Effect of hadronic interaction on the flow of $K^{*0}$

We explore the implications of the late-stage hadronic rescattering phase on the flow of $K^{*0}$. The model calculations are done using a $(3+1)$-dimensional hybrid framework, incorporating both hydrodynamic evolution and hadronic transport that is calibrated to agree with bulk observables including the elusive rapidity differential $v_1$ of light-flavor hadrons. We find that the late-stage hadronic rescattering phase causes significant qualitative modification of the $K^{*0}$ rapidity differential directed flow $v_1$ resulting in $\frac{d{v}_1}{dy}\left(K^{*0}\right)-\frac{d{v}_1}{dy}\left(K^{+}\right)$ and $\frac{d{v}_1}{dy}\left(\varphi \right)-\frac{d{v}_1}{dy}\left(K^{+}\right)$ having opposite signs with the effect being more pronounced in central collisions as compared to peripheral ones due to the larger multiplicity as well as longer duration of the hadronic phase. Further, this effect is enhanced in low-energy collisions owing to a stronger breaking of boost invariance. On the contrary, the influence of the hadronic phase on the $K^{*0}$ elliptic flow $v_2$ is found to be less significant and quantitative.

Figure 1

The rapidity differential directed flow ($v_1$) of $\varphi$ and $K^{*0}$ has been plotted in panels (a) and (b), respectively, for $\mathrm{Au}+\mathrm{Au}$ collisons of $10–40\%$ centrality at $\sqrt{s_{NN}}=27$ GeV. The $v_1$ of the primordial hadrons which are produced directly from the hypersurface is represented by solid lines. The dashed lines represent the $v_1$ calculations of the hadrons after performing the decay of resonances to stable hadrons, whereas the dashed-dotted lines represent the $v_1$ calculations of the hadrons after they pass through the UrQMD hadronic afterburner. The band in each line provides the statistical uncertainty in the calculation.

Figure 2

The rapidity-integrated yield (a) and $v_1$ (b) ratios between hadrons of $p_x>0$ and $p_x<0$ [see Eqs. (13) and (14)] in $\mathrm{Au}+\mathrm{Au}$ collisons of $10–40\%$ centrality at $\sqrt{s_{NN}}=27$ GeV. The rapidity integration has been performed between $0<y<1$. The ratios have been shown for $\varphi$, $K^{*0}$, and $K^{+}$. To show the results obtained under different conditions, specifically, with or without the inclusion of hadronic transport stages for the hadrons, we have plotted the ratios for scenarios involving solely primordial hadrons and their resonance decay contributions (dotted lines), as well as for cases where the hadrons undergo interactions in the hadronic medium (solid lines).

Figure 3

The $p_T$ differential directed flow ($v_1$) has been plotted for $\varphi$ (a) and $K^{*0}$ (b) for $\mathrm{Au}+\mathrm{Au}$ collisons of $10–40\%$ centrality at $\sqrt{s_{NN}}=27$ GeV. The calculation has been done for the particles produced within the rapidity range $0<y<1$. The $v_1$ of the primordial hadrons which are produced directly from the hypersurface is represented by solid lines. The dashed lines represent the $v_1$ calculations of the hadrons after performing the decay of resonances to stable hadrons, whereas the dashed-dotted lines represents the $v_1$ calculations of the hadrons after they pass through the UrQMD hadronic afterburner.

Figure 4

Same as in Fig. 3 but for the $p_T$ differential elliptic flow ($v_2$) of the hadrons produced within the rapidity range $\left|y\right|<0.5$.

Figure 5

The splitting of directed flow slopes ($\frac{d{v}_1}{dy}$) of resonances $\varphi$ and $K^{*0}$ with $K^{+}$ has been plotted as a function of centrality for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=27$ GeV. The shaded bands denote the statistical uncertainties in the model calculations.

Figure 6

The splitting of directed flow slopes ($\frac{d{v}_1}{dy}$) between $K^{*0}$ and $K^{+}$, along with $\varphi$ and $K^{+}$, has been plotted as a function of the collision energy ($\sqrt{s_{NN}}$) for $\mathrm{Au}+\mathrm{Au}$ collisions of $10–40\%$ centrality.