Elliptic flow of $\varphi$ mesons at intermediate $p_T$: Influence of mass versus quark number

We have studied elliptic flow $\left(v_2\right)$ of $\varphi$ mesons in the framework of a multiphase transport (AMPT) model at CERN Large Hadron Collider (LHC) energy. In the realms of AMPT model we observe that $\varphi$ mesons at intermediate transverse momentum $\left(p_T\right)$ deviate from the previously observed [at the BNL Relativistic Heavy Ion Collider (RHIC)] particle type grouping of $v_2$ according to the number of quark content, i.e, baryons and mesons. Recent results from the ALICE Collaboration have shown that $\varphi$ meson and proton $v_2$ has a similar trend, possibly indicating that particle type grouping might be due to the mass of the particles and not the quark content. A stronger radial boost at LHC compared to RHIC seems to offer a consistent explanation to such observation. However, recalling that $\varphi$ mesons decouple from the hadronic medium before additional radial flow is built up in the hadronic phase, a similar pattern in $\varphi$ meson and proton $v_2$ may not be due to radial flow alone. Our study reveals that models incorporating $\varphi$-meson production from $K\overline{K}$ fusion in the hadronic rescattering phase also predict a comparable magnitude of $\varphi$ meson and proton $v_2$ particularly in the intermediate region of $p_T$. Whereas, $v_2$ of $\varphi$ mesons created in the partonic phase is in agreement with quark-coalescence motivated baryon-meson grouping of hadron $v_2$. This observation seems to provide a plausible alternative interpretation for the apparent mass-like behavior of $\varphi$-meson $v_2$. We have also observed a violation of hydrodynamical mass ordering between proton and $\varphi$ meson $v_2$ further supporting that $\varphi$ mesons are negligibly affected by the collective radial flow in the hadronic phase due to the small in-medium hadronic interaction cross sections.

Figure 1

Elliptic flow parameter $v_2$ for pions (${\pi }^{+}+{\pi }^{-}$), kaons ($K^{+}+K^{-}$), phi mesons ($\varphi$), and protons ($p+\overline{p}$) as a function of transverse momentum calculated from the SM version of AMPT (a) with hadronic rescattering (b) without hadronic rescattering in 20–40 % Pb-Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$.

Figure 2

Ratio of $v_2^{\varphi }\left(p_T\right)/v_2^p\left(p_T\right)$ as a function of transverse momentum calculated from the SM version of AMPT with hadronic rescattering (open star) and without hadronic rescattering (solid star) in 20–40 % Pb-Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. Filled boxes represent statistical uncertainties.

Figure 3

Transverse momentum dependence $v_2$ of $\varphi$ mesons calculated from the SM version of AMPT with hadronic rescattering (solid star), without hadronic rescattering (solid circle), and with hadronic rescattering but $K\overline{K}\to \varphi$ forbidden (solid square) in 20–40 % Pb-Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. Filled boxes and the bands represent statistical uncertainties

Figure 4

Elliptic flow parameter $v_2$ for kaons ($K^{+}+K^{-}$), phi mesons ($\varphi$), and protons ($p+\overline{p}$) as a function of transverse momentum calculated from AMPT SM with hadronic rescattering in (a) 20–40 % and (b) 50–80 % centrality classes of Pb-Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$.

Figure 5

Transverse momentum dependence of $\varphi$-meson and pion $v_2$ for 20–40 % Pb-Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. Results obtained from SM version of AMPT model for parton scattering cross section of (a) 3 mb and (b) 1.5 mb without hadronic rescatterings.

Figure 6

Transverse momentum dependence of $\varphi$-meson and proton $v_2$ for 20–40 % Pb-Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. Results obtained from SM version of AMPT model for parton scattering cross section of (a) 3 mb and (b) 1.5 mb without hadronic rescatterings.