---
abstract: 'Production of $\pi^0$ and $\eta$ mesons has been measured at midrapidity in Cu$+$Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV. Measurements were performed in $\pi^0(\eta)\rightarrow\gamma\gamma$ decay channel in the 1(2)-20 GeV/$c$ transverse momentum range. A strong suppression is observed for $\pi^0$ and $\eta$ meson production at high transverse momentum in central Cu$+$Au collisions relative to the $p$$+$$p$ results scaled by the number of nucleon-nucleon collisions. In central collisions the suppression is similar to Au$+$Au with comparable nuclear overlap. The $\eta/\pi^0$ ratio measured as a function of transverse momentum is consistent with $m_T$-scaling parameterization down to $p_T=2$ GeV/$c$, its asymptotic value is constant and consistent with Au$+$Au and $p$$+$$p$ and does not show any significant dependence on collision centrality. Similar results were obtained in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions as well as in $e^+e^-$ collisions in a range of collision energies $\sqrt{s_{_{NN}}}=3$–1800 GeV. This suggests that the quark-gluon-plasma medium produced in Cu$+$Cu collisions either does not affect the jet fragmentation into light mesons or it affects the $\pi^0$ and $\eta$ the same way.'
author:
- 'C. Aidala'
- 'N.N. Ajitanand'
- 'Y. Akiba'
- 'R. Akimoto'
- 'J. Alexander'
- 'M. Alfred'
- 'K. Aoki'
- 'N. Apadula'
- 'H. Asano'
- 'E.T. Atomssa'
- 'T.C. Awes'
- 'B. Azmoun'
- 'V. Babintsev'
- 'A. Bagoly'
- 'M. Bai'
- 'X. Bai'
- 'B. Bannier'
- 'K.N. Barish'
- 'S. Bathe'
- 'V. Baublis'
- 'C. Baumann'
- 'S. Baumgart'
- 'A. Bazilevsky'
- 'M. Beaumier'
- 'R. Belmont'
- 'A. Berdnikov'
- 'Y. Berdnikov'
- 'D. Black'
- 'D.S. Blau'
- 'M. Boer'
- 'J.S. Bok'
- 'K. Boyle'
- 'M.L. Brooks'
- 'J. Bryslawskyj'
- 'H. Buesching'
- 'V. Bumazhnov'
- 'S. Butsyk'
- 'S. Campbell'
- 'V. Canoa Roman'
- 'C.-H. Chen'
- 'C.Y. Chi'
- 'M. Chiu'
- 'I.J. Choi'
- 'J.B. Choi'
- 'S. Choi'
- 'P. Christiansen'
- 'T. Chujo'
- 'V. Cianciolo'
- 'B.A. Cole'
- 'M. Connors'
- 'N. Cronin'
- 'N. Crossette'
- 'M. Csanád'
- 'T. Csörgő'
- 'T.W. Danley'
- 'A. Datta'
- 'M.S. Daugherity'
- 'G. David'
- 'K. DeBlasio'
- 'K. Dehmelt'
- 'A. Denisov'
- 'A. Deshpande'
- 'E.J. Desmond'
- 'L. Ding'
- 'J.H. Do'
- 'L. D’Orazio'
- 'O. Drapier'
- 'A. Drees'
- 'K.A. Drees'
- 'J.M. Durham'
- 'A. Durum'
- 'T. Engelmore'
- 'A. Enokizono'
- 'S. Esumi'
- 'K.O. Eyser'
- 'B. Fadem'
- 'W. Fan'
- 'N. Feege'
- 'D.E. Fields'
- 'M. Finger'
- 'M. Finger,Jr.'
- 'F. Fleuret'
- 'S.L. Fokin'
- 'J.E. Frantz'
- 'A. Franz'
- 'A.D. Frawley'
- 'Y. Fukao'
- 'T. Fusayasu'
- 'K. Gainey'
- 'C. Gal'
- 'P. Gallus'
- 'P. Garg'
- 'A. Garishvili'
- 'I. Garishvili'
- 'H. Ge'
- 'F. Giordano'
- 'A. Glenn'
- 'X. Gong'
- 'M. Gonin'
- 'Y. Goto'
- 'R. Granier de Cassagnac'
- 'N. Grau'
- 'S.V. Greene'
- 'M. Grosse Perdekamp'
- 'Y. Gu'
- 'T. Gunji'
- 'H. Guragain'
- 'T. Hachiya'
- 'J.S. Haggerty'
- 'K.I. Hahn'
- 'H. Hamagaki'
- 'J. Hanks'
- 'S. Hasegawa'
- 'T.O.S. Haseler'
- 'K. Hashimoto'
- 'R. Hayano'
- 'X. He'
- 'T.K. Hemmick'
- 'T. Hester'
- 'J.C. Hill'
- 'K. Hill'
- 'A. Hodges'
- 'R.S. Hollis'
- 'K. Homma'
- 'B. Hong'
- 'T. Hoshino'
- 'N. Hotvedt'
- 'J. Huang'
- 'S. Huang'
- 'T. Ichihara'
- 'Y. Ikeda'
- 'K. Imai'
- 'Y. Imazu'
- 'M. Inaba'
- 'A. Iordanova'
- 'D. Isenhower'
- 'A. Isinhue'
- 'D. Ivanishchev'
- 'B.V. Jacak'
- 'S.J. Jeon'
- 'M. Jezghani'
- 'Z. Ji'
- 'J. Jia'
- 'X. Jiang'
- 'B.M. Johnson'
- 'K.S. Joo'
- 'D. Jouan'
- 'D.S. Jumper'
- 'J. Kamin'
- 'S. Kanda'
- 'B.H. Kang'
- 'J.H. Kang'
- 'J.S. Kang'
- 'J. Kapustinsky'
- 'D. Kawall'
- 'A.V. Kazantsev'
- 'J.A. Key'
- 'V. Khachatryan'
- 'P.K. Khandai'
- 'A. Khanzadeev'
- 'K.M. Kijima'
- 'C. Kim'
- 'D.J. Kim'
- 'E.-J. Kim'
- 'M. Kim'
- 'Y.-J. Kim'
- 'Y.K. Kim'
- 'D. Kincses'
- 'E. Kistenev'
- 'J. Klatsky'
- 'D. Kleinjan'
- 'P. Kline'
- 'T. Koblesky'
- 'M. Kofarago'
- 'B. Komkov'
- 'J. Koster'
- 'D. Kotchetkov'
- 'D. Kotov'
- 'F. Krizek'
- 'B. Kurgyis'
- 'K. Kurita'
- 'M. Kurosawa'
- 'Y. Kwon'
- 'R. Lacey'
- 'Y.S. Lai'
- 'J.G. Lajoie'
- 'A. Lebedev'
- 'D.M. Lee'
- 'G.H. Lee'
- 'J. Lee'
- 'K.B. Lee'
- 'K.S. Lee'
- 'S.H. Lee'
- 'M.J. Leitch'
- 'M. Leitgab'
- 'Y.H. Leung'
- 'B. Lewis'
- 'N.A. Lewis'
- 'X. Li'
- 'X. Li'
- 'S.H. Lim'
- 'M.X. Liu'
- 'S. L[ö]{}k[ö]{}s'
- 'D. Lynch'
- 'C.F. Maguire'
- 'T. Majoros'
- 'Y.I. Makdisi'
- 'M. Makek'
- 'A. Manion'
- 'V.I. Manko'
- 'E. Mannel'
- 'M. McCumber'
- 'P.L. McGaughey'
- 'D. McGlinchey'
- 'C. McKinney'
- 'A. Meles'
- 'M. Mendoza'
- 'B. Meredith'
- 'Y. Miake'
- 'T. Mibe'
- 'A.C. Mignerey'
- 'D.E. Mihalik'
- 'A. Milov'
- 'D.K. Mishra'
- 'J.T. Mitchell'
- 'G. Mitsuka'
- 'S. Miyasaka'
- 'S. Mizuno'
- 'A.K. Mohanty'
- 'S. Mohapatra'
- 'T. Moon'
- 'D.P. Morrison'
- 'S.I. Morrow'
- 'M. Moskowitz'
- 'T.V. Moukhanova'
- 'T. Murakami'
- 'J. Murata'
- 'A. Mwai'
- 'T. Nagae'
- 'S. Nagamiya'
- 'K. Nagashima'
- 'J.L. Nagle'
- 'M.I. Nagy'
- 'I. Nakagawa'
- 'Y. Nakamiya'
- 'K.R. Nakamura'
- 'T. Nakamura'
- 'K. Nakano'
- 'C. Nattrass'
- 'P.K. Netrakanti'
- 'M. Nihashi'
- 'T. Niida'
- 'R. Nouicer'
- 'T. Novák'
- 'N. Novitzky'
- 'A.S. Nyanin'
- 'E. O’Brien'
- 'C.A. Ogilvie'
- 'H. Oide'
- 'K. Okada'
- 'J.D. Orjuela Koop'
- 'J.D. Osborn'
- 'A. Oskarsson'
- 'K. Ozawa'
- 'R. Pak'
- 'V. Pantuev'
- 'V. Papavassiliou'
- 'I.H. Park'
- 'S. Park'
- 'S.K. Park'
- 'S.F. Pate'
- 'L. Patel'
- 'M. Patel'
- 'J.-C. Peng'
- 'W. Peng'
- 'D.V. Perepelitsa'
- 'G.D.N. Perera'
- 'D.Yu. Peressounko'
- 'C.E. PerezLara'
- 'J. Perry'
- 'R. Petti'
- 'C. Pinkenburg'
- 'R.P. Pisani'
- 'M.L. Purschke'
- 'H. Qu'
- 'P.V. Radzevich'
- 'J. Rak'
- 'I. Ravinovich'
- 'K.F. Read'
- 'D. Reynolds'
- 'V. Riabov'
- 'Y. Riabov'
- 'E. Richardson'
- 'D. Richford'
- 'T. Rinn'
- 'N. Riveli'
- 'D. Roach'
- 'S.D. Rolnick'
- 'M. Rosati'
- 'Z. Rowan'
- 'J. Runchey'
- 'M.S. Ryu'
- 'B. Sahlmueller'
- 'N. Saito'
- 'T. Sakaguchi'
- 'H. Sako'
- 'V. Samsonov'
- 'M. Sarsour'
- 'S. Sato'
- 'S. Sawada'
- 'B.K. Schmoll'
- 'K. Sedgwick'
- 'J. Seele'
- 'R. Seidl'
- 'Y. Sekiguchi'
- 'A. Sen'
- 'R. Seto'
- 'P. Sett'
- 'D. Sharma'
- 'A. Shaver'
- 'I. Shein'
- 'T.-A. Shibata'
- 'K. Shigaki'
- 'M. Shimomura'
- 'K. Shoji'
- 'P. Shukla'
- 'A. Sickles'
- 'C.L. Silva'
- 'D. Silvermyr'
- 'B.K. Singh'
- 'C.P. Singh'
- 'V. Singh'
- 'M.J. Skoby'
- 'M. Skolnik'
- 'M. Slunečka'
- 'S. Solano'
- 'R.A. Soltz'
- 'W.E. Sondheim'
- 'S.P. Sorensen'
- 'I.V. Sourikova'
- 'P.W. Stankus'
- 'P. Steinberg'
- 'E. Stenlund'
- 'M. Stepanov'
- 'A. Ster'
- 'S.P. Stoll'
- 'M.R. Stone'
- 'T. Sugitate'
- 'A. Sukhanov'
- 'J. Sun'
- 'Z. Sun'
- 'A. Takahara'
- 'A. Taketani'
- 'Y. Tanaka'
- 'K. Tanida'
- 'M.J. Tannenbaum'
- 'S. Tarafdar'
- 'A. Taranenko'
- 'E. Tennant'
- 'R. Tieulent'
- 'A. Timilsina'
- 'T. Todoroki'
- 'M. Tomášek'
- 'H. Torii'
- 'R.S. Towell'
- 'I. Tserruya'
- 'Y. Ueda'
- 'B. Ujvari'
- 'H.W. van Hecke'
- 'M. Vargyas'
- 'E. Vazquez-Zambrano'
- 'A. Veicht'
- 'J. Velkovska'
- 'R. Vértesi'
- 'M. Virius'
- 'V. Vrba'
- 'E. Vznuzdaev'
- 'X.R. Wang'
- 'D. Watanabe'
- 'K. Watanabe'
- 'Y. Watanabe'
- 'Y.S. Watanabe'
- 'F. Wei'
- 'S. Whitaker'
- 'S. Wolin'
- 'C.P. Wong'
- 'C.L. Woody'
- 'M. Wysocki'
- 'B. Xia'
- 'C. Xu'
- 'Q. Xu'
- 'Y.L. Yamaguchi'
- 'A. Yanovich'
- 'S. Yokkaichi'
- 'J.H. Yoo'
- 'I. Yoon'
- 'Z. You'
- 'I. Younus'
- 'H. Yu'
- 'I.E. Yushmanov'
- 'W.A. Zajc'
- 'A. Zelenski'
- 'S. Zharko'
- 'S. Zhou'
- 'L. Zou'
title: 'Production of $\pi^0$ and $\eta$ mesons in Cu$+$Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV'
---

Introduction
============

Experiments at the Relativistic Heavy Ion Collider (RHIC) [@Arsene:2004fa; @Back:2004je; @Adams:2005dq; @Adcox:2004mh] and later at the Large Hadron Collider (LHC) [@CMS:2012aa; @Abelev:2012hxa; @Aad:2012vca; @Gunji:2016uqe] established the formation of quark-gluon plasma (QGP) in relativistic collisions of heavy ions (). One of the most important tools to investigate the properties of this new medium are identified hadrons at high transverse momenta ($>$5), because they are leading fragments [@jacob1978large] of jets from hard-scattered partons, which, before fragmentation, interacted with the QGP [@Baier:2000mf]. The differential cross section of high-$p_T$ hadron production in elementary $p$+$p$ collisions can be derived using next-to-leading-order perturbative-quantum-chromodynamics formalism [@Owens:1986mp; @Adare:2007dg]:

$$\begin{aligned}
\label{eqcs}
d\sigma_{pp\rightarrow hX}\approx\sum_{abcd}\int 
dx_a dx_b dz_c f_{a/p}(x_a)\otimes f_{b/p}(x_b) \\ 
\otimes \  d\sigma_{ab\rightarrow cd} \otimes D_{c\rightarrow h}(z_c), \nonumber\end{aligned}$$

where $x_{a,b}$ is the initial momentum fraction carried by partons $a$ and $b$, $z_c$ is the final-state momentum fraction of the hadron $h$, $f_{a/p}$ and $f_{b/p}$ are the parton distribution functions (PDFs), $d\sigma_{ab\rightarrow cd}$ is the differential cross section of the initial partons hard scattering, $D_{c\rightarrow h}$ is the fragmentation function (FF) of the hard scattered parton to the final-state hadron.

There are two classes of nuclear effects, which modify the high-$p_T$ hadron production cross section in A+A collisions. The initial state (or cold nuclear matter) effects are related to the presence of a heavy nucleus in the collision and require the modification of the corresponding PDF in Eq. \[eqcs\]. The correction factors for PDFs are usually obtained from the $p$/$d$$+$$A$ data [@Helenius:2012wd; @Eskola:2016oht].

The final-state effects are related to the formation of a hot, dense medium, QGP. While the hard-scattered parton propagates through the medium, it loses a fraction of its energy (jet-quenching) [@Bjorken:1982tu; @Baier:2000mf; @Wang:1994fx] by gluon emission or elastic scatterings with the medium constituents.

Parton energy loss in the QGP is quantified with the jet transport coefficient $\hat{q}$, defined as the squared momentum exchange between the hard parton and the medium per unit path length [@Baier:2000mf]. The relation of $\hat{q}$ to other medium parameters, such as temperature, shear viscosity and entropy, is indicative of the character of the coupling to the medium [@majumder2007small].

Several phenomenological models [@qin2008gy; @chen2011x; @young2012martini; @majumder2012suppression; @xu2014azimuthal] were designed to estimate $\hat{q}$ based on ${\mbox{$R_{AB}$}\xspace}$ measurements at RHIC and the LHC. In the model calculations, the final state effects are usually accounted for by replacing $D_{c\rightarrow h}$ with the medium-modified FF $\widetilde{D}_{c\rightarrow h}$ in Eq. \[eqcs\]. Methods of $\widetilde{D}_{c\rightarrow h}$ estimation are specific for each parton energy model. Also several attempts were made to extract $\hat{q}$ using lattice QCD calculations [@majumder2013calculating; @Panero:2013pla]. The effects of the medium on particle production are usually quantified by the nuclear modification factor (${\mbox{$R_{AB}$}\xspace}$): $$R_{AB}^{\rm cent}({\mbox{$p_T$}\xspace}) = \frac{1}{T_{AB}^{\rm cent}}\frac{dN_{AB}^{\rm cent}/d{\mbox{$p_T$}\xspace}}{d\sigma_{pp}/d{\mbox{$p_T$}\xspace}},$$ where $dN_{AB}^{\rm cent}$ is the particle yield measured in A+B collisions for a given centrality class ($cent$), $d\sigma_{pp}$ is the cross section of the same particle measured in ${\mbox{$p$$+$$p$}\xspace}$ collisions at the same collision energy, $T_{AB}^{\rm cent}$ is the nuclear thickness function for the event class [@Miller:2007ri]. The energy loss of hard-scattered partons causes a reduction of from unity towards smaller values.

Measurement of $\pi^0$ meson production is particularly interesting, because $\pi^0$s are abundantly produced and their yields can be measured up to high $p_T$ with good particle identification, an excellent signal-to-background ratio ($S/B$), and relatively small uncertainties using the electromagnetic calorimeters (EMCal) of the PHENIX detector. The $\eta$ meson has four times heavier mass than $\pi^0$ and an about 50% strangeness content. Thus measurements of $\eta$ allow to study the dependence of jet quenching on the hadron mass and flavor content. Measurement of $\eta/\pi^0$ in ${\mbox{A$+$A}\xspace}$ gives an opportunity to better understand whether fragmentation processes are affected by the presence of the colored medium.

Previously published results on $\pi^0$ and $\eta$ production at PHENIX were obtained in symmetric heavy-ion systems such as ${\mbox{Au$+$Au}\xspace}$ and ${\mbox{Cu$+$Cu}\xspace}$  [@Adler:2006bv; @Adare:2008cg; @Adare:2008qa; @Adare:2008ad; @Adare:2010dc]. Contrarily to that, ${\mbox{Cu$+$Au}\xspace}$ collisions at $\sqrt{s_{_{NN}}}=200$ GeV is the first asymmetric system of heavy nuclei studied at RHIC. Such collisions provide a different collision geometry from the one realized in symmetric systems. In central collisions the Cu nucleus is fully submerged in the Au nucleus, which results in the reduction of nucleon-nucleon interactions in the “corona" region [@Pantuev:2005jt] of the collision (see Fig. \[fig:cartoon\]). In semi-central ${\mbox{Cu$+$Au}\xspace}$ collisions an asymmetry of the nuclear overlap region is present along the axis connecting the centers of the interacting nuclei. These features make ${\mbox{Cu$+$Au}\xspace}$ collision system an important part of the systematic study of the final-state effects in heavy-ion collisions.

In this paper we present $\pi^0$ and $\eta$ meson $p_T$ spectra and nuclear modification factor measurements in ${\mbox{Cu$+$Au}\xspace}$ collisions at $\sqrt{s_{_{NN}}}=200$ GeV. Data were collected in RHIC Year-2012 run with the PHENIX detector.

Data analysis
=============

![Cartoon showing and collisions with comparable . On panel (b) the overlap area is asymmetric, and part of the dilute surfaces of Au and Cu (corona) overlap. []{data-label="fig:cartoon"}](Cartoon_CollisionGeometry.pdf){width="1.0\linewidth"}

   Centrality interval   $\left\langle T_{AB} \right\rangle$ (mb$^{-1}$)   $\left\langle N_{\rm part} \right\rangle$
  --------------------- ------------------------------------------------- -------------------------------------------
      Minimum Bias                       $2.54\pm 0.19$                                  $61.1\pm 2.7$
         0%–10%                           $8.8\pm 0.6$                                  $177.2\pm 5.2$
         10%–20%                          $6.0\pm 0.4$                                  $132.4\pm 3.7$
         0%–20%                           $7.5\pm 0.5$                                  $154.8\pm 4.1$
         20%–40%                          $3.1\pm 0.2$                                   $80.4\pm 3.3$
         40%–60%                         $1.00\pm 0.12$                                  $34.9\pm 2.8$

  : \[tab0\] The average values of the nuclear thickness function $\left\langle 
  T_{AB} \right\rangle$ and the numbers of nucleons participating in the nuclei interaction $\left\langle N_{\rm part} \right\rangle$ in different Cu$+$Au centrality intervals.

A detailed description of the PHENIX experimental set-up can be found elsewhere [@Adcox:2003zm]. Beam-beam counters (BBC, $3.0<|\eta|<3.9$) [@Allen:2003zt] located downstream in both beam directions (north and south), each consisting of 64 Čerenkov-radiator counters, provide the minimum-bias (MB) trigger [@Adler:2003zu] and are also used to determine the event centrality and vertex position along the beam axis ($z_{\rm BBC}$). The MB trigger is formed if two or more BBC counters on each side detect the passage of charged particle(s). The MB trigger efficiency in is 93% of total inelastic collisions. The event centrality is defined by the total charge observed in the BBC. The mean number of participating nucleons (), binary collisions () and the nuclear overlap function () in various centrality intervals are estimated with a Glauber-model Monte-Carlo simulation [@Miller:2007ri] folded with the BBC response. The average values of and for different centrality classes of collisions are listed in Table \[tab0\].

The measurements are based on two data sets. Up to moderate ($<8$) $6.9\times10^{9}$ MB events satisfying a vertex cut of $|z_{\rm BBC}|< 20$ cm are used. To improve statistics and extend the range to higher an additional sample was collected with one of the EMCal hardware triggers (ERT-A). This trigger required the presence of at least one high-energy shower in the EMCal. After offline calibration it was found that the ERT-A trigger reached full efficiency for photons with energy above 4.5–5GeV depending on location in the calorimeter. The accumulated ERT-A data sample after the same $|z_{\rm BBC}|<20$cm vertex cut corresponds to $1.8\times10^{10}$ sampled MB events, which is a factor of three more than the MB sample. MB data is used to measure meson yields at $p_T<8$ GeV/$c$, and ERT-A data set is used at higher momenta.

Reconstruction of $\pi^0$ and $\eta$ mesons is performed via their decay modes $\pi^0\rightarrow\gamma\gamma$ and $\eta\rightarrow\gamma\gamma$. Photons are measured in the EMCal [@Aphecetche:2003zr] located in the two central arms of the PHENIX detector, each covering 90 degrees in azimuth and $|\eta|<0.35$ in pseudorapidity. The EMCal comprises two technologically different subsystems: lead-scintillator sampling calorimeter (PbSc) and lead-glass Čerenkov calorimeter (PbGl), which cover $3/8$ and $1/8$ of the full azimuth, respectively. The PbSc and PbGl subsystems have different linearity, energy resolution ($\delta E/E=2.1\%\oplus8.1\%/\sqrt{E}$ for PbSc and $0.8\%\oplus5.9\%/\sqrt{E}$ for PbGl) and segmentation ($\delta\phi\times\delta\eta \approx 0.01\times0.01 $ for PbSc and $ 
0.008\times0.008 $ for PbGl).

The raw yields of $\pi^0$ and $\eta$ mesons are determined from the $\gamma\gamma$ invariant mass ($m_{\rm inv}$) distribution, in bins of and centrality. The analysis is carried out independently for the PbSc and PbGl subsystems. Photon candidates have to satisfy a shower shape cut [@Aphecetche:2003zr] and are required to have energy ($E_{\gamma}$) larger than 0.4GeV, which helps to further reduce the contribution from other particles, mostly minimum ionizing hadrons. Each $\gamma\gamma$ pair is required to satisfy an asymmetry cut $|\alpha|<0.8$, where $\alpha=|E_{\gamma1}-E_{\gamma2}|/(E_{\gamma1}+E_{\gamma2})$. The asymmetry cut helps to reduce the background from combinatorial $\gamma\gamma$ pairs in the $m_{\rm inv}$ distributions, improving the $S/B$ ratio. A typical invariant mass distribution is shown in Fig. \[fig:FIG0\_InvMass\_Example\].

The $m_{\rm inv}$ distributions contain two peaks in the selected mass region, which correspond to decays of $\pi^0$ and $\eta$. At lower the peaks sit on top of a large combinatorial background. The shape of the background is estimated by event mixing, i.e. from the $m_{\rm inv}$ distribution obtained by combining photons from different events that nevertheless have similar collision vertex and centrality. The mixed event distributions are normalized and subtracted from the real event distributions. The mixed events are normalized outside of the meson peaks from $0.080<m_{\rm inv}<0.085$ and $0.3<m_{\rm inv}<0.4$ GeV/$c^2$ for the and $0.7<m_{\rm inv}<0.8$for the $\eta$. The combinatorial background decreases rapidly with increasing , therefore, mixed event subtraction is carried out only for $p_T$ below 7–10depending on the collision centrality. Above that the background under the peaks is estimated from the average counts in real events outside, but close to the peaks (sideband).

The resulting, combinatorial-subtracted invariant mass distributions are fit to a combination of a Gaussian to describe signal and a polynomial to describe the residual background. First- and second-order polynomials were used in $\pi^0$ and $\eta$ measurements, respectively. Meson raw yields were obtained as the difference between the integral of the bin content in the mass peak regions and the integral of the polynomial fits to the residual background in the same region. The mass peak regions were defined as $m_{\rm inv}=0.10$-$0.17$ and $0.48$-$0.62$ GeV/$c^2$ for $\pi^0$ and $\eta$, respectively.

Acceptance and reconstruction efficiency (efficiency hereafter) are estimated using a [geant3]{}-based [@Brun:1978fy] Monte-Carlo simulation of the PHENIX detector. The simulation was tuned to reproduce the observed mass peaks and widths of $\pi^0$ and $\eta$ in the real data. To account for the effect of underlying events the simulated mesons were embedded in real data in each centrality, then analyzed with the same methods as the real data. Final efficiencies also account for branching ratios of the analyzed decay modes and for the ERT-A trigger efficiency in the corresponding data sample.

Invariant yields of $\pi^0$ and $\eta$ are obtained as follows: $$\frac{1}{N_{\rm event}}\frac{d^2N}{2\pi p_T dp_T dy} = 
\frac{N_{\rm raw}}{2\pi p_T N_{\rm event} \epsilon_{\rm rec} 
\Delta p_T \Delta y},$$

where $N_{\rm raw}$ is the particle raw yield and $\epsilon_{\rm rec}$ is the efficiency (including acceptance and all other corrections), $N_{\rm event}$ is the number of analyzed events.

Systematic uncertainties are classified into three types. Type A represents uncertainties, that are entirely -uncorrelated; these are added in quadrature to the statistical uncertainty. Type B uncertainties are -correlated, but different from point to point, and all data points can move up or down by the same fraction of their Type B uncertainty. Type C represents uncertainties which move all points up or down by the same fraction. Typical values of the estimated systematic and total uncertainties are presented in Tables \[tab1\] and \[tab2\].

  --------------------------- ----------------------------------- ------------------------------------- ----------------------------- -------------------------------------- ---
            Source                                                                                                  Type                                                     
                                        $3.25$ GeV/$c$                        $11$ GeV/$c$                     $3.25$ GeV/$c$                      $11$ GeV/$c$              
          Acceptance                   1.5$\%$(1.5$\%$)                     1.5$\%$(1.5$\%$)                  1.5$\%$(1.5$\%$)                   1.5$\%$(1.5$\%$)             B
         $p_T$ weights                   1$\%$(1$\%$)                         1$\%$(1$\%$)                      1$\%$(1$\%$)                       1$\%$(1$\%$)               B
         Energy scale                    5$\%$(5$\%$)                         9$\%$(9$\%$)                      5$\%$(5$\%$)                       9$\%$(9$\%$)               B
       Energy resolution                 2$\%$(2$\%$)                         2$\%$(2$\%$)                      2$\%$(2$\%$)                       2$\%$(2$\%$)               B
       ERT-A efficiency                       $-$                             1$\%$(1$\%$)                           $-$                         1.3$\%$(1.3$\%$)             B
       Photon conversion               5.2$\%$(5.2$\%$)                     5.2$\%$(5.2$\%$)                  5.2$\%$(5.2$\%$)                   5.2$\%$(5.2$\%$)             C
        Cluster merging                       $-$                            3$\%$(2.5$\%$)                          $-$                               $-$                    B
           PID cuts               4$\%$(4$\%$)$-$6$\%$(4$\%$)          4$\%$(4$\%$)$-$6$\%$(4$\%$)       5$\%$(5$\%$)$-$7$\%$(5$\%$)       5$\%$(5$\%$)$-$7$\%$(5$\%$)        B
     Raw yield extraction                3$\%$(3$\%$)                  3$\%$(3$\%$)$-$4$\%$(4$\%$)           8.13$\%$(8.13$\%$)                  5.3$\%$(5.3$\%$)            
   Reconstruction efficiency   0.8$\%$(1.5$\%$)$-$1.7$\%$(3$\%$)   0.4$\%$(0.7$\%$)$-$0.7$\%$(1.5$\%$)   3$\%$(5$\%$)$-$4$\%$(8$\%$)   0.6$\%$(1.2$\%$)$-$1.03$\%$(1.9$\%$)   A
  --------------------------- ----------------------------------- ------------------------------------- ----------------------------- -------------------------------------- ---

[ccccc]{} Type & $3.25$ GeV/$c$ & $11$ GeV/$c$ & $3.25$ GeV/$c$ & $11$ GeV/$c$\
& &\
Stat & 0.08$\%-$0.2$\%$ & 0.9$\%-$4$\%$ & 3$\%-$5$\%$ & 4$\%-$11$\%$\
Type A & 0.9$\%-$1.8$\%$ & 0.4$\%-$0.9$\%$ & 2$\%-$4$\%$ & 0.6$\%-$0.9$\%$\
Type B & 6$\%-$7$\%$ & 10.1$\%-$10.3$\%$ & 8.7$\%-$9.3$\%$ & 10.7$\%-$11.1$\%$\
Type C & 5.2$\%$ & 5.2$\%$ & 5.2$\%$ & 5.2$\%$\
\
& &\
Type A + Stat. & 1.0$\%-$1.9$\%$ & 2.6$\%-$4.4$\%$ & 4$\%-$6$\%$ & 6$\%-$13$\%$\
Type B & 10.5$\%-$10.7$\%$ & 14.3$\%-$14.4$\%$ & 13.7$\%-$14.1$\%$ & 14.4$\%-$14.7$\%$\
Type C & 12$\%-$23$\%$ & 12$\%-$23$\%$ & 12$\%-$23$\%$ & 12$\%-$23$\%$\
\
& &\
Type A + Stat. & 4$\%-$6$\%$ & 4$\%-$12$\%$ & &\
Type B & 10.9$\%-$11.4$\%$ & 14.7$\%-$15.1$\%$ & &\
Type C & $-$ & $-$ & &\

![Example of an invariant mass plot ($4.5<{\mbox{$p_T$}\xspace}<5.0$). (a) The foreground (photon pairs from the same event) is shown as points, the shaded area is the scaled mixed event background. Insert (b) shows the peak area after mixed event subtraction; the Gaussian fit to the peak and the first order polynomial fit to the residual background are also shown. Insert (c) shows the $\eta$ peak area with the Gaussian fit and second order polynomial for the residual background. []{data-label="fig:FIG0_InvMass_Example"}](FIG1_InvMass_rev3_1cp.pdf){width="1.0\linewidth"}

One of the main sources of systematic uncertainties is the absolute energy calibration of the EMCal. The uncertainty on the absolute scale was estimated to be $1\%$. Due to the steeply falling (power-law) spectrum it corresponds to $\approx2$-$9\%$ uncertainty for the measured yields of $\pi^0$ and $\eta$ mesons, which gradually increases from low to high momentum. At high the measured yields are strongly affected by cluster merging when two photons from a $\pi^0$ decay have a small opening angle and produce partially or fully overlapping showers, which cannot be reconstructed as two individual clusters in the EMCal. Cluster merging results in significant loss of $\pi^0$ reconstruction efficiency at high $p_T$. Due to the different segmentation and Moliere-radius [@Aphecetche:2003zr] the merging effect manifests itself differently in the PbSc and PbGl subsystems. In PbSc the merging starts at $p_T>12$ GeV/$c$, while in PbGl it starts only at $p_T>16$ GeV/$c$. Uncertainties on how well the simulations describe the merging effect result in corresponding uncertainties for the measured $\pi^0$ yields, increase with , reaching $\approx$20$\%$ in PbSc and $\approx$9$\%$ in PbGl at 20 GeV/$c$. Due to the four times heavier mass and larger $\gamma\gamma$ opening angle, the $\eta$ measurements will be influenced by cluster merging only at $p_T>50$ GeV/$c$, which is far beyond the $p_T$ range presented in this analysis. At low $p_T$ (below $\approx$5 GeV/$c$) the main uncertainty for $\pi^0$ and $\eta$ comes from the raw yield extraction due to relatively small $S/B$ ratios. This uncertainty is estimated as the maximum difference between raw yields obtained using different mass regions for mixed event background normalization, different fitting ranges, and different order polynomials for the residual background estimation. Some photons from $\pi^0$ and $\eta$ decays convert into $e^-e^+$ pairs when traversing through detector material. If this happens within the magnetic field, they are bent in opposite directions and can not be reconstructed as a single photon-like cluster in the EMCal. As a result, $\approx25\%$ of $\pi^0$ and $\eta$ mesons are lost. This effect is included in the efficiency calculation. The uncertainty on how accurately it is reproduced in the simulation is estimated to be $5.2\%$, and it is Type-C, because in the relevant energy range the conversion probability is almost constant.

Systematic uncertainties for $\eta/\pi^0$ ratios are included as a quadratic sum of the type-B uncertainties from $\pi^0$ and $\eta$ yields. Because type-C uncertainties of the $\pi^0$ and $\eta$ yields are 100% correlated between these particle measurements for all , this uncertainty cancels in the ratios. The $p_T$-correlated systematic uncertainties for $R_{AB}$ include both uncertainties from Cu$+$Au and $p$+$p$ measurements [@Adare:2007dg].

Invariant yields are obtained separately for PbSc and PbGl subsystems. The results are then averaged with weights defined by the quadratic sum of statistical and those systematic uncertainties that are uncorrelated between the two subsystems. The ratios of the yields obtained in PbSc and PbGl to the averaged ones are presented in panels (b)-(d) and (f)-(h) of Fig. \[fig:FIG1\_CuAu\_CY\]. Only uncorrelated systematic uncertainties are shown in the ratios. Yields obtained in the different subsystems are consistent within statistical and uncorrelated systematic uncertainties. Typical systematic uncertainties for the combined spectra, and $\eta$ $R_{AB}$ and $\eta$/ratio are listed in Table \[tab2\].

To facilitate comparison between different experiments and data sets, the data points of the meson spectra are plotted at the center of each given $p_T$ interval, which, due to the falling spectrum, does not represent the true physical value of the yield at that  [@LAFFERTY1995541]. A bin-shift correction is applied that adjusts the meson yields to their value at the bin center.

![image](FIG2_Yields_rev3_1cp.pdf){width="0.98\linewidth"}

![ Ratios of $\eta$ and $\pi^0$ yields measured as a function of $p_T$ in different centrality intervals of Cu$+$Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV. Dashed curve shows the $m_T$ scaling curve normalized to 0.5 at high momentum (see text). Error bars represent a quadratic sum of statistical and type-A systematic uncertainties for $\pi^0$ and $\eta$ yields. Error boxes represent a quadratic sum of type-B systematic uncertainties for $\pi^0$ and $\eta$ yields. []{data-label="fig:FIG2_CuAu_eta_pi0_rat"}](FIG3_eta_to_pi0_rat_rev3_1cp.pdf){width="1.0\linewidth"}

![image](FIG4_CuAu_pi0_eta_RAB_rev3_1cp.pdf){width="0.99\linewidth"}

![image](FIG5_CuAu_AuAu_CuCu_pi0_RAB_rev3_1cp.pdf){width="0.99\linewidth"}

![image](fig7.pdf){width="0.99\linewidth"}

Results and discussion
======================

Invariant yields in the range 1(2)-20for $\pi^0$ ($\eta$) mesons measured in different centrality intervals and MB collisions are shown in panels (a) and (e) of Fig. \[fig:FIG1\_CuAu\_CY\], respectively. At low the measurement is limited by the rapidly decreasing $S/B$ ratio, and at high by the available statistics.

Spectra of $\pi^0$ and $\eta$ mesons can be fitted with a sum of Hagedorn and power-law functions: $$f(p_T)=T(p_T)\frac{A}{(1+p_T/p_0)^m}+(1-T(p_T))\frac{B}{p^n_T},$$

where $T(p_T)=1/(1+\exp((p_T-t)/w))$, $A$, $p_0$, $m$, $B$, $n$, $t$ and $w$ are free parameters. The parameter $t$ governs at what the second, pure power-law term becomes dominant; $t$ varies between 4–6, depending on centrality. The parameter $w$ varies between 0.05–0.15 and governs the width of transition interval, where the first term loses its dominance and the second term becomes dominant. At high transverse momenta $f(p_T) \propto {\mbox{$p_T$}\xspace}^{-n}$. For in MB collisions $n=8.06 \pm 0.01_{\rm stat} \pm 0.06_{\rm sys}$, for the most central 0%–10% collisions $n=8.02 \pm 0.02_{\rm stat} \pm 0.07_{\rm sys}$, and increases slowly to $n=8.07 \pm 0.02_{\rm stat} \pm 0.06_{\rm sys}$ up to 40% centrality. These numbers are consistent within uncertainties to the values obtained in pure power-law fits at high ($>$8) in 200GeV collisions with similar  [@Adare:2008qa; @Adare:2012wg].

The $\eta/\pi^0$ ratios ($R_{\eta/\pi^0}$) as a function of $p_T$ for different Cu$+$Au centrality intervals are presented in the Fig. \[fig:FIG2\_CuAu\_eta\_pi0\_rat\]. Within uncertainties the measured $R_{\eta/\pi^0}$ are centrality independent in the whole $p_T$ range of measurements. A constant fit to the MB data in the 4$<{\mbox{$p_T$}\xspace}<$20region results in $\eta/{\mbox{$\pi^0$}\xspace}= 0.50 \pm 0.01_{\rm stat} 
\pm 0.02_{\rm sys}$, and the various centrality bins are consistent with this value. The dashed curve in Fig. \[fig:FIG2\_CuAu\_eta\_pi0\_rat\] shows this asymptotically constant fit modified according to $m_T$-scaling. Similar results were obtained in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions as well as in $e^{+}e^{-}$ collisions in a wide range of collision energies $\sqrt{s_{_{NN}}}=3$–1800 GeV [@Busser:1974yj; @Adler:2006bv]. This suggests that QGP medium produced in Cu$+$Au collisions either does not affect the jet fragmentation into light mesons or it affects the and $\eta$ the same way.

Nuclear modification factors of $\pi^0$ and $\eta$ mesons as functions of $p_T$ are shown in Fig. \[fig:FIG3\_CuAu\_pi0\_eta\_RAA\] for different Cu$+$Au centrality intervals. The reference $\pi^0$ meson production cross section in $p$+$p$ collisions was obtained from the 2005 PHENIX $p$+$p$ measurement [@Adare:2007dg]. For $\eta$ meson $R_{AB}$ estimation, the 2006 PHENIX $p$+$p$ measurements were used [@Adare:2010cy]. The $R_{AB}$-s of $\pi^0$ and $\eta$ mesons are consistent within uncertainties in the whole $p_T$ range for every analyzed centrality interval of Cu$+$Au collisions. At $p_T>5$ GeV/$c$ $R_{AB}$ is $\approx 0.4 - 0.5$ in most central collisions. A weak $p_T$ dependence of the measured $R_{AB}$ values can be observed. The suppression of $\pi^0$ and $\eta$ decreases as one moves to more peripheral collisions.

Fig. \[fig:fig5\] compares $R_{AB}$ of $\pi^0$ mesons measured as a function of $p_T$ in ${\mbox{Cu$+$Au}\xspace}$, ${\mbox{Au$+$Au}\xspace}$ [@Adare:2008qa] and ${\mbox{Cu$+$Cu}\xspace}$ [@Adare:2008ad] collisions at $\sqrt{s_{_{NN}}}=200$ GeV and similar $N_{\rm part}$. In central and semi-central ${\mbox{Cu$+$Au}\xspace}$ collisions $\pi^0$ $R_{AB}$ are consistent with those measured in ${\mbox{Au$+$Au}\xspace}$ and ${\mbox{Cu$+$Cu}\xspace}$, if applicable, which suggests that $\pi^0$ suppression mostly depends on the energy density and size of the produced medium. Because in the most central collisions the Cu ion is fully submerged in Au, without any “corona” [@Pantuev:2005jt], but the suppression is the same as in at comparable , the corona-effect is either nonexistent or very small.

In Fig. \[fig:fig6\], the $\pi^0$ and $\eta$ integrated $R_{AB}$’s are shown as a function of $N_{\rm part}$ and compared to ${\mbox{Au$+$Au}\xspace}$. The integration is carried out in two different ranges (${\mbox{$p_T$}\xspace}>5$ and ${\mbox{$p_T$}\xspace}>10$). The results obtained for the two different collision systems are consistent within uncertainties.

Summary
=======

In summary, PHENIX has measured $\pi^0$ and $\eta$ invariant $p_T$-spectra and nuclear modification factors in asymmetric collisions of heavy ions, Cu$+$Au at $\sqrt{s_{_{NN}}}=200$ GeV in a wide $p_T$ range ($1(2)<p_T<20$ GeV/$c$) and for several centrality intervals. In the more central collisions the spectra are similar to those observed in . The asymptotic (high ) value of $\eta/{\mbox{$\pi^0$}\xspace}$ is $0.50 \pm 
0.01_{\rm stat} \pm 0.02_{\rm sys}$, constant, independent of collision centrality, and consistent with the previously measured values in hadron-hadron, hadron-nucleus, nucleus-nucleus as well as $e^{+}e^{-}$ collisions at $\sqrt{s_{_{NN}}}=$3–1800 GeV, suggesting that either the fragmentation of jets into and $\eta$ is unchanged irrespective of the absence or presence of the medium, or it changes the same way, despite the different flavor content. The values of $R_{AB}$ for and $\eta$ are consistent within uncertainties in all analyzed centrality intervals of ${\mbox{Cu$+$Au}\xspace}$ collisions. The suppression pattern of $\pi^0$ in ${\mbox{Cu$+$Au}\xspace}$ collisions is consistent with ${\mbox{Au$+$Au}\xspace}$ and ${\mbox{Cu$+$Cu}\xspace}$ collisions at the same interaction energy and similar values of $N_{\rm part}$.

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 Tecnol[ó]{}gico and Fundaç[ã]{}o de Amparo [à]{} Pesquisa do Estado de S[ã]{}o 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’[É]{}nergie Atomique, and Institut National de Physique Nucl[é]{}aire et de Physique des Particules (France), Bundesministerium für Bildung und Forschung, Deutscher Akademischer Austausch Dienst, and Alexander von Humboldt Stiftung (Germany), J. Bolyai Research Scholarship, EFOP, the New National Excellence Program ([Ú]{}NKP), NKFIH, and OTKA (Hungary), Department of Atomic Energy and Department of Science and Technology (India), Israel Science Foundation (Israel), Basic Science Research Program through NRF of the Ministry of Education (Korea), Physics Department, Lahore University of Management Sciences (Pakistan), Ministry of Education and Science, Russian Academy of Sciences, Federal Agency of Atomic Energy (Russia), VR and Wallenberg Foundation (Sweden), 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.

[40]{}ifxundefined \[1\][ ifx[\#1]{} ]{}ifnum \[1\][ \#1firstoftwo secondoftwo ]{}ifx \[1\][ \#1firstoftwo secondoftwo ]{}““\#1””@noop \[0\][secondoftwo]{}sanitize@url \[0\][‘\
12‘\$12 ‘&12‘\#12‘12‘\_12‘%12]{}@startlink\[1\]@endlink\[0\]@bib@innerbibempty [****,  ()](\doibase 10.1016/j.nuclphysa.2005.02.130) [****,  ()](\doibase
  10.1016/j.nuclphysa.2005.03.084) [****, ()](\doibase 10.1016/j.nuclphysa.2005.03.085) [****,  ()](\doibase
  10.1016/j.nuclphysa.2005.03.086) [****,  ()](\doibase
  10.1140/epjc/s10052-012-1945-x) [****,  ()](\doibase
  10.1016/j.physletb.2013.01.051) [****,  ()](\doibase 10.1016/j.physletb.2013.01.024) [****,  ()](\doibase 10.1016/j.nuclphysa.2016.02.038) [****,  ()](\doibase
  10.1016/0370-1573(78)90177-1) [****,  ()](\doibase 10.1146/annurev.nucl.50.1.37) [****,  ()](\doibase 10.1103/RevModPhys.59.465) @noop [****,  ()]{} @noop [“,” ]{} [****,  ()](\doibase
  10.1140/epjc/s10052-017-4725-9) @noop [“,” ]{} (),  [****,  ()](\doibase
  10.1103/PhysRevD.51.3436) @noop [****,  ()]{} [****,  ()](\doibase 10.1103/PhysRevLett.100.072301) [****,  ()](\doibase 10.1103/PhysRevC.84.034902) @noop [****,  ()]{} @noop [****,  ()]{} @noop [****, ()]{} @noop [****,  ()]{} [****,  ()](\doibase 10.1103/PhysRevLett.112.162001) [****,  ()](\doibase 10.1146/annurev.nucl.57.090506.123020) [****,  ()](\doibase 10.1103/PhysRevC.75.024909) [****,  ()](\doibase 10.1103/PhysRevC.77.064907) [****,  ()](\doibase 10.1103/PhysRevLett.101.232301) [****,  ()](\doibase 10.1103/PhysRevLett.101.162301) @noop [****,  ()]{} [****, ()](\doibase 10.1134/S0021364007020026) [****,  ()](\doibase 10.1016/S0168-9002(02)01950-2) [****,  ()](\doibase 10.1016/S0168-9002(02)01956-3) [****,  ()](\doibase 10.1016/S0168-9002(02)01957-5) [****,  ()](\doibase 10.1016/S0168-9002(02)01954-X) @noop [“,” ]{} (),  [****,  ()](\doibase 10.1016/0168-9002(94)01112-5) @noop [****,  ()]{} [****,  ()](\doibase 10.1103/PhysRevC.87.034911) [****, ()](\doibase 10.1016/0370-2693(75)90450-5)
