of $\geq 99.7$% is found. In this study, the timing resolution is limited by
the spatial resolution of the tracking from the charge readout, not by the
intrinsic light detector timing resolution, which is discussed in Section 4.
Next, Fig. 33 illustrates the relative time offset between the two systems for
the Module-0 prototype, again for a selection of anode-cathode-crossing
tracks. The distribution exhibits a Gaussian core and a tail. The asymmetric
tail of the distribution, captured by a Crystal Ball fit cry , is due to track
truncation near the boundaries of the pixel planes. The Gaussian component of
the Crystal Ball fit is also shown; the standard deviation of the Gaussian,
$0.4\text{\,}~{}$$\mu$s, is identified as the charge readout timing
resolution. The physics requirements for ND-LAr require that the resolution in
the drift dimension be at least as precise as that across the anode plane,
i.e. the pixel pitch divided by $\sqrt{12}$, or
$1.3\text{\,}\mathrm{m}\mathrm{m}$. The resolution extracted in Module-0
corresponds to $0.6\text{\,}\mathrm{m}\mathrm{m}$ at a drift electric field of
$500\text{\,}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$, thus meeting the
requirement.

Figure 32: Charge-light matching efficiency in linear scale (left) and
inefficiency in logarithmic scale (right) for light detector triggers matched
to the arrival time of charge at the anode side of anode-cathode-crossing
tracks. Figure 33: Time offset distribution for light detector triggers
matched to the arrival time of charge at the anode side of anode-cathode-
crossing tracks (charge minus light).

###  5.4 Correlation of the charge and light yield

Matched charge and light events as shown in Figure 34 provide another data
sample which may be used to study the correlation in the relative charge and
light yields in the detector. These yields are related to electric-field
dependent recombination effects.

Figure 34: Charge-light matched event display of a cosmic muon track. The left
two panels show the TPC charge readout, in a $z-y$ project (left) and $x-y$
projection (center left). The right two panels show the light detector
responses for the arrays at $-x$ (center right) and $+x$ (right), with each
bin along the vertical axis representing the strength of signal read by
individual SiPMs.

To describe the recombination mechanism in LAr we formalize the ionization and
excitation states generated by the deposited energy of a traversing particle
as follows:

$N_{i}+N_{ex}=QY+LY,$ (2)

where the sum of available ionization ($N_{i}$) and excitation ($N_{ex}$)
states determines the total number of electrons ($QY$) and photons ($LY$)
generated in LAr. The number of ionization states $N_{i}$ is given by

$N_{i}=\frac{E_{dep}}{W_{i}}\,,\,W_{i}=23.6\,\mathrm{eV},$ (3)

where $W_{i}$ is the ionization work function Shibamura et al. (1975) and
$E_{dep}$ is the deposited energy. In the absence of charge attenuation and
impurities, the total charge $Q$ arriving at the anode depends only on the
initially-produced ionization charge $Q_{0}=N_{i}e$ as

$\displaystyle QY$ $\displaystyle=N_{i}\cdot R_{c},$ (4) $\displaystyle LY$
$\displaystyle=N_{i}\left(1+\frac{N_{ex}}{N_{i}}-R_{c}\right),$ (5)

where the charge recombination factor $R_{c}$ is dependent on the electric
field $\epsilon$, and $e$ is the electron charge. In the presence of
impurities, the electron lifetime correction is applied first; see Eq. 1.
Increasing $\epsilon$ leads to less recombination between argon ions and
ionization electrons, and thus more free charge carriers are present in the
TPC drift field, increasing the total detected charge at the anode plane. At
the same time, a reduced charge recombination factor corresponds to less
scintillation light produced within the TPC, leading to a decrease of the
light yield at higher electric fields, as expressed by Eq. 4. Hence, the
amount of charge yield and the amount of light yield observed in the detector
are expected to be anti-correlated. To describe the recombination of electron-
ion pairs, we focus on the most commonly used models, namely the Box Thomas
and Imel (1987) and the Birks’ models Birks (1951), and compare the results of
Module-0 measurements with those of the ICARUS Amoruso et al. (2004) and
ArgoNeuT Acciarri et al. (2013) experiments. The Box model assumes zero
electron diffusion, zero ion mobility, and a distribution of ionization
electrons that are uniformly produced within a 3D box along the path of the
ionizing particle. The collected charge $Q$ is given by

$Q=Q_{0}\cdot\dfrac{A_{\rm{Box}}}{\xi}\cdot\ln\left(\xi\right),$ (6)

where $Q_{0}$ denotes the primary ionization charge and $\xi$ is

$\xi=\dfrac{N_{0}K_{r}}{4a^{2}\mu\epsilon},$ (7)

where $a$ is the linear size of the charge ‘box’, $N_{0}$ denotes the number
of electrons in the box and $K_{r}$ is the recombination rate constant. $\mu$
and $\epsilon$ define the electron mobility and the electric field,
respectively. Note that in the limit of an infinite electric field intensity
$\epsilon$, the collected charge at the anode plane corresponds to the
initially produced charge, $Q_{0}$. Birks’ model describes the collected
charge $QY$ as

$QY=N_{i}\cdot\frac{A_{\rm{Birks}}}{1+\frac{k_{B}}{\epsilon}\cdot\frac{dE}{dx}}=\frac{Q_{0}}{e}R_{c},$
(8)

where $A_{\rm{Birks}}$ and $k_{B}$ are fitting constants. In this formulation
of the Birks’ model, for infinite electric field intensities
$\epsilon\rightarrow\infty$, the recombination factor does not go to $1$ and
is limited to $R_{c}\rightarrow A$. We can now express the light yield as

$LY=N_{i}\left(1+\frac{N_{ex}}{N_{i}}-\frac{A_{\rm{Birks}}}{1+\frac{k_{B}}{\epsilon}\cdot\frac{dE}{dx}}\right).$
(9)

However, since the fraction of excited states $\frac{N_{ex}}{N_{i}}$ is not
precisely known, the commonly used model for description of the light yield in
scintillating materials uses the following formulation:

$\displaystyle LY$ $\displaystyle=L_{0}\left(1-\alpha
R_{c}\right)=L_{0}R_{L},$ (10) $\displaystyle L_{0}$
$\displaystyle=\frac{E_{dep}}{W_{L}}\,,W_{L}=19.5\,\rm{eV},$ (11)

where $L_{0}$ denotes the number of scintillation photons at zero electric
field intensity, $\alpha$ is a constant fitted to the data and $W_{L}$ is the
scintillation work function Doke et al. (2002). This formulation is used in
this analysis to evaluate the parameters in the Birks’ model for the light
yield.

To study the charge and light correlation in Module-0, data samples at
different electric field intensities ranging from
$0.05\text{\,}\mathrm{kV}\text{\,}{\mathrm{cm}}^{-1}$ to
$1.00\text{\,}\mathrm{kV}\text{\,}{\mathrm{cm}}^{-1}$ were acquired and
analysed. These events contain information about the collected charge and
scintillation light. A selection of vertical through-going tracks, as expected
from MIP muons, was used to extract the collected charge and light per unit
length of the track. For the measurement of the collected charge per unit
track length, the track was divided into 2 cm segments and the total charge
collected each the segment was divided by the segment length. Then, the light
yield per unit track length is extracted as:

$\frac{dL}{dx}=\frac{L_{\mathrm{detected}}}{\int\Omega
dl\times\mathrm{PDE}\times G}.$ (12)

The factors in this expression include the geometrical acceptance $\int\Omega
dl$, the readout gate acceptance $G$, and the overall PDE of each tile
reported in Section 4. The geometrical acceptance was computed based on the
charge data and the track segment position with respect to a light detection
tile, integrated over the track length. The readout gate acceptance is an
estimation of the fraction of photons which reach the SiPM within the readout
integration gate of $500$ ns. The gate acceptance was measured using the
average waveform of the light signals in Module-0 data to be $\sim 64\%$ for
both the LCM and ArCLight modules.

The $dQ/dx$ and $dL/dx$ distributions are well-described by a Landau-convolved
Gaussian function, which is used to extract the most probable value (MPV). We
note that the fits are performed on raw data, i.e. without additional
calibration of the track $dE/dx$. Due to uncorrected charge losses, the
extracted MPV values for charge measurements should be compared with an
effective value of $\sim 1.8$ MeV/cm, while MPVs corresponding to light
measurements correspond to an effective $dE/dx\sim 2.1$ MeV/cm. The dependence
of the charge yield and the light yield MPV values with respect to the
electric field density is illustrated in Fig. 35.

The charge yield and light yield data points were fitted separately to the
Birks’ model, with results shown in Fig. 35 and Tab. 1. We note that for the
light yield fit (Fig. 35, right), per Eq. 10, the $A_{\mathrm{Birks}}$ and
$\alpha_{\mathrm{light}}$ parameters are totally correlated and cannot be
extracted independently. The left panel of Fig. 35 also shows a comparison of
the charge yield data (red points) to fits using a Birks’ model (red curve)
and Box model (green curve), alongside the results from the ICARUS experiment
(blue curve), demonstrating good agreement between the results.

Figure 35: Charge yield as a function of the electric field intensity fitted with the Box and Birks’ models, and compared to ICARUS results (left); Light yield as a function of the electric field intensity fitted separately with the Birks’ model (right). Fit parameters |  $A_{Birks}$ $[$\text{\,}\mathrm{kV}\text{\,}\mathrm{g}\text{\,}{\mathrm{cm}}^{-3}\text{\,}{\mathrm{MeV}}^{-1}$]$ |  $k_{Birks}$ $[$\text{\,}\mathrm{kV}\text{\,}\mathrm{g}\text{\,}{\mathrm{cm}}^{-3}\text{\,}{\mathrm{MeV}}^{-1}$]$
---|---|---
Charge only fit | $0.820\pm 0.011\text{\,}$ | $0.058\pm 0.005\text{\,}$
Light only fit | $0.79\pm 0.45\text{\,}$ | $0.037\pm 0.004\text{\,}$
Combined fit | $0.794\pm 0.008\text{\,}$ | $0.045\pm 0.003\text{\,}$
Table 1: The fitted parameters of the Birks’ model using the Module-0 data.

Next, a combined fit of the Birks’ model to both charge and light yield data
sets was performed. Fig. 36 shows the final result of the correlation study.
The best fit results for the Birks’ model parameters are $A_{Birks}=0.794\pm
0.008$ and $k_{Birks}=0.045\pm 0.003$, with a $\chi^{2}/$ndf of $23.2/35$,
where the number of degrees of freedom calculated based on 19 fit points per
dataset (charge and light) included in the fit and three fit parameters.

Figure 36: Light yield (blue) and charge yield (red) extracted from a
simultaneous fit with the Birks’ model.

Table 2 summarizes the Birks’ model parameters obtained with the Module-0
detector and compares them with the parameters found in the ICARUS and the
ArgoNeuT experiments. The results of the simultaneous fit of the Birks’ model
to the light and charge distributions show reasonable agreement with previous
experiments.

Experiment |  $A_{Birks}$ $[$\text{\,}\mathrm{kV}\text{\,}\mathrm{g}\text{\,}{\mathrm{cm}}^{-3}\text{\,}{\mathrm{MeV}}^{-1}$]$ |  $k_{Birks}$ $[$\text{\,}\mathrm{kV}\text{\,}\mathrm{g}\text{\,}{\mathrm{cm}}^{-3}\text{\,}{\mathrm{MeV}}^{-1}$]$ | Reference
---|---|---|---
ICARUS | $0.800\pm 0.003\text{\,}$ | $0.0486\pm 0.0006\text{\,}$ | Amoruso et al. (2004)
ArgoNeuT | $0.806\pm 0.010\text{\,}$ | $0.052\pm 0.001\text{\,}$ | Acciarri et al. (2013)
Module-0 | $0.794\pm 0.008\text{\,}$ | $0.045\pm 0.003\text{\,}$ | This work
Table 2: Comparison of the ICARUS and ArgoNeuT results with the current study.

###  5.5 Michel electrons

Michel electrons, i.e. electrons from stopped muon decay, constitute a readily
available and versatile tool for the study and characterisation of the
performance of a LArTPC. They are abundant for surface-level detectors exposed
to a large cosmic ray muon flux, and with $\mu\rightarrow
e\overline{\nu}_{e}\nu_{\mu}$ as the almost exclusive decay channel, the
number of events is given by the probability of the muon to come to rest in
the detector. The electrons produced by the decay have a well-characterised
energy spectrum with a cutoff at $\sim 50$ MeV and their topology is
relatively easy to tag: a long muon track ending with a Bragg peak followed by
a short ionization track from the electron at a different angle with respect
to the muon direction. Fig. 1 includes one example of a stopping muon decaying
with a Michel electron in Module-0. The effective muon lifetime of $\sim 2$
$\mu$s is short relative to the TPC drift speed, leading to minimal
displacement of the muon track endpoint and electron track start. However, it
is large relative to the time resolution of the light readout system, allowing
the two signals to be tagged separately: the first light pulse corresponding
to the muon ionization, and the second to the electron, can be easily
separated for a large majority of events due to the excellent timing
resolution of ArCLight and LCM detectors. Fig. 37 shows the event display of a
selected Michel electron candidate, with the two peaks showing the waveforms
of the light detectors located in one of the two half-TPCs.

The Michel electron candidates’ topology is mainly characterised by a long
ionisation trail left over by the crossing muon. An automatic selection
algorithm based on the event topology and the presence of the Bragg peak at
the end of the muon track was developed and applied to the subset of cosmic
data. Visual event validation was performed on selected events to validate the
analysis. The final distribution of the reconstructed Michel electron energy
based on the automated charge reconstruction is shown in Fig. 38. The end
point is near the expected true end point of 53 MeV. The spectrum peaks at
lower energies mainly as a consequence of partial containment, imperfect
clustering, and charge below threshold, particularly from electrons Compton-
scattered by Bremmstrahlung photons radiated from the primary electron Abed
Abud et al. (2023); Foreman et al. (2020); Acciarri et al. (2017).

Figure 37: Event display of a Michel electron candidate shown in a 3D view
(left) and with associated waveforms from photon detectors (right). In the
right panel, orange and blue indicate the two optically isolated semi-TPCs.
The red circles highlight an example the two pulses on the photon detectors
correspond to the entering muon and the electron resulting from its decay.
Figure 38: Charge-based energy spectrum of Michel electron candidates from a
sample of reconstructed muon decays, using the full data set and automated
event reconstruction.

###  5.6 Detector simulation validation with cosmic ray tracks

Finally, selected samples of cosmic ray tracks are compared in detail to a
cosmic ray simulation based on the CORSIKA event generator and the detailed
microphysical detector simulation introduced in Section 5. Starting from the
cosmic ray track reconstruction described there, the track’s start and end
points are found by projecting the 3D points onto the cluster’s principal
components. The DBSCAN+RANSAC fit is applied on outlying hits until all are
placed within a cluster or no hits remain. This is sufficient for studies of
low-level detector response, as it provides a local approximation of the track
trajectory with minimal impact from $\delta$-rays and hard scatters.
Reconstructed tracks may show artificial gaps due to the presence of disabled
channels. Also, cathode-piercing tracks will usually be reconstructed as
separated tracks, due to the non-zero cathode thickness. Thus, tracks with an
angle smaller than $20^{\circ}$ and closer than 10 cm are stitched together
for the following studies. A comparison between the spatial coordinates of the
stitched tracks in data and simulation is shown in Fig. 39.

Figure 39: Start and end coordinates of stitched tracks in data (high and low
threshold runs) and simulation.

Fig. 40 shows a comparison of the $dQ/dx$ for low threshold and high threshold
runs with a sample of simulated cosmic rays. The $dQ/dx$ has been measured for
segments of different lengths, following the procedure described in Section
5.6. The simulation assumes the Birks model for electron recombination and a
gain of 4 mV/$10^{3}$ e- Birks (1951). In the data, the amount of charge that
reaches the anode is corrected by the electron lifetime factor calculated in
Section 5.1.

Figure 40: $dQ/dx$ measured for segments of different lengths for low
threshold runs (black dots), high threshold runs (white dots) and a sample of
simulated cosmic rays (red line). The distributions have been fitted with a
Gaussian-convolved Moyal function (dashed lines).

Next, the $dQ/dx$ as a function of the reconstructed track residual range is
considered. As noted in Section 5.5, for a muon that stops in the detector the
amount of deposited charge per unit length will increase as it approaches the
end point, forming a Bragg peak. Fig. 41 shows an example of a stopping muon
and the subsequent Michel electron. The $dQ/dx$ has been measured by
subdividing the reconstructed track in 10 mm segments (our $dx$) and summing
the charge contained in each segment (the $dQ$). The data show a Bragg peak
near the end of the reconstructed track, where the residual range is close to
zero. The theoretical prediction is obtained by taking the
$\langle\frac{dE}{dx}\rangle$ values tabulated in Ref. Groom et al. (2001) for
muons in LAr, divided by the argon ionization energy (23.6 eV) and multiplied
by the recombination factor ${R}_{\mathrm{Birks}}^{\mathrm{ICARUS}}$,
calculated in Ref. Amoruso et al. (2004).

Figure 41: Top: event display of the anode plane for a selected stopping muon
(blue) and subsequent Michel electron (orange). Bottom: $dQ/dx$ for the
reconstructed muon track as a function of the residual range $dQ/dx$ and the
theoretical curve for muons stopping in liquid argon (red line).

The observed distributions indicate good overall agreement between data and
simulations, in particular with the ability to correctly reproduce the
position of the $dQ/dx$ peak. Module-0 data provide input that can be used to
further tune the detector simulation, including modeling of additional noise
sources and details of the anode response. Meanwhile, the strong overall
agreement in the vertex positioning and calorimetry indicates that the initial
detector response model is able to capture the main features of the cosmic ray
track samples.

##  6 Conclusions

We have reported here the experimental results of exposing the Module-0
demonstrator, a tonne-scale LArTPC with pixel-based charge readout, to cosmic
rays. This new type of neutrino detector is designed to meet the challenges of
the near detector complex of the forthcoming DUNE experiment, which will be
exposed to a very intense beam-related flux of particles. These challenges are
expected to severely hamper the performance of a conventional, wire-readout,
monolithic LArTPC, where reconstruction of complex 3D event topologies using a
small number of 2D projections can lead to unsolvable ambiguities,
particularly when multiple events overlap in the drift direction. The novel
Module-0 design features a combination of new technological solutions: a
pixelated anode to read out the ionization electron signal that provides
native three-dimensional charge imaging, a modular structure with relatively
short drift length, high-performance scintillation light detection systems,
and an innovative approach to field shaping using a low-profile resistive
shell. Module-0 is one of four units that will comprise the $2\times 2$
demonstrator (ProtoDUNE-ND) being installed at Fermilab to be exposed to the
NuMI neutrino beam.

A detailed assessment of this technology has been performed by operating
Module-0, as well as the associated cryogenics, data acquisition, trigger, and
timing infrastructure, at the University of Bern. A large sample of 25 million
self-triggered cosmic ray-induced events was collected and analyzed, along
with an array of dedicated diagnostic data runs. The response of the
78,400-pixel readout system was studied, as well as the performance of the two
independent and complementary light detection systems. The data analysis
demonstrated key physics requirements of this technology, such as the electron
lifetime, the uniformity of the electric field, and the matching/correlation
between the charge and light signals. The reconstruction of particle tracks
and Michel electrons illustrates the physics capabilities, and the comparison
with detailed, microphysical simulations has demonstrated a robust
understanding of the workings of this new type of LArTPC detector. Overall,
these results demonstrate the key design features of the technique and provide
a confirmation of the outstanding imaging capabilities of this next-generation
LArTPC design.

##  7 Acknowledgments

This document was prepared by the DUNE collaboration using the resources of
the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of
Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi
Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359.
This work was supported by CNPq, FAPERJ, FAPEG and FAPESP, Brazil; CFI, IPP
and NSERC, Canada; CERN; MŠMT, Czech Republic; ERDF, H2020-EU and MSCA,
European Union; CNRS/IN2P3 and CEA, France; INFN, Italy; FCT, Portugal; NRF,
South Korea; CAM, Fundación “La Caixa”, Junta de Andalucía-FEDER, MICINN, and
Xunta de Galicia, Spain; SERI and SNSF, Switzerland; TÜBİTAK, Turkey; The
Royal Society and UKRI/STFC, United Kingdom; DOE and NSF, United States of
America. This research used resources of the National Energy Research
Scientific Computing Center (NERSC), a U.S. Department of Energy Office of
Science User Facility operated under Contract No. DE-AC02-05CH11231.

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