Multiplicity dependent $J/ψ$ and $ψ(2S)$ production at forward and backward rapidity in $p$$+$$p$ collisions at $\sqrt{s}=200$ GeV
PHENIX Collaboration N. J. Abdulameer U. Acharya C. Aidala Y. Akiba M. Alfred V. Andrieux S. Antsupov N. Apadula H. Asano B. Azmoun V. Babintsev N. S. Bandara E. Bannikov K. N. Barish S. Bathe A. Bazilevsky M. Beaumier R. Belmont A. Berdnikov Y. Berdnikov L. Bichon B. Blankenship D. S. Blau J. S. Bok V. Borisov M. L. Brooks J. Bryslawskyj V. Bumazhnov S. Campbell R. Cervantes D. Chen M. Chiu C. Y. Chi I. J. Choi J. B. Choi Z. Citron M. Connors R. Corliss N. Cronin M. Csanád T. Csörgő T. W. Danley M. S. Daugherity G. David K. DeBlasio K. Dehmelt A. Denisov A. Deshpande E. J. Desmond A. Dion D. Dixit V. Doomra J. H. Do A. Drees K. A. Drees J. M. Durham A. Durum H. En'yo A. Enokizono R. Esha B. Fadem W. Fan N. Feege D. E. Fields M. Finger, Jr. M. Finger D. Firak D. Fitzgerald S. L. Fokin J. E. Frantz A. Franz A. D. Frawley Y. Fukuda P. Gallus C. Gal P. Garg H. Ge F. Giordano Y. Goto N. Grau S. V. Greene M. Grosse Perdekamp T. Gunji T. Guo H. Guragain T. Hachiya J. S. Haggerty K. I. Hahn H. Hamagaki H. F. Hamilton J. Hanks S. Y. Han S. Hasegawa T. O. S. Haseler T. K. Hemmick X. He J. C. Hill K. Hill A. Hodges R. S. Hollis K. Homma B. Hong T. Hoshino N. Hotvedt J. Huang K. Imai M. Inaba A. Iordanova D. Isenhower D. Ivanishchev B. Jacak M. Jezghani X. Jiang Z. Ji B. M. Johnson D. Jouan D. S. Jumper J. H. Kang D. Kapukchyan S. Karthas D. Kawall A. V. Kazantsev V. Khachatryan A. Khanzadeev C. Kim E. -J. Kim M. Kim D. Kincses E. Kistenev J. Klatsky P. Kline T. Koblesky D. Kotov L. Kovacs S. Kudo K. Kurita Y. Kwon J. G. Lajoie A. Lebedev S. Lee M. J. Leitch Y. H. Leung S. H. Lim M. X. Liu X. Li V. -R. Loggins S. Lökös D. A. Loomis K. Lovasz D. Lynch T. Majoros Y. I. Makdisi M. Makek V. I. Manko E. Mannel M. McCumber P. L. McGaughey D. McGlinchey C. McKinney M. Mendoza A. C. Mignerey A. Milov D. K. Mishra J. T. Mitchell M. Mitrankova Iu. Mitrankov G. Mitsuka S. Miyasaka S. Mizuno P. Montuenga T. Moon D. P. Morrison B. Mulilo T. Murakami J. Murata K. Nagai K. Nagashima T. Nagashima J. L. Nagle M. I. Nagy I. Nakagawa K. Nakano C. Nattrass T. Niida R. Nouicer N. Novitzky T. Novák G. Nukazuka A. S. Nyanin E. O'Brien C. A. Ogilvie J. D. Orjuela Koop M. Orosz J. D. Osborn A. Oskarsson G. J. Ottino K. Ozawa V. Pantuev V. Papavassiliou J. S. Park S. Park M. Patel S. F. Pate D. V. Perepelitsa G. D. N. Perera D. Yu. Peressounko C. E. PerezLara J. Perry R. Petti M. Phipps C. Pinkenburg R. P. Pisani M. Potekhin M. L. Purschke K. F. Read D. Reynolds V. Riabov Y. Riabov D. Richford T. Rinn S. D. Rolnick M. Rosati Z. Rowan A. S. Safonov T. Sakaguchi H. Sako V. Samsonov M. Sarsour S. Sato B. Schaefer B. K. Schmoll K. Sedgwick R. Seidl A. Seleznev A. Sen R. Seto A. Sexton D. Sharma I. Shein T. -A. Shibata K. Shigaki M. Shimomura T. Shioya P. Shukla A. Sickles C. L. Silva D. Silvermyr B. K. Singh C. P. Singh V. Singh M. Slunečka K. L. Smith M. Snowball R. A. Soltz W. E. Sondheim S. P. Sorensen I. V. Sourikova P. W. Stankus S. P. Stoll T. Sugitate A. Sukhanov T. Sumita J. Sun Z. Sun J. Sziklai K. Tanida M. J. Tannenbaum S. Tarafdar G. Tarnai R. Tieulent A. Timilsina T. Todoroki M. Tomášek C. L. Towell R. S. Towell I. Tserruya Y. Ueda B. Ujvari H. W. van Hecke J. Velkovska M. Virius V. Vrba N. Vukman X. R. Wang Y. S. Watanabe C. L. Woody L. Xue C. Xu Q. Xu S. Yalcin Y. L. Yamaguchi H. Yamamoto A. Yanovich I. Yoon J. H. Yoo I. E. Yushmanov H. Yu W. A. Zajc A. Zelenski L. Zou
















































































































































  
 
  
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PHENIX Collaboration  





§ ABSTRACT 



The J/ψ and ψ(2S) charmonium states, composed of cc̅ 
quark pairs and known since the 1970s, are widely believed to serve as 
ideal probes to test quantum chromodynamics in high-energy hadronic 
interactions.  However, there is not yet a complete understanding 
of the charmonium-production mechanism.  Recent measurements of 
J/ψ production as a function of event charged-particle 
multiplicity at the collision energies of both the Large Hadron 
Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC) show 
enhanced J/ψ production yields with increasing multiplicity. One 
potential explanation for this type of dependence is multiparton 
interactions (MPI).  We carry out the first measurements of 
self-normalized J/ψ yields and the ψ(2S) to J/ψ ratio at 
both forward and backward rapidities as a function of self-normalized 
charged-particle multiplicity in p+p collisions at √(s)=200 
GeV. In addition, detailed pythia studies tuned to RHIC energies 
were performed to investigate the MPI impacts. We find that the PHENIX 
data at RHIC are consistent with recent LHC measurements and can only 
be described by pythia calculations that include MPI effects. The 
forward and backward ψ(2S) to J/ψ ratio, which serves as a 
unique and powerful approach to study final-state effects on charmonium 
production, is found to be less dependent on the charged-particle 
multiplicity.



Multiplicity dependent J/ψ and ψ(2S) production at 
forward and backward rapidity in p+p collisions at √(s)=200 GeV
    L. Zou
    September 9, 2024
===================================================================================================================











Charmonium, a bound cc̅ state, has been studied extensively over 
the past several decades, but a clear understanding of its formation 
has not yet been reached.  Several models are currently available to 
describe the evolution of a cc̅ pair into the bound or 
meson, such as the nonrelativistic-quantum-chromodynamics 
(NRQCD) <cit.>, color-evaporation <cit.>, 
color-singlet <cit.>, and 
jet-fragmentation <cit.> models.  
The formation appears to involve both 
perturbative (above the Λ_ QCD scale) and nonperturbative 
(below the Λ_ QCD scale) aspects of QCD.  The initial 
creation of cc̅ pairs through hard scattering can be described as 
perturbative, and their evolution into a color-neutral state is likely 
nonperturbative.

In this Letter, we present PHENIX measurements at the Relativistic 
Heavy Ion Collider (RHIC) of the self-normalized production 
versus self-normalized event multiplicity to study the 
multi-parton-interaction (MPI) effects at forward rapidity as well as 
the to ratio, which is sensitive to final-state 
interactions in collisions at RHIC energies.  We measure inclusive 
and production without separating prompt from nonprompt 
charmonium because the nonprompt contributions are less than 3% of the 
total charmonium production.

The STAR Experiment at RHIC has measured the self-normalized yields as a function of self-normalized charged-particle multiplicity 
at midrapidity in collisions <cit.>.  The results show 
an increase in the yields with increasing multiplicity, a 
dependence suggesting MPI. Additionally, at Large-Hadron-Collider (LHC) 
energies, the ALICE experiment has reported similar results for the 
normalized yields versus event multiplicity at both 
forward rapidity <cit.> and 
midrapidity <cit.>. In addition to potential MPI, the 
to ratio could reveal final-state effects from either hot 
(formation of quark-gluon 
plasma <cit.>), 
or cold (comover-interaction model <cit.>) 
nuclear-matter effects. In early 2024, the LHCb collaboration reported 
the ratio of the normalized to in collisions at 
=13 TeV as a function of multiplicity <cit.>, 
where suppression of promptly produced charmonia is observed at high 
event multiplicity.












The present analysis relies on the data from the PHENIX 
experiment <cit.> obtained using the muon-arms detector 
subsystem covering 1.2<|η|<2.4, which includes the muon tracker 
(MuTr), the muon identifier (MuID), the hadron absorbers, the forward 
silicon vertex detectors 
(FVTX) <cit.> 
in the forward rapidity region and the central arm barrel silicon 
vertex tracker (VTX) <cit.> at |η|<1.0. Two 
beam-beam counters (BBC), covering the full azimuth and 
3.1<|η|<3.9, measure the vertex position along the beamline, 
located at z=±144 cm from the nominal interaction point. The 
BBCs also serve as the minimum-bias (MB) trigger and measure the beam 
luminosity.

The data set used in this analysis was collected in 2015 and 
recorded at =200 GeV center-of-mass energy. The analyzed events 
were selected by the MB trigger and the dimuon triggers, which  
required two or more muon tracks in the MuID. 
The collision vertex was constrained to be within ±10 cm with 
respect to the center of the interaction region.  The total sampled 
luminosity for the data set is 47 pb^-1.







The observable used in this analysis has theoretical <cit.> 
and experimental <cit.> motivations. We first define the 
self-normalized event charged-particle multiplicity , where represents the number of reconstructed charged-particle tracks detected by 
the forward- or backward-rapidity FVTX with 1.2<η<2.4 and 
-2.4<η<-1.2, and ⟨⟩ represents the average for 
MB events. Then the relative yield of , denoted as 
N_J/ψ/⟨N_J/ψ⟩ in a given range, is 
measured by the forward or backward muon arms covering 1.2<y<2.2 and 
-2.2<y<-1.2, respectively:


    N_J/ψ/⟨ N_J/ψ⟩ = N_J/ψ^ raw/N_ evt N_ evt^ total/N_J/ψ^ raw,totalε^ MB_ trig/ε^J/ψ_ trig⟨ε^J/ψ_ trig⟩/⟨ε^ MB_ trig⟩ f_ coll,


where N_J/ψ^ raw is the raw number of signal yield extracted from the dimuon invariant mass fit, and N_ 
evt is the number of recorded MB events for a certain bin. The 
average MB efficiency is ⟨ε^ MB_ 
trig⟩=55±5% and the J/ψ efficiency is 
⟨ε^J/ψ_ trig⟩=79±2%. The 
superscript “total" stands for quantities integrated over all . 
The ϵ^ MB_ trig is the MB trigger efficiency, 
ϵ^J/ψ_ trig is the dimuon trigger efficiency. The 
f_ coll is a correction factor for multiple collisions. The same 
observable is then measured for , and the ratio of relative 
yields is defined as 
(N_ψ(2S)/ N_J/ψ)/⟨N_ψ(2S)/N_J/ψ⟩.
We present the data in terms of the same arms defined as measuring 
and N_J/ψ at the same rapidity range, and opposite arms 
defined as measuring and N_J/ψ at the opposite rapidity 
range. When combining the data from two arms, we define 
1.2<|η|<2.4 for and 1.2<|y|<2.2 for N_J/ψ.





In PHENIX the trigger efficiency has event-multiplicity dependence due 
to finite acceptance of the BBC. The event multiplicity-dependent MB 
and dimuon trigger efficiencies are determined using a data-driven 
approach. The MB trigger efficiency versus event multiplicity was 
evaluated with random-collision-clock triggered events by checking 
whether the MB trigger is fired for events satisfying the MB trigger 
condition. To check the multiplicity dependence of the MB trigger for 
hard-scattering events, we require at least one EMCAL cluster of E>2 
GeV on top of the random-collision-clock trigger





The possibility of multiple-collision events, defined as an event 
having collisions in addition to the one that produced the or , increases with increasing multiplicity. A data-driven method 
is utilized to estimate the fraction of multiple collision events, 
which assumes Poisson statistics and estimates the BBC (MB) trigger 
rate R_ BBC using the following formula:


    R_ BBC = f_BC[1-e^-μϵ_F-e^-μϵ_B-e^-μ(ϵ_F+ϵ_B+ϵ_FB)],


where f_BC is the beam-crossing rate at RHIC, μ is the mean 
number of collisions, ϵ_F (ϵ_B) is the trigger efficiency 
(≈75%) of each BBC at forward (backward) rapidity, and 
ϵ_FB is the trigger efficiency (≈50%) when both BBCs are 
fired. The maximum R_ BBC during the data run is 2.5 MHz, 
corresponding to an ≈10% rate of double collision events. Due to the 
average R_ BBC being ≈1 MHz and the low probability of having 
more than two collisions per beam crossing, only contributions from double 
collisions were considered. The ratio of double to single collisions, 
f_ coll, is evaluated as a function of the measured-BBC-trigger rate 
R_ BBC.








A crystal-ball (CB) function <cit.> is used to model the 
and signal shapes to extract the raw yields from the 
dimuon invariant-mass distribution. The tail parameters α and 
n of the CB function were fixed with values from integrated 
multiplicity data for and simulation studies for ψ(2S). The 
FVTX detector delivers the mass resolution needed for measurements but reduces the acceptance due to a finite matching 
efficiency between the MuTr and FVTX detectors. For 
N_J/ψ/⟨N_J/ψ⟩
 as a function of /⟨⟩ 
shown in Figs. <ref> and <ref>, 
the FVTX detector is not used to maximize signal statistics. For 
measurements with the FVTX detector, a Gaussian function is used 
alongside the CB function to account for the broadening of signal shape 
due to misassociation between the FVTX and MuTr 
detectors <cit.>. The individual multiplicity bins are 
fitted by fixing the shape parameters of the CB function to the 
integrated multiplicity fit results to extract the J/ψ signal 
yield.

For the analysis without the FVTX detector, an exponential decay 
function is used to describe the background. For the ψ(2S) to J/ψ 
ratio, a modified Hagedorn function is used to model the combinatorial 
and correlated-background 
contributions <cit.>. The shape of the 
combinatorial background is estimated with real data using the 
mixed-event method, where opposite sign single muons are selected from 
different events. The combinatorial background normalization is 
obtained from like-sign single muons selected from the same events. The 
correlated background shape is determined using detailed simulation 
studies <cit.> and is implemented in the total fit 
function by fixing three of the five parameters of the modified 
Hagedorn function to constrain the shape.






The sources of systematic uncertainties for the measurements 
include the following: the reconstruction efficiency, the trigger efficiency, the MB trigger efficiency, and the 
multiple-collision-correction factor f_ coll per beam crossing. 
A systematic uncertainty is assigned for the reconstruction 
efficiency based on the largest variation when three different 
z-vertex selections are applied. For the systematic uncertainty 
related to the trigger efficiency, the efficiency as a function 
of is first fit with the following function: f(x) = p_0 + 
p_1e^-p_2x. Then, the efficiency distribution is re-evaluated by 
moving the parameter values by ±1σ of the statistical 
uncertainty in the fit result. The largest difference with respect to 
the nominal value is assigned as the systematic uncertainty. The 
MB-trigger efficiency can be affected by multiple collisions. The 
systematic uncertainty related to the MB-trigger efficiency is 
determined by dividing the trigger efficiency into three different collision rates, determined by the MB trigger: 600–800, 1000–1500, 
and 2000–2500 kHz. The trigger efficiency for the high and low trigger 
rates are compared to the central rate, and the maximum deviation is 
scaled by 1/√(12) (the standard deviation of a uniform 
distribution), which is assigned as the systematic uncertainty.  The 
systematic uncertainty related to the multiple-collision correction 
factor is evaluated by comparing correction factors using an 
alternate method, which is the ratio of probability distributions 
P() between two different trigger rates, less than 500 and 
1000–1500 kHz.



The sources of systematic uncertainty for the normalized to 
ratio include the following: the mixed-event background 
normalization, the signal shapes (fixed CB tail parameters and the 
second Gaussian width), and the correlated background shape.  Most 
systematic uncertainties cancel for the double ratio, including 
uncertainties related to fixing the CB tail parameters, the second 
Gaussian width, and the multiple collision correction factor. The 
correlated background uncertainty was determined by allowing two of the 
five parameters in the fit function to vary and comparing the resulting 
signal yields from each fit.  The determination of the uncertainty in 
the normalization of the mixed-event background follows the methods 
described in Ref. <cit.> and an uncertainty is assigned by 
repeating the fit to the invariant-mass distribution over a mass range 
extended first below and then above the nominal mass range of the fit.












The self-normalized J/ψ yields 
(N_J/ψ/⟨N_J/ψ⟩) as a function of 
self-normalized charged-particle multiplicity () are shown in 
Fig. <ref> and compared to 
STAR <cit.> and ALICE <cit.> 
data.  The J/ψ decay-daughter-muon contributions to the 
charged-particle multiplicity have been subtracted in the PHENIX 
results to remove the auto-correlation effect. Before subtracting the 
J/ψ daughter-muon contributions, The PHENIX results show a 
multiplicity dependence that is similar to the STAR results at 
midrapidity. For ALICE at 13 TeV, the results at forward rapidity are 
systematically lower than at midrapidity, but it is difficult to reach 
conclusions for PHENIX and STAR at 200 GeV due to the larger systematic 
uncertainties.   After subtracting the daughter-muon contributions, 
the yields shift to lower , leading to a significant drop 
of N_J/ψ/⟨ N_J/ψ⟩, which is consistent with the 
results of opposite arms, where is free from the daughter-muon contributions. The PHENIX results with subtraction is 
significantly lower than the ALICE results at forward rapidity, but a 
comparable slope is seen in STAR and ALICE results at midrapidity. Note 
that the auto-correlation correction was not applied to the ALICE and 
STAR results.  The impact on the slope is expected to be more 
significant for the STAR than the ALICE results due to the smaller 
multiplicity.

The self-normalized J/ψ yields are also compared with calculations. In Fig. <ref> where the simulations are 
compared to J/ψ normalized yield in data, the Detroit 
tuned with MPI calculations <cit.> agree with the data 
within ≈1σ while failing to describe the data without 
MPI effects.  Therefore, MPI effects need to be included to accurately 
model production in collisions at RHIC. In addition, 
comparison between the PHENIX and ALICE results at forward rapidity 
indicates that the MPI effects on the multiplicity dependence would be 
even stronger at LHC energies.

The (N_ψ(2S)/N_J/ψ)/⟨ N_ψ(2S)/N_J/ψ⟩ as a 
function of , shown in Fig. <ref>, was measured 
to investigate final-state interaction effects on charmonium production.  
The self-normalized yield ratios of to at forward rapidity are 
shown as a function of normalized charged-particle multiplicity, where the 
charged-particle multiplicity has been measured using both the forward 
(same arms) and backward (opposite arms) FVTX detectors. The 
(N_ψ(2S)/ N_J/ψ)/⟨ N_ψ(2S)/ N_J/ψ⟩ 
measurements are consistent with unity within≈1σ, and no 
significant rapidity dependence is observed. Therefore, final-state 
interactions on charmonium production appear negligible at the measured 
multiplicity range and collision energy.

Furthermore, in Fig. <ref>, the ALICE forward 
rapidity prompt  <cit.> and LHCb prompt and 
nonprompt measurements are included for comparison. The ALICE 
results also demonstrate similar consistency near unity up to 
/⟨⟩=≈6. Recently, LHCb has reported 
suppression of 
(N_ψ(1S)/N_J/ψ)/⟨N_ψ(2S)/N_J/ψ⟩ 
in high multiplicity collisions <cit.>. The final 
state comover effect <cit.> becomes more pronounced at 
high multiplicity, and may result in the increased breakup of compared to due to its lower binding energy.

Finally, Fig. <ref> also shows Detroit 
tuned with MPI effects for the 
(N_ψ(2S)/N_J/ψ)/⟨N_ψ(2S)/N_J/ψ⟩ as a 
function of but without any final-state effects on quarkonia. 
The calculations yield similar results within uncertainties, 
and generally reproduce the data near unity. This indicates that the 
data favors no significant final-state interaction in collisions at 
=200 GeV.






In summary, we have reported multiplicity-dependent studies of and production at forward rapidity in collisions at 
=200 GeV. The self-normalized yields are measured up to 
≈6 units of and reasonable consistency with the STAR 
and ALICE data has been achieved when the and charged particles 
are measured in the same pseudorapidity region. Results of 
self-normalized yields before and after decay-daughter-muon 
subtraction for counting can be well described by the Detroit tuned with MPI. Also, forward self-normalized to yields as a function of forward and backward track multiplicity have 
been studied. Agreements with unity have been observed within 
uncertainties and the results are consistent with each other at 
different rapidity gaps, suggesting no significant final-state 
interactions on charmonium production. The model without 
final-state interactions generally reproduces the self-normalized 
to yields indicating that no such effect occurs in collisions at RHIC energies. 

Consistency with unity is also reported by ALICE. However, LHCb 
observes a suppression of prompt ψ(2S) production at high 
multiplicity, aligning with the prediction of final-state comover 
effects <cit.>. The LHCb results also demonstrate 
consistency with the PHENIX data points within uncertainties. 
Investigations of charmonium production in p+Al and p+Au 
collisions with PHENIX data, particularly in the backward-rapidity 
region, would provide an excellent opportunity to further study 
final-state effects in small collision systems at RHIC energies.














We thank the staff of the Collider-Accelerator and Physics
Departments at Brookhaven National Laboratory and the staff of
the other PHENIX participating institutions for their vital
contributions.  
We acknowledge support from the Office of Nuclear Physics in the
Office of Science of the Department of Energy,
the National Science Foundation,
Abilene Christian University Research Council,
Research Foundation of SUNY, and
Dean of the College of Arts and Sciences, Vanderbilt University
(U.S.A),
Ministry of Education, Culture, Sports, Science, and Technology
and the Japan Society for the Promotion of Science (Japan),
Conselho Nacional de Desenvolvimento Científico e
Tecnológico and Fundação de Amparo à Pesquisa do
Estado de São Paulo (Brazil),
Natural Science Foundation of China (People's Republic of China),
Croatian Science Foundation and
Ministry of Science and Education (Croatia),
Ministry of Education, Youth and Sports (Czech Republic),
Centre National de la Recherche Scientifique, Commissariat
à l'Énergie Atomique, and Institut National de Physique
Nucléaire et de Physique des Particules (France),
J. Bolyai Research Scholarship, EFOP, HUN-REN ATOMKI, NKFIH,
MATE KKF, and OTKA (Hungary), 
Department of Atomic Energy and Department of Science and Technology (India),
Israel Science Foundation (Israel),
Basic Science Research and SRC(CENuM) Programs through NRF
funded by the Ministry of Education and the Ministry of
Science and ICT (Korea).
Ministry of Education and Science, Russian Academy of Sciences,
Federal Agency of Atomic Energy (Russia),
VR and Wallenberg Foundation (Sweden),
University of Zambia, the Government of the Republic of Zambia (Zambia),
the U.S. Civilian Research and Development Foundation for the
Independent States of the Former Soviet Union,
the Hungarian American Enterprise Scholarship Fund,
the US-Hungarian Fulbright Foundation,
and the US-Israel Binational Science Foundation.






















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