CME Search Before Isobar Collisions and Blind Analysis From STAR
Prithwish Tribedy for the STAR collaboration
The 36th Winter Workshop on Nuclear Dynamics
1-7th March, 2020, Puerto Vallarta, Mexico
In part supported by Introduction
Solenoidal Tracker at RHIC (STAR) RHIC has collided multiple ion species; year 2018 was dedicated to search for effects driven by strong electromagnetic fields by STAR Isobars: Ru+Ru, Zr+Zr @ 200GeV (2018) Low energy: Au+Au 27 GeV (2018)
Large systems : U+U, Au+Au @ 200 GeV
P.Tribedy, WWND 2 The Chiral Magnetic Effect (Cartoon Picture)
Quarks Quarks randomly aligned oriented along B
antiquarks I II III IV
More More right left handed handed quarks quarks J || B J || -B
CME converts chiral imbalance to observable electric current P.Tribedy, WWND 2020 3 New Theory Guidance : Complexity Of An Event
Magnetic field map Pb+Pb @ 2.76 TeV Axial charge profile b=11.4 fm, Npart=56
Pb+Pb 2.76 TeV, b=11.4 fm, dN5/dxT [a.u.] 0.3 6 uR>uL 0.2 4 uR 0.1 2 0 0 y [fm] -2 -0.1 -4 -0.2 -6 -0.3 -6 -4 -2 0 2 4 6 x [fm] Based on: Chatterjee, Tribedy, Phys. Rev. C 92, Based on: Lappi, Schlichting, Phys. Rev. D 97, 011902 (2015) 034034 (2018) Going beyond cartoon picture: 1) Fluctuations dominate e-by-e physics, 2) B-field & domain size of axial-charge change with √s P.Tribedy, WWND 2020 4 New Theory Guidance : Complexity Of An Event Pb+Pb @ 2.76 TeV Magnetic field b=11.4 fm, N Axial charge profile Pb+Pb 2.76 TeV, b=11.4 fm, dN5/dxT [a.u.] 0.3 6 u 0.2 4 u 0.1 2 0 0 y [fm] -2 -0.1 -4 -0.2 -6 -0.3 -6 -4 -2 0 2 4 6 x [fm] Based on: Chatterjee, Tribedy, Based on: Lappi, Schlichting, 011902 (2015) 034034 (2018) Going beyond cartoon picture: 1) Fluctuations dominate e-by-e physics, 2) B-field & domain size of axial-charge change with √s P.Tribedy, WWND 2020 5 New Theory Guidance : Complexity Of An Event Pb+Pb @ 2.76 TeV b=11.4 fm, N More Left than Right _+ _+ More Right but B-field _+ downwards More Right than Left Based on: Chatterjee, Tribedy, Based on: Lappi, Schlichting, 011902 (2015) 034034 (2018) Going beyond cartoon picture: 1) Fluctuations dominate e-by-e physics, 2) B-field & domain size of axial-charge change with √s P.Tribedy, WWND 2020 6 #3: PresenceNew ofTheory strong Guidance magnetic : Complexity field Of An Event 18 Magnetic field map Pb+Pb @ 2.76 TeV Axial charge profile b=11.4 fm, Npart=56 Strong B-fields ~10 Gauss are generated18 in non-central heavy ion collisions The BEM field – 10 gauss at the peak y Pb+Pb 2.76 TeV, b=11.4 fm, dN5/dxT [a.u.] McLerran, Skokov, 1305.0774 0.3 • The B field is strong z=0 and short duration due 6 uR>uL Electro-Magnetic fields in heavy ion collisions to the velocity of the 0.2 Electro-Magnetic fields in heavy ionpassing collisions ions 4 uR + x lifetimey [fm] + + + + ++ + + + ++ +++ ++in the+ + QGP extend the + + + + + + + + + + + x + x + + + + + + + ++ + ++ lifetime+ of the B field -2 + + + + + + + + -0.1 – aka Lenz’s Law B B B B – Finite conductivity -4 B✕ ✕ B ⦿ ⦿ -0.2 • Recent calculations B-field direction → perpendicular to collision plane -6 2 B B-field direction → perpendicularB-field to collision magnitude plane → ~Z , ~ γ suggest the lifetime is 2 B-field magnitude → ~Z , ~ γ B-field magnitude → ~ 1/γ , conductivity of the extendedmedium in a plasma -0.3 B-field magnitudeKharzeev, → ~ 1/γ , conductivity McLerran, of the medium and Warringa 0711.0950,but the magnitude is -6 -4 -2 0 2 4 6 Skokov, Illarionov,P Tribedy, RutgersToneev Nuclear Physics 0907.1396 Seminars, Feb 12, 2018reduced x50 36from the P Tribedy, Rutgers Nuclear Physics Seminars, Feb 12, 2018 36 peak at the relevant L. McLerran, V. Skokov, Nucl.Phys. A929 (2014) 814-190 x [fm] Basedtime on: scaleChatterjee, Tribedy, Phys. Rev. C 92, Based on: Lappi, Schlichting, Phys. Rev. D 97, B-field directionJim → Thomas perpendicular011902 (2015) to collision plane 4 034034 (2018) 2 B-field magnitudeGoing → ~Z beyond, ~ γ cartoon picture: 1) Fluctuations dominate e-by-e B-field lifetime →physics, ~ 1/γ , conductivity 2) B-field & of domain the medium size of axial-charge change with √s B-field strength Motivations: → decrease time with forimpact 1) decisive parameter/overlap test, 2) revisit CME search at low √s P Tribedy, Chiral Fluids, July 16-19, 2018P.Tribedy, WWND 2020 8 7 STAR Search For Other B-field Driven Effects “Discovery of Breit-Wheeler Process” STAR, PRL121,132301(2018) STARBreit-Wheeler Collaboration, Process arXiv:1910.12400 e+ Two quasi-real photons colliding to create a see talk by D. Brandenburg real e+-e- pair Tue 3/3 e- 14 eBL ≈ 30 MeV/c, B ~ 10 T, L ~1 fm 2 12 eB > eBC ∼ me ∼ 10 G 9 P.Tribedy, WWND 8 STAR Search For Other B-field Driven Effects “Discovery of Breit-Wheeler Process” STAR, PRL121,132301(2018) STARBreit-Wheeler Collaboration, Process arXiv:1910.12400 e+ Two quasi-real photons colliding to create a see talk by D. Brandenburg real e+-e- pair Tue 3/3 e- 14 eBL ≈ 30 MeV/c, B ~ 10 T, L ~1 fm 2 12 eB > eBC ∼ me ∼ 10 G Polarization of Lambda & Anti-Lambda STAR, J.Adams, QM2019 magnetic 9 spin-orbit STAR Preliminary Independent limits on B-field : important for CME search P.Tribedy, WWND 9 CME Search Using The γ-Correlator Observable + _ Charge separation perpendicular to ΨRP Observables+ for CME search : γ-correlator γα,β = cos(φα + φβ 2Ψ ) + 1 2 RP φφ1− Charge separation across reaction− plane 2 !CME expectation " B + + Voloshin, PRC 70 γ − = cos(π/2 π/2 + 0) = 1 7 (2004) 057901 ++, − γ −− = cos(π/2+π/2 + 0) = 1 -3 -3 C88 (2013) no.6, 064911 ×10 3 ×10 − 〉 〉 ) ) − 1.51 B opposite charge RP Ψ positive charges 1.5 ΨRP 10 , Y7 (ZDC-SMD) Ψ Ψ1 - φ 1 -2 , Y7 (TPC) negative charges × Ψ2 β 1 φ , Y4 (TPC) Ψ " Ψ RP 2 + ) sin( α 〈 STAR collaboration, PRL 103, 251601 0.5 φ 0.5 (2009), PRC 88 (2013) RP cos( 0 〈 0 2 Ψ Charged − -0.5 -0.5 β 2 same charge tracks φ Reaction-plane Ψ , Y7 (ZDC-SMD) + -1 1 + (TPC) -1 φ Ψ2, Y7 2 α 1 Ψ2, Y4 (TPC) _ φ -1.5 -1.5 _ 80 70 60 50 40 30 20 _ 10 0 cos( 80 70 60 50 40 30 20 10 0 Centrality (%)φ1− ! Centrality (%) FIG. 4: (Color online) sin(φα Ψ1) for positive and nega-p+AFIG. measurements 5: (Color online) Three-point indicate correlator, the rapid Eq. 1, rise mea- STAR capability⟨ to measure− ⟩ CME using γ-correlator:st nd tive charges versus centrality for Au+Au collisions at √sNN=in peripheralsured with 1 andevents 2 harmonic→ due event to planes background versus centrality Charged200 GeV. Shaded tracks area representsfrom TPC the systematic (-1<η uncertainty<1) for Au+Au collisions at √sNN=200GeV.Shownwithcrosses for both charge types obtained by comparing correlations are our previous results from the 2004 RHIC run (Y4) [9, 10]. Proxyfrom positive for reaction and negative pseudorapidity.planes: event-planes ThefromSTAR Y4 Collaboration, runZDC-SMD, used a second Phys.Lett. harmonicTPC B798 & event (2019) BBC plane. 134975 Y4 and Y7 Ψ2 results are consistent within statistical errors. Shaded P Tribedy, QCD@HighDensity,P.Tribedy, WWND Nov2020areas 12-14, for the Wuhan, 2nd harmonic 2019 points represent the systematic510 The three-point correlator measured with 1st and 2nd uncertainty of the event plane determination. Systematic un- certainties for the 1st harmonic points are negligible compared harmonic event planes is shown in Fig. 5. We find con- to the statistical ones shown. sistency between correlations obtained with both event plane types. As the pseudorapidity gap between the ZDC-SMD(Ψ1) and the TPC(particles α and β) is rather length through the medium. However, when we weight large ( 7 units in η) , we find “direct” three-particle ∼ all azimuthal regions of charge separation equally, as with effects (clusters) to be an unlikely source for the sig- the msc in Fig. 6, we do not recover a magnitude sym- nal. This is an indication that the signal is likely a gen- metry. uine correlation with respect to the reaction plane. Also The two terms of the msc in Eq. 9 are shown in Fig. 7. shown for comparison in Fig. 5 are our previous results We observe that same and opposite charge correlations from the 2004 RHIC run [9, 10] which are consistent with in the ∆N term have very similar magnitudes, but oppo- the current results within statistical errors. site signs for all centrality bins. This feature is expected The modulated sign correlations are compared with from the construction of the ∆N term due to the rela- the three-point correlator in Fig. 6. It is evident that the tively large and approximately equal positive and nega- msc is able to reproduce the same trend as the three-point tive charge multiplicities. A model calculation including correlator although their magnitudes differ slightly. It is statistical+dynamical fluctuations of particle azimuthal also clear that the correlation magnitude for same charge distributions should be performed in order to rule out pairs is larger than for opposite charge pairs for both -even explanations. The ∆msc term has a similar mag- correlators. The charge combinations of ++ and are Pnitude for same and opposite charge correlations, indi- −− consistent with each other for the msc (not shown here), cating a charge-independent background for the correla- just like the case for the three-point correlator [10]. We tions. Thus, the source of the magnitude asymmetry be- also plot the model calculation of THERMINATOR [21] tween same and opposite charge correlations about zero to be discussed later. as shown in Fig. 6 is isolated in the ∆msc term (Note that Before any possible interaction with the medium, the the sum of both terms yields the total msc). To further CME is expected to generate equal correlation magni- investigate the source of this background, we plot v2/N , tudes for same and opposite charge pairs. It was pre- a simplified estimate of the effect due to momentum− con- viously supposed that medium suppression of back-to- servation and elliptic flow [22]. Here v2 was introduced back phenomena could be responsible for this magnitude in Eq. 2, and the values are from Ref. [23]. N represents asymmetry [9, 10]. Oppositely charged pairs from the the total number of produced particles, but in this prac- CME may not freeze out back-to-back, but instead with tice we only counted those within η < 1. v2/N well one of the particles deflected closer to the event plane due matches the ∆msc term for 0 50%| collisions.| − MEVSIM to multiple scattering within the medium. This is most is a Monte Carlo event generator,− developed for STAR likely to occur for the particle traversing the largest path simulations [24]. A model calculation of MEVSIM with CME Search Using The γ-Correlator Observable + _ Charge separation perpendicular to ΨRP Observables+ for CME search : γ-correlator γα,β = cos(φα + φβ 2Ψ ) + 1 2 RP φφ1− Charge separation across reaction− plane 2 !CME expectation " B + + Voloshin, PRC 70 γ − = cos(π/2 π/2 + 0) = 1 7 (2004) 057901 ++, − γ −− = cos(π/2+π/2 + 0) = 1 -3 -3 C88 (2013) no.6, 064911 ×10 3 ×10 − 〉 〉 ) ) − 1.51 B opposite charge RP Ψ positive charges 1.5 ΨRP 10 , Y7 (ZDC-SMD) Ψ Ψ1 - φ 1 -2 , Y7 (TPC) negative charges × Ψ2 β 1 φ , Y4 (TPC) Ψ " Ψ RP 2 + ) sin( α 〈 STAR collaboration, PRL 103, 251601 0.5 φ 0.5 (2009), PRC 88 (2013) RP cos( 0 〈 0 2 Ψ Charged − -0.5 -0.5 β 2 same charge tracks φ Reaction-plane Ψ , Y7 (ZDC-SMD) + -1 1 + (TPC) -1 φ Ψ2, Y7 2 α 1 Pratt 1002.1758, Pratt, Schlichting, Ψ2, Y4 (TPC) _ φ -1.5 Gavin1011.6053 Bzdak, -1.5Koch, Liao 1008.4919 _ Background expectation80 70 60 50 40 30 20 _ 10 0 cos( 80 70 60 50 40 30 20 10 0 + Centrality (%)φ1− ! Centrality (%) γ − = cos(0 + 0 + 0) = 1 ++, FIG. 4: (Color online) sin(φα Ψ1) for positive and nega- FIG. 5: (Color online) Three-point correlator, Eq. 1, mea- γ −− =STAR cos(0 +capabilityπ + 0) =⟨ to1 measure− ⟩ CME using γ-correlator:st nd tive charges versus centrality− for Au+Au collisions at √sNN= sured with 1 and 2 harmonic event planes versus centrality Neutral resonanceCharged200 GeV. Shaded decaystracks area represents from+ flow TPC the + systematic (-1<η uncertainty<1) for Au+Au collisions at √sNN=200GeV.Shownwithcrosses for both charge types obtained by comparing correlations are our previous results from the 2004 RHIC run (Y4) [9, 10]. momentumProxyfrom conservation positive for reaction and negative can pseudorapidity.planes: mimic CME event-planes Thefrom Y4 runZDC-SMD, used a second harmonicTPC & event BBC plane. Y4 and Y7 Ψ2 results are consistent within statistical errors. Shaded P Tribedy, QCD@HighDensity,P.Tribedy, WWND Nov2020areas 12-14, for the Wuhan, 2nd harmonic 2019 points represent the systematic511 The three-point correlator measured with 1st and 2nd uncertainty of the event plane determination. Systematic un- certainties for the 1st harmonic points are negligible compared harmonic event planes is shown in Fig. 5. We find con- to the statistical ones shown. sistency between correlations obtained with both event plane types. As the pseudorapidity gap between the ZDC-SMD(Ψ1) and the TPC(particles α and β) is rather length through the medium. However, when we weight large ( 7 units in η) , we find “direct” three-particle ∼ all azimuthal regions of charge separation equally, as with effects (clusters) to be an unlikely source for the sig- the msc in Fig. 6, we do not recover a magnitude sym- nal. This is an indication that the signal is likely a gen- metry. uine correlation with respect to the reaction plane. Also The two terms of the msc in Eq. 9 are shown in Fig. 7. shown for comparison in Fig. 5 are our previous results We observe that same and opposite charge correlations from the 2004 RHIC run [9, 10] which are consistent with in the ∆N term have very similar magnitudes, but oppo- the current results within statistical errors. site signs for all centrality bins. This feature is expected The modulated sign correlations are compared with from the construction of the ∆N term due to the rela- the three-point correlator in Fig. 6. It is evident that the tively large and approximately equal positive and nega- msc is able to reproduce the same trend as the three-point tive charge multiplicities. A model calculation including correlator although their magnitudes differ slightly. It is statistical+dynamical fluctuations of particle azimuthal also clear that the correlation magnitude for same charge distributions should be performed in order to rule out pairs is larger than for opposite charge pairs for both -even explanations. The ∆msc term has a similar mag- correlators. The charge combinations of ++ and are Pnitude for same and opposite charge correlations, indi- −− consistent with each other for the msc (not shown here), cating a charge-independent background for the correla- just like the case for the three-point correlator [10]. We tions. Thus, the source of the magnitude asymmetry be- also plot the model calculation of THERMINATOR [21] tween same and opposite charge correlations about zero to be discussed later. as shown in Fig. 6 is isolated in the ∆msc term (Note that Before any possible interaction with the medium, the the sum of both terms yields the total msc). To further CME is expected to generate equal correlation magni- investigate the source of this background, we plot v2/N , tudes for same and opposite charge pairs. It was pre- a simplified estimate of the effect due to momentum− con- viously supposed that medium suppression of back-to- servation and elliptic flow [22]. Here v2 was introduced back phenomena could be responsible for this magnitude in Eq. 2, and the values are from Ref. [23]. N represents asymmetry [9, 10]. Oppositely charged pairs from the the total number of produced particles, but in this prac- CME may not freeze out back-to-back, but instead with tice we only counted those within η < 1. v2/N well one of the particles deflected closer to the event plane due matches the ∆msc term for 0 50%| collisions.| − MEVSIM to multiple scattering within the medium. This is most is a Monte Carlo event generator,− developed for STAR likely to occur for the particle traversing the largest path simulations [24]. A model calculation of MEVSIM with CME Search Using The γ-Correlator Observable + _ Charge separation perpendicular to ΨRP Observables+ for CME search : γ-correlator γα,β = cos(φα + φβ 2Ψ ) + 1 2 RP φφ1− Charge separation across reaction− plane 2 !CME expectation " B + + Voloshin, PRC 70 γ − = cos(π/2 π/2 + 0) = 1 7 (2004) 057901 ++, − γ −− = cos(π/2+π/2 + 0) = 1 -3 -3 C88 (2013) no.6, 064911 ×10 3 ×10 − 〉 〉 ) ) − 1.51 B opposite charge RP Ψ positive charges 1.5 ΨRP 10 , Y7 (ZDC-SMD) Ψ Ψ1 - φ 1 -2 , Y7 (TPC) negative charges × Ψ2 β 1 φ , Y4 (TPC) Ψ " Ψ RP 2 + ) sin( α 〈 STAR collaboration, PRL 103, 251601 0.5 φ 0.5 (2009), PRC 88 (2013) RP cos( 0 〈 0 2 Ψ Charged − -0.5 -0.5 β 2 same charge tracks φ Reaction-plane Ψ , Y7 (ZDC-SMD) + -1 1 + (TPC) -1 φ Ψ2, Y7 2 α 1 Pratt 1002.1758, Pratt, Schlichting, Ψ2, Y4 (TPC) _ φ -1.5 Gavin1011.6053 Bzdak, -1.5Koch, Liao 1008.4919 _ Background expectation80 70 60 50 40 30 20 _ 10 0 cos( 80 70 60 50 40 30 20 10 0 + Centrality (%)φ1− ! Centrality (%) γ − = cos(0 + 0 + 0) = 1 ++, FIG. 4: (Color online) sin(φα Ψ1) for positive andp/d+A nega- measurementsFIG. 5: (Color online) indicate Three-point the correlator, rapid Eq. rise 1, mea- γ −− =STAR cos(0 +capabilityπ + 0) =⟨ to1 measure− ⟩ CME using γ-correlator:st nd tive charges versus centrality− for Au+Au collisions at √ofsNN γ= in peripheralsured with 1 and events 2 harmonic→ due event planesto background versus centrality Neutral resonanceCharged200 GeV. Shaded decaystracks area represents from+ flow TPC the + systematic (-1<η uncertainty<1) for Au+Au collisions at √sNN=200GeV.Shownwithcrosses for both charge types obtained by comparing correlations are our previous results from the 2004 RHIC run (Y4) [9, 10]. momentumProxyfrom conservation positive for reaction and negative can pseudorapidity.planes: mimic CME event-planes ThefromSTAR Y4 Collaboration, runZDC-SMD, used a second Phys.Lett. harmonicTPC B798 & event (2019) BBC plane. 134975 Y4 and Y7 Ψ2 results are consistent within statistical errors. Shaded P Tribedy, QCD@HighDensity,P.Tribedy, WWND Nov2020areas 12-14, for the Wuhan, 2nd harmonic 2019 points represent the systematic512 The three-point correlator measured with 1st and 2nd uncertainty of the event plane determination. Systematic un- certainties for the 1st harmonic points are negligible compared harmonic event planes is shown in Fig. 5. We find con- to the statistical ones shown. sistency between correlations obtained with both event plane types. As the pseudorapidity gap between the ZDC-SMD(Ψ1) and the TPC(particles α and β) is rather length through the medium. However, when we weight large ( 7 units in η) , we find “direct” three-particle ∼ all azimuthal regions of charge separation equally, as with effects (clusters) to be an unlikely source for the sig- the msc in Fig. 6, we do not recover a magnitude sym- nal. This is an indication that the signal is likely a gen- metry. uine correlation with respect to the reaction plane. Also The two terms of the msc in Eq. 9 are shown in Fig. 7. shown for comparison in Fig. 5 are our previous results We observe that same and opposite charge correlations from the 2004 RHIC run [9, 10] which are consistent with in the ∆N term have very similar magnitudes, but oppo- the current results within statistical errors. site signs for all centrality bins. This feature is expected The modulated sign correlations are compared with from the construction of the ∆N term due to the rela- the three-point correlator in Fig. 6. It is evident that the tively large and approximately equal positive and nega- msc is able to reproduce the same trend as the three-point tive charge multiplicities. A model calculation including correlator although their magnitudes differ slightly. It is statistical+dynamical fluctuations of particle azimuthal also clear that the correlation magnitude for same charge distributions should be performed in order to rule out pairs is larger than for opposite charge pairs for both -even explanations. The ∆msc term has a similar mag- correlators. The charge combinations of ++ and are Pnitude for same and opposite charge correlations, indi- −− consistent with each other for the msc (not shown here), cating a charge-independent background for the correla- just like the case for the three-point correlator [10]. We tions. Thus, the source of the magnitude asymmetry be- also plot the model calculation of THERMINATOR [21] tween same and opposite charge correlations about zero to be discussed later. as shown in Fig. 6 is isolated in the ∆msc term (Note that Before any possible interaction with the medium, the the sum of both terms yields the total msc). To further CME is expected to generate equal correlation magni- investigate the source of this background, we plot v2/N , tudes for same and opposite charge pairs. It was pre- a simplified estimate of the effect due to momentum− con- viously supposed that medium suppression of back-to- servation and elliptic flow [22]. Here v2 was introduced back phenomena could be responsible for this magnitude in Eq. 2, and the values are from Ref. [23]. N represents asymmetry [9, 10]. Oppositely charged pairs from the the total number of produced particles, but in this prac- CME may not freeze out back-to-back, but instead with tice we only counted those within η < 1. v2/N well one of the particles deflected closer to the event plane due matches the ∆msc term for 0 50%| collisions.| − MEVSIM to multiple scattering within the medium. This is most is a Monte Carlo event generator,− developed for STAR likely to occur for the particle traversing the largest path simulations [24]. A model calculation of MEVSIM with CME Search@200 GeV & Glimpse From QM2019 13 Motivation : SomeB-field Guidancedifference inFrom Au+Au Models & U+U Motivation : B-field difference in Au+Au & U+U ] B-field scaled by ellipticity U+U (Npart=394) -4 ] U+U (Npart=394) -4 [ fm [ fm Au+AuAu+Au 200 200 GeV GeV 2 50 2 50 U+UU+U 193 193 GeV GeV 40 40 )) 〉 / ε 2 )) 〉 / ε 2 30 B-field is different 30 - Ψ B 20 - Ψ based on : B 20 10 PRC 92, 011902 (2015) in Au+Au and U+U based on : 10 PRC 0 92, 011902 (2015) 2 cos(2( Ψ 0 100 200 300 400 0 - 〈 B Au+Au (Npart=394) Npart 2 cos(2( Ψ 0 100 200 300 400 - 〈 B Au+Au (Npart=394) Npart 11 Towards central events when Au+Au becomes fully overlap, U+UU+U will have& Au+Au provides unique Hydro + manylocal spectators charge left to conservationgenerate B-field. In this scenario, the flow driven charge 0.8 separation will scale with the shape difference. Multiplicity & twonon-flow system (random- configuration to walk)AuAu LCC will + GMCbe the same.AuAu One no LCCtherefore, no GMC finds a model independent way to testify/ 0Towards.7 UUcentral LCC + GMC events whenUUmax no LCC Au+Au no GMC becomes fully overlap,contrast U+U will signal have & background falsify CME. Npart → N , (Δγ/v2*Npart)Au+Au > (Δγ/v2*Npart)U+U will challenge CME. many spectators left to generatepart B-field. In this scenario, the flow driven charge 0.6 (a) } separation will scale with the shape difference. Multiplicity & non-flow (random- { 2 10 2 0.5 Discussion on Au+Au & U+U paper, CME task force meeting /C walk) will be the same. One therefore, finds aMaximum model independent possible way to testify/ max part 0falsify.4 CME. Npart → N , (Δγ/v2*Npart)Au+Au > (Δγ/v2*Npart)U+U will challenge CME. N part background 112 0.3 Schenke, Shen, PT 1901.04378 C 0.2 Discussion on Au+Au & U+U paper, CME task force meeting 10 0.1 Minimum possible 0.0 0 100 200 300 400 background Npart P.Tribedy, WWND 2020 14 Nch C112 FIG. 12. Panel (a): Test of the scaling of K1 as a 2 C2 2 function of centrality in Au+Au and U+U collisions.{ } Panel C132 K1 (b) Test of the scaling of C 2 K . 2{ } 2 Predictions of charge dependent multi-particle correla- tions in isobar collisions (Ru+Ru and Zr+Zr) are shown in Figs. 13 and 14. The two particle correlation func- tions C 2 in Ru+Ru and Zr+Zu collisions scale very 1{ } well with the number of participants Npart. The values of C1 2 Npart are very close to those shown in Au+Au and U+U{ } collisions shown in Fig. 9. The three particle correlations C112/C2 2 are approximately the same in Ru+Ru and Zr+Zr collisions.{ } This is because the hydro- dynamic flow backgrounds in these two collision systems FIG. 11. Panel (a): The di↵erence between opposite-sign are very close to each other as shown in Fig. 5.Our and same-sign three-particle correlation functions C = 112 results provide a realistic background baseline for the C112(OS) C112(SS) is scaled by the value of Npart/C2 2 in every centrality bin in Au+Au and U+U collisions. Panel{ } (b) search of the Chiral Magnetic E↵ect in upcoming RHIC for C132Npart/C2 2 and panel (c) for C123Npart/C3 2 . isobar data. The di↵erence between Ru+Ru and Zr+Zr { } { } Here C2 2 and C3 2 are the second and the third or- visible in Fig. 14 is small in comparison to the expected der Fourier{ } coe cients{ } of the two-particle correlation of all 10 15% di↵erence generated by the CME [37, 84, 85]. ⇠ charged particles. Results with and without imposing local We note that our results for charge dependent correla- charge conservation (LCC) and global momentum conserva- tors calculated including local charge conservation should tion (GMC) are shown. be taken as upper bounds. Although we anticipate a di- rect comparison of RHIC measurements with our predic- tions, any conclusions from such data-model comparison 3 3 170 and“c” are represented by a,b,c,“m”, and “n” are in- 217 Previous works have argued based on these comparisons 171 teger harmonics, and the indices ↵, refer to the charge 218 that backgrounds can be shown to account for all of the 3 170 and“c” are represented by a,b,c,“m”, and “n” are in- 217 Previous works have argued based on these comparisons 172 selection applied to particles “a” and “b”. The combina- 219 observed 1,1,2 [24]. Those arguments however rely 171 teger harmonics, and the indices ↵, refer to the charge 218 that backgrounds can be shown to account for all of the 173 tion ↵, = , is referred to as same-sign (SS) particle 220 on assumptions related to the symmetry of the system: 3 170 and“c” are represented± ± by a,b,c,“m”, and “n” are in- 217 all of the observed 1,1,2 [24]. Those arguments how- 172 selection174 pairs applied and to↵, particles= , is “a referred” and “ tob”. as Theopposite-sign combina- (OS)219 observed221 i.e. that sin(1,1 ,2↵ [24]. )sin( Thosen argumentsn c) = 0 and however to fac- rely 171 teger harmonics, and± ⌥ the indices ↵, refer to the charge 218 ever relyh on assumptions related toi the symmetry of the 173 tion ↵,175 particle= , pairs.is referred Typically, to as the same-sign charge selections (SS) particle are made220 on222 torization: assumptions i.e. related that cos( to the↵ symmetry ) cos(n of then c) system:= 170 and“c”172 areselection represented± ± applied to by particles a,b,c,“ “am””, and and “b”. “n The” are combina- in- 217 all219 system: of the i.e. observed that sin(h 1,1,2 [24].)sin(n Those n arguments) =i 0 and to how- 174 pairs and176 on↵, particle = , “a”is and referred “b” while to as the opposite-sign third particle (OS) “c”in-221 i.e.223 cos( that ↵ sin( ) cos( n )sin( ↵nn c ) . n ) = 0c and to fac- h ih↵ h i c i 171 teger harmonics,173 tion177 cludes↵, = both and±,⌥ positive theis indicesreferred and negative↵ to, asrefer same-sign charges. to the When (SS) charge analyz- particle218 ever220 factorization: relyh on assumptions i.e. that cos( related ↵ to i) thecos(n symmetry n c) of= the 175 particle pairs. Typically,± ± the charge selections are made 222 torization:224 In this i.e. paper, that we willcos(h use↵ charge-dependent, ) cos(n n two- c) =i 172 selection174 pairs178 applieding and higher, to↵, particles mixed= , harmonicsis “ referreda” and however, to“b”. as opposite-sign The we will combina- also apply (OS)219 system:221 cos( ↵ i.e. that ) cos(sin(hn ↵ , ↵ n c)sin() . n ↵ n c ) =i 0 and to 176 on particle “a” and “b±”⌥ while the third particle “c”in- 223 225cos(particleh ↵ correlations ) cos(ih n n n c=) . i cos(n i n j ) , 175 particle179 the charge pairs. selection Typically, to particlethe charge “c”. selections In the case are where madeh ih h i i 173 tion177 ↵, = , is referred to as same-sign (SS) particle 220 factorization:222 In this paper, i.e. that we willcos( use charge-dependent, ) cos(n n two- ) = cludes both positive and negative charges. When analyz- 224 226 Incharge-independent this paper, we two-particle will use charge-dependent,↵DD harmonic coe cients EE two- c 176 on180 m particle±=±n = “ 1,a” the and -correlator “b” while (more the third explicitly particle written “c”in- as 2 h↵, ↵ i 174 pairs178 ing and higher,↵, mixed= , harmonicsis referred however, to as opposite-sign we will also apply (OS) 221227223cos(vparticle2 ↵= correlationscos( ) n cos(i nn ↵j, ) andn c= a) full. suitecos(n↵ of mixed-n ) , 181 n n i j 177 cludes 1,1, both2)± is related positive⌥ to andC1,1 negative,2 by charges. When analyz-225 particleh { } correlations hh ih n↵, ii = i cos(n i n j ) , 175 179 the charge selection to particle “c”. In the case where 228 particle pairs. Typically, the charge selections are made 222 224harmoniccharge-independentIn this correlations paper, weCm,n,m two-particle will+n useto provide charge-dependent,DD harmonic tests of coe sym- cientsEE two- 178 ing higher, mixed harmonics however, we will↵, also apply226 charge-independent two-particle harmonic coe cients 180 C 229 metry2 and factorization assumptions.DD We will present ourEE 176 onm particle= n = “ 1,a” the and↵ ,-correlator “b” while↵ (more the third explicitly particle written1,1 “,2c”in- as 2225 vn 2 = cos(n i n ↵j), and a full suite↵ of mixed- 179 the charge 1 selection,1,2 = cos( to particlea + b “2c ”.2) In the case, where(2)227223vparticle2 = correlationscos(n i n j) and= a full suitecos(n of mixed-n ) , 181 230n analysis{ } forhh Au+Au and U+U↵n, ii collisions, quantify somei j 177 cludes 1,1, both2) is related positive to andC1,1hh negative,2 by charges. ii When ⇡ v2 analyz-2 226{ harmonic} hh correlations Cii to provide tests of sym- 180 m = n = 1, the -correlator (more explicitly{ written} as ↵, m,n,m+n 228224harmonic231charge-independentof the known correlations short-rangeCm,n,m two-particle background+n to provide contributions harmonic tests of and coe sym- cients 227 DD EE 178 ing higher,181 182 where mixed harmonicsis the second however, harmonic we will event↵, also plane apply and metry and factorization assumptions. We will present our 1,1,2) is related2 to C1,1,2 by 232 compare2 our data to background calculations based on Figure 7 & 8: model↵, 2 comparison C1,1,2 229225metry and factorization assumptions. We will present our ↵ v 2 = cos(n n ) and a full suite of mixed- 183 v 2 = cos( ) is the two-particle elliptic 228nanalysis for Au+Aui andj U+U collisions, quantify some 179 the charge selection2 = cos( to particle+i j “2c ”.2) In the case, where(2) 233 1,1{,2} hh a b ii ↵, 230 analysisa{ hydrodynamic} forhh Au+Au model and coupled U+U↵, ii collisions, with global quantify momentum some 184 anisotropyhh coe cient. Clearly, ii we ⇡ usev2 the2C ratio of two226 harmonic229 of the known correlations short-rangeC backgroundto provide contributions tests of and sym- 180 m = n = 1, the ↵ , -correlator↵ (more explicitly written1,1,2 as 234 conservation, resonance decaysm,n,m and+n local charge conser- =↵, cos( + 2 2) { } ↵, , (2)231 of the known short-range background contributions and 185 cumulants1,1,2 C and av2 2 bto determine the corre- 230 compare our data to background calculations based on 182 where is the second1,hh1,2 harmonic eventii ⇡ planev2 21,1, and2 227235metryvation. and Finally, factorization we will make assumptions. use of the mixed-harmonic We will present our 181 1,1,2) is related2 to C1,1,2 by { } 232 186 lator in oppose to directly measuring it using{ an} event- compare our data to background calculations based on Figure 7 & 8: model2 comparison 236231 a hydrodynamic model coupled with global momentum correlations to extract the contribution from correlations 183 v2 2 = cos( i j) is the two-particleObservables elliptic 228 analysis we will for Au+Austudy and with U+U Isobar collisions, data quantify some 0.04 182 where187 plane method.2 is the We 0.6 second argue that harmonic this method event↵, has plane its advan- and233 a hydrodynamic model coupled with global momentum (a) { } hh ii Observables 237we232inconservation,(a) the will reaction study plane resonance and with those decays perpendicular Isobar and local charge to data it. In conser- 184 anisotropy2 coe cient.part Clearly, we use theC ratio of two 229 of the known short-range background contributions and 183 v↵1882, tage2 of= beingcos(↵ independent i j) ofis the the event-plane two-particle1,1,2 resolution elliptic234 conservation, resonance decays and local charge conser- part 0.03 =↵, cos( + 2 ) ↵, , (2) 238233additionvation. to Finally, improving we will our makeunderstanding use of the of mixed-harmonic charge sep- 185 cumulants1,1{,2}C andhh av 2 bto determineii 2 the corre- 230 R-variable : 184 anisotropy189 and1 correspond,1,2 coe cient.2 to 0.4 a well-defined Clearly, we limit use (the the1 low-resolution,1, ratio2 of two235 compare∆ ourφ =( dataφ Ψ to2) background calculations based on hh ii ⇡Gammav2 2 correlator:vation.239 234aration Finally, in heavy we ion will collisions, make use these of data the mixed-harmonic provide a rich × N { } ObservablesObservables we wecorrelations will will studystudy to extract− with with the contributionIsobar IsobarR-variable data from data correlations : 186 ↵, ↵, ↵, ∆φ =(φ Ψ ) 0.02 lator in oppose to directly2 measuringGamma it using {correlator: an} event- 2 + × N 190 231 185 cumulantslimit) [?C] of theand measurement.v2 2 to determine The thecorrelator corre- de-236 240a hydrodynamic model coupled with global momentum 1,1,2 = cos(1,1, 2 +1 ,1 ,2 2 2correlations) 235sourcein the of reaction information to extract− plane for the and future contribution those model perpendicularsin comparisons. from∆φi correlations tosin it.∆φi− In Figure 7 & 8: model/v 0.2comparisonObservables we will study with Isobar data Mixed Harmonics182 In U+U{ } And Au+Au Mixed harmonicswhere187 is in the U+U second harmonic and event Au+Au plane and + 0.04 plane method.1912 We 0.6 argue that this method has its advan- 186 latorfined in inoppose Eq.2 approximates to directlyObservables measuring the -correlator it using with an respect event- 237we232 conservation, will study resonance with decays iIsobar and local chargei data conser- 112 0.01 (a) = cos( + 2 ) in241236(a) theExperiment reaction and plane Analysis and those :∆SWe= perpendicular presentR-variablesin measurements∆φ : to it.sin In ∆φ− 2 part =Gammacos( correlator:) cos( 2 ) additionsin(∆ φ =( to)sin(φ improving Ψ 2) ) our understandingR-variable ofi charge : sep- i 112 STAR 183 v1882 tage2 187 of=192 beingtocos( the independent reaction i j plane) ofis theRP the, i.e. event-plane two-particlecos( a + resolution b elliptic2 RP ) , ↵∆, φ =( φ − ↵Ψ, 2 ) !i p − ! in part ChargeSTAR separation w.r.toplane method. Ψ2 We & argue Ψ thatGamma3 this in method correlator:U+U has its advan- & Au+Au ∆γ Figure 7 & 8: model comparison238233242 0.03 0 addition vation.237ofarationC to Finally, in improving heavyand we ion willin our collisions, 200 make understanding GeV Au+Au use these of+ data theand of+ U+U mixed-harmonicprovide charge col- sep- a rich 0 { } hh ii h i m,n,m+n − ∆S =sin ∆φR-variablesin ∆φ :− 193 where the 0.4 proxy∆γ for is the = secondcos( harmonic+ event2 ) cos ∆φ cos ∆φ− U+U 193 GeV 184 anisotropy189 and188 correspondtage coe of beingcient. to a independent well-defined Clearly,RP we= of limitU+UGamma the usecos( 193 (the event-plane the GeV low-resolution ratio correlator:) cos( of resolution two ) 2 sin( ∆ φ )sin(=(φ Ψ )2) ! i p i+ !i ni 239234aration243238lisions in with heavy the data ion collisions, collected in these the year data 2011 provide and− 2012 a rich Models:Models: signal U+U & &background Au+Au can expectations be two systems × N ModelsModelsObservables tested= testedcos( Observables with + with mixed mixed2 harmonics:)we we harmonicscorrelations willsource will of studystudy information to extract− with with for the future contributionIsobari Isobar modeli sinR-variable∆ comparisons. φdata fromi datai correlationssin ∆: φ− Au+Au 200 GeV 194 plane↵, of the inclusive chargedAu+Au↵ 200, particles. GeV↵ , Therefore,2 ∆φ =(φ Ψ )∆S = i + i 0.02 2 2 Gamma correlator: 2 ∆S = + × N 185 190 limit)189 [? ] of the measurement. The = cos(correlator ) cos( de- ) 244 sin( )sin(v Isobaric ) collisions at 200 GeVcos ∆φ cos ∆φ− cumulantsandC correspond↵1, 1,2 and v2 to2 a well-definedto determine limit1,1, the2 (the 1 low-resolution,1 ,2 corre- 240 sourcerespectively of information by the STAR for detectorfuture⊥! model [38]!ip atsin comparisons.RHIC.∆− φ! Thei n! cur-i sin ∆φ−i B-fields are different in Au+Au & U+U 195at same Npart but= =flowcos(cos( backgrounds + + 2 +22) 235are in239 the)similar reaction− plane and those perpendicularp i− n to it.i In Motivation & Figure.1/v Figure 0.04 7 & 8: model measures 0.2comparison any 0.6112 possible e↵ects of ↵ charge, separation 2 Experiment and Analysis∆S :=We present+ measurements Mixed harmonics in 1U+U,1,2 { }and Au+Au1 2 245 i + i areto different contrast for signal Au+Au & backgroundand U+U(a) 191 of 190CME = cos( ) cos( ) sin(rent(a) work )sin( is an extension ) of our previous work on charge− (b)186 latorfined in inopposelimit) Eq.2 [? approximates to] of directly thepart measurement. measuring the -correlator The it using 1, with1,2 correlator an respect event- de- (b) ↵, Ø Total ↵15M, events∆S after=!cos cutsi ∆φpi −cos!∆iφi nsh 112 0.01 112 = cos( + +2241236 2402) v Isobaric collisions at 200R-variable GeVsin ∆φ : sin ∆φ− ] part = cos(~ + 2 ) ExperimentB and Analysis :∆SWe= presentN( measurements∆S)/N (∆S) part 1 2 additionof C∆φ =( toφ improvingandΨ ) in our 200 understanding GeV Au+Au and ofi U+U charge col- sep- i part 196 2 2 i i driven by the component of= GammaBcos(along 2correlator:[16,) cos( 20].OS Some ) SS246 sin( m,n,m )sin(+n ) ⊥ !R-variablep + − ! : n 0.03 192 191 112 STAR inclusive↵, three-particle correlation (Cm,n,m+n) measure- ChargeSTAR 0.04-4 separation w.r.to187 to the finedΨ reaction in2 Eq.2 plane& approximates Ψ0.6RP 0.4, 3i.e. theincos( -correlator aU+U+ ∆b γ =2 with γRP respect)&, γ Au+Au∆φ =(v Isobaricφ ü− ↵* Ψcollisions, 2)∆'∆CorrelatorS atR 200=(∆ GeVS)=!cosi p∆φ − !cosin∆φ− plane method. We argue that 0.4Gamma this method correlator: has its advan- $+ sh ∆γ Figure3 7 & 8: model comparison 242 241 i i (a) 197 0 2 237of C(a)lisions withand the datain collected 200⊥ GeV! in Au+Au the year+ and 2011! U+U and col- 2012 short-range backgroundpart e↵ectsh such as those due to HBT,i arationm,n,m+ inn heavy ion collisions, thesep N(∆ data−S )+/N providen(∆S ) a richsh 0 × 10 × N − 247 ments [37?Ø].−Total We detect15M events charged∆S after=sin particlesi cuts∆φ withinsin thei ∆φ− 193 where192 to the the proxy reaction∆γ for plane is the , =i.e. secondcos(cos( harmonic ++ event22 ) ) , B cosN∆(⊥φ∆S)/N (⊥∆cosS∆) φ− 2 = cos( ) cos( ) sin( )sin( ) i i part RP U+URP 193 GeV a b RP2 × N 2 × N 0.02 188 i+ i U+U × N 193 GeV OS SS ! sh ! 0.03 0.02 tage of being198 Coulomb independent and di-jets 123 of can= the be event-plane quantifiedcos( 1 and+2 resolution removed from2433lisions 2423respectively) withv theØ Total by data the 15M collected STAR events∆S detectorafter in= cuts the [38]year at 2011p RHIC. and The− 2012 cur- n 3 2 Isobaric collisions at 200 GeV Models 0.4 tested 0.8h ∆withγ = γmixed OS γ SSharmonicsi238248sourcerange ⌘ ofB< information1 and for transverse forR future(∆ momentumiS)=N modeli (sin∆S)∆/N of comparisons.φp(∆Ti S>)0m. i=2 2 sin ∆φ− Models: U+U14 & Au+Au can be two systems194 193 /v =0.2Au+Aucos( 200 +GeV 2 2) ü *$+ ∆' 1.06Correlator⊥ ! p i +! n sh i Au+Au 200 GeV plane where 2 of the the proxy inclusive for chargedRP is the particles. second∆ harmonicγ Therefore,= γ Isobar-mixed event γ 200 GeV R∆(S∆=S)= − m = 3 × N | | ü * ∆' Correlator∆S = 189 116 199charge conservation 123/v within= thiscos( model. As+2 expected, the 2443 2433) v $+ Iso-MixN(∆ 200S GeV )/Nsh(∆S ) − 123 U+U 193 GeV and correspondthis observable to a well-defined by studying limit= its dicos( (the↵erential low-resolution ) dependence cos( − ) on sin(rent work)sin(Isobaric is an extension) collisions of at our 200 previous GeVcos work∆φ on chargecos ∆φ 112 0.01 [fm part Projected B-field (a) ↵, 1 2 respectively249 GeV/c using by the the STAR STAR Time detector Projection! [38]i at ChamberRHIC.! Thei [39] cur-i i 0.01 2 N(p∆S )/N− (∆S n) 0.02 part − ⊥ ! ! × N 194 STAR Preliminary 0.6 239 Ø Total 15M events after cuts p ⊥− nsh⊥ B-fields are different ] Motivation in Au+AuDifferent & B-fieldU+U 195at& same Figure.1 Npart but flow backgrounds are similar Refmult > 7 0.04 plane116 of 0.6 the inclusive charged particles. Therefore, Experiment and Analysis : We present measurements measures2 any possible112 e↵ectsSTAR of charge separation ∆S = 0.04 12 STARAu+Au 200 GeV 1,1,2117 200casechargethe where relative conservation 0.6 local pseudo-rapidity charge within conservation this of two model.↵, of is the enforced As three expected, particles: shows the B Ψ2 1.04 i N⊥+(∆S)/N⊥ (∆Si) /v 245 244 ∆γ to contrast signal-4 & background of CME 0.2 OS SS 250 inclusive three-particle correlation (C ) measure- (a) 190 123 = cos( ) cos( ) sin(rent(a)situated work )sin( is inside an extension a 0.5) Tesla of solenoidal our previous magneticm,n,m work field.+ onn charge We − (b) 1) ↵System, part dependence 0 of B-field & hydro(b) ↵, cos ∆φ cos ∆mφ = 2 ] limit) [? ] of the measurement. 0 0.8 The correlator de- ! i ! i sh × N 0.8 Ø Total ↵15M, 1.06events∆S after= cutsp m = 2− n 0 195 117 × N ∆0.41,γ1,2= γ γ v Isobaric collisions 1.06 R(∆ atS )=200 GeV ∆γ ü * ∆' Correlator 112 0 casemeasures where local any charge possible conservation e↵ects of ischarge enforcedIsobar-mixed separation shows 200240 GeV ] part 2 ~ Isobar-mixed 200 GeV B $+ N(∆S)/N (∆m S= 3) part 0.01 -4 118 2011,1,2 U+U 193 GeV of C and in 200 GeV Au+Aum and = 3 U+U col-sh part U+U 193 GeV 196 drivena by much the⌘. component larger charge of separationB along than [16, without. 20].OS Some While SS 251245 m,n,m+n i Iso-Mix 200+i GeV 10 n ⊥ Iso-Mix! 200 GeV ! 2 × ∆γ 2 246 use track-by-track weights [40, 41] to account for im- 0.03 ∆γ inclusivements three-particle [37? ]. We correlation detect charged (C N particles(∆pS )) measure-/N within(−∆S the) n 112 0.03 50 Projected B-field 191(a) STAR < 1 − ( ∆ S) m,n,m+n part part |η | -4 fined in Eq.2 approximates the -correlator with respect ∆ 1.02S R=(∆S)= 0.04 [ fm 0.6 0.6∆γ = γ γ 118 a,b,c/v ü * ∆' Correlator cos ∆φ cos ∆φ− STAR|η | < 1 a much larger 0.4 charge separation 0.6Au+Au 200 than GeV without. While v Isobaric collisions$+ m at 200 GeVRefmult > 7 ∆γ Au+Au 200 GeV 119 202 0.4 ~ 0.2 Refmult⊥ i> 7 ⊥ sh i 3 2 a,b,c 196 the backgroundIn this paper model we 0 also predicts study that the thetwo charge following separa-2 higher241 ⊥ (a) 197 driven by the component of B along [16, 20]. Some (a)252lisions with theΨ2 data 1.04 collectedΨ ! in the year 2011! and 2012 50 Projected B-field (a)short-range backgroundpart e↵ects such as those due2 to HBT, 246perfectionsrange ⌘ < in1Ψ the and2 detector for transverse 1.04 acceptance momentump andN(∆ momentum−S of)/Npn(∆>S0.2) sh 0 × N 247 [ fm − Ø Total 15M events after cuts T ∆γ × 10 8 U+U 193 GeV ments [37? ]. We detectR charged particlesi within thei 192 119 × N m = 2 2 U+U 193 GeV to the reactionthe background plane model, i.e. 0.8 predictscos( 0.4 that+ the charge2 separa-) , B N(⊥∆S)/N (⊥∆S) )) 〉 / ε 2 part 40 RP a b RP 1.06 0.04 120 203 × N 0.6 B × N 2 × N 0.02 0.04 tion scaled by0.6N /v will 0 be similar in U+U | | × N 0.02 197 short-rangeorder charge112 background dependentpart e↵ correlations, 0.4ects2 such as thoseOS Isobar-mixed dueSS to HBT, 200242 GeV253 Ø Total 15M events∆ 1S after= cuts sh n 0.03 2 (b) 198 Coulomb and di-jets can be quantified and removed from respectively247dependence(b) of by the the detector STAR e detector ciency. Additionally,[38] at RHIC. wem The = 3 cur- 1,n-1,n v 3 Au+Au 200 GeV GeV/cIsobaricusing the collisions STAR Time at 200 Projection GeVN(∆S)/N Chamber(∆S) [39] Au+Au U+U200 GeV Hydro + Max. LCC (c) h U+U Hydro + Max. LCCi 248 n=2(c) B ( ∆ S) R(∆S)=Iso-Mix 200 GeV n range ⌘ < 1 and for transverse 1.02 momentum of p > 0m. =2 2 )) 〉 / ε 40 120 0.4 0.8∆γ = γ OS γ SS T /v /v ü 14 tion scaled by N /v will be similar in U+U * ∆m ' 1.06Correlator⊥ 112 0.2 part part 2 ! ! 193 0.2 $+ ( ∆ S) part 121 6 0.2 ↵ part p − n sh 2 where theand proxy Au+Au for collisions RP is and the roughly second independent harmonic ofIsobar-mixed eventNpart, 200 GeV 1.02 0.6 R(∆S)= 198 -0.2∆γ = γ γ 254 n=3 Ψ m = 3 /v m Refmult > 7 Coulomb × N andcos( di-jets +2 can3 be) quantified and removed from correct| | ourü measurements* ∆' Correlator from the e↵ects of two-track 30 /v c 0.03 Au+Au Hydro + Max. LCC 116 199 ↵, apart 0.2 Au+Au Hydro + Max. LCC 248 $+ N(∆S )/N (∆S ) )) 〉 / ε charge conservation within thisb model. As expected,↵ the 243 Iso-Mix 200 GeV sh 123 0.03 this observable by studying its di↵erential dependence on U+U 193 GeV − rentsituated work insideis an extension a 0.5R Tesla of solenoidal our previous magnetic work field. on chargeWe 112 [fm part 0.04 0.6 249 0.01 Projected B-field (a) 121 hh ii GeV/c using theΨ2 STAR 1.04Ψ Time 0.98 Projection Chamber [39] - Ψ 2 0.01 2 and Au+Au= collisions 0.4 and roughlycos( independent +2 of3 N) ,, N(∆S )/N (∆S ) 0.02 122 0.4 part − 3part B × N a part 30 (b) the1 projected,2,3 magneticvSTAR3 2 field Preliminary 0.6 exhibits 0 a distinctb variation (b) Ø Total 15M events after cuts ⊥ sh⊥ 194 R 1 ] Different B-field 255 Refmult > 7 B plane116 of the inclusive charged particles. Therefore, 199 112 merging that is dominant in central collisions [36]. We es- 4 - Ψ 2 STAR ⊥ ⊥ 12 chargethis conservation observable within by studying this× N model. its di-0.4↵erential As expected, dependence the on 117 200 { } 0.4 ⇡hh1,n-1,n ii 249 B N(∆S)/N (∆S) part n=2 Ψ2 1.04 STARpart Au+Au 200 GeV casethe where relative local pseudo-rapidity charge conservation of two of is the enforced three particles: shows use track-by-trackB weights [40, 41] to account for im- /v 244 B 122 0 × N ∆γ -4 20 0.2 OS SS 250 × N the projected magnetic↵ field exhibits a distinct variation inclusive three-particle correlation (C ) measure- 0.02 1) ↵System, 123 dependence123 0 of B-field 0 50 & hydro 100 situated150 200 inside a 0.5 Tesla solenoidal 1 -3 -2 magnetic-1 m,n,m 0 1 field.+n 2 We 3 m = 2 0.02 n ] with collision system0 0.8 and with varying N . For values - Ψ MC-Glauber 0.03 cos( 3 +2 ) part × N c -0.2 n=3 1.06 m = 2 ↵, 1,n-1,n 3 0.8 256 × N a b × N ↵ timate systematic uncertainties 1.06 R(∆ byS comparing)= data from 0 195 117 200 ∆0.4γ = γ γ n=2 Ψ3( ∆ S) ∆γ ü * ∆' Correlator ″ B 1.02 112 0 20 casemeasures wherethe relative local anyhh pseudo-rapidity charge possible 0.4 conservation e↵ectsii of oftwo ischarge of enforced theIsobar-mixed three separation shows particles: 200 GeV 0.012 Isobar-mixed 200 GeV250 $+ m = 3 /v -4 118 = cos( 3 +2 ) . 0.98 m = 3 2011,1,2 0.2U+U 193 GeV m sh U+U 193 GeV2 MC-Glauber a much⌘. 123 largerwith1,3,2 collision charge separation system2 0.2 and 0.2 with than varying without.a N Whileb. ForN values2 perfections in the detector acceptance∆S and momentum × N v 2 part 251245 Iso-Mix 200 GeV 10 2 n part Iso-Mix 200 GeV 2 × ∆γ 124 /v use track-by-track weights [40, 41] to account for im- U+U 193 GeV of N ∆γ above 100, owing-0.2 to the larger number of spec- n=3ments [37? ]. We detect chargedN particles(∆S )/N within(∆S the) part Ψ 123 112 50 10 Projected B-field (a) STAR < 1⇡hh − ii 257 ( ∆ S) { } part -0.4 di↵erent time periods within a given year and from dif- part |η | 1.02 × N [ fm 0.01 0.6 × N 201 /v 118 a,b,c/v 0.01 m STAR|η 0.02| < 1 a much ⌘ larger. charge separation 0.6Au+Au 200 than GeV without. While R 0.98 Refmult > 7 ∆γ Au+Au 200 GeV 119 202 124 ~ 0.2 251 Refmult⊥ > 7 ⊥ 2 a,b,c Au+AuU+U 193200 GeV 196 of N above 0 100, owing to the larger 0 number 50 of 100 spec- 150 dependence 200 of the detector-3 -2 e ciency.-1 0 Additionally, 1 2 3 we the backgroundIn this paperpart model we also3 predicts study that the thetwo charge following separa- higher 10 driven by125 the component of B along [16, 20]. Some Ψ2 1.04Ψ 50 0 Projected B-field (a) tators in the U+U collisions 0 at a given2 Npart, U+U col-(3)252246perfections258 B inΨ the2Ψ detector3 1.04 acceptance and momentum 0 132 range ⌘ < 1 and for transverse 1 momentum of p > 0.2 [ fm ferent years for which di↵erent tracking algorithms″ have T ∆γ 0.2 123 -0.4 8 202 U+U 0 193 GeV R 1,n-1,n N S 0 Au+Au 200 GeV 119 0 × N ∆ m = 2 /v 2 U+U 193 GeV the background125In this paper model we 0.8 predicts also study 0.4 that the the two charge following separa-part highern=2252 )) 〉 / ε tators in the U+U collisions at a given N , U+U col- 13 40123 1.06 132 0.04 2 cos(2( Ψ 120 203 0.6 part correct ourB measurements from the e↵ects of two-track 0 × N 0.04 0.012 cos(2( Ψ 0 197 short-rangetionorder 126 2) charge112lisions Measure backgroundscaled exhibitdependent by0.6 aN largerpartγ e↵123 correlations, 0.4ects/v projected2which suchwill 0 0 beObservable as magnetic is those similar 100% 50 Isobar-mixed due (B) in w.r.to tofield U+U 100Bkg. HBT, Ψ than 2002 should 150GeV253 be 200 different| | in two isobars, 1 ones-3 -2 w.r.to-1 Ψ3 0are baselines 1 2 3 n 259 2 dependence of the detector e ciency. Additionally, wem = 3 ∆γ 247 been used. We vary our e ciency estimates, the z-vertex 2 × ∆γ 0 (b) ∆γ (b) U+U ZDC(0-2%) 204 Au+Au-0.21,n-1,n 200 GeV n=3GeV/c using theΨ STAR3 Time Projection Chamber [39] Au+Au U+U200 GeV Hydro + Max. LCC (c) The measurement of theseU+U higher, 0.6 0 Au+Au ZDC(0-2%) 198 -0.2 P.Tribedy,254 Aug260n=3 22, 2019, STAR CollaborationΨ meeting, Krakow, Poland 15 /v position of the collision, andm the track selectionRefmult criteria. > 7 30 - 〈 B Flow Background (b)Coulomb205 andcos( di-jets +2 can3 bec) quantified and removed from correct our measurements from the e↵ects of two-track 0.03 Au+Au Hydro + Max. LCC ↵, relationsapart provides 0.2 several testsAu+Au for Hydro CME. + Owing Max. toLCC sym-248 13 0.03 )) 〉 / ε 0 b ↵ 0.04 0.6 127 0.6 ↵ -0.4 Observable w.r.to Ψ2 should situatedbe different inside in two a isobars, 0.5R Tesla ones solenoidal w.r.to Ψ3 are magnetic baselines field. We Au+Au collisions. Therefore, if has a large con- 1.04Ψ - 〈 B 121 hh ii 112 Ψ2 0.98 - Ψ 2 and Au+Au128= collisions 0.4 and roughlycos( independent +2 of3 N) ,, 254 2 × ∆γ part 122 tribution fromcos( 0.4 ∆γ CME,+2 when3 c) compareda at the same3 Npart timateB systematic uncertainties by comparing data from part 30 0.04 Flow(b) Background (b)the1 projected,2,3 ↵, magneticv3 2 a field b0.6 exhibits 0 a< distinct1 ↵ b variation (b)261 0.6 |η 0 | 50 100 150255 We 200 also study the variationR 1 of observables with the lumi- B 199 206 a,b,c merging that is dominant in central-3 -2 collisions-1 0 [36]. 1 We 2 es- 3 4 - Ψ < 1 metryhh for example, the correlationii of the third harmonic |η | this observable by studying× N its di-0.4↵erential dependence on 0 a,b,c 100U+U Hydro 200 + Max. 300 LCC 400 (c) 500 128 = { } 0.4 ⇡hh0 1,n-1,n 100cos(U+U Hydro 200+2 + Max. 3003ii LCC3) ,249 400 (c) 500 tributionpart from CME, when compareda at the same N n=2 part 1,2,3 v 2 b P.Tribedy,part Aug 22,use 2019, track-by-track STARB CollaborationΨ3 weightsmeeting, Krakow, [40, Poland 41] to account15 for im- B 0.4 122 129 3 0 20 × N 255 ″ × N there should be a di↵erence between Au+Au collisions 0.02 123 the projected magnetic↵ field exhibits 0 a distinct 50 variation 100 150 262 di 200↵erent time periods within 1 -3 a given-2 -1 year 0 and 1 from 2 dif- 3 13 0.02 with collision system and n with varying⇡hhN . ForN values ii nosity as quantified by the coincidence rate measuredS by - Ψ MC-Glauber 0.4 { } part 0.03 207 cos( 3 +2 c) -0.2 part n=3 ∆ ↵, 1,n-1,n part Au+Au Hydro + Max. LCC 3 Au+Au Hydropart + Max. LCC256 part Observable w.r.to Ψ2 should be different in two isobars, ones w.r.to Ψ3 are baselines event-plane × N a b ( 3) with the magnetic↵ field is expected to timate systematic uncertainties by comparing data from 0.03 200 129 ↵ n=2 Ψ3( ∆ S) ″ B 20 0.04 the relative130 therehh pseudo-rapidity should 0.4 be 0.6 a diii of↵erence two of between the three Au+Au particles: collisions250 1.02 N = /v cos( 3 +2N ) . 0.98 0.2 0.4 m 2 0.4 123 and U+U2 cos( collisions. 3 +2 This c) provides two generic expecta-2 perfections in the detector acceptance and momentum part MC-Glauber with1,3,2 collision↵, system 0.2a and 0.2b with varyinga N ↵ b. For N values 256 ∆S × N part v 2 part part 263 ferent years for which di↵erent tracking algorithms have part U+U Hydro + Max. LCC (c) 124 2 U+U Hydro + Max.part LCC ZDCs.(c) In relevant figures, systematic uncertainties will U+U 193 GeV of N 208above 100,/v owing-0.2 to the larger number of spec- n=3 part cancel.hh In this case, oneii expects that CME should not Ψ 123 10 130 1,and3,2 = U+U{ collisions.} This⇡hh-0.4 providescos( two a generic3 b +2 expecta-ii 2) 257. di↵erent time periods within a given year and from dif- 15 0.01 × N v 2 P.Tribedy, Aug 22, 2019, STAR Collaboration meeting, Krakow, Poland × N 201 2 0.01 0.2 131 /v 0.02 0.2 ⌘. tions with which to compare our measurements. It must R 0.98 0.03 0.02 Au+AuU+U Au+Au193200 GeV Hydro + Max. LCC 124 of N above 100, owingpart { } to the⇡hh larger 0 Au+Au number 50 Hydro +of 100 Max. spec- LCC 150ii 251264dependence257 200been used. Weof the vary detector our e-3 ciency-2 e ciency.-1 estimates, 0 Additionally, 1 the 2 z-vertex 3 we 3 10 125 part209 × N be shown as shaded boxes while statistic uncertainties × N 2 0 × N 2 tators in131 thecontribute U+U collisions to a 0.4 measurement 0 at a given of N 1part,2,3 ,where U+U col-3 is(3) used258 B Ψ3 13 part 132 tions with which to compare our measurements. It must 1 0.2 0.2 2 0.2 ferent years for which di↵erent tracking algorithms″ have 132 123 -0.4Observable w.r.to Ψ2 should be different in two isobars, ones w.r.to Ψ3 are baselines × N 202 be noted that 0 apart from B-field and flow-driven back- /v (3) 1,n-1,n N S 0 /v Au+Au 200 GeV 0 ∆ × N 2 125Intators this in paper the/v U+U we also collisions study at the a given twoN following, U+Upart higher col- n=2252265258are shown as vertical lines. Table I shows a break-down 13 123 position of the collision, and the track selection criteria. 132 0 2 cos(2( Ψ 210 part correct our measurements from the e↵ects of two-track 2 cos(2( Ψ 126 instead of . The systematics of , such as mag- 0 0.01 /v 0 50 100 150 200 0.01 0.02 0 2)lisions Measure exhibit132 be noted a largerγ123 that2 projectedwhich apart fromObservable magnetic is B-field 100% and (B) 1w.r.to,2 flow-driven, field3 Bkg. Ψ than2 should back-259 be different in two isobars, ones-3 -2 w.r.to-1 Ψ3 0are baselines 1 2 3 /v ∆γ 133 been used. We vary our e ciency estimates, the z-vertex 0 × N 2 × ∆γ U+U 0 ZDC(0-2%) 204 The measurementground, ∆γ 112 ofmeasurements these-0.2 higher, are mixed-harmonic a↵ected by non-flow cor- n=3 Ψ3 112 < 1 P.Tribedy, Aug 22,266 2019, STAR Collaboration meeting, Krakow, Poland 15 2 cos(2( Ψ 203 ″ 132 |η | of the systematic uncertainties for /v in U+U 112 126 259 1,1,2 2 Similar 0 FlowU+Uflow (Hydro+maxLCC) Backgroundbackground(b)U+U (Hydro)orderlisions charge211 exhibitnitude, dependent a largersystem2 projectedcorrelations,0.2 anda,b,c centrality magnetic dependence (B) field will than be en-253 We also study the variation of observables with the lumi- × N < 1 0.6 |η | 127 204 The133 measurement∆γ of these higher, mixed-harmonicN cor- merging that is dominant in central collisions∆S [36]. We es- U+U (Hydro+maxLCC) U+U (Hydro)Au+Au collisions.ground,123 Therefore, measurements 0 if arehas a↵ aected large by con- non-flow 0.98 - 〈 B a,b,cBackground models capture most of the observed112 trends,112 γ112 goingpart to zero in 112 0 Au+Au ZDC(0-2%) 134 backgrounds that132 are not correlated to a globalP.Tribedy, event- Aug260 22, 2019, STAR Collaboration meeting, Krakow, Poland 15 0 ∆γ position of the collision, and the track selection criteria. - 〈 B U+U (Hydro+maxLCC) U+U (Hydro)205 0.01 Flow Background (b) /v 267 0 ∆γ Au+Au (Hydro+maxLCC) Au+Au (Hydro) relations provides several tests for CME. Owing to sym- collisions. 13 0.6 ∆γ U+U ZDC(0-2%) 127 Au+Au212 collisions.tirely↵ driven Therefore, by-0.4 backgroundObservable if that canhas w.r.to be a contrasted large Ψ2 should con- with be260 differentnosity as in quantified two isobars, by the ones coincidence w.r.to Ψ rate3 are measured baselines by - 〈 B Au+Au (Hydro+maxLCC) Au+Au (Hydro)128 205 134 backgrounds that are not correlated112 to a global event- ∆γ relations provides several tests for CME. Owing to sym-254 2 × ∆γ tribution fromcos( ∆γ CME,+2 when3 ) compared at the same N timate systematic uncertainties by comparing data from 132 135 part 0.04 FlowAu+Au Background (Hydro+maxLCC) (b)Au+Au (Hydro)↵, plane,a dominant 0.6 ∆γ c in peripheral events – we assume that 261 0.6 206 b |η 0 | < 1 50↵ 100 150 We 200 also study the variation of observables with the lumi- |η | < 1 Au+Au ZDC(0-2%) (c) metryhh213 for example, the correlation iia,b,c0 of the third harmonic 268261(c) -3 -2 -1 0 1 2 3 0 a,b,cultra-central 100 U+U0 Hydro 200 +0 Max.events 300 100 LCC 400200in not 300 500 unique 400 128 signaturetribution= 135 from1,1,2 .of CME,Under B~0132 certain when0 as compared assumptions 100itcos( U+Uis also Hydro at200+2 of the symmetry +seen sameMax. 3003 LCCN 3 andin) , fac-case 400 ZDCs.ofWe 500 defineγ123 In centralities relevant figures, (0 5%, systematic5 10%, 10 uncertainties20%,...,70 will 0.4 129 1,2,3 206136metryplane, forv3 dominant example,2 in the peripheral correlation eventsa of the –b we thirdP.Tribedy, assume harmonicpart Aug that 22, 2019, STAR CollaborationΨ3 meeting, Krakow, Poland ″ 15 ∆γ there shouldat a fixed be aN di↵erencesuch background between Au+Au will have collisions weak system 255 0.4 U+U ZDC(0-2%) { }part ⇡hh N ii 262 nositydi↵erent as quantified time periods by the within coincidence a given rate year measuredS and from by dif- 13 part 0 0 100 100 200 200 300 300 400 400 207 214 269 ∆ Au+Au Hydro + Max. LCC N part Au+Au Hydropart + Max. LCC part event-planetorization, ( ) with oneObservable can the directly magnetic relate fieldw.r.to background is expectedΨ2 should estimates to be different80%) using in the two probability isobars, distribution ones w.r.to of uncorrected Ψ3 are baselines 3 ∆γ 262 0.04 0.03 0 100 200 300part 400 500129 there207 should136 at a↵ fixed be 0.6 a N dipart↵erencesuch background0 between 100 Au+Au will have200 collisions weak 300 system 400 be shown500 as shaded boxes while statistic uncertainties 0.4 Au+AuN ZDC(0-2%) 130 and U+U137event-planedependence.cos( collisions. 3 (0.4 In+2 This3) this c with) provides work the we magnetic explore two generic suchN field non-flow expecta- is expected back- to part part N N ↵, a b ↵ part 263256 ferent years for which di↵erent tracking algorithms have part U+U Hydro + Max. LCC (c) part 215 U+U Hydro + Max. LCC ZDCs.(c)270 In relevant figures, systematic uncertainties will part 208 cancel.137hh Infrom this the case, third one harmonicii expects plane that to CME the measurements should not us- 263tracks from TPC within ⌘ < 0.5. For each of our 130 1,and3,2 208= U+U138 dependence. collisions. In This this provides workcos( we explore two a generic such3 non-flow+2 expecta- 2) back-. are shown as vertical lines. Table I shows a break-down 0.2 0.2 N 131 tions withcancel.grounds which Inv2 in to this2 detail. compare case, Apart one our expects frommeasurements. the that systemP.Tribedy, CMEb N It dependence must should Aug 22, not 2019, STAR Collaboration meeting,| | Krakow, Poland 15 0.03 0.02 Au+Au 0 Hydro 100 + Max. 200 LCC part 300 400 500 216 part { } 0⇡hhAu+Au 100 Hydro 200 + Max.part 300 LCCii 264400257271been 500 used. We vary our e ciency estimates, the z-vertex 209 138 ing 2 × N which should contain any CME related signal. becentrality shown as intervals, shaded10 boxes we use while a Monte statistic Carlo uncertainties Glauber × N 2 × N 2 FIG. 1. (color online) (a) Predictions from MC-Glauber Taskforce131 presentationcontribute1393)grounds Test to aon 0.4 measurement insymmetry UU detail. paper Apart of draftand from 1,2,3 thefactorizationwhere system 3 dependenceis used 264 of the systematic uncertainties for 1,1,2/v2 in U+U 13 part tions209 withwe expect which some to compare general features our measurements. of measurements It must 0.2 132 contribute2 to 0.2 aObservable measurement ofw.r.to 1,2,1123 Ψwhere2 should 3 is usedbe different in two isobars, ones w.r.to Ψ3 are baselines × N • be noted that apart from B-field and flow-driven back- /v FIG. 1. (color online) (a) Predictions from MC-Glauber (3) /v Data do not conform with either of B-field or Hydro+LCC expectations × N 2 model for projected magneticN field at the center of participant 139 N 265258are shown as vertical lines. Table I shows a break-down • part 210 instead140 ofwe expect. The some systematics general features of of , such112 measurementspart as mag- position265 of the collision, and the track selection criteria. 0.02 0.01 0Mixed harmonics γ123 (100% background)132 be noted210 insteadbased that &2 on ofγ/v apart132 Fig. . 1.provide Anyfrom Owing non-zero B-field to data-driven a decorrelationand result1,2 flow-driven,3 should between therefore back-baselines the be collisions. for γ112 /v model for projected magnetic field at the center of133 participant 2 0 zone at the time of collisions (⌧ =0)inAu+AuandU+Uground, 112 × N measurements are a↵ected by non-flow 112 140 based on Fig. 1. Owing to a decorrelationP.Tribedy, between Aug 22, the266 2019, STAR Collaboration meeting, Krakow, Poland 15 132 of the systematic uncertainties for /v in U+U 112 259 1,1,2 2 0 U+U• (Hydro+maxLCC) U+U (Hydro) 211 nitude,141 direction system2 of0.2 and the B-field centrality and the dependence flow axis, the will projected be en- B- We also study the variation of observables with the lumi- Background × N U+U collisions.models (Hydro+maxLCC)zoneMixed at the The time quantitycapture harmonics of collisions is scaledU+U (⌧most the(Hydro)=0)inAu+AuandU+U γ ellipticity123 (100%of to204the takeThe133 ground, thebackground)observed measurement211 related 112 tomeasurements background. of trends, 0provides these higher, Under areγ data-driven112 mixed-harmonic a↵ certainectedgoing by assumptions non-flow to baseline cor-zero of 266in We define centralities (0 5%, 5 10%, 10 20%,...,70 112 • 134 backgrounds that132 are not correlated to a global event- 0 ∆γ U+U (Hydro+maxLCC)→ U+U (Hydro) 141 direction of the B-field and the flow axis, the projected B- 0.01 γ112Central → 0 in events central events, charge also separation seen for w.r.to γ123,/v cannotΨ2 : U+U be > unique Au+Au signature& strong centrality of267 B-field ∆γ Au+Au (Hydro+maxLCC) Au+Au (Hydro) collisions. ∆γ Backgroundcollisions. The models quantity is scaled capture the ellipticity most to212 take of the the142 field observed is sharply reduced trends, in both very γ112 peripheral going and to very zero260 in U+UAu+Au ZDC(0-2%)shape (Hydro+maxLCC) di↵erence between the twoAu+Au systems. (Hydro) (b) Predictions205 134 backgroundstirely for212 driven by that background are not correlated that can be to contrasted a global event- with nosity267 as quantified by the coincidence rate measured by ∆γ relationssymmetry provides and several factorization, tests for CME. one can Owing relate background to sym- 80%) using the probability distribution of uncorrected 132 • 135 Au+Au (Hydro+maxLCC)→ Au+Au (Hydro) plane, dominant142 field is∆γ sharply in peripheral reduced events in both – very we peripheral assume that and very shapeγ di112↵erence between0 in central the two systems. events, (b) Predictions also forseen143 for γ123, new understanding on background • Au+Auflow ZDC(0-2%) driven background using IP-Glasma+MUSIC+UrQMD213 central Au+Au 0 and U+U collisions. Although very pe- 268261 ultra-central 0 γ 0132dependence events ≠ γ 100112 200in notas 300 expected unique 400 signaturefor B-field,135 1,1213,2 but.of Under B~0Ψ132 3 certain measurements as assumptions it is also of symmetry alsoseen show andin fac-case similar ZDCs.268ofWe dependence. defineγ123 In centralities relevant figures, (0 5%, systematic5 10%, 10 uncertainties20%,...,70 will Backgroundchallenges models capture factorization most206136metry of plane,& the forsymmetryestimates143 dominant example,observed from in the peripheral theassumptions correlation trends, third harmonic events of γ the112 – plane we thirdgoingclaimed assume to harmonic the to measure- that tozero be holdintracks γ at from LHC TPC within ⌘ < 0.5. For each of our ∆γ ultra-central events in not unique signaturecentral of Au+Au B~0 and as U+U it collisions.is also Although seen veryin case pe- of 123 U+U ZDC(0-2%)(Hydro)flow driven simulations background with using and without IP-Glasma+MUSIC+UrQMD including maximumat a fixed144 ripheralNpart such collisions background will have willlarge have three-particle weak system non-flow 0 0 100 100 200 200N 300 300 400 400 214 torization, one can directly relate background estimates 269 80%)4 using the probability distribution| | of uncorrected Taskforce presentation214 on∆γ UU paper draft 262 269 0 100 (Hydro) 200 simulations 300part with and400 without 500 including207 maximum136 atP.Tribedy, a fixedments144 ripheralN part usingWWNDsuch collisions 2 backgroundwhich02020 will should have100 largewill contain have200 three-particle any weak CME300 system non-flow related 400 becentrality shown500 as intervals, shaded15 boxeswe use while a Monte statistic Carlo uncertainties Glauber Au+AuOther ZDC(0-2%)possible centralities e↵ects of localN charge → conservation Background (maxLCC).137event-planedependence. expectations The 145 backgrounds, ( In3) this with work verycaptures the we central magnetic explore collisions most such field may non-flow of is be expectedthe particularly back- observed to trends. ultra-central eventsN part in not unique Replacementsignature215 offor B~0Jie’s slideas it#6 is also seen in case270 of γ123 48 quantitypossible plotted e↵ects on of the localpart y-axis charge is scaled conservation by elliptic (maxLCC). anisotropy137 dependence.from The215 thesignal.145 backgrounds, third PreviousIn harmonic this work very works planewe central have explore to collisions argued the such measurements based may non-flow be on particularly these back- us- com-263tracksare270 model shown from [42, TPCas 43] vertical to within estimate lines.⌘ < the Table0. average5. I For shows number each a break-down of of our par- N 208138cancel.grounds146 In inuseful this detail. for case, disentangling Apart one expects from B-field the that system driven CMEN e dependence↵ects should from notflow | | 0 100 toquantity scale 200 out plotted thepart 300 shape on the di↵erence y-axis 400 is between scaled 500 bythe elliptic models. anisotropy216 Materials for 0 C6 100 200 part 300 400271 500 2 FIG. 1. (color online) (a) Predictions from MC-Glauber 3)138 groundsing Test216 parisons2146which useful insymmetry detail. that for should disentangling backgrounds Apart contain and from B-field any can thefactorization CME be system driven shown related e dependence↵ects to account signal. from flow for264centrality271 ticipating intervals, nucleons1010 weNpart usefor a plottingMonte Carlo our results. Glauber See to scale out the shape diTaskforce↵erence betweenTaskforce presentation the models.209139contribute wepresentation expect147 onrelated someto UU a backgroundmeasurement generalon paper UU features paper –draft while of ofdraft the1 ,2 flow-related,1123 wheremeasurements background3 is used of the systematic uncertainties for 1,1,2/v2 in U+U modelFIG. for 1. projected (color online) magneticN (a) field Predictions at the center from of participant MC-Glauber 139 147 related background – while the flow-relatedN background • part we expect148 remains some large general in these features collisions of the 112 projectedmeasurementspart B-field is 265 Mixed harmonics γ123 (100% background)210140insteadbased & on ofγ132 Fig. . 1.provide Any Owing non-zero to data-driven a decorrelation result should between therefore baselines the be collisions. for γ112 10 zonemodel at the for projected time of collisions magnetic (⌧ field=0)inAu+AuandU+U at the center ofTaskforce participant presentation148 remains2 on largeUU inpaper these collisionsdraft the projected B-field is 140 based149 onhighly Fig. suppressed. 1. Owing to If measurements a decorrelation are between dominated the by 141 direction of the B-field and the flow axis, the projected B- collisions.zone at the The time quantity of collisions is scaled (⌧ the=0)inAu+AuandU+U ellipticity to take the211 related to149 highly background. suppressed. Under If measurements certain assumptions are dominated of by266 We define centralities (0 5%, 5 10%, 10 20%,...,70 • 94 grounds. On the other hand, the validity of the assump-141 150 background the correlations should remain large in ultra- Backgroundγ112Central → 0 in events central models → events, charge capture also separation most seen of for the 142w.r.to γdirection123, observed cannotΨ2 of : the U+U B-field betrends, > andunique Au+Au the flowγ112 axis, signature& going thestrong projected to centrality zero B-of B-field in shapecollisions. di↵erence The94 between quantitygrounds. the Onis two scaled the systems. other the hand, ellipticity (b) Predictions the validity to take for of the the assump-field is sharply150 background reduced the in correlations both very should peripheral remain and large very in ultra- 95 tions made in these analyses are sometimes unclear.212 symmetry It 151 and factorization, one can relate background 267 80%) using the probability distribution of uncorrected 142 field iscentral sharply collisions reduced while in both if they very are peripheral dominated and by signal,very flowshape driven di↵erence background95 tions between made using the in IP-Glasma+MUSIC+UrQMDtwo these systems. analyses (b) are Predictions sometimes for unclear.143 central It Au+Au151 central and collisions U+U while collisions. if they Although are dominated very by pe- signal, • γ132dependence ≠ γ112 challenges96 has alsoas been expected di factorizationcult to account for for B-field, all observations & 213symmetry butestimates with Ψ1523 theymeasurements from should theassumptions third be suppressed harmonic [28, also plane 31–34]. claimed toshow the measure- similarto be268 hold tracksdependence. at from LHC TPC within ⌘ < 0.5. For each of our Backgroundultra-centralflow driven backgroundmodels events using capturein IP-Glasma+MUSIC+UrQMD not unique most ofsignature the143 observedcentral of Au+Au B~0 andtrends, as U+U it collisions.is γalso112 going Although seen to veryin zerocase pe- in of γ123 (Hydro) simulations96 has with also been and di without cult to including account for maximum all observations144 ripheral with 152 collisionsthey should will be have suppressed large three-particle [28, 31–34]. non-flow | | 97 background models. TheTaskforce comparison presentation of di↵erent collid- on 153UU Inpaper this paper, draft we present measurements of an observ- 4 (Hydro) simulations with and without including maximum214 ments144 ripheral using collisions 2 which will should have large contain three-particle any CME non-flow related 269 centrality intervals, we use a Monte Carlo Glauber possible e↵ects of97 background local charge→ models. conservation The comparison (maxLCC). of The di↵erent145 collid- 153 In this paper, we present measurements of an observ- ultra-centralOther centralities events98 ing systems, in however not Background such unique as U+U and Replacementsignature Au+Au expectations maybackgrounds, help of154forable B~0Jie’s similar verycaptures slideas central to but it#6 morecollisionsis most also general may of thanseen bethe particularlyand observedin investigate case of trends γ123 . 48 possible e↵ects of local charge conservation (maxLCC). The215 270 quantity plotted98 oning the systems, y-axis however is scaled such by elliptic as U+U anisotropy and Au+Ausignal. may145 backgrounds, help Previous154 able similar very works central to have but more collisions argued general based may than be on particularlyand these investigate com- model [42, 43] to estimate the average number of par- 99 distinguish background from CME. 146 useful155 for disentangling B-field driven e↵ects from flow quantity plotted on the y-axis is scaled by elliptic anisotropy its centrality dependence in U+U and Au+Au collisions 2 to scale out the shape99 distinguish di↵erence background between from the models. CME. 216 parisons146Materialsuseful155 that forits disentanglingfor centrality backgrounds C6 dependence B-field can be in driven U+U shown e and↵ects to Au+Au account from collisions flow for 271 ticipating nucleons10 Npart for plotting our results. See to scale out100 the shapeSince we di↵ expecterence the between measurementsTaskforce the models. of presentation , more147 specif-related156 background onincluding UU ultra-centralpaper – while draft the collisions. flow-related We extend background our analysis 100 Since we expect the measurements of , more147 specif-related156 backgroundincluding ultra-central – while the collisions. flow-related We extend background our analysis 101 ically 1,1,2 to be a↵ected by B-field driven e↵148ectsremains and 157 largeto higher in these harmonics collisions in order the to 1) projected provide a B-field more detailed is 157 to higher harmonics in order to 1) provide a more detailed 10 101 ically 1,1,2 to be aTaskforce↵ected by B-field presentation driven e↵148ectsremains and 158on largeUU inpaper these collisionsdraft the projected B-field is 102 a dominant flow-driven background, we demonstrate149 highly the suppressed.and complete If picture measurements of the two-particle are dominated correlations by rela- 158 and complete picture of the two-particle correlations rela- 102 a dominant flow-driven background, we demonstrate149 highly the159 tive suppressed. to the reaction If measurements plane, 2) to provide are dominated an experimental by 94 grounds. On103 themotivation other hand, of this the work validity using Fig. of the 1. In assump- top panel150 ofbackground Fig. 1 the correlations should remain large in ultra- 103 motivation of this work using Fig. 1. In top panel of Fig. 1 159 tive to the reaction plane, 2) to provide an experimental 94 grounds. On104 thewe show other model hand, calculations the validity of of projections the assump- of the150 mag-background160 baseline the for correlations background should expectations, remain 3) large to cross-check in ultra- 95 tions made in these analyses are sometimes unclear. It 151 central collisions while if they are dominated by signal, 104 we show model calculations of projections of the mag- 160 baseline for background expectations, 3) to cross-check 95 tions made105 innetic these field analyses on to the are participant-plane sometimes unclear. that determines It 151 central161 our collisions conclusions, while and if 4) they to allow are dominatedfor tests of symmetry by signal, and 96 has also been di cult to account for all observations with 152 they should161 our be conclusions, suppressed and [28, 4) to31–34]. allow for tests of symmetry and 105 netic field on to the2 participant-plane that determines162 factorization assumptions that will be described further 96 has also been106 the di ellipticcult to flow account axis B forcos(2( all observations B 2)) divided with 152 by the 97 2 they should be suppressed [28, 31–34]. background models.106 the elliptic The comparison flow axish B ofcos(2( di↵ erent B collid-2i)) divided153 byIn the this162 paper,factorization we present assumptions measurements that will be of describedan observ- further 107 ellipticity of the initial overlap region " that drives the 163 below. We analyze mixed-harmonic, charge-dependent 97 background models. The comparisonh of di↵erent collid-i 153 In this paper, we present measurements of an observ- 98 ing systems, however107 ellipticity such of as the U+U initial and overlap Au+Au region may" helpthat154 drivesable the similar163 below. to but We more analyze general mixed-harmonic, than and charge-dependent investigate 108 magnitude of elliptic flow. In the lower panel we show hy- 164 three-particle azimuthal correlations using the observ- 98 ing systems, however such as U+U and Au+Au may help 154 able similar164 to but more general than and investigate 99 distinguish background108 magnitude from of elliptic CME. flow. In the lower panel we155 show hy- three-particle azimuthal correlations using the observ- 109 drodynamic predictions for the flow related backgroundits centrality165 able [17, dependence 35–37] in U+U and Au+Au collisions 99 distinguish background109 drodynamic from predictions CME. for the flow related background155 its centrality165 able [17, dependence 35–37] in U+U and Au+Au collisions 100 Since we expect110 with the and measurements without charge of conservation , more enforced specif- for156 including U+U ultra-central↵, collisions.↵ We extend our analysis 110 with and without charge conservation enforced for156 including U+U ultra-centralCm,n,m↵, +n = collisions.cos(m a +↵ Wen b extend (m + ourn) c analysis) (1) 100 Since we111 expect the measurements of , more specif-157 101 ically 1,1,2 toand be Au+Au a↵ected collisions by B-field as a driven function e↵ects of the and collisionto cen- higher harmonicsCm,n,m in+n order=hh cos( tom 1) providea + n b a more(m + detailedn) iic) (1) 111 and Au+Au collisions as a function of the collision157 cen- hh ii 101 ically 1,1112,2 tralityto be a represented↵ected by by B-fieldN driven– the e number↵ects and of nucleonsto higher166 where harmonics the inner in average order to is 1) taken provide over a all more sets detailed of unique 102 a dominant flow-driven background, wepart demonstrate the 158 and complete picture of the two-particle correlations rela- 112 trality represented by Npart – the number of nucleons 166 where the inner average is taken over all sets of unique 102 a dominant113 flow-drivenparticipating background, in the collision. we demonstrate In the hydrodynamic the 158 and cal- complete167 triplets, picture and the of outer the two-particle average is taken correlations over all rela- events 103 159 tive to the reaction plane, 2) to provide an experimental motivation of this113 participating work using Fig. in the 1. collision. In top panel In the of hydrodynamic Fig. 1 cal- 167 triplets, and the outer average is taken over all events 114 culation, the correlation length between charge pairs159 tive is to168 weighted the reaction by the plane, number 2) to of provide triplets in an each experimental event. The 103 motivation of this work using Fig. 1. In top panel of Fig. 1160 104 we show model114 calculationsculation, the correlation of projections length of between the mag- chargebaseline pairs is 168 forweighted background by the expectations, number of triplets 3) to in cross-check each event. The 115 169 104 we show modelset calculationsto zero leading of to projections the largest possible of the mag- e↵ect of160 localbaselineazimuthal for background angles of expectations, the momenta of3) particles to cross-check “a”,“b”, 105 netic field on115 toset the to participant-plane zero leading to the that largest determines possible e↵ect161 our of local conclusions,169 azimuthal and angles4) to allow of the for momenta tests of symmetry of particles and “a”,“b”, 105 netic field on to the2 participant-plane that determines 161 our conclusions, and 4) to allow for tests of symmetry and 106 the elliptic flow axis B cos(2( B 2)) divided by the 162 factorization assumptions that will be described further 2 162 factorization assumptions that will be described further 106 the elliptic flow axish B cos(2( B 2i)) divided by the163 below. We analyze mixed-harmonic, charge-dependent 107 ellipticity of the initialh overlap region " thati drives the 107 ellipticity of the initial overlap region " that drives the 163 below. We analyze mixed-harmonic, charge-dependent 108 magnitude of elliptic flow. In the lower panel we show hy- 164 three-particle azimuthal correlations using the observ- 108 magnitude of elliptic flow. In the lower panel we show hy- 164 three-particle azimuthal correlations using the observ- 109 drodynamic predictions for the flow related background 165 able [17, 35–37] 109 drodynamic predictions for the flow related background 165 able [17, 35–37] 110 with and without charge conservation enforced for U+U ↵, ↵ 110 with and without charge conservation enforced for U+U Cm,n,m↵, +n = cos(m a + n b (m + n) c) (1) 111 ↵ and Au+Au collisions as a function of the collision cen- Cm,n,m+n =hh cos(m a + n b (m + n) iic) (1) 111 and Au+Au collisions as a function of the collision cen- hh ii 112 trality represented by Npart – the number of nucleons 166 where the inner average is taken over all sets of unique 112 trality represented by Npart – the number of nucleons 166 where the inner average is taken over all sets of unique 113 participating in the collision. In the hydrodynamic cal- 167 triplets, and the outer average is taken over all events 113 participating in the collision. In the hydrodynamic cal- 167 triplets, and the outer average is taken over all events 114 culation, the correlation length between charge pairs is 168 weighted by the number of triplets in each event. The 114 culation, the correlation length between charge pairs is 168 weighted by the number of triplets in each event. The 115 set to zero leading to the largest possible e↵ect of local 169 azimuthal angles of the momenta of particles “a”,“b”, 115 set to zero leading to the largest possible e↵ect of local 169 azimuthal angles of the momenta of particles “a”,“b”, Use ΨPP and ΨRP to solve Bkg and CME Ø ΨPP maximizes flow, è flow background Ø ΨRP maximizes the magnetic field (B), è CME signal Ø ΨPP and ΨRP are correlated, but not identical due to geometry fluctuations CorrelationØ Δγ w.r.t. TPC Along ΨEP (proxy Participant of ΨPP ) and ZDC Ψ1 (proxy vs. of Ψ RPSpectators) contain different Planes fractions of CME and Bkg H-J. Xu, et alΨ, CPCB 42 (2018)H-J. 084103 Xu, et al, CPC 42 (2018) 084103 Δγ {ψ TPC}= CME{ψ TPC}+ Bkg{ψ TPC} Two-component ψ B assumption Δγ {ψ ZDC}= CME{ψ ZDC}+ ExploitBkg{ψ ZDC} the correlation of B- CME{ } a *CME{ }, Bkg{ } a * Bkg{ } ψ ψ TPC = ψ ZDfieldC withψ ZDC participants= ψ TPC vs. PP ΨPP~ΨTPC spectatorassum planese Bkg v: ∝ 2 ψ Small CME fraction & RP b a = v {ψ } / v {ψ }, A = Δγ {ψ } / Δγ {ψ } 2 ZDC 2 TPC dominanceZDC of backgroundTPC BothΨSP are~Ψ experimentalZDC measurements J. Zhao, QM 2019 f (CME) CME{ }/ { } ( A / a 1) / (1/ a2 1) Fraction of CME-like signals EP can= be extractedψ TPC Δγ ψ TPC = − − based on the following three assumptions: Figure 1: (Color online) Sketch of a heavyQM2019, ion Wuhan collision projected onto the transverse plane 7 ∆γtot = ∆γCME + ∆γbkg J. Zhao (perpendicular to the beam direction). RP is the reaction plane (impact parameter, b) CME direction, PP the participant plane∆γ direction(SP) (ofv interacting2(PP) nucleons, denoted by the solid CME = circles), and B the magnetic field∆γ direction(PP) (mainlyv2(SP from) spectator protons, denoted by the open circles together with spectatorbkg neutrons). ∆γ (SP) v2(SP) bkg = ∆γ (PP) v2(PP) small-system collisions [33, 30, 31], invariant mass study [34], and by new also see: Voloshin, Phys. Rev. C 98, 054911 (2018) observables [35, 36]. The lhc data seem to suggest that the cme signal is P.Tribedy, WWND 2020 16 small and consistent with zero [31, 32], while the situation at rhic is less clear [8]. 96 96 To better gauge background contributions, isobaric 44Ru+44Ru (RuRu) 96 96 and 40Zr+40Zr (ZrZr) collisions have been proposed [37] and planned at rhic in 2018. Their QCD backgrounds are expected to be almost the same because of the same mass number, whereas the atomic numbers, hence B,di↵er by 10%. These expectations are qualitatively confirmed by studies [38] with Woods-Saxon (ws)nucleardensities;thecme signal over background could be improved by a factor of seven in comparative measurements of RuRu and ZrZr collisions than each of them individually. A recent study by us [39] has shown, however, that there could exist large uncertainties on the di↵erences in both the overlap geometry eccentricity (✏2 )andB due to nuclear density deviations from ws. As a result, the isobaric collisions may not provide a clear-cut answer to the existence or the lack of the cme. 4 Using Balance Function To Search For CME Use Signed Balance Function for boosted charge pairs in three steps: Y. Lin , QM 2019 0 20 40 60 80 0 20 40 60 80 B r AuAu 200GeV AVFD (30-40%) AuAu 200GeV AVFD (30-40%) 1) Count1) Count pair pair’s momentum momentum ordering ordering inin ppyy : R Real r LCC = 33%, r Real LCC = 33% 1.015 rest rest 1.015 Real r n /s=0.2, a ≈2% Shuffled n /s=0.2, a 2% lab 5 1 5 1≈ Shuffled r n /s=0.1, a ≈1% n /s=0.1, a ≈1% rest 5 1 |η| < 0.5 5 1 Shuffled r n /s=0, a =0 n /s=0, a =0 lab 5 1 1.0005 5 1 1.0005 1.01 1.01 |η| < 0.5 2) Count net ordering (e.g. excess of 2) Count net ordering (excess of STAR pos. leading neg. ) for each event : preliminary pos. leading neg.) for each event: 1.005 1.005 1 1 1 1 STAR preliminary 3) Look3) Look for for enhanced enhanced event-by-evente-by-e fluctuations 0 20 40 60 80 0 20 40 60 80 fluctuation of net ordering in y direction. of net ordering in y-direction: Centrality (%) Centrality (%) (>1 with CME) Both rrest and RB are larger than model calculation with no CME. A. Tang, arXiv:1903.04622 Data difficult to explain by only backgrounds. P.Tribedy, WWND 2020 17 Centrality (%) Other Observable 18 Alternate observable to study CME Alternate observable to study CME N. Magdy, et al. v !"# ∆% Correlator N. Magdy, et al.PRC 97, 061901 (2018) v !"#Alternate∆% Correlator Observable To Study CME PRC 97, 061901 (2018) Ø The !". ∆% correlator measures the magnitude of charge separation parallel to the B-field, Ø The ! ∆% correlator measures the magnitude of charge separation parallel to the B-field, ".We use R ( ∆ relative S ) correlator to that to for study charge charge separation separation perpendicular to the B-field relativeΨm to that for charge separation perpendicular to the B-field C (∆S) '" ∆% Ψm NoteN. that Magdy, both et al. and ) are insensitive to the RΨ (∆(S)= ,m=2, 3 )'"! ∆% '"! ∆% ! '"∆(%∆%= m , + = 2,3 Note that both ' PRC∆ 97,% 061901and ' (2018)∆% are insensitive to the "# ) CΨ (∆S) "! "! !"# ∆% = ) ', + =∆2%,3 m⊥ CME-driven charge separation (but not to background) ' ∆% "( CME-driven charge separation (but not to background) "( RΨ (∆S) charge separation parallel/perpendicular to B-field (CME sensitive) 2 N. Magdy for the STAR Ø→Measurements for ! show: N. Magdy for the STAR RØΨ3Measurements(∆S) baseline, for ! insensitiveshow: to" #CME but sensitive to background Collaboration QM-2019 → "# Collaboration QM-2019 Au+Au (a) U+U (a)(a)(b) Au+AuU+U m = 2 (c)(b) Au+AuCu+Au Au+Aum =200 2 GeV (c) Cu+Au (a) U+U (a)(a)(b) Au+AuU+U m = 2 (c)(b) Au+AuCu+Au m = 2001.1 2 GeV (b) (c) Cu+Au d+Au (a)(c) q2% = 0-20% (b) 1.1 (b) d+Au〈 N 〉 ∼ 20 ± 2 (a)(c) q2% = 0-20% (b) 0.1 0-20% m = 3 0-20% m = 3 m 〈= N 3 〉 ∼ 20 ± 2 m = ch3 p+Au 0.1 20-40% 0.1 0-20% 00-20%-20% 0-20% N. Magdy, QM 2019 ch p+Au Au+Au 200 GeV 20-40%Au+Au 200 GeV 0.1 ″ ) ″ ) 40-60% ″ ) ″ ) 1.05 1.05 1.05 1.05 40-60% 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 20-50% 40-100% 20-50% 40-100% ″ ) ″ ) ″ ) 1.05 1.05 ″ ) 1.04 1.04 ( ∆ S ( ∆ S 0.08 ( ∆ S ( ∆ S STAR PreliminarySTAR Preliminary STAR Preliminary STAR Preliminary STAR Preliminary STAR 0.08 Preliminary { 2 } 0.08 { 2 } 0.08 m m m m ( ∆ S ( ∆ S 2 2 ( ∆ S ( ∆ S 2 2 2 2 v v Ψ Ψ Ψ Ψ Ψ Ψ Ψ Ψ R R R R R R R R 1 1 1 1 1 1 1 1 1 1 0.06 1 1 1 1 0.06 1 1 0.06 0.06 0.95 0.95 -2 -1 0 1 2 0 20 40 60 80 -3 -2 -1 0 1 2 3 -3 -2-2 -1-1 00 11 22 33 -3-2 -2-1-1-2 00 -11 1 2 2 0 3 1-2 -1 2 0 1 2 ″ 00 -2 -1 0 1q % 2 0 20 40 60 80 -3 -2″ -1 0 1 2 3 -3 ″″-2-2 -1-1 00 11 22 33 ″-3″-2 -2-1-1-2″00 00 -11 1 2 2 0 3 ″ 1-2 -1 2 0 ∆∆S 1S 2 ″ 00 2 q % S ″ SS ″″ SS ∆∆SS ″″ ″00 S ″ ∆∆SS 2 ∆ ∆S ∆∆ ∆∆SS ∆∆ ∆∆SS ∆∆SS∆ ∆S ü DifferentDifferent response response for for ü Different responseü Different Differentfor small response response for üsmall forThe !Ψ2 is notü stronglyThe ! is not strongly ü Different response for p/d+Au and Au+Au Ψ2 !ΨR2Ψand2 &!RΨ3Ψ3 (p(d)+Au) and large (Au+Au) influenced by the v2 background !Ψ2 and !Ψ3 (p(d)+Au) and large (Au+Au) influenced by the v2 background Observation consistent with expectation for CME-driven charge separation Ø!"# results are consistent with the expectation for CME-driven Ø! resultsP.Tribedy, WWNDare consistent 2020 with the expectation19 for CME-driven "# charge separation. charge separation. 1 1 New Developments: CME Search At Low √s 20 The First Measurements At RHIC: BES-I data Charge separation vanishes at the lowest energy L. Adamczyk et al. (STAR Collaboration), PRL 113 (2014) 052302. 4 10 2.76 TeV Pb+Pb 10 200 GeV Au+Au 10 62.4 GeV Au+Au10 39 GeV Au+Au 4 10 10 5 5 5 5 × MEVSIM ] 〉 ) ⟩× 0 0 0 0 ) RP 2 ψ -2 -5 -5 -5 -5 2 Ψ β φ − + α 2 40 27 GeV Au+Au40 19.6 GeV Au+Au40 11.5 GeV Au+Au40 7.7 GeV Au+Au φ φ opposite charge 30 30 30 30 + same charge cos( 1 〈 20 20 20 20 φ ≡ γ 10 10 10 10 [ cos( ⟨ 0 0 0 0 80 60 40 20 0 80 60 40 20 0 80 60 40 20 0 80 60 40 20 0 % Most central Centrality % Figure 13: Three-pointWhy does correlator charge as a function separation of centrality disappear for Au+Au collisions at lower at 7.7-200 √s GeV ? [106], and for Pb+Pb collisions at 2.76 TeV [129]. Note that the vertical scales are di↵erent for di↵erent rows. The systematicIs this errors because (grey bars) bearsignal the same vanishes meaning asor in background Fig. 12. Charge independent vanishes? results from theMany model calculationsnew insights of MEVSIM since [135] 2014 are shown on as how grey curves. to handle background P.Tribedy, WWND 2020 21 of the charge-independent background. 4.1.1 CME background studies The ambiguity in the interpretation of experimental results comes from a possible background of (the reaction plane dependent) correlations not related to the CME. As illustrated in Fig. 3 of Ref [106], the two-particle correlator, cos( ) , which in the absence of any other correlations except ⌘h ↵ i the CME should be proportional to a↵a , shows the “wrong” ordering. That indicates the existence of an overwhelming background in hoveri any possible CME e↵ect. In correlator those background correlations are strongly suppressed (at the level of v2)butstillmightbesignificant.Thefactthatno event generator can explain the data says that either the experimental results are indeed due to the CME, or that all existing event generators do not include all the possible physics. There exist several attempts to identify the physics which might be responsible for the experimental observations. The most notable in this respect is the paper [113] where the authors show that the di↵erence between the same- and opposite-charge correlations as measured by STAR can be explained within a Blast Wave model that includes charge conservation along with radial and elliptic flow with parameters tuned to the data. Local charge conservation (LCC) assumes that the pairs of opposite charges are created very close in space at the late stage of the system evolution with developed anisotropic flow. Radial boost of the pair due to transverse expansion leads to particle collimation in azimuth and pseudorapidity [138, 139]. Then, due to elliptic flow, opposite-charge pairs became stronger correlated in-plane than out-of-plane, which causes splitting in value of correlator between same- and opposite-charge pairs [113] as observed in the data. While in [113] the authors were able to describe the data rather closely, there exist many questions to this particular analysis. Firstly we note that the local charge conservation (LCC) mechanism leads to strong correlation between opposite charge pairs, while experimentally + is very close to zero. 24 STAR Capability For CME Search At Low Energy 1000 Au+Au 27 GeV Event# Run# 19157004 6/6/18 02:01:10 EDT Beam-Beam Counter https://www.star.bnl.gov/~dmitry/edisplay/ © (West) Beam-Beam Counter (3.3<η<5.1) (East) (0<φ<2π) (-5.1<η<-3.3) (0<φ<2π) Time Projection Chamber (-1<η<1) (0<φ <2π) P.Tribedy, WWND 2020 22 STAR Capability For CME Search At Low Energy 1000 Au+Au 27 GeV Event# Run# 19157004 6/6/18 02:01:10 EDT Event Plane Detector https://www.star.bnl.gov/~dmitry/edisplay/ © (West) Event Plane Detector (2.1<η<5.1) (East) (0<φ<2π) (-5.1<η<-2.1) (0<φ<2π) Time Projection P ⇤ = Sˆ⇤ JˆsysChamber · (-1<η<1) D E PSTAR(~r, Upgradesp~)= Sˆ for(0< 2018,!ˆφ(<2~r) π #1:) Event Plane Detector ⇤ ⇤ · D E Sˆ !ˆ ⇠ · D E 8 sin( ⇤ 1) Event Plane Detector : A major upgrade for BES-II, p P H = (1) ⇡↵H fully installed in 2018, factor of two increase in EP ⌦ REP ↵ resolution, reduction in non flow due to η-gap ↵ = 0.642 ⇤,⇤ ± Measurements of large v1@forward η at low ⇤ + ⇤ STAR Preliminary √s→ new capability at STAR Pz = Sˆ⇤ zˆ P.Tribedy, WWND 2020 · 23 D 1 E 1 P doubling resolution ⟷ four-fold increase in run length ⇤ p R (3 weeks required, instead of 3 months…) Ultra-relativistic nuclear collisions: where the spectators flow? Sergei A. Voloshin and TakafumiSTAR Niida 1Event Plane detector acceptance: 2.1<|η|<5.1 1Wayne State University, 666 W. Hancock, Detroit, MI 48201 Beam rapidity for Au+Au 27 GeV, Ybeam =3.4 In high energy heavy ion collisions, the directed flow of particles is conventionally measured with respect to that of the projectile spectators, which is defined as positive x direction. But it is not Sign change of v1@Ybeam known if the spectators deflect in the “outward” direction or “inward” – toward the center line of the collision. In this Letter we discuss how the measurements of the directed flow at mid-rapidity, 0.15 especially in asymmetric collision such as Cu+Au, can be used to answer this question. We show PHOBOS that the existing data strongly favor the case that the spectators, in the ultrarelativistic collisions, Ybeam = 3.4 on average deflect outwards. Au+Au 0-40% Fig: Phys. Rev. C 94, 021901 (2016) 19.6 GeV https://drupal.star.bnl.gov/STAR/ 0.1 PACS numbers: 25.75.Ld, 25.75.Gz, 05.70.Fh 62.4 GeV EPD starnotes/public/sn0666 130 GeV SPECTATOR 200 GeV In an ultrarelativistic nuclear collision only part of all PROTONS 0.05 nucleons from the colliding nuclei experience a truly in- X ( η ) 1 PHOBOS collab. PRL v elastic collision. Some of nucleons, called spectators, stay 97 (2006) 012301 mostly intact (or might experience a transition to an ex- cited state). Nevertheless, those nucleons do experience a Z 0 nonzero momentum transfer and deflect from the original nucleus trajectory. The direction of such projectile nu- FORWARD cleon (“spectator”) deflection is conventionally taken as a positive x direction in the description of any anisotropic PARTICIPANTS -0.05 -5 -4 -3 -2 -1 0 1 2 particle production (anisotropic flow [1]). At the same time, while this direction has been measured experimen- η - ybeam tally at very low collision energies, nothing is known on which 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- of the spectator protons. cleon wave function in the nucleus, as well as momentum In this article we show how the study of the charge par- distribution of the nucleons confined in a nucleus [2]. It ticle directedWe flowcan at midrapidity use two measured planes relative to the from EPD as proxies for ΨRP spectator deflection direction (directed flow) can help to is also important for the interpretation of the anisotropic st flow measurements. In particular, the knowledge of the answerΨ the1 question(η > of Y whichbeam direction): 1 the spectators-order are plane, proton-rich (spectators, beam-fragments) spectator flow is requited for determination of the di- deflected on average. We do not distinguish between low nd rection of the magnetic field created in the collision as and highΨp2T (spectatorsη < Y inbeam this study,): though2 -order in principle plane of forward produced particle well as the system orbital momentum. The latter, for this question can be studied experimentally. example, is needed for the measurements of the so-called The main idea of our approach is based on the ob- global polarization [3–5]. servation that in the case of asymmetric initial density P.Tribedy, WWND 2020 24 The only (known to authors) direct determination of distribution in the system, the high(er) transverse mo- the spectator nucleons deflection direction was performed mentum particles on average are flowing/emitted in the at the energies E/A 100 MeV by measuring of the po- direction of the largest density gradient, while the lower ⇠ p particles flow in the opposite direction [9, 10]. If the arXiv:1604.04597v2 [nucl-th] 21 Apr 2016 larization of emitted photons [6]. It was observed (see T also [7, 8]) that around this energy the direction of the mean transverse momentum of all particles is zero (e.g at deflection direction changes from the “in-ward” (due to midrapidity region in symmetric collisions) then the av- attractive potential at lower energies) to the “out-ward” erage, integrated over all transverse momenta, directed at higher energies. No similar measurements was per- flow is in the same direction as that of low pT particles. formed at higher collision energies. Theoretically, this Then the strategy in the establishing the direction of question is also not well understood. As recently has the spectator flow becomes straight-forward. First, one been shown in [2], the direction of the spectator deflec- has to measure the directed flow of particles at midrapid- tion is likely dependent on the nucleon transverse mo- ity with respect to the spectator deflection. Comparing mentum. These calculations show that at relatively large that to the initial density gradients calculated relative to transverse momentum (more than 200 MeV) the nucle- the position of spectators, one can determine the direc- ons are likely deflected inwards, while⇠ at low transverse tion of spectator flow. The direction of the highest den- momentum they might deflect outwards. One reason for sity gradient in the system has to be determined with the latter might be the Coulomb interaction (repulsion) the help of a model, but this appears to be a very robust New Measurement Of Charge Separation: 27 GeV Charge separation normalized by v2 for planes at |η| + + Ψ2 participants + Ψ2(participants) Ψ1Ψ protons1(proton) _ _ _ _ So which plane shows more charge separation? P Tribedy, QCD@HighDensity, Nov 12-14, Wuhan, 2019 20 No significant difference in the scaled charge separation w.r.t. spectator proton & produced particle event planes. P.Tribedy, WWND 2020 25 A Decisive Tests Of CME Using Isobar Collisions 26 Decisive Tests Of CME Using Isobar Collisions Phys.Rev.Lett. 105 (2010) 172301 STAR’s proposal and projections https://drupal.star.bnl.gov/STAR/system/files/ STAR_BUR_Run1718_v22_0.pdf Figure 5–4: Magnitude (left axis) and significance (right axis) of the relative difference in the projected γ×Npart between Isobar 96 96 44Ru+ 44Ru and B B 96 96 40Zr+ 40Zr at 200 collisions GeV. We use the relative difference in Neutron eccentricity as the Extra baseline. Electro-Magnetic fields in heavy ion collisionsElectro-MagneticElectro-Magnetic fields in fields heavy in heavy ion collisions ion collisionsElectro-Magnetic fields in heavy ion collisions Proton 18 18 18 18 Strong B-fields ~10 Gauss are generated in non-centralStrong heavy B-fieldsion collisionsStrong ~10 B-fieldsGauss ~10are Gaussgenerated are generated in non-central in non-central heavy ionheavyStrong collisions ion B-fields collisions ~10 Gauss are generated in non-central heavy ion collisions y y y y z=0 Proton z=0 B z=0 B B z=0 B + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + x + + + + x + + 5σ difference in Δγ observable + + + + + + + ++ + + + x + + + + x Table 5.1 lists the expected relationship between Ru+Ru and Zr+Zr in terms of + + + + + + ++++ + + + + + + 96 40+ 96 40++ + + + 96 44+ 96 44++ + + + B B B B experimental observables for elliptic flow, CME, CMW and CVE, assuming that the Zr BZr B Ru RuB B if signal is at 20% level ✕ ✕ chiral effects are major physics mechanisms for the corresponding observables. With this ⦿ ✕ ⦿ ✕ ⦿ ⦿ assumption for the CMW observable, we have carried out a 700M-event projection for B-field direction → perpendicular to collision plane B-field direction → perpendicular to collision plane the slope parameter r, and found the r ratio of Ru+Ru over Zr+Zr to be 1.08 ± 0.08 for B-field magnitude → ~Z 2, ~ γ B-field directionB-field → magnitude perpendicular → ~Z 2to, ~ collision γ plane B-field direction → perpendicular to collision plane ~10% larger B-field2 in Ru+Ru but similar 2background as Zr+Zr makes B-field magnitude → ~ 1/γ , conductivity of the medium B-field magnitudeB-field →magnitude ~Z , ~ γ → ~ 1/γ , conductivity of the medium B-field magnitude → ~Z , ~ γ 20−60% collisions, which is only a 1σ effect. The CVE does not explicitly depend on the B-field magnitude → ~ 1/γ , conductivity of the medium B-field magnitude → ~ 1/γ , conductivity of the medium magnetic field, so to the 1st-order we expect the same amount of baryon-number P Tribedy, Rutgers Nuclear Physics Seminars, Feb 12, 2018 isobar36 P Tribedy, collisions Rutgers Nuclear Physics Seminars ,ideal Feb 12, 2018 to make36 a decisive test of CME P Tribedy, Rutgers Nuclear Physics Seminars, Feb 12, 2018 36 P Tribedy, Rutgers Nuclear Physics Seminars, Feb 12, 2018 separation36 for Ru+Ru and Zr+Zr. Shi et al. Annals Phys. 394 (2018) 50-72 arXiv:1711.02496 [nucl-th] 96 96 96 96 Many more model studies on Sun et al. Phys.Rev. C98 (2018) no.1, 014911 arXiv:1803.06043Observable 44 [nucl-th]Ru+44 Ru vs 40 Zr+40 Zr Xu et al. Phys.Rev.Lett. 121 (2018) no.2, 022301 arXiv:1710.03086flow [nucl-th] ≈ the observability of CME with Deng et al. Phys.Rev. C97 (2018) no.4, 044901 arXiv:1802.02292CME [nucl-th] > Schenke et al., Phys.Rev. C99 (2019), 044908 arXiv:1901.04378CMW [nucl-th] > Isobar collisions have come up Hammelmann et al, arXiv:1901.04378 CVE = P.Tribedy, WWND 2020 Table 5.1: The expected relationship between Ru+Ru and Zr+Zr27 in terms of experimental observables for elliptic flow, CME, CMW and CVE. Assuming 80% data collection efficiency we estimate needing 3.5 weeks of RHIC operation per collision system to collect 1.2B events. An extra collision energy point will help understand the beam-energy dependence of the true CME signal. It is feasible to also have the isobaric collisions at 27 GeV. The observed charge separation at 27 GeV is very similar to, if not bigger than, that at 200 GeV. However for the same centrality bin, the multiplicity at 27 GeV is lower than that at 200 GeV by a factor of 1.6. Therefore, to reach the same significance level as 200 GeV, we need to increase the number of events by a factor of 4 (1.63 due to the two particles and the resolution of the event plane involved in the γ correlator). 67 Data taking for isobar collisions: Details Of TheZrZr, Data RuRu Taking at √ sOfNN The=200 Isobar GeV Run Zr Ru Zr Ru Zr Ru Zr Ru Zr ZDC Rate (Hz) Collected (3.1B) Delivered luminosity 20 hrs Requested Goal: minimize the We took more systematics,similar Ru Ru data than what we run conditions for requested Zr Zr Consistentlyboth species stable luminosity • with long (~20 hr) store length Ru Ru • Min-bias data taking rates ~2k Hz (initial estimate 1.5k Hz) Zr Zr “Blind” offline data analysis (Zr vs • Ru) will be performed Two important steps: Ru Ru 1) Fill-by-fill switching 2) Blinding of data P.Tribedy, WWND 28 12 Data takingData for isobartaking collisions: for isobar collisions: IsobarIsobar dataZrZr,Data collection RuRu takingRunZrZr, atfor √ &andisobar sRuRuNN Blind =200blind collisions: at GeV analysis√ Analysiss NN=200 GeV From STAR Isobar ZrZr,data RuRucollection at √ sandNN=200 analysis GeV Multiple institutions Zr Ru Zr Ru Zr Ru Zr Ru Zr Zr Ru Zr Ru Zr Ru Zr Ru activelyZr participating in ZDC Rate (Hz) Collected (3.1B) Zr Ru Zr Ru Zr Ru Zr Ru Zr 20 hrs ZDC Rate (Hz) Delivered luminosity Requested the blind analysis which ZDC Rate (Hz) JH, Lee, RHIC AGS meet 2018 Collected (3.1B) Delivered luminosity 20 hrs Delivered luminosity 20 hrs Requested is done in four steps 3.1B events for bothIsobar Ru+Ru, Zr+Zr Blind collected Analysis over 8 weeksFlow Chart Goal is to eliminate Blind analysis3.1B events ongoing for both by fourRu+Ru, independent Zr+Zr collected groups over ( 8BNL-Fudan weeks ,UIC-SBU,UCLA,Purdue) Plans for blind analyses of the data was laid down from the beginning Step-I Step-II Step-III Step-IV “predetermined bias” • Consistently stable luminosity with longConsistently (~20 hr) stable store luminosity length Isobar-Blind STAR collaboration, arXiv:1911.00596 • with longMock (~20 data hr) store lengthIsobar-Mixed Isobar-Unblind Analysis 0.556 Min-bias dataConsistentlychallenge taking rates ~2k stable HzAnalysis luminosity 46035 47084 47088 47164 48270 50248 57288 • • Analysis 0.554 (initialMin-bias estimatewith dataTest 1.5k datalong taking Hz) (~20 rates ~2khr)QA, physics Hzstore & codelength Run-by-run QA, full • Full analysis 0.552 (initial estimatestructure 1.5k Hz) freezing analysis 〉 [GeV] (One run is Ru+Zr) (Ru and Zr T (27 GeV files) (One run is Ru/Zr) 0.55 “Blind” offline data analysis (Zr vs 〈 p • “Blind”Min-bias offline data data analysis taking (Zr vs rates ~2k Hz separated) Ru) •will be performed 0.548 Ru) •will(initial be performed estimate 1.5k Hz) Mixed-blind Mean Mean±5σ 0.572 Jan March May Aug 44052 44275 45183 49330 57224 58205 58335 FirstAll blind steps analysis, newof thedetector blind (EPD) manyanalysis challenges, were currently tested between Step-IIwith & III 0.564 • “Blind” offlineP.Tribedy, data Aug 22, analysis 2019, STAR (ZrCollaboration vs meeting, Krakow, Poland 14 0.556 S&T review, Prithwish 〉 [GeV] 6 mockRu) datawill be performedsample and documented T 〈 p 0.548 12 12 Unmixed-blind Mean Mean±5σ 0.54 0.556 45034 48011 56045 60012 60024 61017 62037 0.552 〉 [GeV] T 〈 p P.Tribedy, Aug 22, 2019, STAR Collaboration meeting, Krakow, Poland 12 17 0.548 Un-blind Mean Mean±5σ 0 1 2 3 4 5 6 7 Run-Index P.Tribedy, WWND 29 Summary Very exciting time at RHIC 1) Comprehensive set of measurements on CME, several new approaches indicate dominance of background and small CME signals but no decisive tests yet 3) Isobar data taking was a success, bind analysis is ongoing by STAR We will hopefully have the answer to CME in a few months P.Tribedy, WWND 2020 30 Thanks 31 Backup 32 The First Measurements At RHIC: BES-I data Charge separation vanishes at the lowest energy L. Adamczyk et al. (STAR Collaboration), PRL 113 (2014) 052302. 4 10 2.76 TeV Pb+Pb 10 200 GeV Au+Au 10 62.4 GeV Au+Au10 39 GeV Au+Au 4 10 10 5 5 5 5 × MEVSIM ] 〉 ) ⟩× 0 0 0 0 ) RP 2 ψ -2 -5 -5 -5 -5 2 Ψ β φ − + α 2 40 27 GeV Au+Au40 19.6 GeV Au+Au40 11.5 GeV Au+Au40 7.7 GeV Au+Au φ φ opposite charge 30 30 30 30 + same charge cos( 1 〈 20 20 20 20 φ ≡ γ 10 10 10 10 [ cos( ⟨ 0 0 0 0 80 60 40 20 0 80 60 40 20 0 80 60 40 20 0 80 60 40 20 0 % Most central Centrality % Figure 13: Three-pointWhy does correlator charge as a function separation of centrality disappear for Au+Au collisions at lower at 7.7-200 √s GeV ? [106], and for Pb+Pb collisions at 2.76 TeV [129]. Note that the vertical scales are di↵erent for di↵erent rows. The systematicIs this errors because (grey bars) bearsignal the same vanishes meaning asor in background Fig. 12. Charge independent vanishes? results from theMany model calculationsnew insights of MEVSIM since [135] 2014 are shown on as how grey curves. to handle background P.Tribedy, WWND 2020 33 of the charge-independent background. 4.1.1 CME background studies The ambiguity in the interpretation of experimental results comes from a possible background of (the reaction plane dependent) correlations not related to the CME. As illustrated in Fig. 3 of Ref [106], the two-particle correlator, cos( ) , which in the absence of any other correlations except ⌘h ↵ i the CME should be proportional to a↵a , shows the “wrong” ordering. That indicates the existence of an overwhelming background in hoveri any possible CME e↵ect. In correlator those background correlations are strongly suppressed (at the level of v2)butstillmightbesignificant.Thefactthatno event generator can explain the data says that either the experimental results are indeed due to the CME, or that all existing event generators do not include all the possible physics. There exist several attempts to identify the physics which might be responsible for the experimental observations. The most notable in this respect is the paper [113] where the authors show that the di↵erence between the same- and opposite-charge correlations as measured by STAR can be explained within a Blast Wave model that includes charge conservation along with radial and elliptic flow with parameters tuned to the data. Local charge conservation (LCC) assumes that the pairs of opposite charges are created very close in space at the late stage of the system evolution with developed anisotropic flow. Radial boost of the pair due to transverse expansion leads to particle collimation in azimuth and pseudorapidity [138, 139]. Then, due to elliptic flow, opposite-charge pairs became stronger correlated in-plane than out-of-plane, which causes splitting in value of correlator between same- and opposite-charge pairs [113] as observed in the data. While in [113] the authors were able to describe the data rather closely, there exist many questions to this particular analysis. Firstly we note that the local charge conservation (LCC) mechanism leads to strong correlation between opposite charge pairs, while experimentally + is very close to zero. 24 Unique advantage of EPD at 27 GeV STAR Event Plane detector acceptance: 2.1<|η|<5.1 Beam rapidity for Au+Au 27 GeV, Ybeam =3.4 EPD detects both participants & spectators P.Tribedy, WWND 2020 34 STAR capability for CME search at low energy 1000 Au+Au 27 GeV Event# Run# 19157004 6/6/18 02:01:10 EDT Event Plane Detector https://www.star.bnl.gov/~dmitry/edisplay/ © (West) Event Plane Detector (2.1<η<5.1) (East) (0<φ <2π) (-5.1<η<-2.1) (0<φ <2π) Time Projection Chamber (-1<η<1) (0<φ <2π) We measure charge-dependent azimuthal correlators using TPC and EPD P.Tribedy, WWND 2020 35