Directed flow in asymmetric nucleus-nucleus collisions and the inverse Landau-Pomeranchuk-Migdal effect

It is proposed to identify a strong electric field—created during relativistic collisions of asymmetric nuclei—via the observation of pseudorapidity and transverse momentum distributions of hadrons with the same mass but opposite charge. The results of detailed calculations within the parton-hadron string dynamics (PHSD) approach for the charge-dependent directed flow $v_1$ are presented for semicentral Cu+Au collision at $\sqrt{s_{NN}}=200$ GeV incorporating the inverse Landau-Pomeranchuk-Migdal (iLPM) effect, which accounts for a delay in the electromagnetic interaction with the charged degrees of freedom. By including the iLPM effect, we achieve a reasonable agreement of the PHSD results for the charge splitting in $v_1\left(p_T\right)$ in line with the recent measurements by the STAR Collaboration for Cu+Au collisions at $\sqrt{s_{NN}}=200$ GeV while an instant appearance and coupling of electric charges at the hard collision vertex overestimates the splitting by about a factor of 10. We predict that the iLPM effect should practically disappear at energies of $\sqrt{s_{NN}}\approx 9$ GeV, which should lead to a significantly larger charge splitting of $v_1$ at the future FAIR/NICA facilities.

Figure 1

Time dependence of the electric field components $E_x$ and $E_y$ as generated by pointlike charges (dash-dotted line) in the central point of the overlap region $(x,y,z)=(0,0,1\mathrm{fm})$ for $\mathrm{Cu}+\mathrm{Au}$ at $b=5\mathrm{fm}$ and $\sqrt{s_{NN}}=200\mathrm{GeV}$. The solid and dotted lines correspond to the fields from the Lorentz contracted ball-like charge distributions (see text).

Figure 2

Pseudorapidity distributions within the pseudorapidity interval $\left|\eta \right|<3$ for positive and negative pions (a) and kaons (b) created in Cu+Au collisions at $\sqrt{s_{NN}}=200$ GeV in the impact parameter interval 4.4–9.5 fm. The histograms are the result of the standard PHSD transport approach without EMF, and the symbols are obtained when the electromagnetic force is additionally included.

Figure 3

Illustration of the inverse LPM effect. The dashed line displays the insensitivity to the electromagnetic field during the formation time for ${\tau }_f^{em}$ of a participant $\pi$; the wavy lines denote the electric field.

Figure 4

Charge-dependent $p_T$ distributions of positive and negative hadrons (top) and their difference $\mathrm{\Delta }{v}_1$ (bottom) from asymmetric Cu+Au collisions at $\sqrt{s_{NN}}=200$ GeV and various centralities including the inverse LPM effect with ${\tau }_f^{\mathrm{em}}={\tau }_f/10$. The experimental data (stars) are taken from Ref. [16].

Figure 5

Charge-dependent transverse momentum $p_T$ dependence of the directed flow for pions from asymmetric Cu+Au collisions at $\sqrt{s_{NN}}=200$ GeV (left) and $\sqrt{s_{NN}}=9$ GeV (right). The backward and forward emitted pions are plotted in panels (a) and (c) for 200 GeV and panels (b) and (d) for 9 GeV, respectively. The inverse LPM effect is taken into account with ${\tau }_f^{\mathrm{em}}=(1/10){\tau }_f$ and shown by full symbols. Other parameters employed and the notation are as in Fig. 2.