Gluon Emission Research Articles

Non-global logarithms up to four loops at finite-Nc for V/H+jet processes at hadron colliders

We extend our previous work [1] on calculating non-global logarithms in e+e− annihilation to Higgs/vector boson production in association with a single hard jet at hadron colliders. We analytically compute non-global coefficients in the jet mass distribution up to four loops using the anti-kt jet algorithm. Our calculations are performed in the eikonal approximation, assuming strong energy ordering for the emitted gluons, thus capturing only the leading logarithms of the distribution. We compare our analytical results with the all-orders large-Nc numerical solution. In general, the gross features of the non-global logarithm distribution observed in the e+e− case remain valid for the V/H+jet processes.

Study of intrinsic-kT in the Parton Branching Method

The work presented here focuses on the production of Drell-Yan lepton pairs in hadron-hadron collisions with very low transverse momentum which is sensitive to the contribution from the non-perturbative transverse motion of partons inside hadrons as well as to the multiple soft gluon emissions which have to be resumed. To study the two contributions, we use Parton Branching Method which describes the evolution of transverse momentum dependent parton distributions and provides very precise predictions for inclusive observables such as the Drell–Yan cross section as a function of transverse momentum. In this study, we tune a parameter that describes the internal transverse motion of partons within hadron (intrinsic-kT) depending on the soft gluon contribution which is varied applying a lower limit to the transverse momentum of the emitted parton in branching up to 2 GeV. It will be shown that the parameter presented by the width of the Gaussian distribution increases with the minimal transverse momentum. This means that by reducing the contribution of soft gluons, more intense internal transverse motion is required (larger intrinsic-kT) to describe experimental data. Moreover, it was observed that the value of the intrinsic-kT increases with the collision energy and such a trend is more pronounced when the minimum transverse momentum of the parton at the branching is higher.

Seeing beauty in the quark-gluon plasma with energy correlators

Heavy quarks created in heavy-ion collisions serve as an excellent probe of the produced quark-gluon plasma (QGP). The radiation pattern of jets formed from heavy quarks as they traverse the QGP exhibits a particularly interesting structure due to the interplay of two competing effects: the suppression of small-angle radiation, also known as the “dead-cone” effect, and the enhancement of emitted gluons by medium-induced radiation. In this , we propose a new observable, based on the energy correlator approach to jet substructure, which will allow us to disentangle the two scales associated to these two phenomena and to determine under which conditions the dead cone is filled by medium-induced radiation. Combined with the forthcoming high-statistics measurements of heavy-flavor jets, this work provides a novel tool to unravel the dynamics of the QGP. Published by the American Physical Society 2024

Revisiting azimuthal angular asymmetries in diffractive di-jet production

We explore the impact of initial state soft gluon radiations on the azimuthal angle asymmetries in photo-production of hard di-jet via coherent diffraction in ultraperipheral heavy ion collisions, as well as in electron-proton (ep) and electron-nucleus (eA) collisions. The primary production mechanism is identified as the diffractive production of two hard jets, accompanied by a collinear gluon emission along the beam direction. In contrast, the diffractive exclusive di-jet production, where the initial state radiation is absent, is suppressed due to color transparency. Our analysis shows that azimuthal asymmetries, traditionally attributed to final state gluon emissions, are reduced by the presence of initial state radiations. The sensitivity of azimuthal asymmetries to both initial and final state radiations suggests that they could provide novel insights into the mechanisms of di-jet production in diffractive processes.

Exponentiation of soft quark effects from the replica trick

In this paper, we show that multiple maximally soft (anti-)quark and gluon emissions exponentiate at the level of either the amplitude or cross-section. We first show that such emissions can be captured by introducing new soft emission operators, which serve to generalise the well-known Wilson lines describing emissions of maximally soft gluons. Next, we prove that vacuum expectation values of these operators exponentiate using the replica trick, a statistical-physics argument that has previously been used to demonstrate soft-gluon exponentiation properties in QCD. The obtained results are general, i.e. not tied to a particular scattering process. We illustrate our arguments by demonstrating the exponentiation of certain real and virtual corrections affecting subleading partonic channels in deep-inelastic scattering.

Fermion self-energy and damping rate in a hot magnetized plasma

We derive a general expression for the fermion self-energy in a hot magnetized plasma by using the Landau-level representation. In the one-loop approximation, the Dirac structure of the self-energy is characterized by five different functions that depend on the Landau-level index n and the longitudinal momentum pz. We derive general expressions for all five functions and obtain closed-form expressions for their imaginary parts. The latter receive contributions from three types of on shell processes, which are interpreted in terms of Landau-level transitions, accompanied by a single photon (gluon) emission or absorption. By making use of the imaginary parts of the self-energy functions, we also derive the Landau-level dependent fermion damping rates Γn(pz) and study them numerically in a wide range of model parameters. We also demonstrate that the two-spin degeneracy of the Landau levels is lifted by the one-loop self-energy corrections. While the spin splitting of the damping rates is small, it may be important for some spin and chiral effects. We argue that the general method and the numerical results for the rates can have interesting applications in heavy-ion physics, astrophysics, and cosmology, where strongly magnetized QED or QCD plasmas are ubiquitous. Published by the American Physical Society 2024

Analysis of the gluon distribution with next-to-leading order splitting function at small-x* *Supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB34030301), the National Natural Science Foundation of China (12375073), the Major Project of Basic and Applied Basic Research in Guangdong Province (2020B0301030008), the Basic Research Program (Natural Science) of Guizhou Province, China(QKHJC-ZK[2023]YB027), and the Education

An approximated solution for the gluon distribution from DGLAP evolution equations with the NLO splitting function in the small-x limit is presented. We first obtain simplified forms of the LO and NLO splitting functions in the small-x limit. With these approximated splitting functions, we obtain the analytical gluon distribution using the Mellin transform. The free parameters in the boundary conditions are obtained by fitting the CJ15 gluon distribution data. We find that the asymptotic behavior of the gluon distribution is consistent with the CJ15 data; however, the NLO results considering the "ladder" structure of gluon emission are slightly better than the LO results. These results indicate that the corrections from NLO have a significant influence on the behavior of the gluon distribution in the small-x region. In addition, we investigate the DGLAP evolution of the proton structure function using the analytical solution of the gluon distribution. The differential structure function reveals that our results have a similar tendency to the CJ15 data at small-x.

Heavy quark diffusion and radiation at intermediate momentum

Heavy quark diffusion and radiation are discussed in an intermediate-momentum regime where finite mass effects can be significant. Diffusion processes are described in the Fokker-Planck approximation for soft momentum transfer, while radiative ones are taken into account by nearly collinear gluon emission from a single scattering in the Boltzmann equation. There are also radiative corrections to the transverse momentum diffusion coefficient, which are O(g2) suppressed more than the leading-order diffusion coefficient but logarithmically enhanced. Numerical results show that the heavy quark distribution function depends on the energy loss mechanism so that the medium modifications by diffusion and radiation are distinguishable. The nuclear modification factor is estimated by employing the heavy quark diffusion coefficient which is constrained by lattice quantum chromodynamics data. The suppression factor exhibits a transition from diffusion at low momentum to radiation at high momentum. The significance of the radiative effects at intermediate momentum depends on the diffusion coefficient and the running coupling constant. Published by the American Physical Society 2024

Small-x factorization from effective field theory

We derive a factorization theorem that allows for resummation of small-x logarithms by exploiting Glauber operators in the soft collinear effective field theory. Our analysis is carried out for the hadronic tensor Wμν in deep inelastic scattering, and leads to the definition of a new gauge invariant soft function Sμν that describes quark and gluon emission in the central region. This soft function provides a new framework for extending resummed calculations for coefficient functions to higher logarithmic orders. Our factorization also defines impact factors by universal collinear functions that are process independent, for instance being identical in small-x DIS and Drell-Yan.

Jets in e+A SIDIS and Denominator Regularization

We compute the in-medium jet broadening to leading order in energy in the opacity expansion. At leading order in αs the elastic energy loss gives a jet broadening that grows with ln E. The next-to-leading order in αs result is a jet narrowing, due to destructive LPM interference effects, that grows with ln2 E. We find that in the opacity expansion the jet broadening asymptotics are— unlike for the mean energy loss—extremely sensitive to the correct treatment of the finite kinematics of the problem; integrating over all emitted gluon transverse momenta leads to a prediction of jet broadening rather than narrowing. We compare the asymptotics from the opacity expansion to a recent twist-4 derivation and find a qualitative disagreement: the twist-4 derivation predicts a jet broadening rather than a narrowing. Comparison with current jet measurements cannot distinguish between the broadening or narrowing predictions. We comment on the origin of the difference between the opacity expansion and twist-4 results.We also introduce a novel regularization scheme in quantum field theory, denominator regularization (den reg). Den reg is as simple to apply as the usual dimensional regularization, works simply with a minimal subtraction scheme, and manifestly 1) maintains Lorentz invariance, 2) maintains gauge invariance, 3) maintains supersymmetry, 4) correctly predicts the axial anomaly, and 5) yields Green functions that satisfy the Callan-Symanzik equation. Den reg also naturally enables regularization in asymmetric spacetimes, finite spacetimes, curved spacetimes, and in thermal field theory.

Transverse momentum dependent shape function for J/ψ production in SIDIS

It has been shown previously that the transverse momentum dependent (TMD) factorization of heavy quarkonium production requires a TMD shape function. Its perturbative tail can be extracted by matching the cross sections valid at low and high transverse momenta. In this article we compare the order-αs TMD expressions with the order- {alpha}_s^2 collinear ones for J/ψ production in semi-inclusive deep inelastic scattering (SIDIS), employing nonrelativistic QCD in both cases. In contrast to previous studies, we find that the small transverse momentum limit of the collinear expressions contains discontinuities. We demonstrate how to properly deal with them and include their finite contributions to the TMD shape functions. Moreover, we show that soft gluon emission from the low transverse momentum Born diagrams provide the same leading order TMD shape functions as required for the matching. Their revised perturbative tails have a less divergent behavior as compared to the TMD fragmentation functions of light hadrons. Finally, we investigate the universality of TMD shape functions in heavy quarkonium production, identify the need for process dependent factorization and discuss the phenomenological implications.

Optimizing the Parton Showers in PYTHIA8 for Xe–Xe collision at 5.44 TeV

We present the doubly differential invariant yield of primary charged particles [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text] in Xe–Xe collisions at [Formula: see text] = 5.44 TeV, as a function of [Formula: see text] in kinematic region of [Formula: see text] and for the pseudorapidity interval of [Formula: see text] by using PYTHIA8 tuned to different Parton Showers like Simple Showers (Time-Like, Space-Like), DIRE and VINCIA Showers. The predictions of hard and soft QCD processes of Parton Showers are then compared with the ALICE data at different centrality classes of 0–5%, 50–60% and 70–80%. The observed deviations are connected with the kinematics involved and are mostly due to the color coherence and soft gluon emission from parton pairs. As PYTHIA8 does not take into account the Cronin effect, thus the deviation at low [Formula: see text] is due to Cronin effect. The nuclear modification factor is constructed and it is observed that the signal is less than unity or suppression is seen which is coming from Parton Showers.

Event-by-event multiplicity fluctuations and correlations in ring-like and jet-like events in 197Au–AgBr collisions at 11.6 A GeV/c

Event-by-event (ebe) multiplicity fluctuations and correlations amongst the charged particles emitted in the forward–backward symmetric pseudorapidity ([Formula: see text]) windows of varying widths and positions are investigated by analyzing the experimental data on [Formula: see text]Au–AgBr collisions at 11.6[Formula: see text]A[Formula: see text]GeV/[Formula: see text]. The findings are compared with the predictions of relativistic transport model, urqmd and independent particle emission (or mixed event) model. It is observed that the fluctuations in ebe mean pseudorapidity values and those reflected from the fluctuations strength measure, [Formula: see text] are relatively higher as compared to those expected from the statistically independent particle emission model. The study of the variance, [Formula: see text] of a suitably defined forward–backward asymmetry variable [Formula: see text] as a function of [Formula: see text] window width and position indicates the presence of strong short-range correlations, which might arise due to isotropic decay of cluster-like objects either in forward or backward [Formula: see text] region. Furthermore, analyses of events having ring-like and jet-like substructures, carried out separately, suggest that the major contribution to the observed fluctuations in the data sample are due to ring-like events, while the contributions from the jet-like events appear to be rather small. The observed difference in the behavior of correlation strengths from the two types of events might be due to the enhanced emission of Cherenkov gluons, giving rise to the ring-like substructure. The mixed event analysis further confirms that the observed fluctuations are the distinct feature of the data, which disappear after event mixing.

Soft gluon emission from heavy quark scattering in strongly interacting quark-gluon plasma

We apply the Low's theorem to soft gluon emission from heavy quark scattering in the nonperturbative strongly interacting quark-gluon plasma (sQGP). The sQGP is described in terms of the dynamical quasi-particles and adjusted to reproduce the EoS from lQCD at finite temperature and chemical potential. Since the emitted gluon is soft and of long wavelength, it does not provide information on the detailed structure of the scattering, and only the emission from incoming and outgoing partons is enough. It simplifies the calculations making the scattering amplitude factorizable into the elastic scattering and the emission of soft gluon. Imposing a proper upper limit on the emitted gluon energy, we obtain the guage-invariant scattering cross sections of heavy quarks with the massive partons of the medium as well as their transport coefficients (momentum drag and diffusion) in the QGP and compare with those from the elastic scattering without gluon emission.

Stronger C -odd color charge correlations in the proton at higher energy

The non-forward eikonal scattering matrix for dipole-proton scattering at high energy obtains an imaginary part due to a $C$-odd three gluon exchange. We present numerical estimates for the perturbative Odderon amplitude as a function of dipole size, impact parameter, their relative azimuthal angle, and light-cone momentum cutoff $x$. The proton is approximated as $\psi_\mathrm{qqq}|qqq\rangle + \psi_\mathrm{qqqg}|qqqg\rangle$, where $\psi_\mathrm{qqq}$ is a non-perturbative three quark model wave function while the gluon emission is computed in light-cone perturbation theory. We find that the Odderon amplitude increases as $x$ decreases from 0.1 to 0.01. At yet lower $x$, the reversal of this energy dependence would reflect the onset of universal small-$x$ renormalization group evolution.

Leading order, next-to-leading order, and nonperturbative parton collision kernels: Effects in static and evolving media

Energetic partons traveling in a strongly interacting medium lose energy by emitting radiation and through collisions with medium constituents. Non-perturbative, next-to-leading order and leading order collision kernels are implemented within AMY-McGill formalism. The resulting gluon emission rates are then evaluated and compared by considering scattering occurring in a brick of quark-gluon plasma, as well as in a realistic simulation of Pb-Pb, collisions at $\sqrt{s}=2.76$ ATeV using MARTINI. We find that the variations in quenching of hard partons resulting from using different kernels can be important, depending on the overall value of the strong coupling constant $\alpha_s$.

Back-to-back inclusive dijets in DIS at small x: Sudakov suppression and gluon saturation at NLO

Back-to-back dijet cross-sections in deeply inelastic scattering (DIS) at small xBj are suppressed by many-body multiple scattering and screening effects arising from gluon saturation at high parton densities. They are similarly sensitive in these kinematics to large Sudakov logarithms from soft gluon radiation. Uncovering novel physics in this DIS channel therefore requires understanding the interplay of the two phenomena. In this work, we compute the small xBj inclusive dijet DIS cross-section in back-to-back kinematics at next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). Our result includes, for the first time, all real and virtual NLO contributions to the impact factor. These include all Sudakov double and single logarithm contributions, as well as all other finite mathcal{O} (αs) terms that contribute at this order. We demonstrate explicitly that resummations of small x and Sudakov logarithms can be performed simultaneously in the CGC EFT. This requires that the JIMWLK kernel for small x evolution of the Weizsäcker-Williams (WW) gluon distribution satisfies a kinematic constraint imposed by lifetime ordering of successive gluon emissions; the corresponding modifications to the kernel, corresponding to resummations of large double transverse logarithms, are precisely of the type required to stabilize JIMWLK evolution beyond leading logarithmicaccuracy. We compute the azimuthal harmonics of the NLO back-to-back distributions and show their sensitivity to both the unpolarized and linearly polarized WW gluon distributions. Finally, we discuss how TMD factorization is broken by an emergent saturation scale at small x.

Gluon dipole factorisation for diffractive dijets

Within the colour dipole picture for deep inelastic scattering at small Bjorken x, we study the production of a pair of relatively hard jets via coherent diffraction. By “relatively hard” we mean that the transverse momenta of the two jets — the quark (q) and the antiquark ( overline{q} ) generated by the decay of the virtual photon — are much larger than the target saturation momentum Qs(Yℙ) evaluated at the rapidity gap Yℙ. We argue that the typical final-state configurations are such that the hard qoverline{q} dijets are accompanied by a semi-hard gluon jet, with a transverse momentum of the order of Qs(Yℙ). The presence of this third jet ensures that the scattering is strong and thus avoids the strong suppression of exclusive (hard) dijet production due to colour transparency. For such “2+1” jet configurations, we demonstrate that both the emission of the semi-hard gluon and its scattering with the hadronic target can be factorised in terms of an effective gluon-gluon dipole. This effective description, originally proposed in [1–7], builds a bridge between the colour dipole picture and the transverse-momentum dependent (TMD) version of the collinear factorisation: the cross-section for diffractive 2+1 jets can be written as the product between a hard factor describing the qoverline{q} dijets and a semi-hard factor expressing the unintegrated gluon distribution of the Pomeron. The latter is controlled by gluon dipole scattering in the black disk limit and hence is strongly sensitive to gluon saturation. By integrating out the kinematics of the 3 jets, we obtain the qoverline{q}g contribution to the diffractive structure function in collinearly-factorised form.

Medium Effects for Hadron-Tagged Jets in Proton–Proton Collisions

We study the medium modification factor {{I}_{{pp}}} within the light-cone path integral approach to induced gluon emission. We use parametrization of the running coupling {{alpha }_{s}}(Q,T) which has a plateau around Q sim kappa T. We calculate {{I}_{{pp}}} with no free parameters using κ fitted to the LHC data on the nuclear modification factor {{R}_{{AA}}}. We find that the theoretical multiplicity dependence of the ratio {{I}_{{pp}}}{text{/}}langle {{I}_{{pp}}}rangle for 5.02 TeV pp collisions agrees reasonably with the recent preliminary ALICE data [1].

Role of initial gluon emission in double J/ψ production at central rapidities

We consider the process of double $J/\ensuremath{\psi}$ production in $pp$ collisions at the LHC in the framework of the ${k}_{T}$-factorization approach. We focus on the gluon fragmentation mechanism which is related to multiple gluon emission in the initial state. The initial state emission is treated according to Catani-Ciafaloni-Fiorani-Marchesini evolution equation, and applies to both single and double parton scattering cases. We show the importance of fragmentation contributions to $J/\ensuremath{\psi}$ pair production and perform a comparison between theoretical predictions and the latest ATLAS data collected at $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$. We find that the effects of multiple gluon emission are essential for both single- and multiparton interaction processes. Finally, we highlight the problem of correct choice of the factorization scale with respect to numerical stability of the calculations and the consistency with noncollinear evolution equations.