Revisiting transverse momentum broadening in dense QCD media

We reconsider the problem of transverse momentum broadening of a highly energetic parton suffering multiple scatterings in dense colored media, such as the thermal quark-gluon plasma or large nuclei. In the framework of Molière’s theory of multiple scattering we rederive a simple analytic formula, to be used in jet quenching phenomenology, that accounts for both the multiple soft and hard Rutherford scattering regimes. Further, we discuss the sensitivity of momentum broadening to modeling of the nonperturbative infrared sector by presenting a detailed analytic and numerical comparison between the two widely used models in phenomenology: the Hard Thermal Loop and the Gyulassy-Wang potentials. We show that for the relevant values of the parameters the nonuniversal, model dependent contributions are negligible at LHC, RHIC and EIC energies, thus consolidating the predictive power of jet quenching theory.

Figure 1

Momentum broadening probability distribution at different orders in Molière’s-expansion (see Eq. (25) compared to the exact result for GW [see Eq. (8)] with $\lambda =0.1$ corresponding to ($Q_{s0}^2=30{\mathrm{GeV}}^2$, $m_D^2=0.13{\mathrm{GeV}}^2$). In this and following figures $k_T\equiv |\mathit{k}|$.

Figure 2

Top: ratio between the $(0)+(1)$ result and the exact GW varying the expansion parameter $\lambda$ [see Eq. (26)]. Bottom: same as top panel but for the $(0)+(1)+(2)$ result. $\lambda =0.15$, 0.2, 0.25 corresponds to ($Q_{s0}^2=4{\mathrm{GeV}}^2$, $m_D^2=0.3{\mathrm{GeV}}^2$), ($Q_{s0}^2=4{\mathrm{GeV}}^2$, $m_D^2=0.5{\mathrm{GeV}}^2$), and ($Q_{s0}^2=1.5{\mathrm{GeV}}^2$, $m_D^2=1{\mathrm{GeV}}^2$) respectively.

Figure 3

Ratio between ${\mathcal{P}}^{\mathrm{HTL}}(\mathit{k},L)$ and ${\mathcal{P}}^{\mathrm{GW}}(\mathit{k},L)$ as a function of the Debye mass $m_D^2$ for $Q_{s0}^2=4.8{\mathrm{GeV}}^2$ (same value used in the other plots of this section).

Figure 4

Ratio of the leading power (LP) (solid) and next-to-leading power (NLP) expansions to the full GW (top) and HTL (bottom) potentials for different $m_D^2$. Notice that the orange, dashed line in the top panel fully overlaps with the reference black line.

Figure 5

Impact of the NLP term in Molière’s scheme at (1) order [using Eq. (33)] for GW (top) and HTL (bottom) potentials for different $m_D^2$.

Figure 6

Top: momentum broadening probability distribution at different orders in Molière’s expansion, see Eq. (25), compared to the exact result for GW and HTL potentials at LHC conditions. Middle: ratio between GW and HTL results. Bottom: ratio between $(0)+(1)$ (orange) and $(0)+(1)+(2)$ (purple) truncations with respect to the GW result.

Figure 7

Same as Fig. 6 but for RHIC.

Figure 8

Same as Fig. 6 but for the future EIC. Note that we do not consider the HTL potential as a thermal medium at the EIC is not expected.