Nuclear Theory·nucl-th

Friday·April 14, 2023

10 papers—6 primary·4 cross-listed

07
[Submitted on 12 Apr 2023] (cross-list from hep-ph)
Analytic Solution for the Revised Helicity Evolution at Small $x$ and Large $N_{c}$ : New Resummed Gluon-Gluon Polarized Anomalous Dimension and Intercept
Jeremy Borden🇺🇸 · Yuri V. Kovchegov🇺🇸
We construct an exact analytic solution of the revised small- $x$ helicity evolution equations derived recently. The equations we solve are obtained in the large- $N_{c}$ limit (with $N_{c}$ the number of quark colors) and are double-logarithmic (summing powers of $α_{s} ln^{2} (1/ x)$ with $α_{s}$ the strong coupling constant and $x$ the Bjorken $x$ variable). Our solution provides small- $x$ , large- $N_{c}$ expressions for the flavor-singlet quark and gluon helicity parton distribution functions (PDFs) and for the $g_{1}$ structure function, with their leading small- $x$ asymptotics given by \begin{align} \Delta \Sigma (x, Q^2) \sim \Delta G (x, Q^2) \sim g_1 (x, Q^2) \sim \left( \frac{1}{x} \right)^{\alpha_h} , \notag \end{align} where the exact analytic expression we obtain for the intercept $α_{h}$ can be approximated by $α_{h} = 3.66074 \frac{α _{s} N _{c}}{2 π}$ . Our solution also yields an all-order (in $α_{s}$ ) resummed small- $x$ anomalous dimension $Δ γ_{GG} (ω)$ which agrees with all the existing fixed-order calculations (to three loops). Notably, our anomalous dimension is different from that obtained in the infrared evolution equation framework developed earlier by Bartels, Ermolaev, and Ryskin (BER), with the disagreement starting at four loops. Despite the previously reported agreement at two decimal points based on the numerical solution of the same equations, the intercept of our large- $N_{c}$ helicity evolution and that of BER disagree beyond that precision, with the BER intercept at large $N_{c}$ given by a different analytic expression from ours with the numerical value of $α_{h}^{B E R} = 3.66394 \frac{α _{s} N _{c}}{2 π}$ . We speculate on the origin of this disagreement.
Comments:
22 pages, 3 figures
Subjects:
High Energy Physics — Phenomenology (hep-ph); Nuclear Theory (nucl-th)
arXiv:
2304.06161 [pdf]
PRD(2023)·41 citations
08
[Submitted on 13 Apr 2023] (cross-list from hep-ph)
Bayesian inference of the path-length dependence of jet energy loss
Jordan Wu🇺🇸 · Weiyao Ke🇺🇸 · Xin-Nian Wang🇺🇸
A simple model for medium modification of the jet function can be used to extract the jet energy loss distribution through a parameterized form. We carry out a comprehensive Bayesian analysis of the world data on single inclusive jet spectra in heavy-ion collisions at both RHIC and LHC energies. We extract the average jet energy loss $⟨ Δ E ⟩$ as a function of jet transverse momentum $p_{T}$ for each collision system and centrality independently. Assuming jet energy loss is proportional to the initial parton density $ρ \sim d N_{ch} / d η / π R_{eff}^{2}$ as estimated from the pseudorapidity density of charged hadron multiplicity $d N_{ch} / d η$ and the effective system size $R_{eff} \sim N_{part}^{1/3}$ given by the number of participant nucleons $N_{part}$ , the scaled average jet energy loss $⟨ Δ E ⟩ / ρ \sim R_{eff}^{0.59} p_{T}^{0.13} ln p_{T}$ for jet cone-size $R = 0.4$ is found to have a momentum dependence that is slightly stronger than a logarithmic form while the system size or length dependence is slower than a linear one. The fluctuation of jet energy loss is, however, independent of the initial parton density or the system size.
Comments:
9 pages with 10 figures final version published in Phys. Rev. C 108 (2023) 3, 034911
Subjects:
High Energy Physics — Phenomenology (hep-ph); Nuclear Theory (nucl-th)
arXiv:
2304.06339 [pdf]
PRC(2023)·17 citations
09
[Submitted on 13 Apr 2023] (cross-list from hep-ph)
Kinematical higher-twist corrections in $γ^{*} \to M_{1} M_{2} γ$ : Neutral meson production
Bernard Pire🇫🇷 · Qin-Tao Song🇨🇳
We carry out the calculation of kinematical higher-twist corrections to the cross section of $γ^{*} \to M_{1} M_{2} γ$ up to twist 4, where $M_{i}$ is a scalar or pseudoscalar neutral meson. The three independant helicity amplitudes are presented in terms of the twist-2 generalized distribution amplitudes (GDAs), which are important non-perturbative quantities for understanding the 3D structure of hadrons. Since this process can be measured by BESIII in $e^{+} e^{-}$ collisions, we perform the numerical estimate of the kinematical higher-twist corrections by using the kinematics of BESIII. We adopt the $π π$ GDA extracted from Belle measurements and the asymptotic $π π$ GDA to study the size of the kinematical corrections in the case of pion meson pair, and a model $η η$ GDA is used to see the impact of target mass corrections $O (m^{2} / s)$ for $γ^{*} \to η η γ$ . Our results show that the kinematical higher-twist corrections account for $\sim 20%$ of the cross sections at BESIII on the average, and it is necessary to include them if one tries to extract GDAs from experimental measurements precisely. We also comment the case of $π^{0} η$ production which is important for the search of hybrid mesons.
Comments:
13 pages, 7 figures, title changed, added comment on $π η$ production, published in PRD107(2023), 114014
Subjects:
High Energy Physics — Phenomenology (hep-ph); High Energy Physics — Experiment (hep-ex); Nuclear Experiment (nucl-ex); Nuclear Theory (nucl-th)
arXiv:
2304.06389 [pdf]
PRD(2023)·9 citations
10
[Submitted on 13 Apr 2023] (cross-list from hep-ph)
Anisotropic flow and the valence quark skeleton of hadrons
Meijian Li🇪🇸 · Wenyang Qian🇪🇸 · Bin Wu🇪🇸 · Hong Zhang🇨🇳
We study transverse momentum anisotropies, in particular, the elliptic flow $v_{2}$ due to the interference effect sourced by valence quarks in high-energy hadron-hadron collisions. Our main formula is derived as the high-energy (eikonal) limit of the impact-parameter dependent cross section in quantum field theory, which agrees with that in terms of the impact parameter in the classical picture. As a quantitative assessment of the interference effect, we calculate $v_{2}$ in the azimuthal distribution of gluons at a comprehensive coverage of the impact parameter and the transverse momentum in high-energy pion-pion collisions. In a broad range of the impact parameter, a sizable amount of $v_{2}$ , comparable with that produced due to saturated dense gluons or final-state interactions, is found to develop. In our calculations, the valence sector of the pion wave function is obtained numerically from the Basis Light-Front Quantization, a non-perturbative light-front Hamiltonian approach. And our formalism is generic and can be applied to other small collision systems like proton-proton collisions.
Subjects:
High Energy Physics — Phenomenology (hep-ph); Nuclear Theory (nucl-th)
arXiv:
2304.06557 [pdf]
JHEP(2023)·4 citations

Affiliations

first authorsco-authorsvia INSPIRE

Analytic Solution for the Revised Helicity Evolution at Small x and Large Nc​: New Resummed Gluon-Gluon Polarized Anomalous Dimension and Intercept

Bayesian inference of the path-length dependence of jet energy loss

Kinematical higher-twist corrections in γ∗→M1​M2​γ: Neutral meson production

Anisotropic flow and the valence quark skeleton of hadrons

Affiliations

Analytic Solution for the Revised Helicity Evolution at Small $x$ and Large $N_{c}$ : New Resummed Gluon-Gluon Polarized Anomalous Dimension and Intercept

Kinematical higher-twist corrections in $γ^{*} \to M_{1} M_{2} γ$ : Neutral meson production