An AdS/CFT Calculation of Screening in a Hot Wind

Abstract

One of the challenges in relating experimental measurements of the suppression in the number of J/ψmesons produced in heavy ion collisions to lattice QCD calculations is that whereas the lattice calculations treat J/ψmesons at rest, in a heavy ion collision a c\bar c pair can have a significant velocity with respect to the hot fluid produced in the collision. The putative J/ψfinds itself in a hot wind. We present the first rigorous non-perturbative calculation of the consequences of a wind velocity v on the screening length L_s for a heavy quark-antiquark pair in hot N=4 supersymmetric QCD. We find L_s(v,T) = f(v)[1-v^2]^{1/4}/πT with f(v) only mildly dependent on v and the wind direction. This L_s(v,T)\sim L_s(0,T)/\sqrtγ velocity scaling, if realized in QCD, provides a significant additional source of J/Ψsuppression at transverse momenta which are high but within experimental reach.

Figures (3)

• Figure 1: String world sheet for wind with velocity $v=0.7$ blowing at an angle $\theta=45^\circ$ relative to the dipole. The solution has integration constants $p=1.325$ and $q=1.109$, which correspond to $\theta=45^\circ$ and $\ell=0.689$. (This $\ell$ is the maximum possible for this $v$ and $\theta$.) $\sigma\propto x_1$ extends from $-(\ell/2)\sin\theta$ to $+(\ell/2)\sin\theta$. (a) $y(\sigma)$. (b) $z(\sigma)-\sigma$ is the deviation of the string world sheet away from $z=\sigma$, the straight line at $\theta=45^\circ$ between the quark and the antiquark.
• Figure 2: The dependence of the screening length on the wind velocity $v$. (a) $\ell=L\pi T$, given in Eq. \ref{['ellvsq']}, as a function of the integration constant $q$ for six different values of $v$: 0, 0.5, 0.7, 0.8, 0.9, 0.95 (top to bottom). We see the peak of this curve, $\ell_{\rm max}$, dropping with $v$. All curves are for a wind blowing in the direction perpendicular to the dipole. (b) $f(v)=\ell_{\rm max}\sqrt{\gamma}=L_s \pi T \sqrt{\gamma}$ versus $v$ for a wind blowing perpendicular to the dipole (lower curve) or parallel to the dipole (upper curve).
• Figure 3: A $1/\sqrt{\gamma}$-velocity scaling of the screening length in QCD would imply a $J/\Psi$ dissociation temperature $T_{\rm diss}(p_T)$ that decreases significantly with $p_T$, while that for the heavier $\Upsilon$ is affected less at a given $p_T$. The $\Upsilon$ curve is schematic: we have increased $T_{\rm diss}(0)$ over that for the $J/\psi$ by a factor corresponding to its smaller size in vacuum.