Status of CME Search Before Isobar Collisions and Methods of Blind Analysis From STAR

Finding a conclusive experimental evidence of the Chiral Magnetic Effect (CME) has become one of the major scientific goals of the heavy-ion physics program at the Relativistic Heavy Ion Collider (RHIC). The existence of CME will be a leap towards an understanding of the QCD vacuum, establishing a picture of the formation of deconfined medium where chiral symmetry is restored and will also provide unique evidence of the strongest known electromagnetic fields created in relativistic heavy-ion collisions [2, 3]. The impact of such a discovery goes beyond the community of heavy-ion collisions and will possibly be a milestone in physics. Also, as it turns out, the remaining few years of RHIC run and analysis of already collected data probably provides the last chance for dedicated CME searches in heavy-ion collisions in the foreseeable future.

Over the past years significant efforts from the STAR as well as other collaborations have been dedicated towards developing new methods and observables to isolate the possible CME-driven signal and non-CME background contributions in the measurements of charge separation across the reaction plane. The most widely studied experimental observable in this context is the $\gamma$-correlator, defined as $\langle\cos(\phi_{a}^{\alpha}+\phi_{b}^{\beta}-2\Psi_{RP})\rangle$, where $\phi_{a}$ and $\phi_{b}$ denote the azimuthal angles of charged particles, $\alpha$ and $\beta$ are labels for the charge of the particles and $\Psi_{RP}$ is the reaction plane angle [4]. The angle $\Psi_{RP}$ is expected to be strongly correlated to the direction of the magnetic field that enables the $\gamma$-correlator to be sensitive to signals of CME, more specifically, CME leads to a difference between same sign (SS,  $\alpha=\beta$) and opposite sign (OS, $\alpha\neq\beta$) charge correlations: $\Delta\gamma=\gamma_{\rm OS}-\gamma_{\rm SS}$. The STAR time projection chamber (TPC) has a wide acceptance at mid-rapidity ($|\eta|\!<\!1$) that is used to detect $\phi_{a}$ and $\phi_{b}$. And, in STAR the proxy for $\Psi_{RP}$ can be played by: 1) second-order harmonic anisotropy plane $\Psi_{2}$ of produced particles at mid-rapidity measured by TPC, 2) the first-order plane due to the spectator neutrons ($\Psi_{\textsc{zdc}}$) detected by the zero degree calorimeters (ZDC), 3) the forward $\Psi_{2}$ plane using the STAR beam beam counter BBCs and 4) very recently using both the first and second-order harmonic anisotropy planes using the forward Event Plane Detector (EPDs). Each of these planes are expected to have more or less measurable correlations to B-field and serves their purpose for the CME search. The first measurement of non-zero $\Delta\gamma$ by the STAR collaboration goes back to  [5] where connections to several expectations from CME driven signals of charge separation was identified. Most importantly, the first measurement from STAR [5] also identified several possible contributions from non-CME effects in the experimental observation of non-zero $\Delta\gamma$. Several subsequent measurements from RHIC and LHC have confirmed this observation and provided many additional insights in that direction [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. In this contribution, I will focus only on RHIC results and refer to LHC results wherever necessary.

A major challenge that the $\gamma$-correlator faces towards detecting signals of CME involves large non-CME background sources that are: 1) correlated to $\Psi_{RP}$ and 2) independent of $\Psi_{RP}$. The distinction between the two sources must be carefully noted as they are crucial to the interpretation of several key measurements performed at both RHIC and LHC.

Small collision systems provide unique data-driven ways to measure charge separation in the background scenario. This is based on the idea that the direction of B-field is uncorrelated to the elliptic anisotropy plane of the produced particle with respect to which $\Delta\gamma$ is measured [12, 19]. In low-multiplicity or min-bias collisions of small systems such planes are dominated by non-flow correlations from di-jets or momentum conservation. However, tell-tale signatures of collectivity have been observed in high multiplicity events of small collision systems – the origin of which has been a widely discussed topic in our community. There are a few scenarios that decide whether the elliptic anisotropy plane measured in the experiment will be: 1) correlated to a geometric plane of participants if collectivity is due to hydrodynamics flow, 2) uncorrelated or less correlated to geometric plane if collectivity is due to non-hydrodynamic but other initial state momentum space correlations, e.g. from CGC or escape mechanism and, 3) dominated by non-flow from di-jets and momentum conservation if no collectivity is observed [20]. Why is this important for CME search? It is important as these scenarios determine the nature of non-CME background that will dominate the measurements of $\Delta\gamma$ in small systems. It is also important to know what kind of baseline measurement do these small systems provide because our ultimate goal is to interpret measurements in heavy-ion collisions. For example, in the first scenario hydrodynamic flow driven background combined with local charge conservation will be the dominant source, important for heavy-ion measurements in most centralities. For the second and third scenarios reaction plane independent background will be the dominant source, important for peripheral and smaller sized heavy-ion collisions. Nevertheless, the expectation is that CME signal in all such scenarios will be small as the B-field in small collision systems are weakly correlated to elliptic anisotropy plane other than some specific scenarios like what was discussed in Ref [21]. So in summary, small systems have the potential to provide baseline measurements for heavy-ion collisions where CME signals are expected to disappear but different background sources will be present. The CMS measurement was the first to show that in overlapping multiplicity $\Delta\gamma$ measurements are quantitatively similar between p+Pb and Pb+Pb [12]. STAR measurements performed in p+Au and d+Au systems show similar and in fact larger charge separation measured in terms of the scaled quantity $\Delta\gamma/v_{2}\times N_{\rm ch}$ than the same in Au+Au measurements [15]. Such observations are striking as they tell us that a very large value of $\Delta\gamma$ is expected even for $100\%$ background scenario.

The following question is often asked. Does measurement in small systems completely rule out CME? Why do we still pursue the CME search? There are several reasons for not abandoning CME search in heavy-ion collisions based on the observations from small collision systems. It is already known that $\Delta\gamma$ in heavy-ion collisions suffer from major background, the possible existence of CME driven signal has become more of a quantitative question. Therefore only a quantitative baseline will serve our purpose. So a better question to ask is whether small system measurements can provide direct quantitative baseline for heavy-ions. Heavy-ion measurements for CME search are performed where the system size, multiplicity do not necessarily overlap with that of small systems. It is not straightforward to extrapolate the quantitative background baselines for $\Delta\gamma$ into such unknown territories where change of physics is eminent. For example, $\Delta\gamma$ measured for $N_{\rm ch}=10$ in p/d+Au maybe a good baseline for A+A at the same multiplicity but may not serve as quantitative baselines for $\Delta\gamma$ in Au+Au at $N_{\rm ch}=100$. One may try to make a projection under some working assumptions but that will lead to a qualitative baseline and defeats the major purpose of using small systems as direct quantitative baselines. This is where isobar collisions come in – that ensures measurements in two systems with very similar size and shape are compared. It is also difficult to conclude that the case of CME is ruled out entirely based on the raw $\Delta\gamma$ measurements between p/d+Au and Au+Au. In lieu of which several variants of $\Delta\gamma$, as well as alternative observable such as $R-$observable, signed balance function has been developed to quantify the signals of CME [22, 23]. The measurements based on $R-$observable show qualitative difference in p/d+Au and Au+Au  [24] – that is discussed in the following section.

With the aforesaid introduction on the challenges to disentangle CME from non-CME background I would like to now proceed with the possible solutions to overcome such a problem. Many cleaver ideas have been proposed and applied to existing data. The general consensus is that measurement from the isobar collisions (Ru+Ru that has $10-18\%$ higher B-field than Zr+Zr) provides the best solution to this problem. In following sections of this conference proceedings I would like to mention a few such recent efforts such as: 1) Differential measurements of $\Delta\gamma$ to identify and quantify backgrounds, 2) measurement of higher order harmonics of $\gamma$-correlator, 3) exploiting the relative charge separation across participant and spectator planes, 4) the use of R-observable to measure charge separation and 5) the use of signed balance function. The first three approaches are based on aforementioned three-particle correlator and the last two employ slightly different approaches to quantify charge separation. There have been many more developments in the recent times and also many LHC measurements have been performed but I will specifically focus on these five approaches because they will be explored with the isobar data. The following five sections describe these procedures in brief with comments on the outlook for isobar blind analysis (see [1] for more details).

In order to proceed in this section it is better to rewrite the conventional $\gamma$-correlator by a more general notation as $\gamma_{112}=\langle\cos(\phi_{a}^{\alpha}+\phi_{b}^{\beta}-2\Psi_{2})\rangle$. The idea is to measure charge separations across the third harmonic event plane by constructing a new correlator $\Delta\gamma_{123}=\gamma_{123}(OS)-\gamma_{123}(SS)$, where $\gamma_{123}=\langle\cos(\phi_{a}^{\alpha}+2\phi_{b}^{\beta}-3\Psi_{3})\rangle$ that was introduced by CMS collaboration in Ref [14]. Since the $\Psi_{3}$ plane is random and not correlated to B-field direction (see Fig.1), $\gamma_{123}$ is purely driven by non-CME background, the contribution of which should go as $v_{3}/N$. This is very useful to contrast signal and background scenario by comparing the measurements in two isobaric collision systems. Since Ru+Ru has larger B-field than Zr+Zr but have comparable background, the case for CME would be as follows: $(\Delta\gamma_{112}/v_{2})^{\rm Ru+Ru}/(\Delta\gamma_{112}/v_{2})^{\rm Zr+Zr}>1$ and $(\Delta\gamma_{112}/v_{2})^{\rm Ru+Ru}/(\Delta\gamma_{112}/v_{2})^{\rm Zr+Zr}>(\Delta\gamma_{123}/v_{3})^{\rm Ru+Ru}/(\Delta\gamma_{123}/v_{3})^{\rm Zr+Zr}$. Fig.1 (left) shows the measurement of these observables in U+U and Au+Au collisions. Within the uncertainties of the measurements, no significant difference in the trend of $\Delta\gamma_{112}/v_{2}$ and $\Delta\gamma_{123}/v_{3}$ is observed for the two collision systems except for the very central events. Predictions from hydrodynamic model calculations with maximum possible strength of local charge conservation [17] is shown on the same plot. Overall observation indicates background dominate the measurements and a similar analysis of the isobar data is highly anticipated.

This analysis makes use of the fact that B-field driven signal is more correlated to spectator plane in contrast to flow-driven background which is maximum along the participant planes. The idea was first introduced in Ref [29] and later on followed up in Ref [30]. It requires measurement of $\Delta\gamma$ with respect to the plane of produced particles, a proxy for participant plane as well as with respect to the plane of spectators. In STAR the two can be done by using $\Psi_{2}$ from TPC and $\Psi_{1}$ from ZDC respectively. The approach is based on three main assumptions: 1) measured $\Delta\gamma$ has contribution from signal and background that can be expressed as $\Delta\gamma=\Delta\gamma^{\rm bkg}+\Delta\gamma^{\rm sig}$, 2) the background contribution to $\Delta\gamma$ should follow the scaling $\Delta\gamma^{\rm bkg}(\textsc{tpc})/\Delta\gamma^{\rm bkg}(\textsc{zdc})=v_{2}(\textsc{tpc})/v_{2}(\textsc{zdc})$ and, 3) the signal contribution to $\Delta\gamma$ should follow the scaling $\Delta\gamma^{\rm sig}(\textsc{tpc})/\Delta\gamma^{\rm sig}(\textsc{zdc})=v_{2}(\textsc{zdc})/v_{2}(\textsc{tpc})$. The first two have been known to be working assumptions, widely used for a long time and can be used to test the case of CME [30] if $\left(\Delta\gamma/v_{2}\right)(\textsc{zdc})/\left(\Delta\gamma/v_{2}\right)(\textsc{tpc})>1$. The validity of the last one was studied and demonstrated in Ref [29]. Using all three equations one can extract [28] the fraction of possible CME signal $f_{\textsc{cme}}=\Delta\gamma^{\rm sig}/\Delta\gamma$ in a fully data-driven way as shown in Fig.1(right). This analysis will be done with the isobar data and the case for CME will be $f_{\textsc{cme}}^{\rm Ru+Ru}>f_{\textsc{cme}}^{\rm Zr+Zr}>0$.

The $R$-observable is actually a distribution, introduced in Ref [22], and defined as the ratio of two distribution functions of the quantity $\Delta S$ parallel and perpendicular to B-field direction defined as $R_{\Psi_{m}}(\Delta S)=C_{\Psi_{m}}(\Delta S)/C^{\perp}_{\Psi_{m}}(\Delta S)$. Here $\Delta S$ measures the difference in the dipole moment of the positive and negative charge in an event (see Ref [22] for details). The shape of $R_{\Psi_{2}}(\Delta S)$ will be sensitive to CME as well as non-CME background whereas $R_{\Psi_{3}}(\Delta S)$ is purely driven by non-CME background and serves as a baseline. Model calculations have established several unique features of this observable: 1) presence of CME signal will lead to a concave shape of the $R_{\Psi_{2}}(\Delta S)$, 2) increasing strength of CME signal will increase the concavity of $R_{\Psi_{2}}(\Delta S)$, 3) in presence of CME, the concavity of $R_{\Psi_{2}}(\Delta S)$ will be larger than that of $R_{\Psi_{3}}(\Delta S)$. The measurement of $R_{\Psi_{m}}$ is shown in Fig.2. The quantity $\Delta S^{\prime\prime}$ shown is a slight variant of $(\Delta S)$ that incorporates correction for particle number fluctuations and event plane resolution. The observation of Fig.2 indicates more concave shape for $R_{\Psi_{2}}$ compared to $R_{\Psi_{3}}$ in Au+Au whereas flat or convex shapes for p/d+Au indicates that the measurements are consistent with expectations of CME [24]. For isobar collisions the case of CME will be confirmed if: 1) a concave shape is observed for the ratio of the observables $R_{\Psi_{2}}(\Delta S)^{\rm Ru+Ru}/R_{\Psi_{2}}(\Delta S)^{\rm Zr+Zr}$ and 2) the concavity should be weaker for $R_{\Psi_{3}}(\Delta S)^{\rm Ru+Ru}/R_{\Psi_{3}}(\Delta S)^{\rm Zr+Zr}$.

A very recently proposed observable to search for CME is the signed balance function (SBF) [23]. The idea is to account for the ordering of the momentum of charged pairs measured by the width of SBF that is expected to be different for out-of-plane as compared to in-plane measurement captured in the ratio $r_{\rm lab}$. In addition, one can also account for the boost due to collective expansion of the system that forces all pairs to move in the same direction and measure the ratio in pair’s rest frame $r_{\rm rest}$. In presence of CME, the individual ratios as well as the double ratio $R_{B}=r_{\rm rest}/r_{\rm lab}$ is expected to be greater than unity. The preliminary measurements shown in Fig.2 (right) from STAR in Au+Au 200 GeV seem to be consistent with CME expectation. This observable will be studied with the isobar data in STAR but not as a part of the blind analysis and the CME expectation will be: 1) $r({\rm Ru+Ru})>r({\rm Zr+Zr})$, and 2) $R_{B}({\rm Ru+Ru})>R_{B}({\rm Zr+Zr})$.

Regardless of the outcome of the measurements with the isobar program, that will be performed at the top RHIC energy, one question will remain [1]. What happens at lower collision energy? In this context a new idea has emerged. The newly installed event-plane detector (EPD) upgrade provides a new capability at STAR towards CME search at lower collision energy and for the Beam Energy Scan phase-II program [38]. The idea is simple, at lower energies EPD acceptance ($2.1<|\eta|<5.1$) falls in the region of beam rapidity ($Y_{\rm beam}$) and can measure the plane of strong directed flow ($\Psi_{1}$) of spectator protons, beam fragments and stopped protons, therefore strongly correlated to the B-field direction (See fig4). The next step is to measure $\Delta\gamma$ with respect to $\Psi_{1}$ and compare it with the measurement of $\Delta\gamma$ along $\Psi_{2}$ planes from outer regions of EPD and TPC at mid-rapidity that are weakly correlated to the B-field directions. A test of CME scenario will be to see if large difference is observed in the measurements. First preliminary measurements from STAR as shown in Fig 4 is dominated by uncertainty but seems to show a lot of prospects for the CME search at lower energies.

Despite several challenges experimental efforts have been continued towards disentangling the CME signals from non-CME background in the measurement of charge separation across reaction plane. The highly anticipated results from the blind analysis of isobar collisions data provides us the best opportunity to make a decisive test of the CME in heavy-ion collisions.