Paper home page of probing EM-field by v1

PRX report and responses: round 2
Paper v8.1:
https://drupal.star.bnl.gov/STAR/system/files/main_16.pdf
responses: https://drupal.star.bnl.gov/STAR/system/files/Responses_round2.pdf

PRX report and responses: round 1
Paper v7.1: https://drupal.star.bnl.gov/STAR/system/files/Manuscript_v7.1.pdf
responses: https://drupal.star.bnl.gov/STAR/system/files/Replies_to_editor_v4.pdf

Paper v6.1: https://drupal.star.bnl.gov/STAR/system/files/GPC337_paper6.1.pdf
Paper draft v6: drupal.star.bnl.gov/STAR/system/files/Observation_of_the_electromagnetic_effect_via_charge_dependent_directed_flow_in_Au_Au_Ru_Ru_and_Zr_Zr_collisions_at__200_GeV.pdf

Reply to Collaboration Review and new draft (sent to star-paper list)
Paper draft v5.1: https://drupal.star.bnl.gov/STAR/system/files/GPC337_paper_v5.1.pdf
Reply: https://drupal.star.bnl.gov/STAR/system/files/Reply%20to%20collaboration%20review.pdf

Reply to Collaboration Review and new draft (sent to GPC)
Paper draft v5:
https://drupal.star.bnl.gov/STAR/system/files/GPC337_paper_v5.pdf
Reply: https://drupal.star.bnl.gov/STAR/system/files/Reply%20to%20collaboration%20review%20.pdf

Collaboration Review:
Paper draft v4.1: https://drupal.star.bnl.gov/STAR/system/files/GPC337_paper_v4.1.pdf

GPC337 (Aug 9, 2022)
Notes and response: https://drupal.star.bnl.gov/STAR/system/files/Reply%20to%20GPC%20Aug%209%202022.pdf
paper draft v4: https://drupal.star.bnl.gov/STAR/system/files/GPC337_paper_v4.pdf

GPC337 (Aug 3, 2022)
Notes and response: drupal.star.bnl.gov/STAR/system/files/Reply%20to%20GPC337%20Aug%203%20_2.pdf
paper draft v3: drupal.star.bnl.gov/STAR/system/files/GPC337_paper_v3.pdf

GPC337 (July 6, 2022)
Notes and response: https://drupal.star.bnl.gov/STAR/system/files/Response%20to%20the%20comments%20from%20GPC%20337%20meeting%20on%20July%206%202022.pdf
paper draft v2: https://drupal.star.bnl.gov/STAR/system/files/GPC337_paper_v2.pdf

PWGC review: https://drupal.star.bnl.gov/STAR/system/files/PWGC_0.pdf
Replies to PWGC: https://drupal.star.bnl.gov/STAR/system/files/RepliesToPWGC.pdf

PWG Presentations:

Observation of the electromagnetic field effect via charge-dependent directed flow in heavy-ion collisions at the Relativistic Heavy Ion Collider

PAs: Jinhui Chen, Aditya Prasad Dash, YuGang Ma, Diyu Shen, Subhash Singha, Aihong Tang, Dhananjaya Thakur and Gang Wang

Target journal:
Physical Review X

Abstract:

Non-central collisions between ultra-relativistic heavy nuclei can produce strong magnetic fields on the order of $10^{18}$ Gauss, and the evolution of the electromagnetic field could leave an imprint on the final-state particles. In particular, particles and  anti-particles with opposite charges will receive opposite contributions to their rapidity-odd directed flow, $v_1(\mathsf{y})$. Here we present the charge-dependent measurements of $dv_1/d\mathsf{y}$ near midrapidity for  $\pi^{\pm}$, $K^{\pm}$, and $p(\bar{p})$ in Au+Au and isobar ($_{44}^{96}$Ru+$_{44}^{96}$Ru and  $_{40}^{96}$Zr+$_{40}^{96}$Zr) collisions at $\sqrt{s_{NN}}=$ 200 GeV, and in Au+Au at 27 GeV, recorded by the STAR detector at the Relativistic Heavy Ion Collider. The combined dependence of the $v_1$ signal on collision system, particle species, and collision centrality can be qualitatively and semi-quantitatively understood as several effects on constituent quarks. While the results in central events can be explained by the $u$ and $d$ quarks transported from initial-state nuclei, those in peripheral events reveal the contributions from the Faraday induction and Coulomb effect for the first time in such experiments.

Figures:

                                                                      Figure 1Figure 1

Fig 1:  
Sketch of a heavy-ion collision. The impact parameter and the beam direction are along the $x$ and $z$ axes, respectively. The $x$-$z$ plane is called the reaction plane. Participating nucleons in the overlap region create a hot and dense medium of  quark-gluon plasma. Spectator nuclear fragments generate strong electromagnetic fields.        

                                                                                                                                                    
                                                                                 
Fig 2: 
Schematic side view of a heavy-ion collision. The dashed lines represent the motion of quarks due to the QGP expansion.The black solid lines indicate the Hall effect, where the magnetic field exerts the Lorentz force on moving charges. The impact of the Coulomb field from spectators and the Faraday field induced by the fast decay of the magnetic field is marked by red lines.

                                                                             

Fig 3: Illustration of different contributions to $\Delta(dv_1/dy)$ between protons and anti-protons versus centrality.  Panel (a) sketches the transported-quark effect. Panel (b) depicts the electromagnetic-field 

contribution, dominated by the Faraday/Coulomb effect. Panel (c)  speculates the superposition of the two effects in the final observable.

                                                                                                 Figure4bFigure4b


Fig 4: Panel (a): the ionization energy loss $dE/dx$ of charged particles as a function of momentum in TPC. The solid lines are the corresponding Bichsel function. Panel (b): the mass-squared as a function of momentum in TOF. The dashed boxed areas indicate the pion, kaon and proton candidates.

                                                                                             
 
Fig 5:
 
$v_1$ for protons and anti-protons as a function of rapidity in (a) Au+Au collisions at $\sqrt{s_{NN}}=$ 200 GeV, (b) isobar (Ru+Ru and Zr+Zr) collisions at $\sqrt{s_{NN}}=$ 200 GeV, and (c) Au+Au collisions at $\sqrt{s_{NN}}=$ 27 GeV in the centrality interval of 50--80\%. Protons and anti-protons are marked with solid and open circles, respectively. Panels (d), (e) and (f) show $\Delta v_1 \equiv v_1^{p} - v_1^{\bar{p}}$ versus rapidity. The $d\Delta v_1/d\mathsf{y}$ values are obtained with linear fits (solid lines). Systematic uncertainties are indicated with shaded bands. 


                                                                                         
                                                                                             
Fig 6: The $\Delta v_1$ slope, $\Delta dv_1/dy$, between positively charged and negatively charged pion, kaon and proton as a function of centrality in (a) Au+Au collisions and (b) Ru+Ru and Zr+Zr collisions at $\sqrt{s_{NN}}=$ 200 GeV. Slopes are obtained by fitting $\Delta v_1$ in -0.8 $<y<$ 0.8 with a linear function. Different open markers are used to indicate experimental measurement, and a blue solid line stands for theoretical prediction on $v_1$ splitting of proton induced by electromagnetic field effect in the transverse momentum range of 1 $<p_T<$ 2 GeV/c, in Au+Au collisions at $\sqrt{s_{NN}}=$ 200 GeV\cite{Gursoy:2018yai}.  The shaded bands indicate systematic uncertainties. For visual coherence, the predictions are scaled by a factor of 0.5. 

Conclusions:

The charge-dependent directed flow provides a probe to the transported quarks, as well as the Hall, Faraday, and Coulomb effects in heavy-ion collisions.
We have presented the $v_1$ measurements for $\pi^\pm$, $K^\pm$, and $p$($\bar{p}$) in Au+Au and isobar (Ru+Ru and Zr+Zr) collisions at $\sqrt{s_{NN}}=$ 200 GeV, \textcolor{blue}{and Au+Au collisions at $\sqrt{s_{NN}}=$ 27 GeV.}  The slope difference, $\Delta(dv_1/d\mathsf{y})$, between protons and anti-protons, \textcolor{blue}{as well as between $K^+$ and $K^-$}, changes from positive values in central collisions to negative in peripheral collisions.\textcolor{blue}{The measured proton $\Delta(dv_1/d\mathsf{y})$ values in the centrality range of 50--80\% are $[-1.89 \pm 0.35({\rm stat.}) \pm 0.09({\rm syst.})] \times 10^{-3}$ in Au+Au collisions at 200 GeV, $[-3.28 \pm 0.53({\rm stat.}) \pm 0.27({\rm syst.})] \times 10^{-3}$ in isobar collisions at 200 GeV, and $[-1.87 \pm 0.11({\rm{stat.}}) \pm 0.03(\rm{syst.})] \times 10^{-2}$ in Au+Au collisions at 27 GeV.}
While the positive $\Delta(dv_1/d\mathsf{y})$ for \textcolor{blue}{protons and kaons} in central collisions \blue{can be} attributed to the transported-quark contributions, the significant negative values in peripheral events are consistent with the electromagnetic field effects with the dominance of the Faraday induction + Coulomb effect~\cite{Gursoy:2014aka,Gursoy:2018yai}. \textcolor{blue}{This charge splitting is stronger in collisions at $\sqrt{s_{NN}}=$ 27 GeV, corroborating the idea that the electromagnetic field decays more slowly at low energies.}
\textcolor{blue}{Compared with protons, pions and kaons have smaller $\Delta(dv_1/d\mathsf{y})$ magnitudes, which is understandable in view of factors such as mean $p_T$ and the formation time.}
Further studies on the beam energy dependence of this observable are underway, with more data accumulated in the RHIC BES-II program.