Status of CME Search Before Isobar Collisions and Methods of Blind Analysis From STAR
SStatus of CME Search Before Isobar Collisions andMethods of Blind Analysis From STAR
Prithwish Tribedy for the STAR collaboration
Physics Department, Brookhaven National Laboratory, Upton, NYE-mail: [email protected]
Abstract.
The STAR collaboration is currently pursuing the blind analysis of the data forisobar collisions that was performed at RHIC in the year 2018 to make a decisive test of theChiral Magnetic Effect (CME) [1]. Why is it so difficult to detect signals of CME in theexperiment? Do we really understand different sources of background? Why observing similarcharge separation between p/d+A and A+A does not stop us from pursuing the search forCME? In this contribution, I attempt to address some of these questions and briefly outlinea few recent STAR analyses based on new methods and observables to isolate the possibleCME-driven signal and non-CME background contributions at the top RHIC energy. Finally,I describe the procedure for the blind analysis of the isobar data. An outstanding questionremains – what happens if we go down in energy? I address this by discussing how the newevent-plane detector (EPD) upgrade provides a new capability at STAR towards CME searchusing the data from the RHIC BES-II program.
1. Introduction
Finding a conclusive experimental evidence of the Chiral Magnetic Effect (CME) has becomeone of the major scientific goals of the heavy-ion physics program at the Relativistic Heavy IonCollider (RHIC). The existence of CME will be a leap towards an understanding of the QCDvacuum, establishing a picture of the formation of deconfined medium where chiral symmetryis restored and will also provide unique evidence of the strongest known electromagnetic fieldscreated in relativistic heavy-ion collisions [2, 3]. The impact of such a discovery goes beyondthe community of heavy-ion collisions and will possibly be a milestone in physics. Also, as itturns out, the remaining few years of RHIC run and analysis of already collected data probablyprovides the last chance for dedicated CME searches in heavy-ion collisions in the foreseeablefuture.Over the past years significant efforts from the STAR as well as other collaborations havebeen dedicated towards developing new methods and observables to isolate the possible CME-driven signal and non-CME background contributions in the measurements of charge separationacross the reaction plane. The most widely studied experimental observable in this context isthe γ -correlator, defined as (cid:104) cos( φ αa + φ βb − RP ) (cid:105) , where φ a and φ b denote the azimuthal anglesof charged particles, α and β are labels for the charge of the particles and Ψ RP is the reactionplane angle [4]. The angle Ψ RP is expected to be strongly correlated to the direction of themagnetic field that enables the γ -correlator to be sensitive to signals of CME, more specifically,CME leads to a difference between same sign (SS, α = β ) and opposite sign (OS, α (cid:54) = β )charge correlations: ∆ γ = γ OS − γ SS . The STAR time projection chamber (TPC) has a wide a r X i v : . [ nu c l - e x ] S e p cceptance at mid-rapidity ( | η | <
1) that is used to detect φ a and φ b . And, in STAR the proxy forΨ RP can be played by: 1) second-order harmonic anisotropy plane Ψ of produced particles atmid-rapidity measured by TPC, 2) the first-order plane due to the spectator neutrons (Ψ zdc )detected by the zero degree calorimeters (ZDC), 3) the forward Ψ plane using the STARbeam beam counter BBCs and 4) very recently using both the first and second-order harmonicanisotropy planes using the forward Event Plane Detector (EPDs). Each of these planes areexpected to have more or less measurable correlations to B-field and serves their purpose forthe CME search. The first measurement of non-zero ∆ γ by the STAR collaboration goes backto [5] where connections to several expectations from CME driven signals of charge separationwas identified. Most importantly, the first measurement from STAR [5] also identified severalpossible contributions from non-CME effects in the experimental observation of non-zero ∆ γ .Several subsequent measurements from RHIC and LHC have confirmed this observation andprovided many additional insights in that direction [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. In thiscontribution, I will focus only on RHIC results and refer to LHC results wherever necessary.A major challenge that the γ -correlator faces towards detecting signals of CME involveslarge non-CME background sources that are: 1) correlated to Ψ RP and 2) independent of Ψ RP .The distinction between the two sources must be carefully noted as they are crucial to theinterpretation of several key measurements performed at both RHIC and LHC.
2. Major challenges in isolating background
The possible background contamination due to the first source of Ψ RP dependent correlationwas already alluded to in the reference where γ -correlator was first proposed [4]. At thattime only neutral resonance particles were identified as the major source of such backgroundalbeit thought to be sub-dominant. When a flowing neutral resonance decays it enhances theprobability of a pair of opposite sign particles to move together along Ψ RP . Such correlationslead to non-zero magnitudes of ∆ γ mimicking CME. Later on, a more severe source of Ψ RP dependent background due to correlated production of a pair of opposite charged particles dueto local charge conservation (LCC) was proposed [16]. Parametrically, if v is the elliptic flowand N is the multiplicity the background contribution from resonance and LCC should go as∆ γ bkg ∼ v /N [4] that is also verified by many model calculations [17]. Recently, many modelsthat incorporate the same basic picture of particle production conserving charge locally froma flowing neutral matter, are able to very well explain measurements of ∆ γ without invokingthe physics of CME. Despite the success of background models experimental search of CMEcontinued because of a number of reasons. Model predictions have large systematics sinceexact mechanism of hardronization is poorly understood, limited constraints from independentmeasurements are available. Above all, even the most state-of-the art background models failto explain all qualitative features of the data (e.g. ∆ γ in central collisions, see Fig.1). Whilethe models continue to refine their predictive power, over many years this largely lead to amajor effort in beating the background sources in the measurement of charge separation alongΨ RP . It is worth to mention that pheomenological predictions based on anomalous viscoushydrodynamics are now available that include both CME signal and background contributionand can be used to test the sensitivity of different observables [18]. The second major sources of non-CME background to ∆ γ arises from reaction plane independentnon-flow correlations. The possibility of such background was discussed in the first publicationof charge separation from STAR [5]. One possible source of such background was identified tobe three-particle correlations induced by mini-jet fragmentation which is known to: 1) influencethe determination of event plane, 2) introduce more opposite charge correlation than sameharge correlations. The combination of these two artifacts are supposed to lead to non-zero∆ γ and mimic CME signals. In Ref [5], an indication of larger contribution of reaction planeindependent background can already be seen in: 1) the sharp increasing strength of ∆ γ towardsperipheral events and, 2) large ∆ γ in Cu+Cu than in Au+Au system at the same centrality.Both observations can be supported by hijing calculation.
3. Using small systems to estimate data driven background
Small collision systems provide unique data-driven ways to measure charge separation in thebackground scenario. This is based on the idea that the direction of B-field is uncorrelated to theelliptic anisotropy plane of the produced particle with respect to which ∆ γ is measured [12, 19].In low-multiplicity or min-bias collisions of small systems such planes are dominated by non-flowcorrelations from di-jets or momentum conservation. However, tell-tale signatures of collectivityhave been observed in high multiplicity events of small collision systems – the origin of whichhas been a widely discussed topic in our community. There are a few scenarios that decidewhether the elliptic anisotropy plane measured in the experiment will be: 1) correlated to ageometric plane of participants if collectivity is due to hydrodynamics flow, 2) uncorrelated orless correlated to geometric plane if collectivity is due to non-hydrodynamic but other initialstate momentum space correlations, e.g. from CGC or escape mechanism and, 3) dominated bynon-flow from di-jets and momentum conservation if no collectivity is observed [20]. Why is thisimportant for CME search? It is important as these scenarios determine the nature of non-CMEbackground that will dominate the measurements of ∆ γ in small systems. It is also important toknow what kind of baseline measurement do these small systems provide because our ultimategoal is to interpret measurements in heavy-ion collisions. For example, in the first scenariohydrodynamic flow driven background combined with local charge conservation will be thedominant source, important for heavy-ion measurements in most centralities. For the second andthird scenarios reaction plane independent background will be the dominant source, importantfor peripheral and smaller sized heavy-ion collisions. Nevertheless, the expectation is that CMEsignal in all such scenarios will be small as the B-field in small collision systems are weaklycorrelated to elliptic anisotropy plane other than some specific scenarios like what was discussedin Ref [21]. So in summary, small systems have the potential to provide baseline measurementsfor heavy-ion collisions where CME signals are expected to disappear but different backgroundsources will be present. The CMS measurement was the first to show that in overlappingmultiplicity ∆ γ measurements are quantitatively similar between p+Pb and Pb+Pb [12]. STARmeasurements performed in p+Au and d+Au systems show similar and in fact larger chargeseparation measured in terms of the scaled quantity ∆ γ/v × N ch than the same in Au+Aumeasurements [15]. Such observations are striking as they tell us that a very large value of ∆ γ is expected even for 100% background scenario.The following question is often asked. Does measurement in small systems completely rule outCME? Why do we still pursue the CME search? There are several reasons for not abandoningCME search in heavy-ion collisions based on the observations from small collision systems. Itis already known that ∆ γ in heavy-ion collisions suffer from major background, the possibleexistence of CME driven signal has become more of a quantitative question. Therefore only aquantitative baseline will serve our purpose. So a better question to ask is whether small systemmeasurements can provide direct quantitative baseline for heavy-ions. Heavy-ion measurementsfor CME search are performed where the system size, multiplicity do not necessarily overlapwith that of small systems. It is not straightforward to extrapolate the quantitative backgroundbaselines for ∆ γ into such unknown territories where change of physics is eminent. For example,∆ γ measured for N ch = 10 in p/d+Au maybe a good baseline for A+A at the same multiplicitybut may not serve as quantitative baselines for ∆ γ in Au+Au at N ch = 100. One may try tomake a projection under some working assumptions but that will lead to a qualitative baselinend defeats the major purpose of using small systems as direct quantitative baselines. This iswhere isobar collisions come in – that ensures measurements in two systems with very similarsize and shape are compared. It is also difficult to conclude that the case of CME is ruled outentirely based on the raw ∆ γ measurements between p/d+Au and Au+Au. In lieu of whichseveral variants of ∆ γ , as well as alternative observable such as R − observable, signed balancefunction has been developed to quantify the signals of CME [22, 23]. The measurements basedon R − observable show qualitative difference in p/d+Au and Au+Au [24] – that is discussed inthe following section.
4. The way forward
With the aforesaid introduction on the challenges to disentangle CME from non-CMEbackground I would like to now proceed with the possible solutions to overcome such aproblem. Many cleaver ideas have been proposed and applied to existing data. The generalconsensus is that measurement from the isobar collisions (Ru+Ru that has 10 −
18% higherB-field than Zr+Zr) provides the best solution to this problem. In following sections of thisconference proceedings I would like to mention a few such recent efforts such as: 1) Differentialmeasurements of ∆ γ to identify and quantify backgrounds, 2) measurement of higher orderharmonics of γ -correlator, 3) exploiting the relative charge separation across participant andspectator planes, 4) the use of R-observable to measure charge separation and 5) the use ofsigned balance function. The first three approaches are based on aforementioned three-particlecorrelator and the last two employ slightly different approaches to quantify charge separation.There have been many more developments in the recent times and also many LHC measurementshave been performed but I will specifically focus on these five approaches because they will beexplored with the isobar data. The following five sections describe these procedures in brief withcomments on the outlook for isobar blind analysis (see [1] for more details).
5. Differential measurements of ∆ γ to identify and quantify background Differential measurements of ∆ γ with invariant mass and relative pseudorapidity provideinteresting prospects to identify and quantify the sources of flow and non-flow drivenbackgrounds. The idea to use invariant mass is simple and was first introduced in Ref [25].Resonances are widely identified by observing structures in the invariant mass spectra of thedecay daughters. Take a pair of opposite sign pions for example, a large fraction of them comefrom the neutral resonances that show up in the invariant mass spectrum of m inv ( π + + π − ). If werestrict the analysis to pairs of pions, differential measurements of ∆ γ with m inv ( π + + π − ) shouldalso show similar peak like structures if background from neutral resonances dominate the chargeseparation. Indeed similar peak structures are observed and a careful analysis is performed bySTAR collaboration to extract the possible fraction of CME signals from measurements [26].This analysis relies on the assumption that CME signals do not show peak like structures in m inv ( π + + π − ) therefore calls for more theoretical inputs in this direction. The relative pseudorapidity dependence of azimuthal correlations are widely studied to identifysources of long-range components that are dominated by early time dynamics as compared tolate time correlations that are prevented by causality to appear as short-range correlations.The same can be extended to charge dependent correlations that provides the impetus toexplore the dependence of ∆ γ on the pseudorapidity gap between the charge carrying particles∆ η ab = | η a − η b | in (cid:104) cos( φ αa + φ βb − RP ) (cid:105) . Such measurements have been performed in STARwith Au+Au and U+U data. It turns out that the possible sources of short-range correlationsdue to photon conversion of e + − e − , HBT and Coulomb effects can be identified and described as igure 1. (Left) Measurement of charge separation along second and third order event planesin Au+Au and U+U collisions. (Right) Fraction of possible CME signal in the measurement of∆ γ with respect to spectator and participant planes [28].Gaussian peaks at small ∆ η ab , the width and magnitude of which strongly depend on centralityand system size. Going to more peripheral centrality bins, it becomes harder and harder toidentify such components as they overlap with sources of di-jets fragmentation that dominatesboth same-sign and opposite sign correlations. An effort to decompose different components of∆ γ via study of ∆ η ab can be challenging although a clear sign of different sources of correlationsare visible in change of shape of individual same-sign and opposite sign measurements of γ -correlator [27].In any case, these differential measurements of ∆ γ in isobar collisions provide the prospectto extract the m inv ( π + + π − ) and ∆ η dependence of CME signals that will provide much deeperinsights on the origin of the effect.
6. Mixed harmonics measurements with second and third order event planes
In order to proceed in this section it is better to rewrite the conventional γ -correlator by a moregeneral notation as γ = (cid:104) cos( φ αa + φ βb − ) (cid:105) . The idea is to measure charge separations acrossthe third harmonic event plane by constructing a new correlator ∆ γ = γ ( OS ) − γ ( SS ),where γ = (cid:104) cos( φ αa + 2 φ βb − ) (cid:105) that was introduced by CMS collaboration in Ref [14].Since the Ψ plane is random and not correlated to B-field direction (see Fig.1), γ is purelydriven by non-CME background, the contribution of which should go as v /N . This is veryuseful to contrast signal and background scenario by comparing the measurements in twoisobaric collision systems. Since Ru+Ru has larger B-field than Zr+Zr but have comparablebackground, the case for CME would be as follows: (∆ γ /v ) Ru+Ru / (∆ γ /v ) Zr+Zr > γ /v ) Ru+Ru / (∆ γ /v ) Zr+Zr > (∆ γ /v ) Ru+Ru / (∆ γ /v ) Zr+Zr . Fig.1 (left) shows themeasurement of these observables in U+U and Au+Au collisions. Within the uncertainties ofthe measurements, no significant difference in the trend of ∆ γ /v and ∆ γ /v is observedfor the two collision systems except for the very central events. Predictions from hydrodynamicmodel calculations with maximum possible strength of local charge conservation [17] is shownon the same plot. Overall observation indicates background dominate the measurements and asimilar analysis of the isobar data is highly anticipated. .Tribedy, WWND 2020 R Ψ m ( ∆ S ″ ) ∆ S ″ R Ψ (Au+Au) 0-20%R Ψ (Au+Au) 0-20%R Ψ (d+Au) 〈 N ch 〉 ∼ ± / Nuclear Physics A 00 (2020) 1–4 we also randomized each particle’s charge while keep the total number of charged particles (positive andnegative) in event unchanged. Such events and they are called shu ✏ ed events, and they are analyzed in thesame way as what real events are analyzed. As shown in 5, SBF observables for shu ✏ ed events are at unityas expected. In the centrality of 30-40%, r rest and R B from data are both larger than the AFVD calculationwithout CME (the case of a = cult to be explained by background-only model. Centrality (%) r AuAu 200GeV rest
Real r lab
Real rAuAu 200GeV rest
Real r lab
Real r rest
Shuffled r lab
Shuffled r LCC = 33% rest /s=0, r n rest /s=0.1, r n rest /s=0.2, r nAVFD (30~40%)| < 0.5 η | preliminarySTARCentrality (%) Centrality (%) B R AuAu 200GeVRealAuAu 200GeVRealShuffled /s=0 n /s=0.1 n /s=0.2 n| < 0.5 η | STAR preliminary Fig. 5. (Color online) r rest , r lab and R B as a function of centrality from Au + Au 200 GeV at STAR.
3. Summary
We reviewed tests of SBF with toy models, and gave an update on studies made with two realisticmodels. Toy model simulation studies show that the two observables, r rest and R B , respond in oppositedirections to signal and backgrounds arising from resonance v and ⇢ . If both r rest and R B are larger thanunity, then it can be regarded as a case in favor of the existence of CME. In Au + Au collisions at 200 GeV, r rest , r lab and R B are found to be larger than unity, and larger than AVFD model calculation with no CMEimplemented. Our results are di cult to be explained by a background-only scenario. Acknowledgments
We thank S. Shi and J. Liao for providing AVFD Beta1.0 source code. In particularwe thank the RHIC Operations Group and RCF at BNL. Y. Lin is supported by the China ScholarshipCouncil (CSC). This work is supported by the Fundamental Research Funds for the Central Universitiesunder Grant No. CCNU19ZN019 and the Ministry of Science and Technology (MoST) under Grant No.2016YFE0104800.
References [1] D. Kharzeev, R. D. Pisarski, M. H. Tytgat, Possibility of spontaneous parity violation in hot QCD, Physical Review Letters 81(3) (1998) 512.[2] D. E. Kharzeev, L. D. McLerran and H. J. Warringa, Nucl. Phys. A , 227 (2008); D. E. Kharzeev, J. Liao, S. A. Voloshin andG. Wang, Prog. Part. Nucl. Phys. , 1 (2016); K. Hattori, X. G. Huang, Nucl. Sci. Tech. , 26 (2017).[3] A. H. Tang, Probe Chiral Magnetic E ↵ ect with Signed Balance Function. Chin. Phys. C 44 No.5 054101 (2020);[4] A. Bzdak, V. Koch and J. Liao, Lect. Notes Phys. , 503 (2013); S. Pratt, S. Schlichting and S. Gavin, Phys. Rev. C ,024909 (2011); S. Schlichting and S. Pratt, Phys. Rev. C , 014913 (2011); F. Wang, Phys. Rev. C , 064902 (2010); F. Wangand J. Zhao, Phys. Rev. C , no. 5, 051901 (2017); Y. Feng, J. Zhao and F. Wang, Phys. Rev. C , no. 3, 034904 (2018).[5] B.Abelev,M.Aggarwal, at al. Physical Review C, 79 (2009) 034909; J. Adams, C. Adler, at al. Physical Review letters 92 (2004)092301; F. Q. Wang, J. Zhao, Physical Review C, 95 (2017) 051901 .[6] Z. W. Lin, C. M. Ko, B. A. Li, B. Zhang and S. Pal, Multiphase transport model for relativistic heavy ion collisions. Phys. Rev.C , 064901 (2005), and private comunication with Zi-Wei Lin and Guo-Liang Ma.[7] Y. Jiang, S. Shi, Y. Yin and J. Liao, Chin. Phys. C , no. 1, 011001 (2018); S. Shi, Y. Jiang, E. Lilleskov and J. Liao, AnnalsPhys. , 50 (2018). / Nuclear Physics A 00 (2020) 1–4 we also randomized each particle’s charge while keep the total number of charged particles (positive andnegative) in event unchanged. Such events and they are called shu ✏ ed events, and they are analyzed in thesame way as what real events are analyzed. As shown in 5, SBF observables for shu ✏ ed events are at unityas expected. In the centrality of 30-40%, r rest and R B from data are both larger than the AFVD calculationwithout CME (the case of a = cult to be explained by background-only model. Centrality (%) r AuAu 200GeV rest
Real r lab
Real rAuAu 200GeV rest
Real r lab
Real r rest
Shuffled r lab
Shuffled r LCC = 33% rest /s=0, r n rest /s=0.1, r n rest /s=0.2, r nAVFD (30~40%)| < 0.5 η | preliminarySTARCentrality (%) Centrality (%) B R AuAu 200GeVRealAuAu 200GeVRealShuffled /s=0 n /s=0.1 n /s=0.2 n| < 0.5 η | STAR preliminary Fig. 5. (Color online) r rest , r lab and R B as a function of centrality from Au + Au 200 GeV at STAR.
3. Summary
We reviewed tests of SBF with toy models, and gave an update on studies made with two realisticmodels. Toy model simulation studies show that the two observables, r rest and R B , respond in oppositedirections to signal and backgrounds arising from resonance v and ⇢ . If both r rest and R B are larger thanunity, then it can be regarded as a case in favor of the existence of CME. In Au + Au collisions at 200 GeV, r rest , r lab and R B are found to be larger than unity, and larger than AVFD model calculation with no CMEimplemented. Our results are di cult to be explained by a background-only scenario. Acknowledgments
We thank S. Shi and J. Liao for providing AVFD Beta1.0 source code. In particularwe thank the RHIC Operations Group and RCF at BNL. Y. Lin is supported by the China ScholarshipCouncil (CSC). This work is supported by the Fundamental Research Funds for the Central Universitiesunder Grant No. CCNU19ZN019 and the Ministry of Science and Technology (MoST) under Grant No.2016YFE0104800.
References [1] D. Kharzeev, R. D. Pisarski, M. H. Tytgat, Possibility of spontaneous parity violation in hot QCD, Physical Review Letters 81(3) (1998) 512.[2] D. E. Kharzeev, L. D. McLerran and H. J. Warringa, Nucl. Phys. A , 227 (2008); D. E. Kharzeev, J. Liao, S. A. Voloshin andG. Wang, Prog. Part. Nucl. Phys. , 1 (2016); K. Hattori, X. G. Huang, Nucl. Sci. Tech. , 26 (2017).[3] A. H. Tang, Probe Chiral Magnetic E ↵ ect with Signed Balance Function. Chin. Phys. C 44 No.5 054101 (2020);[4] A. Bzdak, V. Koch and J. Liao, Lect. Notes Phys. , 503 (2013); S. Pratt, S. Schlichting and S. Gavin, Phys. Rev. C ,024909 (2011); S. Schlichting and S. Pratt, Phys. Rev. C , 014913 (2011); F. Wang, Phys. Rev. C , 064902 (2010); F. Wangand J. Zhao, Phys. Rev. C , no. 5, 051901 (2017); Y. Feng, J. Zhao and F. Wang, Phys. Rev. C , no. 3, 034904 (2018).[5] B.Abelev,M.Aggarwal, at al. Physical Review C, 79 (2009) 034909; J. Adams, C. Adler, at al. Physical Review letters 92 (2004)092301; F. Q. Wang, J. Zhao, Physical Review C, 95 (2017) 051901 .[6] Z. W. Lin, C. M. Ko, B. A. Li, B. Zhang and S. Pal, Multiphase transport model for relativistic heavy ion collisions. Phys. Rev.C , 064901 (2005), and private comunication with Zi-Wei Lin and Guo-Liang Ma.[7] Y. Jiang, S. Shi, Y. Yin and J. Liao, Chin. Phys. C , no. 1, 011001 (2018); S. Shi, Y. Jiang, E. Lilleskov and J. Liao, AnnalsPhys. , 50 (2018). Figure 2. (Left) The R-observable shown for different collision systems, concave shape isconsistent with CME expectation [24]. (Right) The two main quantities r and R B derived fromsigned balance function, deviation from unity is consistent with CME expectation [31].
7. Charge separation along participant and spectator planes
This analysis makes use of the fact that B-field driven signal is more correlated to spectatorplane in contrast to flow-driven background which is maximum along the participant planes.The idea was first introduced in Ref [29] and later on followed up in Ref [30]. It requiresmeasurement of ∆ γ with respect to the plane of produced particles, a proxy for participantplane as well as with respect to the plane of spectators. In STAR the two can be doneby using Ψ from TPC and Ψ from ZDC respectively. The approach is based on threemain assumptions: 1) measured ∆ γ has contribution from signal and background that canbe expressed as ∆ γ = ∆ γ bkg + ∆ γ sig , 2) the background contribution to ∆ γ should followthe scaling ∆ γ bkg ( tpc ) / ∆ γ bkg ( zdc ) = v ( tpc ) /v ( zdc ) and, 3) the signal contribution to ∆ γ should follow the scaling ∆ γ sig ( tpc ) / ∆ γ sig ( zdc ) = v ( zdc ) /v ( tpc ). The first two have beenknown to be working assumptions, widely used for a long time and can be used to test the caseof CME [30] if (∆ γ/v ) ( zdc ) / (∆ γ/v ) ( tpc ) >
1. The validity of the last one was studied anddemonstrated in Ref [29]. Using all three equations one can extract [28] the fraction of possibleCME signal f cme = ∆ γ sig / ∆ γ in a fully data-driven way as shown in Fig.1(right). This analysiswill be done with the isobar data and the case for CME will be f Ru+Ru cme > f
Zr+Zr cme >
8. Alternate measure: The novel R-observable
The R -observable is actually a distribution, introduced in Ref [22], and defined as the ratio oftwo distribution functions of the quantity ∆ S parallel and perpendicular to B-field directiondefined as R Ψ m (∆ S ) = C Ψ m (∆ S ) /C ⊥ Ψ m (∆ S ). Here ∆ S measures the difference in the dipolemoment of the positive and negative charge in an event (see Ref [22] for details). The shape of R Ψ (∆ S ) will be sensitive to CME as well as non-CME background whereas R Ψ (∆ S ) is purelydriven by non-CME background and serves as a baseline. Model calculations have establishedseveral unique features of this observable: 1) presence of CME signal will lead to a concaveshape of the R Ψ (∆ S ), 2) increasing strength of CME signal will increase the concavity of R Ψ (∆ S ), 3) in presence of CME, the concavity of R Ψ (∆ S ) will be larger than that of R Ψ (∆ S ).The measurement of R Ψ m is shown in Fig.2. The quantity ∆ S (cid:48)(cid:48) shown is a slight variant of(∆ S ) that incorporates correction for particle number fluctuations and event plane resolution.The observation of Fig.2 indicates more concave shape for R Ψ compared to R Ψ in Au+Auwhereas flat or convex shapes for p/d+Au indicates that the measurements are consistent withexpectations of CME [24]. For isobar collisions the case of CME will be confirmed if: 1) aoncave shape is observed for the ratio of the observables R Ψ (∆ S ) Ru+Ru /R Ψ (∆ S ) Zr+Zr and 2)the concavity should be weaker for R Ψ (∆ S ) Ru+Ru /R Ψ (∆ S ) Zr+Zr .
9. Alternate measure: The signed Balance function
A very recently proposed observable to search for CME is the signed balance function (SBF) [23].The idea is to account for the ordering of the momentum of charged pairs measured by the widthof SBF that is expected to be different for out-of-plane as compared to in-plane measurementcaptured in the ratio r lab . In addition, one can also account for the boost due to collectiveexpansion of the system that forces all pairs to move in the same direction and measure theratio in pairs rest frame r rest . In presence of CME, the individual ratios as well as the double ratio R B = r rest /r lab is expected to be greater than unity. The preliminary measurements shown inFig.2 (right) from STAR in Au+Au 200 GeV seem to be consistent with CME expectation. Thisobservable will be studied with the isobar data in STAR but not as a part of the blind analysis andthe CME expectation will be: 1) r (Ru + Ru) > r (Zr + Zr), and 2) R B (Ru + Ru) > R B (Zr + Zr).
10. Steps for blind analysis of the isobar data from STAR
It is better to start with a short background on the activities that preceded the isobar blindanalysis in STAR. The idea of colliding isobar, particularly Ru+Ru and Zr+Zr to make a decisivetest of CME was proposed by Voloshin in Ref [32], the same paper which also proposed to useUranium collisions to disentangle signal and background of CME. The possible difference inthe signals relies on 10 −
18% higher B-field in Ru+Ru compared to Zr+Zr [33] in contrastto about 4% difference in flow driven background [17]. Such estimates are sensitive to detailsof shapes, charge distribution and neutron skin thickness of the two isobar nuclei [33, 34, 35].In the 2017-18 RHIC beam user request [36] STAR collaboration therefore proposed to collectdata for two 3.5 week runs in the year 2018. The projection was based on the prospect ofachieving five-sigma significance or better in a scenario where the measurement of ∆ γ has 80%non-CME background. This however corresponds to the fact that the systematic uncertainty inthe measurements has to be within a few percent and below the statistical significance of themeasurements, something that has never been attempted before in the correlation measurementsfrom STAR. This started a large scale collaboration wide effort in synergy with the RHIC collideraccelerator department to plan for the isobar running in the year 2018. Based on the studiesof previous years of data from Au+Au and U+U collisions several major sources of systematicsin the measurement of ∆ γ were identified. The major sources include: run-to-run variation ofdetector response due to loss of acceptance, change in efficiency and variation in luminosity thataffects the number of reconstructed tracks in the Time Projection Chamber. This eventuallyleads to uncorrectable systematic uncertainties in ∆ γ . In order to minimize such systematics theproposal were to: 1) switch species in RHIC between stores e.g., in orders like Ru+Ru, Zr+Zr,Ru+Ru and so on and, 2) keep long stores to level the luminosity aiming for specific rates inthe coincidence measurements of beam fragments by the STAR zero-degree calorimeters. Theaim was to maintain exact balance of run and detector conditions for the two species so thatobservations in the two systems are equally affected and can later on be largely eliminated inthe ratios of observables. With the successful conclusion of the isobar run in the year 2018 STAR experiment collectedmore than 3 billion events for each isobar species. The next step was to develop the plans for ablind analysis, the main idea behind which is to eliminate predetermined biases. A total of fiveinstitutional groups are expected to perform the analysis of the data. The analysts from eachgroup will focus on a specific aspect of the analysis described in the previous section although .Tribedy, Aug 22, 2019, STAR Collaboration meeting, Krakow, Poland Isobar Blind Analysis Flow Charts
Isobar-Unblind AnalysisIsobar-Blind Analysis
Run-by-run QA, full analysis(One run is Ru/Zr)
Mock datachallenge
Test data structure(27 GeV files)
Isobar-Mixed Analysis
QA, physics & code freezing(One run is Ru+Zr) Full analysis(Ru and Zr separated)
IsobarBlind-analysisteam Software & Calibrationteam AnalysisBlinding Committee
Figure 3.
The steps of isobar blind analysis. This cartoon is based on the procedure for theblind analysis of isobar data that have been outlined in Ref [37].in many cases there are substantial overlap in some analyses that will help cross check theresults. An important part of the blind analysis is the blinding of the data. The details of theblinding of the data structure is decided by members of a blinding-committee who are not partof the team of analysts and will work in close collaboration with STAR experts who are partof the production team. The idea is to provide the analysts the access to data in files wherespecies-specific information are disguised or removed before the final step of unblinding. Acareful consideration is taken by the blinding-committee to make sure the essential informationavailable to do the analysis specific quality assurance of the data by the analysts. Some ofthe quality assurance, calibration and centrality determination that require species informationare done only by STAR experts who are not a part of the team of analysts. Above all, themain goal of the committee is to make sure that under no circumstances physics analysts canaccess un-blinded data that can jeopardize the blind analysis. For example, all the data setsare produced with pseudo-run-number that cannot be used by the analysts to retrieve the exactspecies information.
The detailed procedure for the blind analysis of isobar data have been outlined in Ref [37].Figure.3 is a cartoon that summarizes the four steps and the main idea.In the zeroth step shown in (by orange circle) the extreme left of Fig.3 is the mock datachallenge which is not exactly a step of the isobar data analysis but a crucial step to familiarizethe analysts with the technicalities of the data structures that have been specifically designedfor blind analysis.The first step shown in Fig.3 (by green circle) as the “isobar-mixed analysis” or “mixed-blindanalysis” is truly the first step of blind analysis. This is also the most challenging steps fromthe point of view of the analysts. In this step the analysts are provided with data sample whereeach run comprise of events that are mix samples from two species. In this step the analystsperform the full quality assurance (QA) and physics analysis of the data, document every detailsof steps of the procedure and freeze the codes. After the completion of this step no changesto the analysis code is permissible. Also, no changes in the analysis procedure is allowed. Theonly permissible change in the following step is to reject bad runs or pile-up events. However,in order to avoid predetermined bias in analysis such rejection cannot be done arbitrarily andan automated algorithm must be developed in this step and the related codes have to be frozen.The stability of the automated QA algorithm is tested with some of the existing data sets ofAu+Au and U+U collisions.The second step shown in Fig.3 (by blue circle) is referred to as the “isobar-blind analysis”or “unmixed-blind analysis”. From this step on-wards the analysts are allowed to run theirpreviously frozen codes. The main purpose of this step is to perform run-by-run QA of the .Tribedy, WWND 2020 Ultra-relativistic nuclear collisions: where the spectators flow?
Sergei A. Voloshin and Takafumi Niida Wayne State University, 666 W. Hancock, Detroit, MI 48201
In high energy heavy ion collisions, the directed flow of particles is conventionally measured withrespect to that of the projectile spectators, which is defined as positive x direction. But it is notknown if the spectators deflect in the “outward” direction or “inward” – toward the center line ofthe collision. In this Letter we discuss how the measurements of the directed flow at mid-rapidity,especially in asymmetric collision such as Cu+Au, can be used to answer this question. We showthat the existing data strongly favor the case that the spectators, in the ultrarelativistic collisions,on average deflect outwards. PACS numbers: 25.75.Ld, 25.75.Gz, 05.70.Fh
In an ultrarelativistic nuclear collision only part of allnucleons from the colliding nuclei experience a truly in-elastic collision. Some of nucleons, called spectators, staymostly intact (or might experience a transition to an ex-cited state). Nevertheless, those nucleons do experience anonzero momentum transfer and deflect from the originalnucleus trajectory. The direction of such projectile nu-cleon (“spectator”) deflection is conventionally taken as apositive x direction in the description of any anisotropicparticle production (anisotropic flow [1]). At the sametime, while this direction has been measured experimen-tally at very low collision energies, nothing is known onwhich direction the spectators really deflect at high en-ergies – toward the center of the collision, or outwards.Note that this question is not of a pure “academic” inter-est, it is intimately related to understanding of the nu-cleon wave function in the nucleus, as well as momentumdistribution of the nucleons confined in a nucleus [2]. Itis also important for the interpretation of the anisotropicflow measurements. In particular, the knowledge of thespectator flow is requited for determination of the di-rection of the magnetic field created in the collision aswell as the system orbital momentum. The latter, forexample, is needed for the measurements of the so-calledglobal polarization [3–5].The only (known to authors) direct determination ofthe spectator nucleons deflection direction was performedat the energies E/A ⇠
100 MeV by measuring of the po-larization of emitted photons [6]. It was observed (seealso [7, 8]) that around this energy the direction of thedeflection direction changes from the “in-ward” (due toattractive potential at lower energies) to the “out-ward”at higher energies. No similar measurements was per-formed at higher collision energies. Theoretically, thisquestion is also not well understood. As recently hasbeen shown in [2], the direction of the spectator deflec-tion is likely dependent on the nucleon transverse mo-mentum. These calculations show that at relatively largetransverse momentum (more than ⇠
200 MeV) the nucle-ons are likely deflected inwards, while at low transversemomentum they might deflect outwards. One reason forthe latter might be the Coulomb interaction (repulsion) ZX of the spectator protons.In this article we show how the study of the charge par-ticle directed flow at midrapidity measured relative to thespectator deflection direction (directed flow) can help toanswer the question of which direction the spectators aredeflected on average. We do not distinguish between lowand high p T spectators in this study, though in principlethis question can be studied experimentally.The main idea of our approach is based on the ob-servation that in the case of asymmetric initial densitydistribution in the system, the high(er) transverse mo-mentum particles on average are flowing/emitted in thedirection of the largest density gradient, while the lower p T particles flow in the opposite direction [9, 10]. If themean transverse momentum of all particles is zero (e.g atmidrapidity region in symmetric collisions) then the av-erage, integrated over all transverse momenta, directedflow is in the same direction as that of low p T particles.Then the strategy in the establishing the direction ofthe spectator flow becomes straight-forward. First, onehas to measure the directed flow of particles at midrapid-ity with respect to the spectator deflection. Comparingthat to the initial density gradients calculated relative tothe position of spectators, one can determine the direc-tion of spectator flow. The direction of the highest den-sity gradient in the system has to be determined withthe help of a model, but this appears to be a very robust a r X i v : . [ nu c l - t h ] A p r η =Y beam SPECTATOR PROTONSFORWARD PARTICIPANTS
Figure 4. (Left) Figure showing EPD detector acceptance cover beam rapidity and detectingboth forward participants and spectators in 27 GeV Au+Au collisions. (Right) γ -correlatorsscaled by v across different event-planes and double ratio of spectators/participant event planeswhich should be unity for no-CME scenario.data sample. For this the analysts are provided with files each of which contain data froma single species that is either Ru or Zr. However, there are two conditions: the files containlimited number of events that cannot lead to any statistically significant result and the speciesinformation is not revealed. Although a pseudo-run-number is used for each file, the timeordering is preserved with a unique mapping that is unknown to the analysts. It is important tomaintain the time ordering to identify time-dependent changes in detectors and run conditionsas a part of the run-by-run quality assurance. With this limited data sample the analysts needrun the frozen automated algorithm to identify bad runs. A similar automated algorithm is alsoused for identifying and rejecting bad runs. After this step no more changes are allowed in termsof QA.The final step of isobar blind analysis is shown by red circle in Fig.3 is referred to as “isobar-unblind” analysis. In this step the species information will be revealed and the physics resultswill be produced by the analysts using the previously frozen codes. The finding from this stepwill be directly submitted for publication without any kind of alteration. If a mistake is foundin the analysis code, the erroneous results will also accompany the corrected results.
11. Post-isobar era and prospects for CME search at lower collision energies
Regardless of the outcome of the measurements with the isobar program, that will be performedat the top RHIC energy, one question will remain [1]. What happens at lower collision energy?In this context a new idea has emerged. The newly installed event-plane detector (EPD) upgradeprovides a new capability at STAR towards CME search at lower collision energy and for theBeam Energy Scan phase-II program [38]. The idea is simple, at lower energies EPD acceptance(2 . < | η | < .
1) falls in the region of beam rapidity ( Y beam ) and can measure the plane of strongdirected flow (Ψ ) of spectator protons, beam fragments and stopped protons, therefore stronglycorrelated to the B-field direction (See fig4). The next step is to measure ∆ γ with respect toΨ and compare it with the measurement of ∆ γ along Ψ planes from outer regions of EPDand TPC at mid-rapidity that are weakly correlated to the B-field directions. A test of CMEscenario will be to see if large difference is observed in the measurements. First preliminarymeasurements from STAR as shown in Fig 4 is dominated by uncertainty but seems to show alot of prospects for the CME search at lower energies.
2. Summary
Despite several challenges experimental efforts have been continued towards disentangling theCME signals from non-CME background in the measurement of charge separation across reactionplane. The highly anticipated results from the blind analysis of isobar collisions data providesus the best opportunity to make a decisive test of the CME in heavy-ion collisions.
13. Reference [1] STAR 2020 BUR https://drupal.star.bnl.gov/STAR/system/files/BUR2020_final.pdf [2] Kharzeev D and Pisarski R D 2000
Phys.Rev.
D61
Preprint hep-ph/9906401 )[3] Kharzeev D 2006
Phys.Lett.
B633
Preprint hep-ph/0406125 )[4] Voloshin S A 2004
Phys. Rev.
C70
Preprint hep-ph/0406311 )[5] Abelev B I et al. (STAR) 2009
Phys. Rev. Lett.
Preprint )[6] Abelev B I et al. (STAR) 2010
Phys. Rev.
C81
Preprint )[7] Abelev B et al. (ALICE) 2013
Phys. Rev. Lett.
Preprint )[8] Adamczyk L et al. (STAR) 2013
Phys. Rev.
C88
Preprint )[9] Adamczyk L et al. (STAR) 2014
Phys. Rev.
C89
Preprint )[10] Adamczyk L et al. (STAR Collaboration) 2014
Phys.Rev.Lett.
Preprint )[11] Adam J et al. (ALICE) 2016
Phys. Rev.
C93
Preprint )[12] Khachatryan V et al. (CMS) 2016
Phys. Rev. Lett [Phys. Rev. Lett.118,122301(2017)] (
Preprint )[13] Acharya S et al. (ALICE) 2018
Phys. Lett.
B777
Preprint )[14] Sirunyan A M et al. (CMS) 2018
Phys. Rev.
C97
Preprint )[15] Adam J et al. (STAR) 2019
Phys. Lett. B
Preprint )[16] Pratt S 2010 (
Preprint )[17] Schenke B, Shen C and Tribedy P 2019
Phys. Rev.
C99
Preprint )[18] Jiang Y, Shi S, Yin Y and Liao J 2018
Chin. Phys. C Preprint )[19] Belmont R and Nagle J 2017
Phys. Rev. C Preprint )[20] Schenke B, Shen C and Tribedy P 2020
Phys. Lett. B
Preprint )[21] Kharzeev D, Tu Z, Zhang A and Li W 2018
Phys. Rev. C Preprint )[22] Magdy N, Shi S, Liao J, Ajitanand N and Lacey R A 2018
Phys. Rev. C Preprint )[23] Tang A 2020
Chin. Phys. C Preprint )[24] Adam J et al. (STAR) 2020 (
Preprint arXiv:2006.04251 )[25] Zhao J, Li H and Wang F 2019
Eur. Phys. J. C
168 (
Preprint )[26] Adam J et al. (STAR) 2020 (
Preprint arXiv:2006.05035 )[27] Tribedy P (STAR) 2017
Nucl. Phys. A
Preprint )[28] Zhao J (STAR) 2020 (
Preprint )[29] Xu H j, Zhao J, Wang X, Li H, Lin Z W, Shen C and Wang F 2018
Chin. Phys.
C42
Preprint )[30] Voloshin S A 2018
Phys. Rev.
C98
Preprint )[31] Lin Y (STAR) 2020 (
Preprint )[32] Voloshin S A 2010
Phys. Rev. Lett.
Preprint )[33] Deng W T, Huang X G, Ma G L and Wang G 2018
Phys. Rev. C Preprint )[34] Xu H J, Wang X, Li H, Zhao J, Lin Z W, Shen C and Wang F 2018
Phys. Rev. Lett.
Preprint )[35] Hammelmann J, Soto-Ontoso A, Alvioli M, Elfner H and Strikman M 2019 (
Preprint )[36] STAR 2017 BUR https://drupal.star.bnl.gov/STAR/system/files/STAR_BUR_Run1718_v22_0.pdf [37] Adam J et al. (STAR) 2019 (
Preprint )[38] Adams J et al.
Preprint1912.05243