Is $\hat{q}$ a physical quantity or just a parameter? and other unanswered questions in High-$p_T$ Physics

Abstract

The many different theoretical studies of energy loss of a quark or gluon traversing a medium have one thing in common: the transport coefficient of a gluon in the medium, $\hat{q}$, which is defined as the mean 4-momentum transfer$^2$, $\left<q^2\right>$, by a gluon to the medium per gluon mean free path, $\lambda_{\rm mfp}$. In the original BDMPSZ formalism, the energy loss of an outgoing parton, $-dE/dx$, per unit length ($x$) of a medium with total length $L$, due to coherent gluon bremsstrahlung, is proportional to the $\left< q^2\right>$ and takes the form: ${-dE/dx }\simeq \alpha_s \left<{q^2(L)}\right>=\alpha_s\, \mu^2\, L/\lambda_{\rm mfp} =\alpha_s\, \hat{q}\, L\ $ , where $\mu$, is the mean momentum transfer per collision. Thus, the total energy loss in the medium goes like $L^2$. Additionally, the accumulated momentum$^2$, $\left<{k_{\perp}^2}\right>$, transverse to a gluon traversing a length $L$ in the medium is well approximated by $\left<{k_{\perp}^2}\right>\approx\left<{q^2(L)}\right>=\hat{q}\, L$. A simple estimate shows that the $\left<{k_{\perp}^2}\right>\approx\hat{q}\,L$ should be observable at RHIC at $\sqrt{s_{NN}}=200$ GeV via the broadening of di-hadron azimuthal correlations resulting in an azimuthal width $\sim\sqrt{2}$ larger in Au$+$Au than in $p+p$ collisions . Measurements relevant to this issue will be discussed as well as recent STAR jet results presented at QM2014. Other topics to be discussed include the danger of using forward energy to define centrality in $p(d)+$A collisions for high $p_T$ measurements, the danger of not using comparison $p+p$ data at the same $\sqrt{s}$ in the same detector for $R_{AA}$ or lately for $R_{pA}$ measurements.