Among the various candidates for dark matter DM ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context KAGRA has a unique feature due to differing compositions of its mirrors enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for inlineformulammlmath displayinlinemmlmiUmmlmimmlmo stretchyfalsemmlmommlmn1mmlmnmmlmsubmmlmo stretchyfalsemmlmommlmrowmmlmiBmmlmimmlmommlmommlmiLmmlmimmlmrowmmlmsubmmlmathinlineformula gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline which takes into account the stochastic nature of ultralight DM upper bounds on the coupling strength between the inlineformulammlmath displayinlinemmlmiUmmlmimmlmo stretchyfalsemmlmommlmn1mmlmnmmlmsubmmlmo stretchyfalsemmlmommlmrowmmlmiBmmlmimmlmommlmommlmiLmmlmimmlmrowmmlmsubmmlmathinlineformula gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments this study demonstrates the applicability of our method to the lowermass vector DM search which is made difficult in this measurement by the short observation time compared to the autocorrelation timescale of DM.
['Experiments in gravity', 'cosmology', 'cosmic rays', 'Astrophysics - Cosmology and Nongalactic Astrophysics', 'General Relativity and Quantum Cosmology', 'High Energy Physics - Phenomenology']
Ultralight vector dark matter search using data from the KAGRA O3GK run
{'Ultralight vector dark matter search using data from the KAGRA O3GK run': "A. W. Criswell , 89 J. C. G. Crockett-Gray, 11 M. Croquette , 114 R. Crouch, 4 S. G. Crowder, 162 J. R. Cudell , 111 T. J. Cullen, 2 A. Cumming , 26 E. Cuoco, 52, 163, 20 M. Cusinato , 135 P. Dabadie, 123 T. Dal Canton , 35 S. Dall'Osso , 60 G. D'alya , 84 B. D'Angelo , 51 S. Danilishin , 31, 32 S. D'Antonio, 86 K. Danzmann, 14, 13, 14 K. E. Darroch, 116 L. P. Dartez, 4 A. Dasgupta, 83 S. Datta , 54 V. Dattilo, 52 A. Daumas, 63 N. Davari, 164, 130 I. Dave, 95 A. Davenport, 98 M. Davier, 35 T. F. Davies, 27 D. Davis , 2 L. Davis, 27 M. C. Davis , 94 E. J. Daw , 165 M. Dax , 1 J. De Bolle , 84 M. Deenadayalan, 15 J. Degallaix , 166 M. De Laurentis , 29, 6 S. Del'eglise , 114 V. Del Favero , 75 F. De Lillo , 115 D. Dell'Aquila , 164, 130 W. Del Pozzo , 77, 20 F. De Marco , 60, 107 F. De Matteis , 132, 86 V. D'Emilio , 19 N. Demos, 30 T. Dent , 124 A. Depasse , 115 N. DePergola, 94 R. De Pietri , 167, 168 R. De Rosa , 29, 6 C. De Rossi , 52 R. De Simone, 150 A. Dhani, 1 S. Dhurandhar, 15 R. Diab, 40 M. C. D'ıaz , 161 M. Di Cesare , 29 G. Dideron, 169 N. A. Didio, 70 T. Dietrich , 1 L. Di Fiore, 6 C. Di Fronzo , 33 F. Di Giovanni , 135 M. Di Giovanni, 107, 60 T. Di Girolamo , 29, 6 D. Diksha, 32, 31 A. Di Michele , 78 J. Ding , 63, 170 S. Di Pace , 107, 60 I. Di Palma , 107, 60 F. Di Renzo , 153 Divyajyoti , 171 A. Dmitriev , 110 Z. Doctor , 71 E. Dohmen, 4 P. P. Doleva, 116 L. Donahue, 172 L. D'Onofrio , 60 F. Donovan, 30 K. L. Dooley , 19 T. Dooney, 68 S. Doravari , 15 O. Dorosh, 173 M. Drago , 107, 60 J. C. Driggers , 4 Y. Drori, 2 J.-G. Ducoin, 174, 63 L. Dunn , 129 U. Dupletsa, 39 D. D'Urso , 164, 130 H. Duval , 175 P.-A. Duverne, 35 S. E. Dwyer, 4 C. Eassa, 4 M. Ebersold , 176, 28 T. Eckhardt , 76 G. Eddolls , 26 B. Edelman , 69 T. B. Edo, 2 O. Edy , 122 A. Effler , 59 J. Eichholz , 12 H. Einsle, 44 M. Eisenmann, 22 R. A. Eisenstein, 30 A. Ejlli , 19 M. Emma , 55 E. Engelby, 50 A. J. Engl, 18 L. Errico, 29, 6 R. C. Essick , 177 H. Estell'es , 1 D. Estevez , 61 T. Etzel, 2 M. Evans , 30 T. Evstafyeva, 16 B. E. Ewing, 9 J. M. Ezquiaga , 125 F. Fabrizi , 57, 58 F. Faedi, 58, 57 V. Fafone , 132, 86 S. Fairhurst , 19 P. C. Fan , 172 A. M. Farah , 125 B. Farr , 69 W. M. Farr , 178, 179 G. Favaro , 80 M. Favata , 180 M. Fays , 111 M. Fazio, 90 J. Feicht, 2 M. M. Fejer, 18 E. Fenyvesi , 74, 181 D. L. Ferguson , 147 I. Ferrante , 77, 20 T. A. Ferreira, 11 F. Fidecaro , 77, 20 A. Fiori , 20, 77 I. Fiori , 52 M. Fishbach , 177 R. P. Fisher, 116 R. Fittipaldi, 182, 105 V. Fiumara, 183, 105 R. Flaminio, 28 S. M. Fleischer , 184 L. S. Fleming, 185 E. Floden, 89 E. M. Foley, 89 H. Fong, 138 J. A. Font , 135, 136 B. Fornal , 186 P. W. F. Forsyth, 12 K. Franceschetti, 167 N. Franchini, 63 S. Frasca, 107, 60 F. Frasconi , 20 A. Frattale Mascioli , 107, 60 Z. Frei , 187 A. Freise , 32, 99 O. Freitas , 188, 135 R. Frey , 69 W. Frischhertz, 59 V. V. Frolov, 59 G. G. Fronz'e , 25 M. Fuentes-Garcia , 2 S. Fujii, 152 I. Fukunaga, 189 P. Fulda, 40 M. Fyffe, 59 W. E. Gabella , 190 B. Gadre , 68 J. R. Gair , 1 S. Galaudage , 8, 191 S. Gallardo, 192 B. Gallego, 192 R. Gamba , 93 A. Gamboa , 1 D. Ganapathy , 30 A. Ganguly , 15 S. G. Gaonkar, 15 B. Garaventa , 51, 193 J. Garcia-Bellido , 112 C. Garc'ıa-N'u˜nez, 185 C. Garc'ıa-Quir'os , 176 J. W. Gardner , 12 K. A. Gardner, 138 J. Gargiulo , 52 A. Garron , 91 F. Garufi , 29, 6 C. Gasbarra , 132, 86 B. Gateley, 4 V. Gayathri , 10 G. Gemme , 51 A. Gennai , 20 J. George, 95 R. George, 147 O. Gerberding , 76 L. Gergely , 194 N. Ghadiri, 50 Archisman Ghosh , 84 Shaon Ghosh , 180 Shrobana Ghosh, 13, 14 Suprovo Ghosh , 15 Tathagata Ghosh , 15 L. Giacoppo, 107, 60 J. A. Giaime , 11, 59 K. D. Giardina, 59 D. R. Gibson, 185 D. T. Gibson, 16 C. Gier , 90 P. Giri , 20, 77 F. Gissi, 87 S. Gkaitatzis , 77, 20 J. Glanzer, 11 A. E. Gleckl, 50 F. Glotin, 35 J. Godfrey, 69 P. Godwin, 2 N. L. Goebbels , 76 E. Goetz , 138 J. Golomb, 2 S. Gomez Lopez , 107, 60 B. Goncharov , 39 G. Gonz'alez , 11 P. Goodarzi, 126 A. W. Goodwin-Jones , 27 M. Gosselin, 52 A. S. Gottel , 19 R. Gouaty , 28 D. W. Gould, 12 S. Goyal , 21 B. Grace, 12 A. Grado , 195, 6 V. Graham , 26 A. E. Granados , 89 M. Granata , 166 V. Granata , 62 L. Granda Argianas, 94 S. Gras, 30 P. Grassia, 2 C. Gray, 4 R. Gray , 26 G. Greco, 46 A. C. Green , 32, 99 S. M. Green, 122 S. R. Green , 1 A. M. Gretarsson, 43 E. M. Gretarsson, 43 D. Griffith, 2 W. L. Griffiths , 19 H. L. Griggs , 53 G. Grignani, 78, 46 A. Grimaldi , 102, 103 C. Grimaud, 28 H. Grote , 19 A. S. Gruson, 50 D. Guerra , 135 D. Guetta , 196, 60 G. M. Guidi , 57, 58 A. R. Guimaraes, 11 H. K. Gulati, 83 F. Gulminelli , 197, 198 A. M. Gunny, 30 H. Guo , 186 W. Guo , 27 Y. Guo , 32, 31 Anchal Gupta , 2 Anuradha Gupta , 199 Ish Gupta , 9 N. C. Gupta, 83 P. Gupta, 32, 68 S. K. Gupta, 40 T. Gupta , 82 N. Gupte, 1 R. Gurav, 126 J. Gurs, 76 N. Gutierrez, 166 F. Guzman , 128 D. Haba, 3 M. Haberland, 1 L. Haegel , 63 G. Hain, 116 S. Haino, 200 E. D. Hall , 30 E. Z. Hamilton, 176 G. Hammond , 26 W.-B. Han , 201 M. Haney , 176, 32 J. Hanks, 4 C. Hanna, 9 M. D. Hannam, 19 O. A. Hannuksela , 137 A. G. Hanselman , 125 H. Hansen, 4 J. Hanson, 59 R. Harada, 36 T. Harder, 44 K. Haris, 32, 68 T. Harmark , 131 J. Harms , 39, 113 G. M. Harry , 202 I. W. Harry , 122 B. Haskell, 85 C.-J. Haster , 203 J. S. Hathaway, 204 K. Haughian , 26 H. Hayakawa, 45 K. Hayama, 205 J. Healy , 204 A. Heffernan , 91 A. Heidmann , 114 M. C. Heintze, 59 J. Heinze , 110 J. Heinzel, 30 H. Heitmann , 44 F. Hellman , 206 P. Hello, 35 A. F. Helmling-Cornell , 69 G. Hemming , 52 M. Hendry , 26 I. S. Heng , 26 E. Hennes , 32 J.-S. Hennig, 31, 32 M. Hennig, 31, 32 C. Henshaw , 53 A. Hernandez, 180 T. Hertog, 101 M. Heurs , 13, 14 A. L. Hewitt , 16, 207 S. Higginbotham, 19 S. Hild, 31, 32 P. Hill, 90 S. Hill, 26 Y. Himemoto , 208 A. S. Hines, 128 N. Hirata, 22 C. Hirose, 209 J. Ho, 142 S. Hoang, 35 S. Hochheim, 13, 14 D. Hofman, 166 N. A. Holland, 32, 99 K. Holley-Bockelmann, 190  \nI. J. Hollows , 165 Z. J. Holmes , 88 D. E. Holz , 125 C. Hong, 18 J. Hornung, 69 S. Hoshino, 209 S. Hourihane, 2 E. J. Howell , 27 C. G. Hoy , 122 D. Hoyland, 110 C. A. Hrishikesh, 132 H.-F. Hsieh , 141 C. Hsiung, 210 H. C. Hsu, 142 S.-C. Hsu , 48, 141 W.-F. Hsu , 101 P. Hu, 190 Q. Hu , 26 H. Y. Huang , 142 Y.-J. Huang , 9 Y. Huang, 30 Y. T. Huang, 48 A. D. Huddart, 211 B. Hughey, 43 D. C. Y. Hui , 212 V. Hui , 28 R. Hur, 69 S. Husa , 91 R. Huxford, 9 T. Huynh-Dinh, 59 A. Iakovlev , 213 G. A. Iandolo, 31 A. Iess , 163, 20 K. Inayoshi , 214 Y. Inoue, 142 G. Iorio , 80 J. Irwin , 26 M. Isi , 178, 179 M. A. Ismail , 142 Y. Itoh , 189, 215 M. Iwaya, 152 B. R. Iyer , 21 V. JaberianHamedan , 27 P.-E. Jacquet , 114 S. J. Jadhav, 216 S. P. Jadhav , 155 T. Jain, 16 A. L. James , 19 P. A. James, 116 R. Jamshidi, 33 A. Z. Jan , 147 K. Jani , 190 L. Janiurek, 26 J. Janquart, 68, 32 K. Janssens , 106, 44 N. N. Janthalur, 216 S. Jaraba , 112 P. Jaranowski , 217 P. Jasal, 37 R. Jaume , 91 W. Javed, 19 A. Jennings, 4 W. Jia, 30 J. Jiang , 40 H.-B. Jin , 218, 219 K. Johansmeyer, 180 G. R. Johns, 116 N. A. Johnson, 40 R. Johnston, 26 N. Johny, 13, 14 D. H. Jones , 12 D. I. Jones, 220 R. Jones, 26 S. Jose, 171 P. Joshi, 9 L. Ju , 27 K. Jung , 221 J. Junker , 13, 14 V. Juste, 61 T. Kajita , 222 C. Kalaghatgi, 68, 32, 223 V. Kalogera , 71 M. Kamiizumi , 45 N. Kanda , 215, 189 S. Kandhasamy , 15 G. Kang , 224 J. B. Kanner, 2 S. J. Kapadia, 15 D. P. Kapasi , 12 S. Karat, 2 C. Karathanasis , 38 S. Karki , 97 R. Kashyap, 9 M. Kasprzack , 2 W. Kastaun, 13, 14 J. Kato, 151 T. Kato, 152 S. Katsanevas, 52, ∗ E. Katsavounidis, 30 W. Katzman, 59 T. Kaur, 27 R. Kaushik , 95 K. Kawabe, 4 D. Keitel , 91 J. Kelley-Derzon, 40 J. Kennington , 9 R. Kesharwani, 15 J. S. Key , 225 S. Khadka, 18 F. Y. Khalili , 100 F. Khan , 13, 14 I. Khan, 226, 34 T. Khanam, 158 E. A. Khazanov, 213 M. Khursheed, 95 W. Kiendrebeogo , 44, 227 N. Kijbunchoo , 88 C. Kim, 228 J. C. Kim, 229 K. Kim , 230 M. H. Kim, 231 S. Kim , 212 W. S. Kim, 232 Y.-M. Kim , 230 C. Kimball , 71 N. Kimura, 45 M. Kinley-Hanlon , 26 M. Kinnear, 19 J. S. Kissel , 4 T. Kiyota, 189 S. Klimenko, 40 T. Klinger, 19 A. M. Knee , 138 N. Knust , 13, 14 P. Koch, 13, 14 S. M. Koehlenbeck , 18 G. Koekoek, 32, 31 K. Kohri , 233 K. Kokeyama , 19 S. Koley , 39 P. Kolitsidou , 110 M. Kolstein , 38 K. Komori , 36 A. K. H. Kong , 141 A. Kontos , 234 M. Korobko , 76 R. V. Kossak, 13, 14 X. Kou, 89 A. Koushik, 106 N. Kouvatsos , 64 M. Kovalam, 27 N. Koyama, 209 D. B. Kozak, 2 S. L. Kranzhoff, 31, 32 V. Kringel, 13, 14 N. V. Krishnendu , 21 A. Kr'olak , 235, 173 G. Kuehn, 13, 14 P. Kuijer , 32 S. Kulkarni , 199 A. Kulur Ramamohan , 12 A. Kumar, 216 Praveen Kumar , 124 Prayush Kumar , 21 Rahul Kumar, 4 Rakesh Kumar, 83 J. Kume , 80, 81, 36 K. Kuns , 30 S. Kuroyanagi , 112, 236 S. Kuwahara, 36 K. Kwak , 221 K. Kwan, 12 G. Lacaille, 26 P. Lagabbe, 28 D. Laghi , 121 S. Lai, 145 A. H. Laity, 160 M. H. Lakkis, 33 E. Lalande, 237 M. Lalleman , 106 M. Landry, 4 B. B. Lane, 30 R. N. Lang , 30 J. Lange, 147 B. Lantz , 18 A. La Rana , 60 I. La Rosa , 91, 107, 28 A. Lartaux-Vollard , 35 P. D. Lasky , 8 J. Lawrence, 158 M. Laxen , 59 A. Lazzarini , 2 C. Lazzaro, 80, 81 P. Leaci , 107, 60 S. LeBohec, 186 Y. K. Lecoeuche , 138 H. M. Lee , 229 H. W. Lee , 238 K. Lee , 231 R.-K. Lee , 141 R. Lee, 30 S. Lee , 230 Y. Lee, 142 I. N. Legred, 2 J. Lehmann, 13, 14 L. Lehner, 169 A. Lemaˆıtre, 239 M. Lenti , 58, 240 M. Leonardi , 241, 22 E. Leonova , 96 M. Lequime, 34 N. Leroy , 35 M. Lesovsky, 2 N. Letendre, 28 M. Lethuillier , 153 C. Levesque, 237 Y. Levin, 8 K. Leyde, 63 A. K. Y. Li, 2 K. L. Li , 140 T. G. F. Li, 137, 101 X. Li , 148 Chien-Yu Lin, 142, 141 Chun-Yu Lin , 242 E. T. Lin , 141 F. Lin, 142 H. Lin, 142 L. C.-C. Lin , 140 F. Linde, 223, 32 S. D. Linker, 133, 192 T. B. Littenberg, 243 A. Liu , 137 G. C. Liu , 210 Jian Liu , 27 F. Llamas, 161 J. Llobera-Querol , 91 R. K. L. Lo , 2 J.-P. Locquet, 101 L. London, 96 A. Longo , 57, 58 D. Lopez, 176 M. Lopez Portilla, 68 M. Lorenzini , 132, 86 V. Loriette, 35 M. Lormand, 59 G. Losurdo , 20 T. P. Lott IV , 53 J. D. Lough , 13, 14 H. A. Loughlin, 30 C. O. Lousto , 204 M. J. Lowry, 116 H. Luck, 14, 13, 14 D. Lumaca , 86 A. P. Lundgren, 122 A. W. Lussier , 237 L.-T. Ma, 141 S. Ma, 148 M. Ma'arif , 142 R. Macas , 122 M. MacInnis, 30 R. R. Maciy, 13, 14 D. M. Macleod , 19 I. A. O. MacMillan , 2 A. Macquet , 38 D. Macri, 30 K. Maeda, 151 S. Maenaut , 101 I. Maga˜na Hernandez, 10 S. S. Magare, 15 C. Magazz'u , 20 R. M. Magee , 2 E. Maggio , 1 R. Maggiore, 32, 99 M. Magnozzi , 51, 193 M. Mahesh, 76 S. Mahesh, 244 M. Maini, 160 S. Majhi, 15 E. Majorana, 107, 60 C. N. Makarem, 2 J. A. Malaquias-Reis, 17 S. Maliakal, 2 A. Malik, 95 N. Man, 44 V. Mandic , 89 V. Mangano , 60, 107 B. Mannix, 69 G. L. Mansell , 70, 30 M. Manske , 10 M. Mantovani , 52 M. Mapelli , 80, 81 F. Marchesoni, 47, 46, 245 D. Mar'ın Pina , 37, 72, 246 F. Marion , 28 S. M'arka , 159 Z. M'arka , 159 C. Markakis , 144 A. S. Markosyan, 18 A. Markowitz, 2 E. Maros, 2 A. Marquina , 157 S. Marsat , 121 F. Martelli , 57, 58 I. W. Martin , 26 R. M. Martin , 180 B. B. Martinez, 128 M. Martinez, 38, 247 V. Martinez , 123 A. Martini, 102 K. Martinovic, 64 J. C. Martins , 17 D. V. Martynov, 110 E. J. Marx, 30 L. Massaro, 31, 32 A. Masserot, 28 M. Masso-Reid , 26 M. Mastrodicasa, 60 S. Mastrogiovanni , 60 M. Mateu-Lucena , 91 M. Matiushechkina , 13, 14 M. Matsuyama, 189 N. Mavalvala , 30 N. Maxwell, 4 G. McCarrol, 59 R. McCarthy, 4 D. E. McClelland , 12 S. McCormick, 59 L. McCuller , 2 G. I. McGhee, 26 K. B. M. McGowan, 190 M. Mchedlidze, 180 C. McIsaac , 122 J. McIver , 138 K. McKinney, 162 A. McLeod , 27 T. McRae, 12 S. T. McWilliams, 244 D. Meacher , 10 A. K. Mehta, 1 Q. Meijer, 68 A. Melatos, 129 S. Mellaerts , 101 A. Menendez-Vazquez , 38 C. S. Menoni , 98 R. A. Mercer , 10 L. Mereni, 166 K. Merfeld, 69 E. L. Merilh, 59 J. R. M'erou , 91 J. D. Merritt, 69 M. Merzougui, 44  \nS. Sajith Menon, 196, 107, 60 K. Sakai, 278 M. Sakellariadou , 64 T. Sako, 151 S. Sakon , 9 O. S. Salafia , 156, 120, 119 F. Salces-Carcoba , 2 L. Salconi, 52 M. Saleem , 89 F. Salemi , 107, 60 M. Sall'e , 32 S. Salvador , 198, 197, 108 A. Sanchez, 4 E. J. Sanchez, 2 J. H. Sanchez , 71 L. E. Sanchez, 2 N. Sanchis-Gual , 279, 135 J. R. Sanders, 280 E. M. Sanger, 1 T. R. Saravanan, 15 N. Sarin, 8 A. Sasli , 270 P. Sassi , 46, 78 B. Sassolas , 166 H. Satari, 27 R. Sato, 209 S. Sato, 151 Y. Sato, 151 O. Sauter , 40 R. L. Savage , 4 T. Sawada , 45 H. L. Sawant, 15 S. Sayah, 28 D. Schaetzl, 2 M. Scheel, 148 J. Scheuer, 71 M. G. Schiworski , 88 P. Schmidt , 110 S. Schmidt , 68 R. Schnabel , 76 M. Schneewind, 13, 14 R. M. S. Schofield, 69 K. Schouteden, 101 H. Schuler, 9 B. W. Schulte, 13, 14 B. F. Schutz, 19, 13, 14 E. Schwartz , 19 J. Scott , 26 S. M. Scott , 12 T. C. Seetharamu, 26 M. Seglar-Arroyo , 38 Y. Sekiguchi , 281 D. Sellers, 59 A. S. Sengupta , 282 D. Sentenac, 52 E. G. Seo , 26 J. W. Seo , 101 V. Sequino, 29, 6 A. Sergeev, 213 M. Serra , 60 G. Servignat , 261 Y. Setyawati , 68 T. Shaffer, 4 U. S. Shah , 53 M. S. Shahriar , 71 M. A. Shaikh , 229 B. Shams, 186 L. Shao , 214 A. K. Sharma, 21 P. Sharma, 95 S. Sharma-Chaudhary, 97 P. Shawhan , 118 N. S. Shcheblanov , 283, 239 B. Shen, 118 Y. Shikano , 284, 285 M. Shikauchi, 36 K. Shimode , 45 H. Shinkai , 286 J. Shiota, 254 D. H. Shoemaker , 30 D. M. Shoemaker , 147 R. W. Short, 4 S. ShyamSundar, 95 A. Sider, 33 H. Siegel , 159, 178, 179 M. Sieniawska, 115 D. Sigg , 4 L. Silenzi , 46, 47 M. Simmonds, 88 L. P. Singer , 75 A. Singh, 199 D. Singh , 9 M. K. Singh , 21 A. Singha , 31, 32 A. M. Sintes , 91 V. Sipala, 164, 130 V. Skliris , 19 B. J. J. Slagmolen , 12 T. J. Slaven-Blair, 27 J. Smetana, 110 J. R. Smith , 50 L. Smith , 26 R. J. E. Smith , 8 W. J. Smith, 190 J. Soldateschi , 240, 287, 58 S. N. Somala , 288 K. Somiya , 3 K. Soni , 15 S. Soni , 30 V. Sordini, 153 F. Sorrentino, 51 N. Sorrentino , 77, 20 R. Soulard, 44 T. Souradeep, 15, 289 A. Southgate, 19 E. Sowell, 158 V. Spagnuolo, 31, 32 A. P. Spencer , 26 M. Spera , 80, 81 P. Spinicelli, 52 A. K. Srivastava, 83 F. Stachurski , 26 D. A. Steer , 63 J. Steinlechner, 31, 32 S. Steinlechner , 31, 32 N. Stergioulas , 270 P. Stevens, 35 M. StPierre, 160 L. C. Strang, 129 G. Stratta , 290, 291, 60, 292 M. D. Strong, 11 A. Strunk, 4 R. Sturani, 293 A. L. Stuver , 94 M. Suchenek, 85 S. Sudhagar , 15, 85 N. Sueltmann, 76 A. G. Sullivan , 159 K. D. Sullivan, 11 L. Sun , 12 S. Sunil, 83 A. Sur , 85 J. Suresh , 36, 115 P. J. Sutton , 19 Takamasa Suzuki , 209 Takanori Suzuki, 3 B. L. Swinkels , 32 A. Syx, 61 M. J. Szczepa'nczyk , 40 P. Szewczyk , 117 M. Tacca , 32 H. Tagoshi , 152 S. C. Tait , 26 H. Takahashi , 294 R. Takahashi , 22 A. Takamori , 49 K. Takatani, 189 H. Takeda , 295 M. Takeda, 189 C. J. Talbot, 90 C. Talbot, 30 M. Tamaki, 152 N. Tamanini , 121 D. Tanabe, 142 K. Tanaka, 296 S. J. Tanaka , 254 T. Tanaka , 295 A. J. Tanasijczuk, 115 D. Tang, 27 S. Tanioka , 70 D. B. Tanner, 40 L. Tao , 40 R. D. Tapia, 9 E. N. Tapia San Mart'ın , 32 R. Tarafder, 2 C. Taranto, 132, 86 A. Taruya , 297 J. D. Tasson , 172 M. Teloi, 33 R. Tenorio , 91 H. Themann, 192 A. Theodoropoulos, 135 M. P. Thirugnanasambandam, 15 L. M. Thomas , 110 M. Thomas, 59 P. Thomas, 4 J. E. Thompson , 148 S. R. Thondapu, 95 K. A. Thorne, 59 E. Thrane, 8 J. Tissino , 39 A. Tiwari, 15 Shubhanshu Tiwari , 176 Srishti Tiwari , 15 V. Tiwari , 110 M. R. Todd, 70 A. M. Toivonen , 89 K. Toland , 26 A. E. Tolley , 122 T. Tomaru , 22 K. Tomita, 189 T. Tomura , 45 C. Tong-Yu, 142 A. Toriyama, 254 N. Toropov , 110 A. Torres-Forn'e , 135, 136 C. I. Torrie, 2 M. Toscani , 121 I. Tosta e Melo , 298 E. Tournefier , 28 A. A. Trani , 36 A. Trapananti , 47, 46 F. Travasso , 47, 46 G. Traylor, 59 J. Trenado , 37 M. Trevor, 118 M. C. Tringali , 52 A. Tripathee , 79 L. Troiano, 299, 105 A. Trovato , 42, 249 L. Trozzo, 6 R. J. Trudeau, 2 T. T. L. Tsang , 19 R. Tso, 148, † S. Tsuchida , 300 L. Tsukada, 9 T. Tsutsui , 36 K. Turbang , 175, 106 M. Turconi , 44 C. Turski, 84 H. Ubach , 37, 72 A. S. Ubhi, 110 T. Uchiyama , 45 R. P. Udall , 2 T. Uehara , 301 K. Ueno , 36 C. S. Unnikrishnan, 252 T. Ushiba , 45 A. Utina , 31, 32 M. Vacatello , 20, 77 H. Vahlbruch , 13, 14 N. Vaidya , 2 G. Vajente , 2 A. Vajpeyi, 8 G. Valdes , 128 J. Valencia, 91 M. Valentini , 99, 32 S. A. Vallejo-Pe˜na, 276 S. Vallero, 25 V. Valsan , 10 N. van Bakel, 32 M. van Beuzekom , 32 M. van Dael , 32, 302 J. F. J. van den Brand , 31, 99, 32 C. Van Den Broeck, 68, 32 D. C. Vander-Hyde, 70 M. van der Sluys , 32, 68 A. Van de Walle, 35 J. van Dongen , 32, 99 K. Vandra, 94 H. van Haevermaet , 106 J. V. van Heijningen , 115 J. Vanosky, 2 M. H. P. M. van Putten , 303 Z. van Ranst , 31, 32 N. van Remortel , 106 M. Vardaro, 31, 32 A. F. Vargas, 129 V. Varma , 1 M. Vas'uth , 74 A. Vecchio , 110 G. Vedovato, 81 J. Veitch , 26 P. J. Veitch , 88 S. Venikoudis, 115 J. Venneberg , 13, 14 P. Verdier , 153 D. Verkindt , 28 B. Verma, 134 P. Verma, 173 Y. Verma , 95 S. M. Vermeulen , 2 D. Veske , 159 F. Vetrano, 57 A. Veutro, 60 A. M. Vibhute , 4 A. Vicer'e , 57, 58 S. Vidyant, 70 A. D. Viets , 304 A. Vijaykumar , 21 A. Vilkha, 204 V. Villa-Ortega , 124 E. T. Vincent , 53 J.-Y. Vinet, 44 S. Viret, 153 A. Virtuoso , 249, 42 S. Vitale , 30 H. Vocca, 78, 46 D. Voigt , 76 E. R. G. von Reis, 4 J. S. A. von Wrangel, 13, 14 S. P. Vyatchanin , 100 L. E. Wade, 67 M. Wade , 67 K. J. Wagner , 204 R. C. Walet, 32 M. Walker, 116 G. S. Wallace, 90 L. Wallace, 2 H. Wang , 267 J. Z. Wang, 79 W. H. Wang, 161 Z. Wang, 142 G. Waratkar , 139 R. L. Ward, 12 J. Warner, 4 M. Was , 28 T. Washimi , 22 N. Y. Washington, 2 D. Watarai, 36 K. E. Wayt, 67 B. Weaver, 4 C. R. Weaving, 122 S. A. Webster, 26 M. Weinert, 13, 14 A. J. Weinstein , 2 R. Weiss, 30 C. M. Weller, 48 R. A. Weller , 190 F. Wellmann, 13, 14 L. Wen, 27 P. Weßels, 13, 14 K. Wette , 12 J. T. Whelan , 204 D. D. White, 50 B. F. Whiting , 40 C. Whittle , 30 J. B. Wildberger, 1 O. S. Wilk, 67  \n- D. Wilken , 13, 14, 14 K. Willetts, 19 D. Williams , 26 M. J. Williams , 26 N. S. Williams, 110 J. L. Willis , 2 B. Willke , 14, 13, 14 M. Wils , 101 C. C. Wipf, 2 G. Woan , 26 J. Woehler, 31, 32 J. K. Wofford , 204 N. E. Wolfe, 30 D. Wong, 138 H. T. Wong , 142 H. W. Y. Wong , 137 I. C. F. Wong , 137 J. L. Wright, 12 M. Wright , 26  \n141  \nC. Wu ,  \nD. S. Wu  \n,  \nH. Yamamoto  \n,  \nR. Yamazaki  \n,  \nZ. Yarbrough  \n,  \nJ. Yoo  \n,  \n149  \n2  \n254  \n11  \n13, 14  \nH. Wu ,  \nK. Yamamoto  \n,  \nS. Yan,  \n18  \n151  \n141  \nD. M. Wysocki  \n,  \n151  \n10  \nL. Xiao  \n,  \n2  \nT. S. Yamamoto  \n,  \n186  \nM. Yamamoto,  \n110  \nT. Yan,  \nS.-W. Yeh,  \nH. Yu  \n,  \n52  \n148  \n141  \nF. W. Yang  \n,  \nA. B. Yelikar  \n,  \nH. Yuzurihara  \n,  \n81  \nJ.-P. Zendri,  \nR. Zhang  \n,  \nT. Zelenova,  \nL. Zhang,  \nY. Zheng  \n,  \n2  \n97  \nH. Zhong  \n,  \n40  \nM. Zeoli,  \nT. Zhang,  \n89  \n45  \n204  \nF. Yang,  \n159  \nS. M. C. Yeung,  \nA. Zadro˙zny,  \n111, 115  \n110  \nS. Zhong,  \n27  \n173  \nM. Zerrad,  \nY. Zhang  \n,  \nR. Zhou,  \n206  \n12  \nV. A. Xu  \n,  \n236  \n30  \nY. Xu  \n,  \nT. Yamamoto  \n,  \nK. Z. Yang  \n,  \n10  \nX. Yin,  \n30  \n116  \n71  \nA. J. Zannelli,  \n34, 226  \nM. Zevin  \n,  \nC. Zhao  \n,  \nZ.-H. Zhu  \n,  \n27  \n89  \n45  \nL.-C. Yang,  \nJ. Yokoyama  \n,  \n43  \n176  \nN. Yadav  \n,  \n85  \n152  \nS. Yamamura,  \n145  \n36  \nY. Yang  \n,  \n145  \n45  \nT. Yokozawa,  \nM. Zeeshan  \n,  \n159  \nM. Zanolin,  \nA. C. Zhang,  \nYue Zhao,  \n127, 305  \n186  \nJ. Zhang  \n,  \nYuhang Zhao  \n,  \nM. E. Zucker,  \n30, 2  \n204  \n12  \n152, 22, 63  \nand J. Zweizig  \n(The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration)  \nT. Fujimori, 189 H. Fujimoto , 267 T. Fujita , 306, 36 Y. Manita , 295 I. Obata , 307 and H. Takidera 267  \n1  \n13  \nMax Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany  \n2  \nLIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA  \n3 Graduate School of Science, Tokyo Institute of Technology,  \n2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan  \n4 LIGO Hanford Observatory, Richland, WA 99352, USA  \n5 Dipartimento di Farmacia, Universit'a di Salerno, I-84084 Fisciano, Salerno, Italy  \n6 INFN, Sezione di Napoli, I-80126 Napoli, Italy  \n7 University of Warwick, Coventry CV4 7AL, United Kingdom  \n8 OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia  \n9 The Pennsylvania State University, University Park, PA 16802, USA  \n10 University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA  \n11 Louisiana State University, Baton Rouge, LA 70803, USA  \n12 OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia  \nMax Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany  \n14 Leibniz Universitat Hannover, D-30167 Hannover, Germany  \n- 15 Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India  \n16 University of Cambridge, Cambridge CB2 1TN, United Kingdom  \nInstituto Nacional de Pesquisas Espaciais, 12227-010 S˜ao Jos'e dos Campos, S˜ao Paulo, Brazil  \n18 Stanford University, Stanford, CA 94305, USA  \n19 Cardiff University, Cardiff CF24 3AA, United Kingdom  \n20 INFN, Sezione di Pisa, I-56127 Pisa, Italy  \nInternational Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India  \n22  \nGravitational Wave Science Project, National Astronomical Observatory of Japan,  \n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan  \n23 Advanced Technology Center, National Astronomical Observatory of Japan,  \n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan  \n24 Dipartimento di Fisica, Universit'a degli Studi di Torino, I-10125 Torino, Italy  \n25 INFN Sezione di Torino, I-10125 Torino, Italy  \n26 SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom  \n27 OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia  \n28 Univ. Savoie Mont Blanc, CNRS, Laboratoire d'Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France  \n29 Universit'a di Napoli 'Federico II', I-80126 Napoli, Italy  \n30 LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  \n31 Maastricht University, 6200 MD Maastricht, Netherlands  \n32 Nikhef, 1098 XG Amsterdam, Netherlands  \n33 Universit'e Libre de Bruxelles, Brussels 1050, Belgium  \n34 Institut Fresnel, Aix Marseille Universit'e, CNRS, Centrale Marseille, F-13013 Marseille, France  \n35 Universit'e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France  \n36 University of Tokyo, Tokyo, 113-0033, Japan.  \n37 Institut de Ci'encies del Cosmos (ICCUB), Universitat de Barcelona (UB),  \nc. Mart'ı i Franqu'es, 1, 08028 Barcelona, Spain  \n38 Institut de F'ısica d'Altes Energies (IFAE), The Barcelona Institute of Science and Technology,  \nCampus UAB, E-08193 Bellaterra (Barcelona), Spain  \n39 Gran Sasso Science Institute (GSSI), I-67100 L'Aquila, Italy  \n40 University of Florida, Gainesville, FL 32611, USA  \n41 Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit'a di Udine, I-33100 Udine, Italy  \n42 INFN, Sezione di Trieste, I-34127 Trieste, Italy  \n21  \n17  \n2  \n43 Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA  \n44 Universit'e Cˆote d'Azur, Observatoire de la Cˆote d'Azur, CNRS, Artemis, F-06304 Nice, France 45 Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan 46 INFN, Sezione di Perugia, I-06123 Perugia, Italy 47 Universit'a di Camerino, I-62032 Camerino, Italy 48 University of Washington, Seattle, WA 98195, USA 49 Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan 50 California State University Fullerton, Fullerton, CA 92831, USA 51 INFN, Sezione di Genova, I-16146 Genova, Italy 52 European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy 53 Georgia Institute of Technology, Atlanta, GA 30332, USA 54 Chennai Mathematical Institute, Chennai 603103, India 55 Royal Holloway, University of London, London TW20 0EX, United Kingdom 56 The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan 57 Universit'a degli Studi di Urbino 'Carlo Bo', I-61029 Urbino, Italy 58 INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy 59 LIGO Livingston Observatory, Livingston, LA 70754, USA 60 INFN, Sezione di Roma, I-00185 Roma, Italy 61 Universit'e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France 62 Dipartimento di Fisica 'E.R. Caianiello', Universit'a di Salerno, I-84084 Fisciano, Salerno, Italy 63 Universit'e Paris Cit'e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France 64 King's College London, University of London, London WC2R 2LS, United Kingdom 65 Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea 66 Universit'e libre de Bruxelles, 1050 Bruxelles, Belgium 67 Kenyon College, Gambier, OH 43022, USA 68 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands 69 University of Oregon, Eugene, OR 97403, USA 70 Syracuse University, Syracuse, NY 13244, USA 71 Northwestern University, Evanston, IL 60208, USA 72 Departament de F'ısica Qu'antica i Astrof'ısica (FQA), Universitat de Barcelona (UB), c. Mart'ı i Franqu'es, 1, 08028 Barcelona, Spain 73 Dipartimento di Medicina, Chirurgia e Odontoiatria 'Scuola Medica Salernitana', Universit'a di Salerno, I-84081 Baronissi, Salerno, Italy 74 Wigner RCP, RMKI, H-1121 Budapest, Hungary 75 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA 76 Universitat Hamburg, D-22761 Hamburg, Germany 77 Universit'a di Pisa, I-56127 Pisa, Italy 78 Universit'a di Perugia, I-06123 Perugia, Italy 79 University of Michigan, Ann Arbor, MI 48109, USA 80 Universit'a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy 81 INFN, Sezione di Padova, I-35131 Padova, Italy 82 Montana State University, Bozeman, MT 59717, USA 83 Institute for Plasma Research, Bhat, Gandhinagar 382428, India 84 Universiteit Gent, B-9000 Gent, Belgium 85 Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland 86 INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy 87 Dipartimento di Ingegneria, Universit'a del Sannio, I-82100 Benevento, Italy 88 OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia 89 University of Minnesota, Minneapolis, MN 55455, USA 90 SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom 91 IAC3-IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain 92 Departamento de Matem'aticas, Universitat Aut'onoma de Barcelona, 08193 Bellaterra (Barcelona), Spain 93 Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitat Jena, D-07743 Jena, Germany 94 Villanova University, Villanova, PA 19085, USA 95 RRCAT, Indore, Madhya Pradesh 452013, India 96 GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands 97 Missouri University of Science and Technology, Rolla, MO 65409, USA 98 Colorado State University, Fort Collins, CO 80523, USA  \n99 Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands  \n100 Lomonosov Moscow State University, Moscow 119991, Russia  \n101 Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium 102 Universit'a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy 103 INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy 104 Bar-Ilan University, Ramat Gan, 5290002, Israel 105 INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy 106 Universiteit Antwerpen, 2000 Antwerpen, Belgium 107 Universit'a di Roma 'La Sapienza', I-00185 Roma, Italy 108 Centre national de la recherche scientifique, 75016 Paris, France 109 Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France 110 University of Birmingham, Birmingham B15 2TT, United Kingdom 111 Universit'e de Li'ege, B-4000 Li'ege, Belgium 112 Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain 113 INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy 114 Laboratoire Kastler Brossel, Sorbonne Universit'e, CNRS, ENS-Universit'e PSL, Coll'ege de France, F-75005 Paris, France 115 Universit'e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium 116 Christopher Newport University, Newport News, VA 23606, USA 117 Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland 118 University of Maryland, College Park, MD 20742, USA 119 Universit'a degli Studi di Milano-Bicocca, I-20126 Milano, Italy 120 INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy 121 L2IT, Laboratoire des 2 Infinis - Toulouse, Universit'e de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France 122 University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom 123 Universit'e de Lyon, Universit'e Claude Bernard Lyon 1, CNRS, Institut Lumi'ere Mati'ere, F-69622 Villeurbanne, France 124 IGFAE, Universidade de Santiago de Compostela, 15782 Spain 125 University of Chicago, Chicago, IL 60637, USA 126 University of California, Riverside, Riverside, CA 92521, USA 127 Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China 128 Texas A&M University, College Station, TX 77843, USA 129 OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia 130 INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy 131 Niels Bohr Institute, Copenhagen University, 2100 København, Denmark 132 Universit'a di Roma Tor Vergata, I-00133 Roma, Italy 133 University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy 134 University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA 135 Departamento de Astronom'ıa y Astrof'ısica, Universitat de Val'encia, E-46100 Burjassot, Val'encia, Spain 136 Observatori Astron'omic, Universitat de Val'encia, E-46980 Paterna, Val'encia, Spain 137 The Chinese University of Hong Kong, Shatin, NT, Hong Kong 138 University of British Columbia, Vancouver, BC V6T 1Z4, Canada 139 Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India 140 Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan 141 National Tsing Hua University, Hsinchu City 30013, Taiwan 142 National Central University, Taoyuan City 320317, Taiwan 143 OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia 144 Queen Mary University of London, London E1 4NS, United Kingdom 145 Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan 146 Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan 147 University of Texas, Austin, TX 78712, USA 148 CaRT, California Institute of Technology, Pasadena, CA 91125, USA 149 Cornell University, Ithaca, NY 14850, USA 150 Dipartimento di Ingegneria Industriale (DIIN), Universit'a di Salerno, I-84084 Fisciano, Salerno, Italy 151 Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan 152 Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan 153 Universit'e Lyon, Universit'e Claude Bernard Lyon 1, CNRS,  \nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France  \n167  \n201  \n156  \n157  \n154 INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy  \n155 OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia  \nINAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy  \nDepartamento de Matem'aticas, Universitat de Val'encia, E-46100 Burjassot, Val'encia, Spain  \n158 Texas Tech University, Lubbock, TX 79409, USA  \n159 Columbia University, New York, NY 10027, USA  \n160 University of Rhode Island, Kingston, RI 02881, USA  \n161 The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA  \n162 Bellevue College, Bellevue, WA 98007, USA  \n163 Scuola Normale Superiore, I-56126 Pisa, Italy  \n164 Universit'a degli Studi di Sassari, I-07100 Sassari, Italy  \nThe University of Sheffield, Sheffield S10 2TN, United Kingdom  \n166 Universit'e Lyon, Universit'e Claude Bernard Lyon 1,  \nCNRS, Laboratoire des Mat'eriaux Avanc'es (LMA),  \nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France  \nDipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit'a di Parma, I-43124 Parma, Italy  \n168 INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy  \n169 Perimeter Institute, Waterloo, ON N2L 2Y5, Canada  \n170 Corps des Mines, Mines Paris, Universit'e PSL, 60 Bd Saint-Michel, 75272 Paris, France  \n171  \nIndian Institute of Technology Madras, Chennai 600036, India  \n172  \nCarleton College, Northfield, MN 55057, USA  \n173 National Center for Nuclear Research, 05-400 ' Swierk-Otwock, Poland  \n174 Institut d'Astrophysique de Paris, Sorbonne Universit'e, CNRS, UMR 7095, 75014 Paris, France  \n175 Vrije Universiteit Brussel, 1050 Brussel, Belgium  \n176  \nUniversity of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland  \n177 Canadian Institute for Theoretical Astrophysics,  \nUniversity of Toronto, Toronto, ON M5S 3H8, Canada  \n178 Stony Brook University, Stony Brook, NY 11794, USA  \nCenter for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA  \n180  \nMontclair State University, Montclair, NJ 07043, USA  \n181 Institute for Nuclear Research, H-4026 Debrecen, Hungary  \n182 CNR-SPIN, I-84084 Fisciano, Salerno, Italy  \n183 Scuola di Ingegneria, Universit'a della Basilicata, I-85100 Potenza, Italy  \n184 Western Washington University, Bellingham, WA 98225, USA  \n185 SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom  \n186 The University of Utah, Salt Lake City, UT 84112, USA  \n187 Eotvos University, Budapest 1117, Hungary  \n188 Centro de F'ısica das Universidades do Minho e do Porto,  \nUniversidade do Minho, PT-4710-057 Braga, Portugal  \n189 Department of Physics, Graduate School of Science,  \nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,  \nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan  \n190  \nVanderbilt University, Nashville, TN 37235, USA  \n191 Universit'e Cˆote d'Azur, Observatoire de la Cˆote d'Azur, CNRS, Lagrange, F-06304 Nice, France  \n192 California State University, Los Angeles, Los Angeles, CA 90032, USA  \n193 Dipartimento di Fisica, Universit'a degli Studi di Genova, I-16146 Genova, Italy  \n194 University of Szeged, D'om t'er 9, Szeged 6720, Hungary  \n195 INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy  \n196  \nAriel University, Ramat HaGolan St 65, Ari'el, Israel  \n197  \nUniversit'e de Normandie, ENSICAEN, UNICAEN,  \nCNRS/IN2P3, LPC Caen, F-14000 Caen, France  \n198 Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar'echal Juin, F-14050 Caen, France  \n199 The University of Mississippi, University, MS 38677, USA  \n200 Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan  \nShanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China  \n202 American University, Washington, DC 20016, USA  \n203 University of Nevada, Las Vegas, Las Vegas, NV 89154, USA  \n204  \nRochester Institute of Technology, Rochester, NY 14623, USA  \n205 Department of Applied Physics, Fukuoka University,  \n8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan  \n206 University of California, Berkeley, CA 94720, USA  \n207  \nUniversity of Lancaster, Lancaster LA1 4YW, United Kingdom  \n208 College of Industrial Technology, Nihon University,  \n1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan  \n179  \n165  \n209 Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan  \n210 Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan 211 Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom 212 Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea 213 Institute of Applied Physics, Nizhny Novgorod, 603950, Russia 214 Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China 215 Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan 216 Directorate of Construction, Services & Estate Management, Mumbai 400094, India 217 University of Biaglyph[suppress]lystok, 15-424 Biaglyph[suppress]lystok, Poland 218 National Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road, Chaoyang District, Beijing, China 219 School of Astronomy and Space Science, University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, China 220 University of Southampton, Southampton SO17 1BJ, United Kingdom 221 Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea 222 Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan 223 Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands 224 Chung-Ang University, Seoul 06974, Republic of Korea 225 University of Washington Bothell, Bothell, WA 98011, USA 226 Aix Marseille Universit'e, Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France 227 Laboratoire de Physique et de Chimie de l'Environnement, Universit'e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso 228 Ewha Womans University, Seoul 03760, Republic of Korea 229 Seoul National University, Seoul 08826, Republic of Korea 230 Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea 231 Sungkyunkwan University, Seoul 03063, Republic of Korea 232 National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea 233 Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan 234 Bard College, Annandale-On-Hudson, NY 12504, USA 235 Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland 236 Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan 237 Universit'e de Montr'eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada 238 Inje University Gimhae, South Gyeongsang 50834, Republic of Korea 239 NAVIER, ' Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall'ee, France 240 Universit'a di Firenze, Sesto Fiorentino I-50019, Italy 241 Department of Physics, University of Trento, via Sommarive 14, Povo, 38123 TN, Italy 242 National Center for High-performance computing, National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science Park, Hsinchu City 30076, Taiwan 243 NASA Marshall Space Flight Center, Huntsville, AL 35811, USA 244 West Virginia University, Morgantown, WV 26506, USA 245 School of Physics Science and Engineering, Tongji University, Shanghai 200092, China 246 Institut d'Estudis Espacials de Catalunya, c. Gran Capit'a, 2-4, 08034 Barcelona, Spain 247 Institucio Catalana de Recerca i Estudis Avan¸cats (ICREA), Passeig de Llu'ıs Companys, 23, 08010 Barcelona, Spain 248 Tsinghua University, Beijing 100084, China 249 Dipartimento di Fisica, Universit'a di Trieste, I-34127 Trieste, Italy 250 Institute for Photon Science and Technology, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan 251 INFN Cagliari, Physics Department, Universit'a degli Studi di Cagliari, Cagliari 09042, Italy 252 Tata Institute of Fundamental Research, Mumbai 400005, India 253 Hobart and William Smith Colleges, Geneva, NY 14456, USA 254 Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan  \n255 Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France 256 Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan 257 Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India 258 Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA 259 University of Stavanger, 4021 Stavanger, Norway 260 Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 261 Laboratoire Univers et Th'eories, Observatoire de Paris, 92190 Meudon, France 262 Observatoire de Paris, 75014 Paris, France 263 Universit'e PSL, 75006 Paris, France 264 Universit'e de Paris Cit'e, 75006 Paris, France 265 Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan 266 Niigata Study Center, The Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122, Japan 267 Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 268 CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India 269 Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy 270 Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece 271 Museo Storico della Fisica e Centro Studi e Ricerche 'Enrico Fermi', I-00184 Roma, Italy 272 Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit'a degli Studi Roma Tre, I-00146 Roma, Italy 273 INFN, Sezione di Roma Tre, I-00146 Roma, Italy 274 Universit'a di Trento, Dipartimento di Matematica, I-38123 Povo, Trento, Italy 275 Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit'e, 4 rue Alfred Kastler BP 20722 44307 Nantes C ' EDEX 03, France 276 Universidad de Antioquia, Medell'ın, Colombia 277 Departamento de F'ısica - ETSIDI, Universidad Polit'ecnica de Madrid, 28012 Madrid, Spain 278 Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan 279 Departamento de Matem'atica da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications, 3810-183 Aveiro, Portugal 280 Marquette University, Milwaukee, WI 53233, USA 281 Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan 282 Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India 283 Laboratoire MSME, Cit'e Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall'ee Cedex 2, France 284 Graduate School of Science and Technology, Gunma University, 4-2 Aramaki, Maebashi, Gunma 371-8510, Japan 285 Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA 286 Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan 287 INAF, Osservatorio Astrofisico di Arcetri, I-50125 Firenze, Italy 288 Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India 289 Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India 290 Institut fur Theoretische Physik, Johann Wolfgang Goethe-Universitat, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany 291 Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy 292 INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy 293 Universidade Estadual Paulista, 01140-070 Campinas, S˜ao Paulo, Brazil 294 Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 8-15-1 Todoroki, Setagaya, Tokyo 158-0082, Japan 295 Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan 296 Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan 297 Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan  \n298 University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy  \n299  \nDipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit'a di Salerno, I-84084 Fisciano, Salerno, Italy 300 National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan 301 Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan 302 Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands 303 Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea 304 Concordia University Wisconsin, Mequon, WI 53097, USA 305 School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China 306 Waseda Institute for Advanced Study, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku, Tokyo 169-8050, Japan 307 Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan  \nAmong the various candidates for dark matter (DM), ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context, KAGRA has a unique feature due to differing compositions of its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for U (1) B -L gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds on the coupling strength between the U (1) B -L gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments, this study demonstrates the applicability of our method to the lower-mass vector DM search, which is made difficult in this measurement by the short observation time compared to the auto-correlation time scale of DM.", 'I. INTRODUCTION': 'Recently, a number of novel dark matter (DM) searches using laser interferometric gravitational wave (GW) detectors have been proposed [1-6] and conducted [7-11]. Because of their extremely high sensitivity to the differential length changes of their arms in the frequency range O (10 -10 3 ) Hz, they can probe the interaction between the detector and DMs, which have masses of O (10 -14 -10 -11 ) eV/ c 2 and therefore oscillate coherently within this frequency band. Vector DM (or so-called dark photon DM) interacts with test masses of the interferometer, for example, via a coupling to the baryon ( B ) or baryon minus lepton ( B -L ) number current. Because of the non-relativistic dispersion (under the standard halo model [12, 13]), the vector DM field exerted on the test masses behave as an oscillating dark electric force, inducing a measurable change in the differential length of the arm cavity. Vector DMs of this type, which we refer to as U (1) B and U (1) B -L gauge boson, were previously searched in Ref. [9] by using the latest observational data from the Advanced LIGO [14-16] and Virgo [17, 18] detectors. Remarkably, the constraint on the coupling strength of vector DM to baryons from GW interferometers surpasses those from existing experiments such as the Eot-Wash torsion balance [19, 20] and MICROSCOPE [21-23], by orders of magnitude for certain fre-q  \nency bands. Similarly, dilatonic DM, whose interaction alters the apparent electron mass or the fine structure constant, was probed with data from the GEO600 interferometer [10, 24, 25]. These searches highlight the potential of GW detectors as direct probes of ultralight DM.  \nA Japanese laser interferometric GW detector, KAGRA [26-28], can also probe the vector DM interaction, but in a relatively unique way compared to the previous searches. For the Advanced LIGO and Virgo detectors, all the mirrors (including test masses) are made of the same material (fused silica), in other words, they have a common charge-to-mass ratio with respect to the dark electric field. Because the spatial variation scale (so-called coherence length) of the ultralight DM field is O (10 5 -10 8 )km in our target mass range, all mirrors of each detector, which are separated only a few kilometers, respond to the vector field nearly identically. In contrast, KAGRA employs sapphire for cryogenic test masses and fused silica for room temperature auxiliary mirrors. Therefore, owing to the difference in the chargeto-mass ratios, those mirrors respond differently to the vector field, and the vector DM signal in the (differential) length change can be enhanced for auxiliary length monitors [3, 29]. Especially in the case of U (1) B -L , where the difference in charge-mass ratio is relatively large, these channels are shown to have better sensitivity to vector DM than existing experiments in certain low frequency bands, when KAGRA reaches design sensitivity [3].  \nIn this work, we conduct an ultralight vector DM search with KAGRA using the data of its auxiliary length  \nchange monitors during the first joint observation run together with GEO600 (O3GK) [30]. Although the detector was in operation for two weeks during O3GK, the durations of the contiguous data segments were at most about 7 hours [31]. For our target mass range, this duration can be comparable to or smaller than the socalled coherence time, within which the amplitude and the phase of DM can be regarded as a constant. Since each such measurement is one realization of a random field, their stochasticity needs to be taken into account, especially when setting the upper bound on the coupling strength of the ultralight DM. Therefore, our pipeline is constructed based on a recent study [32], which thoroughly investigates the stochastic nature of the ultralight vector DM. Using the detection statistic discussed in Ref. [32], we numerically derive upper limits on the coupling strength incorporating the stochastic nature of the DM. On the other hand, various noise lines [31] result in a false detection as a DM signal. In order to distinguish outliers, we have implemented veto procedures making use of expected features of ultralight DM signals.  \nThe rest of the paper is organized as follows. We first introduce our model of ultralight vector DM and discuss its stochastic nature in Sec. II. After describing our search method in Sec. III, the results of our analysis using O3GK data are presented in Sec. IV. Sec. V provides a discussion of these results and of the prospects for future searches.', 'A. Vector Dark Matter Model': "In this work, we consider a ultralight vector dark matter field A µ ( t, x ), which is regarded as a gauge boson of U (1) D gauge symmetry with D being a label for a charge, such as B and B -L . We assume it interacts with ordinary matter through the coupling to the U (1) D current J µ D . The Lagrangian density L is then given as  \nL = -ε 0 c 2 4 F µν F µν + ε 0 2 ( m A c 2 ℏ ) 2 A µ A µ -ϵ D eJ µ D A µ , (1)  \nwhere F µν = ∂ µ A ν -∂ ν A µ is the field strength, c is the speed of light, ℏ is the reduced Planck constant, m A is the mass of the vector field, ε 0 is the permittivity of vacuum and ϵ D is the gauge coupling constant normalized by the electromagnetic coupling constant. Since the temporal component of the vector field A 0 is negligibly small, we consider only its spatial components ⃗ A = ( A x , A y , A z ) in the following discussion.  \nAssuming the standard halo model, the local density of DM is ρ DM ∼ 0 . 4 GeV / cm 3 , and its virial velocity is v vir ≃ 220 km / sec around the solar system in our Galaxy [12, 13]. These profiles imply that DM would have an extremely large number density for the mass range 10 -22 eV /c 2 ≲ m ≲ 1eV /c 2 and behave as a classical wave oscillating at about the Compton frequency  \nf c = m A c 2 / 2 π ℏ . Then, one can describe it as the superposition of plane waves with different velocities ⃗v ( i,n ) and phases θ ( i,n ) as  \nA i ( t, ⃗x ) = A √ N N ∑ n =1 cos ( 2 πf c ( 1 + v 2 ( i,n ) / 2 c 2 ) t -ℏ -1 m A ⃗v ( i,n ) · ⃗x + θ ( i,n ) ) , (2)  \nwhere θ ( i,n ) is a random variable following a uniform distribution over [0 , 2 π ] and A ≡ √ 2 ρ DM ℏ 2 /ε 0 3 m 2 A c 4 . Note that, for simplicity, the absence of correlation between the direction of ⃗ A and ⃗v is assumed. Here ⃗v ( i,n ) follows the DM velocity distribution of the standard halo model [13]:  \nf SHM ( ⃗v ) d 3 ⃗v = 1 ( πv 2 vir ) 3 / 2 exp [ -( ⃗v + ⃗v ⊙ ) 2 v 2 vir ] d 3 ⃗v, (3)  \nwith the solar velocity | ⃗v ⊙ | ≃ 232 km / sec. This distribution results in the velocity dispersion of the DM as ¯ v 2 = v 2 ⊙ + (3 / 2) v 2 vir ≃ O (10 -6 c 2 ). In such a nonrelativistic regime, the time derivative of the field dominates over the spatial derivative. Hence, it can be regarded as a oscillating dark 'electric' field, which induces displacements of the test masses in GW interferometers as δ x i = ϵ D e ( Q/M ) ˙ A i .  \nAnother feature is that there appears a length scale, called 'coherence length', which is evaluated as L = 2 π ℏ /m A √ ¯ v 2 ∼ 10 7 km (10 -13 eV · c -2 /m A ). This scale characterizes the spatial variation of the ultralight DMs. As we will see below, the separation of test masses here is much shorter than L , we can take ⃗x = 0 in Eq. (2) without loss of generality and hereafter neglect the position dependence of the vector field.", 'B. Auxiliary length channels of KAGRA': "From 2020 April 7 to 2020 April 21, KAGRA conducted its first joint observation run (O3GK) [30, 31], together with GEO600. The configuration of KAGRA interferometer during O3GK is shown in Fig. 1. Similarly to that of LIGO and Virgo, it is based on a Michelson interferometer with a Fabry-P'erot cavity in two perpendicular arms. Each arm cavity is formed by the input test mass (ITM) and the end test mass (ETM). The main channel to monitor the differential changes caused by GWs is called the differential arm length (DARM). The differential length between the beam splitter (BS) and two ITMs are controlled so that the Michelson fringe will be at the dark fringe at the anti-symmetric port, and the channel to monitor the differential Michelson interferometer length is called MICH. The power recycling mirror (PRM) and two ITMs form a power recycling cavity to effectively enhance the input power. The channel to monitor the power recycling cavity length is called PRCL.  \nFIG. 1. The schematic of the KAGRA interferometer. ITM (ETM): input (end) test mass, BS: beam splitter, PRM: power recycling mirror, SRM: signal recycling mirror.  \n<!-- image -->  \nDuring O3GK, a signal recycling mirror (SRM) was tilted, and the signal recycling cavity was not formed [33]. Instead, this tilted SRM introduced an optical loss of 70%, which led to degraded shot noise for the DARM readout. Two auxiliary channels, MICH and PRCL were recorded using different interferometer sensing ports, and were not affected by this optical loss. Using the length symbols in Fig. 1, changes in DARM, MICH and PRCL can be written as  \nδL DARM = δ ( L x -L y ) , (4)  \nδL MICH = δ ( l x -l y ) , (5)  \nδL PRCL = δ [( l x + l y ) / 2 + l p ] , (6)  \nrespectively. Note that each length parameter is given as L x = L y = 3000m, l x = 26 . 7m, l y = 23 . 3m and l p = 41 . 6m, all of which are much shorter than the coherence length of DM.  \nPrevious vector DM searches using LIGO and Virgo focused on DARM channels with the highest displacement sensitivity. This sensitivity is equivalent to the sensitivity to vector DM interactions for both LIGO and Virgo employing room temperature fused silica mirrors for all the mirrors. This situation, however, drastically changes for KAGRA, which employs cryogenic sapphire mirrors for the test masses. As pointed out in Ref. [3], MICH and PRCL contain both the fused silica mirrors such as PRM and BS, and the sapphire test masses that respond differently to the vector DM due to the different chargeto-mass ratio. This results in the enhancement of the (differential) length change caused by vector DM in those channels. Since the difference becomes larger especially for the U (1) B -L gauge boson, hereafter we focus on the D = B -L case.", "C. Signal in the KAGRA's auxiliary length channels": "Since the frequency of each plane wave is localized near the Compton frequency as f i = f c √ 1 + v 2 i /c 2 ∼ f c (1 + O (10 -6 )), it is convenient to work in the Fourier space. Let us consider the Fourier transform of the signal in X channel with duration T and center time t 0 :  \n˜ h X ( f ; t 0 ) ≡ ∫ t 0 + T/ 2 t 0 -T/ 2 dt h X ( t )e -2 π i f ( t -t 0 + T/ 2) . (7)  \nTo simplify the discussion, T is taken to be much shorter than the time scale of Earth's rotation. As discussed in [32], the oscillating length changes of an arm cavity can be decomposed into three contributions referred to as charge asymmetry, spatial difference and finite light traveling time [8]. For auxiliary length monitors of interest here, the dominant contribution is the one from charge asymmetry expressed as  \n˜ h X ( f ; t 0 ) = i ϵ D e 2 πf ∆ ( Q D M ) l i X ( t 0 ) ˜ A i ( f ; t 0 ) , (8)  \nwhere ∆( Q D /M ) is the difference of charge to mass ratio between two mirrors (BS and ITMX/Y) and in our case, it is ∆( Q B -L /M ) ∼ 0 . 009 /m n with m n being the neutron mass [3]. The vector l i X ( t 0 ) is given as  \nl i X ( t ) =    n i ( t ) -m i ( t ) , ( X = MICH) 1 2 ( n i ( t ) + m i ( t ) ) , ( X = PRCL) , (9)  \nwhere n i and m i are unit vectors pointing along the orthogonal arm axes depicted in Fig. 1. Here ˜ A i ( f ; t 0 ) is the Fourier transform of the field amplitude. Since it is a superposition of a huge number of partial waves, the central limit theorem assures that ˜ A i ( f ; t 0 ) and consequently ˜ h X ( f ; t 0 ) follow a Gaussian distribution. Note that, when the DM density and the distance between the test masses are fixed, this type of contribution results in a larger field amplitude and hence in a larger signal for the lower frequencies [3, 32]. This is the reason why MICH and SRCL (not available in O3GK) has, under the design sensitivity, the capability of limiting the DM coupling beyond existing limits in the lower frequency band.  \nAt this point, it is convenient to introduce the so-called coherence time  \nτ ≡ 2 π/m A v 2 vir ∼ 0 . 3 day ( 10 -13 eV · c -2 m A ) , (10)  \nwhich quantifies the characteristic correlation lifetime of the DM field at different times ⟨ ˜ h ∗ X ( f ; t 0 ) ˜ h X ( f ; t 1 ) ⟩ . Let T be the duration of a single chunk of data and N ch be the number of equal-length chunks. For higher mass ranges, in general, the coherence time becomes shorter than the duration of each chunk as τ < T . In this case,  \nthe amplitude and phase of the DM randomly evolve within the chunks. While this decoherence reduces the growth of the signal-to-noise (SNR) ratio in amplitude as ∝ ( N ch T ) 1 / 4 [32], each data chunk can be regarded as an independent measurement of DM, and in fact the statistical treatment can be simplified [32]. For a lower mass range ( τ > T ), however, the correlation of the DM field between different data chunks cannot be neglected. This issue will be addressed in the following section describing the search pipeline.  \nFinally, let us give a concrete expression of the signal covariance ⟨ ˜ h ∗ X ( f ; t 0 ) ˜ h X ( f ; t 1 ) ⟩ used in our analysis. By combining Eqs. (2) and (3), it is derived as  \n〈 ˜ h ∗ X ( f ; t 0 ) ˜ h X ( f ; t 1 ) 〉 = ϵ 2 D e 2 A 2 T 2 v 3 vir 32 π 5 2 f 2 v 3 ⊙ { ∆ ( Q D M )} 2 ×  \nl i X ( t 0 ) l X,i ( t 1 )e -v 2 ⊙ v 2 vir +2 π i f DM ( t 1 -t 0 ) ( I ( x + ) -I ( x -)) . (11)  \nHere I ( x ) is a function of the DM frequency and the time  \nI ( x ) = X 2 8 [ √ πX e X 2 / 4 { erf ( x X -X 2 ) + erf ( x X + X 2 )} -4e -x 2 /X 2 sinh( x ) ] , (12)  \nwhere we use the following parametrization,  \nx = 2 v ⊙ v 2 vir v, X = 2 v ⊙ v vir √ 1 -i πv 2 vir c -2 f DM ( t 1 -t 0 ) , (13)  \nand  \nv ± c ≡ √ 2 ( f ± 1 / (2 T ) f DM -1 ) , x ± ≡ 2 v ⊙ v 2 vir v ± . (14)  \nFor t 0 = t 1 , our I ( x ) coincides with the function ∆ s ( f n ) in Ref. [32], which gives the deterministic part of the spectral shape.", 'A. Detection statistics': "Here we introduce, and slightly extend, the detection statistic discussed in Ref. [32]. It is based on the existing methods of continuous GW searches [34-36] that also look for a narrow band signal similarly to our case. For comprehensive reviews of those method, see e.g. Refs. [37-39] The search method discussed in Ref. [32] is generally applicable to the ultralight DM searches using a single detector and interested readers could refer to Ref. [40] for the application of this detection statistic to the ultralight axion search.  \nAs we discussed in Sec. II, the spectrum of the DM signal is localized within the narrow frequency band f c ≤ f ≲ f c (1+ κ 2 v 2 vir /c 2 ) where κ is O (1) constant and we set  \nκ = 3 . 17 to guarantee that the fractional loss of signal power becomes less than 1%. For each single data chunk, we sum up the spectra over this frequency range:  \nρ i ( f c ) ≡ ∑ f c ≤ f n ≤ f c (1+ κ 2 v 2 vir /c 2 ) 4 | ˜ d ( f n ; t i ) | 2 TS ( f n ; t i ) , (15)  \nwhere T again is the duration of the data chunks, ˜ d ( f n ; t i ) represents the Fourier transform of the i -th data chunk and S ( f n ; t i ) is the one-sided noise power spectral density (PSD) around t = t i . Note that in order to neglect the effect of Earth's rotation as in Sec. II, T should be small enough and hereafter we take T = 30 min.  \nIn our pipeline, S ( f n ; t i ) is estimated from ˜ d ( f n ; t i ) by applying the running median and then converting it to the mean value by multiplying a correction factor (see App.A of Ref. [41]). In the median estimation, 180 neighboring frequency bins corresponding to 0 . 1Hz band width are involved so that the effect of DM signal with narrow bandwidth can be smeared out. The number of bins involved in ρ i ( f c ) is given as  \nN bin = ⌈ κ ¯ v 2 f c ∆ f ⌉ = ⌈ κ T τ ⌉ , (16)  \nwhere ⌈ x ⌉ represents the minimum integer larger than x . By performing the summation over all chunks, we can define the detection statistics ρ as  \nρ ( f c ) ≡ N ch ∑ i ρ i ( f c ) , (17)  \nwhere N ch represents the number of chunks. Under the assumption of the stationarity and Gaussian distribution of noise, ρ follows a χ 2 distribution with 2 N bin N ch degrees of freedom in the absence of signal. We chose the threshold to be the 95% percentile of this distribution.", 'B. Upper limit estimation': "In this study, we derive upper limits based on the frequentist's method where β %confidence level upper limit is derived through the integration of the likelihood function L ( ρ ( f c ); ϵ β % D ) as  \n1 -β 100 = ∫ ρ obs 0 dρ L ( ρ ( f c ); ϵ β % D ) . (18)  \n̸  \n̸  \nOne might expect the central limit theorem to be applicable to ρ ( f c ) since the number of chunks is relatively large. There is, however, a non-vanishing cross-correlation between different segments ⟨ ρ i ρ j ⟩| i = j = 0 for | t i -t j | < τ . This correlation prevents the convergence to a Gaussian distribution especially for lower-mass DM and makes the analytical expression of L ( ρ ( f c ); ϵ D ) complicated [32]. In fact, this analytical expression suffers from numerical instability for intermediate regimes where the coherence  \ntime and the duration of chunks are comparable. In our pipeline, therefore, the 95% upper limit on the coupling constant was numerically derived as follows.  \nAssuming that only Gaussian noise ˜ n ( f n ; t i ) and ultralight DM signals are present in the data, it can be expressed as ˜ d ( f n ; t i ) = ˜ n ( f n ; t i ) + ˜ h X ( f n ; t i ). Therefore, dependence of ρ on the coupling constant can be decomposed as  \nρ ( f c ; ϵ D ) = ∑ t i ,f n 4 TS ( | ˜ n | 2 +2Re [ ˜ n ∗ ˜ h X ] + | ˜ h X | 2 ) = N 2 + ϵ D N · S + ϵ 2 D S 2 . (19)  \nHere N 2 represents contributions from 2 N bin N ch unit Gaussian variables since the noise component in ρ is normalized by the PSD. On the other hand, S 2 represents contributions solely from the Gaussian signal ˜ h X ( f n ; t i ) (also normalized by noise PSD) whose correlation function is given as Eq. (11) under the standard halo model assumption. N·S is the contribution from the cross term of the unit Gaussian and the normalized signal. For a fixed DM mass (or f c ), we simulated 10 5 realizations of N 2 , S 2 , N ·S from the covariance of the DM signal (11) and the estimated noise PSD S n ( f n ; t i ). Then we can obtain a histogram of ρ that approximates the likelihood L ( ρ ( f c ); ϵ D ) and depends on the value of ϵ D . Then the value of ϵ D , for which the observed value of the detection statistics ρ obs ( f c ) coincides with the 5% percentile of this realization, is identified as the 95% upper limit. We would like to emphasize that our method does not suffer from the numerical instability mentioned above and that it is applicable to arbitrary masses of DM.", 'A. Data': "We analyzed the O3GK data collected from the KAGRA detector in the observation mode, and the data from GEO600 is not used. During the O3GK run, the KAGRA detector had duty factors, the fraction of time the detector is in the observing mode to the total time, of ∼ 53%. The length channels considered in this study are the differential Michelson interferometer length (MICH) and the power recycling cavity length (PRCL). For both the MICH and PRCL channels, calibrations of data were performed offline for this study, whose parameters and information will be summarized in Ref. [42]. For the frequency band we used for the analysis, calibration uncertainty in MICH and PRCL channels are 20-30% in amplitude.  \nThe amplitude spectral densities (ASDs), derived from S ( f n ; t i ), of these channels during O3GK are plotted in Fig 2. We should note that, for the last few days of O3GK, alignments of mirrors were dithered at significantly large amplitude for the beam position control [31]. These injected lines were accompanied by a large number  \nof sidebands. Since our pipeline simply searches power excesses within narrow bandwidth, it is not straightforward to distinguish those noise lines from the DM signals. Hence the segments from the last three days of the O3GK, where the efficiency of the DM search was spoiled, were not included in our analysis. Consequently, the number of 30 minute chunks subject to our pipeline was 217.  \nFIG. 2. ASDs of the MICH and PRCL estimated from the first 30 min chunk during O3GK.  \n<!-- image -->  \nAnother limitation is that the vibration isolation systems for mirrors in MICH and PRCL were simplified compared to those in the full-design [31]. Consequently, there are many noise peaks in the lower frequency range, where the KAGRA's auxiliary degrees of freedom become more and more sensitive. Although our pipeline can be used in the lower frequency range ≲ 10Hz, the analysis was performed over the frequency range from 15 Hz to 1015 Hz for this demonstration analysis.", 'B. Candidates and veto procedure': 'In Fig. 3, the detection statistics ρ ( f c ) computed in our pipeline are shown respectively for MICH and PRCL. As expected from the many lines in ASDs shown in Fig. 2, more non-Gaussian power excess within an expected signal bandwidth is observed in the PRCL data. Under the 5% False-Alarm-Probability derived from χ 2 distribution for Gaussian noise, 1944 and 4133 lines are identified as candidates for MICH and PRCL, respectively. These candidates are then subject to the veto analysis as follows. First, according to the expected narrow band feature of DM signal, the peak of ρ ( f c ) should also have a comparable width if it has DM origin. As illustrated in the top panel of Fig. 4, candidates with a width more than two times broader than the expected DM signal width were vetoed. We also vetoed lines that were less than the peak width away from the vetoed peaks of ρ , as  \nFIG. 4. A schematic picture of the veto procedure. For both cases, the vertical red lines denote surviving candidates after two veto procedure. ( Top panel ) Green vertical bands indicate the broad peak structures vetoed by the bandwidth criterion. ( Bottom panel ) The yellow vertical lines represent candidates with power excess that fails coincidence requirements.  \n<!-- image -->  \nFIG. 3. The detection statistics ρ computed from 217 halfhour chunks during O3GK with MICH ( top panel ) and PRCL ( bottom panel ) channel. A step appears about every 200 Hz because of the increase in N bin , which varies from 1 to 6. The step height depends on the number of chunks.  \n<!-- image -->  \nthere is a possibility that they originated from the same source as those broad peaks.  \nSecond, in contrast to transient noise, expected to produce outliers in the O3GK data, DM signals should be more persistent on average, albeit with random statistical fluctuations. In the analysis, we chronologically divide the whole data chunks into two subsets and perform the same analyses within the first half 108 chunks and the second half 108 chunks. Then we take a coincidence between the candidates found in those two subsets to exclude transients that only appear during a limited duration. However, it must be noted that this procedure inevitably vetoes weaker DM signals with which ρ ( f c ) exceeds the detection threshold only after summing over all the chunks. Furthermore, unless the signal coherence time is sufficiently shorter than the data length of the subset, the field amplitude (and therefore the value of ρ ( f c )) can be significantly different for each subset. By examining the spectrum, we found that in the case of present data, such lines with the values of ρ close to the threshold are mostly sidebands of more intense lines, but this issue must be considered in future studies. For possible improvements to this veto procedure, see the discussion below.  \nAfter applying these two veto procedures, 77 lines remain as candidates in the MICH data while 202 lines remain in the PRCL data. Many of them are in the low frequency range below 100 Hz, where there are many lines due to injected signals and the suspension noise. By referring to, for example, the Appendix A. of Ref [31] discussing the noise lines of DARM during O3GK, we found that 57 out of 77 lines in the MICH data and 54 out of 202 lines in the PRCL data come from known lines. Note that there were few dedicated studies of the line identification for MICH and PRCL channels during O3GK, and lines of unknown origin still remain. Therefore, for our future reference, the candidate lines identified in this study are listed in Ref. [43].', 'C. Upper limit': 'There are several lines that have passed our pipeline detection criteria, but they cannot be claimed as DM signals given the current level of displacement sensitivity shown in Fig. 2 and the much shorter total observation time, compared to those assumed in Ref. [3]. With the  \nscaling of SNR ∝ ( N ch T ) 1 / 4 , their prediction on upper limits derived by setting SNR = 1 can be scaled to give an order of magnitude estimate of the upper limits we can derive from ρ . By comparing the design sensitivity (Fig. 2 in Ref. [3]) with our Fig. 2 and considering another suppression factor of ( N ch · 30min / 1yr) 1 / 4 ∼ 0 . 01 1 / 4 that comes from the difference between the real and assumed observation time, we expect that the upper limit on ϵ B -L from O3GK data will be at best O (10 -20 ). This is much weaker than those derived from the Eot-Wash torsion balance [19, 20] and MICROSCOPE [21-23], predicting 10 -24 to 10 -23 in the frequency band of our interest.  \nTherefore, the upper limit estimation here should be considered as a demonstration of our pipeline, which can accurately analyze low-frequency regions and highfrequency regions as well. As such a demonstration, upper limits on the coupling constant are derived over the whole frequency range analyzed in this study. Note that in principle, upper limits can be derived even for ρ ( f c ) that exceed the detection threshold.  \nFIG. 5. 95% upper limit on the B -L gauge coupling constant derived from MICH data (blue line) and PRCL data (orange line). Many narrow peaks observed in lower mass range are due to unknown line artifacts in the lower frequency range.  \n<!-- image -->  \nIn Fig. 5, 95% upper limits on the coupling constant ϵ B -L are shown. Here the constraint is smoothed by collecting the maximum value of ρ ( f c ) within a 0.1Hz bandwidth. For clarity, uncertainty of the calibration is not displayed. Let us stress that the stochastic nature of DMis properly taken into account in deriving this bound, by using the covariance of DM signal (11) for simulating the realization of ρ ( f c ). As demonstrated in Ref. [32], for example, incorrect deterministic treatment predicts a non-central χ 2 distribution of ρ ( f c ) and overestimates the upper bound by up to a factor of 3 in low mass (or long coherence time) regions. We also found that our result is consistent with the above rough estimate on the upper limit based on the SNR scaling, which is also a consequence of the stochastic nature of ultralight DMs [3, 32].  \nAs expected, these upper limits derived from the KA-  \nGRA O3GK data are weaker than previous published limits by several orders of magnitude. Again, this is owing to both the current noise level of the KAGRA detector and the limited duration of the measurement time. In order to reach the unexplored parameter space, reduction of the dominant low-frequency noise and longer stable detector operation are indispensable.', 'V. DISCUSSION': 'In this work, an ultralight vector DM search with KAGRA was conducted for the first time by using the KAGRA data from the O3GK run. Our pipeline design is guided by a recent study on the stochastic nature of the ultralight vector DM [32]. Consequently, the KAGRA O3GK data, which has a relatively short measurement time compared to the DM coherence time for low DM masses, can be analyzed.  \nWefound that our pipeline can discriminate candidates for vector DM signal from the broad peaks and transient lines, which are expected to have an instrumental origin. Nonetheless, there are several lines with unspecified origin meeting our criteria, especially for the lower frequency range. We expect that the number of such lines will decrease in upcoming observations because of, for example, an updated system for the suspension control and an improved understanding of the noise. Although the upper limits derived in this analysis are weaker than previous ones, they are found to be consistent with the prediction given in prior studies [3, 32]. Achieving the designed sensitivity and future upgrades of the KAGRA detector [44] will allow us to fully appreciate its unique feature as a vector DM detector exploiting the mirrors made of different materials to yield new constraints.  \nThere are several directions for improving our DM search pipeline. First, as outlined in Sec. II, our analysis is performed assuming the equilibration of vector polarization. Depending on the production mechanism, however, only a specific polarization mode might be produced. Therefore, the formalism beyond this assumption may allow us to probe the cosmological origin of vector DM. Second, while the bandwidth criterion for the veto analysis is quite robust, the appropriateness of taking coincidence between subsets of whole data should depend on the strength and coherence time of the signal being searched for. Since the covariance of the vector DM signal is known, it is possible to implement a test to check whether the candidates follow a distribution consistent with the given covariance. This could provide a more robust way to distinguish a DM signal from the noise lines. Finally, our pipeline can be extended to include the analysis of the DARM channel data, which has been used in DM searches in other GW detectors.', 'ACKNOWLEDGEMENTS': "This material is based upon work supported by NSF's LIGO Laboratory which is a major facility fully funded by the National Science Foundation. The authors also gratefully acknowledge the support of the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS) and the Netherlands Organization for Scientific Research (NWO), for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, the Department of Science and Technology, India, the Science & Engineering Research Board (SERB), India, the Ministry of Human Resource Development, India, the Spanish Agencia Estatal de Investigaci'on (AEI), the Spanish Ministerio de Ciencia e Innovaci'on and Ministerio de Universidades, the Conselleria de Fons Europeus, Universitat i Cultura and the Direcci'o General de Pol'ıtica Universitaria i Recerca del Govern de les Illes Balears, the Conselleria d'Innovaci'o, Universitats, Ci'encia i Societat Digital de la Generalitat Valenciana and the CERCA Programme Generalitat de Catalunya, Spain, the National Science Centre of Poland and the European Union - European Regional Development Fund; Foundation for Polish Science (FNP), the Swiss National Science Foundation (SNSF), the Russian Foundation for Basic Research, the Russian Science Foundation, the European Commission, the European Social Funds (ESF), the European Regional Development Funds (ERDF), the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian Scientific Research Fund (OTKA), the French Lyon Institute of Origins (LIO), the Belgian Fonds de la Recherche Scientifique (FRS-FNRS), Actions de Recherche Concert'ees (ARC) and Fonds Wetenschappelijk Onderzoek - Vlaan-  \n- [1] A. 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Advanced Research Networks, JSPS Grantin-Aid for Scientific Research (S) 17H06133 and 20H05639 , JSPS Grant-in-Aid for Transformative Research Areas (A) 20A203: JP20H05854, the joint research program of the Institute for Cosmic Ray Research, University of Tokyo, National Research Foundation (NRF), Computing Infrastructure Project of Global Science experimental Data hub Center (GSDC) at KISTI, Korea Astronomy and Space Science Institute (KASI), and Ministry of Science and ICT (MSIT) in Korea, Academia Sinica (AS), AS Grid Center (ASGC) and the National Science and Technology Council (NSTC) in Taiwan under grants including the Rising Star Program and Science Vanguard Research Program, Advanced Technology Center (ATC) of NAOJ, and Mechanical Engineering Center of KEK.  \nAdditional acknowledgements for support of individual authors may be found in the following document: https://dcc.ligo.org/LIGO-M2300033/public . 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