Gluon Momentum Research Articles

Screening properties of quark-gluon plasma obtained from distribution and correlation functions of the constituent quasiparticle model

Based on the constituent quasiparticle model of quark-gluon plasma (QGP), the matrix elements of the density operator and the Wigner function in the color phase space are presented in form of color path integrals over Wiener and SU(3) group Haar measures. Monte Carlo calculations of quark and gluon momentum distributions and spatial pair distribution functions have been carried out for the strongly coupled QGP plasma in thermal equilibrium at zero baryon chemical potential. The Debye screening mass and the running coupling constant have been obtained from the spatial pair distribution function and are in agreement with the available lattice QCD data. At densities related to the average interparticle distance more than 0.4 fm the gluon bound states in the form of glueballs have been found. Comparison with the Maxwell Boltzmann distribution shows significant influence of interparticle interaction on high energy asymptotics of the momentum distribution functions, resulting in appearance of quantum tails. The new color pair correlation function has been introduced, and related new color screening mass has been discussed.

Parton energy loss and the generalized jet transport coefficient

We revisit radiative parton energy loss in deeply inelastic scattering (DIS) off a large nucleus within the perturbative QCD approach. We calculate the gluon radiation spectra induced by double parton scattering in DIS without collinear expansion in the transverse momentum of initial gluons as in the original high-twist approach. The final radiative gluon spectrum can be expressed in terms of the convolution of hard partonic parts and unintegrated or transverse momentum dependent (TMD) quark-gluon correlations. The TMD quark-gluon correlation can be factorized approximately as a product of initial quark distribution and TMD gluon distribution which can be used to define the generalized or TMD jet transport coefficient. Under the static scattering center and soft radiative gluon approximation, we recover the result by Gylassy-Levai-Vitev (GLV) in the first order of the opacity expansion. The difference as a result of the soft radiative gluon approximation is investigated numerically under the static scattering center approximation.

QCD evolution of the orbital angular momentum of quarks and gluons: Genuine twist-three part

We present the numerical solution of the one-loop QCD evolution equation for the genuine twist-three part of the orbital angular momentum (OAM) distributions of quarks and gluons inside a longitudinally polarized nucleon. This is based on the observation that the evolution is identical to that of the Efremov-Teryaev-Qiu-Sterman function for transverse single spin asymmetry. Together with the known evolution of the Wandzura-Wilczek part, the one-loop evolution of OAM distributions is now practically under control. We also study, for the first time, the scale dependence of the potential angular momentum defined as the difference between the Ji and Jaffe-Manohar definitions of OAM.

Longitudinal double-spin asymmetry for inclusive jet and dijet production in pp collisions at s=510 GeV

We report the first measurement of the inclusive jet and the dijet longitudinal double-spin asymmetries, $A_{LL}$, at midrapidity in polarized $pp$ collisions at a center-of-mass energy $\sqrt{s} = 510$ GeV. The inclusive jet $A_{LL}$ measurement is sensitive to the gluon helicity distribution down to a gluon momentum fraction of $x\approx 0.015$, while the dijet measurements, separated into four jet-pair topologies, provide constraints on the $x$ dependence of the gluon polarization. Both results are consistent with previous measurements made at $\sqrt{s}= 200$ GeV in the overlapping kinematic region, $x > 0.05$, and show good agreement with predictions from recent next-to-leading order global analyses.

The quark-gluon vertex and the QCD infrared dynamics

The Dyson–Schwinger quark equation is solved for the quark-gluon vertex using the most recent lattice data available in the Landau gauge for the quark, gluon and ghost propagators, the full set of longitudinal tensor structures in the Ball-Chiu vertex, taking into account a recently derived normalisation for a quark-ghost kernel form factors and the gluon contribution for the tree level quark-gluon vertex identified on a recent study of the lattice soft gluon limit. A solution for the inverse problem is computed after the Tikhonov linear regularisation of the integral equation, that implies solving a modified Dyson–Schwinger equation. We get longitudinal form factors that are strongly enhanced at the infrared region, deviate significantly from the tree level results for quark and gluon momentum below 2 GeV and at higher momentum approach their perturbative values. The computed quark-gluon vertex favours kinematical configurations where the quark momentum p and the gluon momentum q are small and parallel. Further, the quark-gluon vertex is dominated by the form factors associated to the tree level vertex gamma _mu and to the operator 2 , p_mu + q_mu . The higher rank tensor structures provide small contributions to the vertex.

QCD calculations of B \u2192 \u03c0, K form factors with higher-twist corrections

We update QCD calculations of B → π, K form factors at large hadronic recoil by including the subleading-power corrections from the higher-twist B-meson light-cone distribution amplitudes (LCDAs) up to the twist-six accuracy and the strange-quark mass effects at leading-power in Λ/mb from the twist-two B-meson LCDA ϕB+(ω, μ). The higher-twist corrections from both the two-particle and three-particle B-meson LCDAs are computed from the light-cone QCD sum rules (LCSR) at tree level. In particular, we construct the local duality model for the twist-five and -six B-meson LCDAs, in agreement with the corresponding asymptotic behaviours at small quark and gluon momenta, employing the method of QCD sum rules in heavy quark effective theory at leading order in αs. The strange quark mass effects in semileptonic B → K form factors yield the leading-power contribution in the heavy quark expansion, consistent with the power-counting analysis in soft-collinear effective theory, and they are also computed from the LCSR approach due to the appearance of the rapidity singularities. We demonstrate explicitly that the SU(3)-flavour symmetry breaking effects between B → π and B → K form factors, free of the power suppression in Λ/mb, are suppressed by a factor of {alpha}_sleft(sqrt{m_bLambda}right) in perturbative expansion, and they also respect the large-recoil symmetry relations of the heavy-to-light form factors at least at one-loop accuracy. An exploratory analysis of the obtained sum rules for B → π, K form factors with two distinct models for the B-meson LCDAs indicates that the dominant higher-twist corrections are from the Wandzura-Wilczek part of the two-particle LCDA of twist five gB−(ω, μ) instead of the three-particle B-meson LCDAs. The resulting SU(3)-flavour symmetry violation effects of B → π, K form factors turn out to be insensitive to the non-perturbative models of B-meson LCDAs. We further explore the phenomenological aspects of the semileptonic B → πℓν decays and the rare exclusive processes B → Kνν, including the determination of the CKM matrix element |Vub|, the normalized differential q2 distributions and precision observables defined by the ratios of branching fractions for the above-mentioned two channels in the same intervals of q2.

Transverse-Momentum-Dependent Distributions with Jets.

We investigate the use of jets to measure transverse-momentum-dependent distributions (TMDs). The example we use to present our framework is the dijet momentum decorrelation at lepton colliders. Translating this momentum decorrelation into an angle θ≪1, we analyze the factorization of the cross section for the cases θ≫R, θ∼R, and θ≪R, where R is the jet radius. Critically, for the winner-take-all axis, the jet TMD has the same double-scale renormalization group evolution as TMD fragmentation functions for all radii R. TMD fragmentation functions in factorization theorems may then simply be replaced by the jet TMDs we calculate, and all ingredients to perform the resummation to next-to-next-to-leading logarithmic accuracy are available. Our approach also applies to semi-inclusive deep inelastic scattering, where a jet instead of a hadron is measured in the final state, and we find a clean method to probe the intrinsic transverse momentum of quarks and gluons in the proton that is less sensitive to final-state nonperturbative effects.

Ghost-gluon vertex in the presence of the Gribov horizon

We consider Yang-Mills theories quantized in the Landau gauge in the presence of the Gribov horizon via the refined Gribov-Zwanziger (RGZ) framework. As the restriction of the gauge path integral to the Gribov region is taken into account, the resulting gauge field propagators display a nontrivial infrared behavior, being very close to the ones observed in lattice gauge field theory simulations. In this work, we explore a higher correlation function in the refined Gribov-Zwanziger theory: the ghost-gluon interaction vertex, at one-loop level. We show explicit compatibility with kinematical constraints, as required by the Ward identities of the theory, and obtain analytical expressions in the limit of vanishing gluon momentum. We find that the RGZ results are nontrivial in the infrared regime, being compatible with lattice Yang-Mills simulations in both SU(2) and SU(3), as well as with solutions from Schwinger-Dyson equations in different truncation schemes, Functional Renormalization Group analysis, and the renormalization group-improved Curci-Ferrari model.

Nucleon Spin and Momentum Decomposition Using Lattice QCD Simulations.

We determine within lattice QCD the nucleon spin carried by valence and sea quarks and gluons. The calculation is performed using an ensemble of gauge configurations with two degenerate light quarks with mass fixed to approximately reproduce the physical pion mass. We find that the total angular momentum carried by the quarks in the nucleon is J_{u+d+s}=0.408(61)_{stat}(48)_{syst} and the gluon contribution is J_{g}=0.133(11)_{stat}(14)_{syst}, giving a total of J_{N}=0.54(6)_{stat}(5)_{syst} that is consistent with the spin sum. For the quark intrinsic spin contribution, we obtain 1/2ΔΣ_{u+d+s}=0.201(17)_{stat}(5)_{syst}. All quantities are given in the modified minimal subtraction scheme at 2GeV. The quark and gluon momentum fractions are also computed and add up to ⟨x⟩_{u+d+s}+⟨x⟩_{g}=0.804(121)_{stat}(95)_{syst}+0.267(12)_{stat}(10)_{syst}=1.07(12)_{stat}(10)_{syst}, thus satisfying the momentum sum.

Gluon momentum fraction of the nucleon from lattice QCD

We perform a direct calculation of the gluon momentum fraction of the nucleon using maximally twisted mass fermion ensembles with $N_f=2+1+1$ flavors at a pion mass of about $370\,\mathrm{MeV}$ and a lattice spacing of $a\approx 0.082\,\mathrm{fm}$ and with $N_f=2$ flavors at the physical pion mass and a lattice spacing of $a\approx 0.093\,\mathrm{fm}$. In the definition of the gluon operator we employ stout smearing to obtain a statistically significant result for the bare matrix elements. In addition, we perform a lattice perturbative calculation including 2 levels of stout smearing to carry out the mixing and the renormalization of the quark and gluon operators. We find, after conversion to the $\overline{\mathrm{MS}}$ scheme at a scale of $2\,\mathrm{GeV}$: $\langle x\rangle^R_g {=} 0.284(23)(23)$ for pion mass of about $370\,\mathrm{MeV}$ and $\langle x\rangle^R_g {=} 0.283(23)(15)$ for the physical pion mass.

Impact of momentum anisotropy and turbulent chromo-fields on thermal particle production in quark\u2013gluon-plasma medium

Momentum anisotropy present during the hydrodynamic evolution of the Quark–Gluon Plasma (QGP) in RHIC may lead to the chromo-Weibel instability and turbulent chromo-fields.The dynamics of the quark and gluon momentum distributions in this case is governed by an effective diffusive Vlasov equation (linearized). The solution of this linearized transport equation for the modified momentum distribution functions lead to the mathematical form of non-equilibrium momentum distribution functions of quarks/antiquarks and gluons. The modifications to these distributions encode the physics of turbulent color fields and momentum anisotropy. In the present manuscript, we employ these distribution functions to estimate the thermal dilepton production rate in the QGP medium. The production rate is seen to have appreciable sensitivity to the strength of the anisotropy.

Feasibility Studies for Single Transverse-Spin Asymmetry Measurements at a Fixed-Target Experiment Using the LHC Proton and Lead Beams (AFTER@LHC)

The measurement of Single Transverse-Spin Asymmetries, A_N, for various quarkonium states and Drell–Yan lepton pairs can shed light on the orbital angular momentum of quarks and gluons, a fundamental ingredient of the proton-spin puzzle. The AFTER@LHC proposal combines a unique kinematic coverage and large luminosities thanks to the Large Hadron Collider beams to deliver precise measurements, complementary to the knowledge provided by collider experiments such as at RHIC. In this paper, we report on sensitivity studies for J/psi , varUpsilon and Drell–Yan A_N done using the performance of LHCb-like or ALICE-like detectors, combined with polarised gaseous hydrogen and helium-3 targets. In particular, such analyses will provide us with new insights and knowledge about transverse-momentum-dependent parton distribution functions for quarks and gluons and on twist-3 collinear matrix elements in the proton and the neutron.

Wilson lines, Grassmannians and gauge invariant off-shell amplitudes in mathcal{N}=4 SYM

In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in mathcal{N}=4 SYM. For the off-shell amplitudes with one leg off-shell we present a conjecture for their Grassmannian integral representation in spinor helicity, twistor and momentum twistor parameterizations. The presented conjecture is successfully checked against BCFW results for MHVn, NMHV4 and NMHV5 off-shell amplitudes. We have also verified that our Grassmannian integral representation correctly reproduces soft (on-shell) limit for the off-shell gluon momentum. It is shown that the (deformed) off-shell amplitude expressions could be also obtained using quantum inverse scattering method for auxiliary mathfrak{g}mathfrak{l}left(4Big|4right) super spin chain.

Contribution of orbital angular momentum to the nucleon spin

We have calculated the orbital angular momentum of quarks and gluons in the nucleon. The calculations are carried out in the next to leading order utilizing the so-called valon model. It is found that the average quark orbital angular momentum is positive, but small, and the average gluon orbital angular momentum is negative and large. We also report on some regularities about the total angular momentum of the quarks and the gluon, as well as on the orbital angular momentum of the separate partons. We have also provided partonic angular momentum, [Formula: see text] as a function of [Formula: see text].

Zero-momentum correlator in SU(2) Landau gauge gluodynamics under various boundary conditions

We make new simulations of S U (2) zero spatial momentum (ZM) gluon correlator in Landau gauge gluodynamics paying special attention to possible lattice artefacts and Gribov copy effect. In particular we started investigation of the correlator dependence on the choice of boundary conditions (BCs) by comparing results for periodic and zerofield (ZF) boundary conditions at various β values. Time behaviour of the ZM correlator for ZF BCs corresponds to approximately constant in time effective gluon mass thus providing additional evidence in favour of decoupling behaviour of momentum-dependent gluon propagator in the IR region. We have found that at fixed lattice sizes and β values the ZM gluon correlator and effective gluon mass for periodic and ZF boundary conditions can differ considerably.

Quark and Gluon Orbital Angular Momentum: Where Are We?

The orbital angular momentum of quarks and gluons contributes significantly to the proton spin budget and attracted a lot of attention in the recent years, both theoretically and experimentally. We summarize the various definitions of parton orbital angular momentum together with their relations with parton distributions functions. In particular, we highlight current theoretical puzzles and give some prospects.

Inclusive cross section and double-helicity asymmetry forπ0production at midrapidity inp+pcollisions ats=510 GeV

PHENIX measurements are presented for the cross section and double-helicity asymmetry ($A_{LL}$) in inclusive $\pi^0$ production at midrapidity from $p$$+$$p$ collisions at $\sqrt{s}=510$~GeV from data taken in 2012 and 2013 at the Relativistic Heavy Ion Collider. The next-to-leading-order perturbative-quantum-chromodynamics theory calculation is in excellent agreement with the presented cross section results. The calculation utilized parton-to-pion fragmentation functions from the recent DSS14 global analysis, which prefer a smaller gluon-to-pion fragmentation function. The $\pi^{0}A_{LL}$ results follow an increasingly positive asymmetry trend with $p_T$ and $\sqrt{s}$ with respect to the predictions and are in excellent agreement with the latest global analysis results. This analysis incorporated earlier results on $\pi^0$ and jet $A_{LL}$, and suggested a positive contribution of gluon polarization to the spin of the proton $\Delta G$ for the gluon momentum fraction range $x>0.05$. The data presented here extend to a currently unexplored region, down to $x\sim0.01$, and thus provide additional constraints on the value of $\Delta G$. The results confirm the evidence for nonzero $\Delta G$ using a different production channel in a complementary kinematic region.

Lattice QCD Green’s functions in maximally Abelian gauge: Infrared Abelian dominance and the quark sector

On lattice gauge field configurations with 2+1 dynamical quark flavors, we investigate the momentum space quark and gluon propagators in the combined maximally Abelian plus $U(1)_3\times U(1)_8$ Landau gauge. We extract the gluon fields from the lattice link variables and study the diagonal and off-diagonal gluon propagators. We find that the infrared region of the transverse diagonal gluon propagator is strongly enhanced compared to the off-diagonal propagator. The Dirac operator from the Asqtad action is inverted on the diagonal and off-diagonal gluon backgrounds separately. In agreement with the hypothesis of infrared Abelian dominance, we find that the off-diagonal gluon background hardly gives rise to any non-trivial quark dynamics while the quark propagator from the diagonal gluon background closely resembles its Landau gauge counterpart.

Hard Exclusive Meson Production at COMPASS

The concept of Generalized Parton Distributions (GPDs) combines two-dimensional spatial information given by form factors, with longitudinal momentum information from Parton Distribution Functions. GPDs provide comprehensive description of the nucleon structure involving a wealth of new information. For instance, according to Ji’s sum rule, the GPDs [Formula: see text] and [Formula: see text] enable access to the total angular momenta of quarks, antiquarks and gluons. While [Formula: see text] can be approached using measurements of electroproduction cross sections, asymmetry measurements in hard exclusive meson production off transversely polarized targets can help to constrain the GPD [Formula: see text] and chiral-odd GPDs. In 2007 and 2010 the COMPASS experiment at CERN collected data by scattering a [Formula: see text] muon beam off a transversely polarized NH3 target. Exclusive vector-meson production [Formula: see text] with a [Formula: see text] or [Formula: see text] meson in the final state is studied and five single-spin and three double-spin azimuthal asymmetries are measured.

Gauge Invariance, Lorentz Covariance and Canonical Quantization in Nucleon Structure Studies

There are different operators of quark and gluon momenta, orbital angular momenta, and gluon spin in the nucleon structure study. The precise meaning of these operators are studied based on gauge invariance, Lorentz covariance and canonical quantization rule. The advantage and disadvantage of different definitions are analyzed. A gauge invariant canonical decomposition of the total momentum and angular momentum into quark and gluon parts is suggested based on the decomposition of the gauge potential into gauge invariant (covariant) physical part and gauge dependent pure gauge part. Challenges to this proposal are answered. \keywords{Physical and pure gauge potentials; Gauge invariant canonical quark and gluon momenta, orbital angular momenta and spins; Homogeneous and non-homogeneous Lorentz transformations; Gauge invariant decomposition and gauge invariant extension; Classical and quantum measurements.