Abstract
We compute the correction to the energy loss of a hard parton due to short separation distances between the creation of the particle and the in-medium scattering center that stimulates bremsstrahlung radiation, to first order in opacity. In deriving the result we make full use of the large formation time assumption, which results in a significant reduction of the number of diagrams contributing to the small separation distance correction. An asymptotic analysis of our small separation distance correction term finds that the correction dominates at large $\sim 100$ GeV parent parton energies; scales like $L$ with the size of the system for small $L$, but like $L^0$ at larger $L$; and breaks color triviality. An extensive numerical investigation of the correction term confirms the aforementioned analytic findings, reveals that the correction term does not go to zero for large $L$, finds that the correction is sensitive to the mass of the parent parton, and shows a crucial dependence of the energy loss on a proper treatment of the physics of separation distances on the order of the Debye screening length. However, an examination of the large formation time approximation shows that it is violated for much of the phase space of the emitted radiation, implying a need to investigate the sensitivity of jet quenching results from relaxing this approximation. Our result constitutes an important step toward understanding partonic energy loss in small colliding systems.
Highlights
Recent startling results from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) show that key signatures of quark-gluon plasma (QGP) formation are found in high-multiplicity p + p and p/d + A collision systems
In order to further quantify the sensitivity of the energy loss to early time physics, we plot in Fig. 9 ratios of relative energy loss computed using three different scattering center distributions to the relative energy loss computed using the full step function, for the large-separation-distance DGLV result on the left, and the present small-separationdistance correction on the right, all for an E = 10 GeV bottom quark
Our result constitutes an important step toward the understanding of partonic energy loss in small colliding systems
Summary
Recent startling results from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) show that key signatures of quark-gluon plasma (QGP) formation are found in high-multiplicity p + p and p/d + A collision systems. In the usual Djordjevic, Gyulassy, Levai, and Vitev (DGLV) opacity expansion [32,33], for instance, the energy-loss derivation assumes a large separation distance z ≡ z1 − z0 ∼ λmfp 1/μ between the initial production position z0 of the hard parent parton and the position z1 where it scatters off a QGP medium quasiparticle. In this article we modify the usual DGLV approach (see Sec. II for details) by removing the second implication of the large-separation-distance assumption and retaining terms that were previously suppressed under the large-separationdistance assumption: We derive a generalization of the N = 1 in opacity DGLV radiative energy-loss result [35,36] by including all previously neglected terms assumed small under the scale ordering z 1/μ; see Fig. 1. All current jet quenching models that include radiative energy loss based on pQCD must individually assess their sensitivity to the large-formation-time and large system size approximations when making quantitative comparisons with data
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