Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userImproved opacity expansion at NNLO for medium induced gluon radiation
67
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
When an energetic parton propagates in a hot and dense QCD medium it loses energy by elastic scatterings or by medium-induced gluon radiation. The gluon radiation spectrum is suppressed at high frequency due to the LPM effect and encompasses two regimes that are known analytically: at high frequencies $omega >omega_c = hat q L^2$, where $hat q $ is the jet quenching transport coefficient and $L$ the length of the medium, the spectrum is dominated by a single hard scattering, whereas the regime $omega <omega_c$ is dominated by multiple low momentum transfers. In this paper, we extend a recent approach (dubbed the Improved Opacity Expansion (IOE)), which allows an analytic (and systematic) treatment beyond the multiple soft scattering approximation, matching this result with the single hard emission spectrum. We calculate in particular the NNLO correction analytically and numerically and show that it is strongly suppressed compared to the NLO indicating a fast convergence of the IOE scheme and thus, we conclude that it is sufficient to truncate the series at NLO. We also propose a prescription to compare the GW and the HTL potentials and relate their parameters for future phenomenological works.
rate research
Read More
We present a new expansion scheme to compute the rate for parton splittings in dense and finite QCD media. In contrast to the standard opacity expansion, our expansion is performed around the harmonic oscillator whose characteristic frequency depends on the typical transverse momentum scale generated in the splitting. The first two orders account for the high frequency regime that is dominated by single hard scatterings together with the regime of multiple soft scatterings at low frequency. This work generalizes the findings of Ref. cite{Mehtar-Tani:2019tvy} beyond the leading logarithmic approximation allowing to account also for the Bethe-Heitler regime and compare to the full numerical results from Ref. cite{CaronHuot:2010bp}. We investigate the sensitivity of our results to varying the separation scale that defines the leading order. Finally, the application to Monte Carlo event generators is discussed.
We revisit the calculation of the medium-induced gluon radiative spectrum and propose a novel expansion scheme that encompasses the two known analytic limits: i) the high frequency regime dominated by a single hard scattering that corresponds to the leading order in the standard opacity expansion, ii) the low frequency regime that is dominated by multiple soft scatterings. Our approach is based on expanding around the harmonic oscillator instead of vacuum in the leading logarithmic approximation. We compute the first two orders in this improved opacity expansion and show that they account for the aforementioned limits.
We calculate the fully differential medium-induced radiative spectrum at next-to-leading order (NLO) accuracy within the Improved Opacity Expansion (IOE) framework. This scheme allows us to gain analytical control of the radiative spectrum at low and high gluon frequencies simultaneously. The high frequency regime can be obtained in the standard opacity expansion framework in which the resulting power series diverges at the characteristic frequency $omega_csim hat q L^2$. In the IOE, all orders in opacity are resumed systematically below $omega_c$ yielding an asymptotic series controlled by logarithmically suppressed remainders down to the thermal scale $T ll omega_c$, while matching the opacity expansion at high frequency. Furthermore, we demonstrate that the IOE at NLO accuracy reproduces the characteristic Coulomb tail of the single hard scattering contribution as well as the Gaussian distribution resulting from multiple soft momentum exchanges. Finally, we compare our analytic scheme with a recent numerical solution, that includes a full resummation of multiple scatterings, for LHC-inspired medium parameters. We find a very good agreement both at low and high frequencies showcasing the performance of the IOE which provides for the first time accurate analytic formulas for radiative energy loss in the relevant perturbative kinematic regimes for dense media.
Medium-induced gluon radiation from massless and massive quarks is treated in the same formalism. The dead cone which regulates gluon radiation from massive quarks in the vacuum at small angles, is filled in the medium but constitutes a small fraction of the available phase space. Our study indicates that the energy loss for charmed hadrons at RHIC should be smaller than for light hadrons, but still sizable.
We calculate in this paper the perturbative gluon transverse momentum dependent parton distribution functions (TMDPDFs) and fragmentation functions (TMDFFs) using the exponential regulator for rapidity divergences. We obtain results for both unpolarized and linearly polarized distributions through next-to-next-to leading order in strong coupling constant, and through ${cal O}(epsilon^2)$ in dimensional regulator (finding discrepancy for the linearly polarized gluon TMDPDFs with a previous result in the literature). We find a nontrivial momentum conservation sum rule for the linearly polarized component for both TMDPDFs and TMDFFs in the ${cal N}=1$ super-Yang-Mills theory. The TMDFFs are used to calculate the two-loop gluon jet function for the energy-energy correlator in Higgs gluonic decay in the back-to-back limit.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
