Influence of electromagnetic fields on the generation of the directed and elliptic flows of heavy quarks in relativistic heavy-ion collisions

We study the impact of self-generated electromagnetic fields (EMF) on the momentum evolution of charm quarks in the partonic and hadronic medium created in heavy-ion collisions at energies available at the Relativistic Heavy Ion Collier (RHIC), using the parton-hadron-string dynamics (PHSD) off-shell transport approach. In the quark-gluon plasma (QGP) phase, the charm quark interacts with the off-shell partons, whose mass and widths are given by the dynamical quasiparticle model (DQPM), which can reproduce the lattice QCD thermodynamics. The background electromagnetic fields are computed dynamically within the PHSD considering both the spectators and participants protons as well as newly produced charged hadrons, quarks, and antiquarks, which reflects naturally the electric conductivity <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>σ</a:mi> <a:mi>el</a:mi> </a:msub> </a:math> of the medium. We study the directed and elliptic flow of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>D</b:mi> </b:math> mesons in the presence of electromagnetic fields. We find that electromagnetically induced <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>v</c:mi> <c:mn>1</c:mn> </c:msub> </c:math> splitting in the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>D</d:mi> </d:math> meson through <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msup> <e:mi>D</e:mi> <e:mn>0</e:mn> </e:msup> </e:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msup> <f:mover> <f:mi>D</f:mi> <f:mo>¯</f:mo> </f:mover> <f:mn>0</f:mn> </f:msup> </f:math> mesons is consistent with the experimental data. Furthermore, we notice that the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msub> <g:mi>v</g:mi> <g:mn>1</g:mn> </g:msub> </g:math> splitting in the heavy quark as a function of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msub> <h:mi>p</h:mi> <h:mi>T</h:mi> </h:msub> </h:math> is more prominent as a probe of the produced electromagnetic fields. However, we find only a small impact of electromagnetic fields on the heavy quark elliptic flow <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:msub> <i:mi>v</i:mi> <i:mn>2</i:mn> </i:msub> </i:math> .