Soft Gluon Limit Research Articles

Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass

We present a direct lattice QCD calculation of the x-dependence of the pion distribution amplitude (DA), which is performed using the quasi-DA in large momentum effective theory on a domain-wall fermion ensemble at physical quark masses and spacing a ≈ 0.084 fm. The bare quais-DA matrix elements are renormalized in the hybrid scheme and matched to MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{MS}} $$\\end{document} with a subtraction of the leading renormalon in the Wilson-line mass. For the first time, we include threshold resummation in the perturbative matching onto the light-cone DA, which resums the large logarithms in the soft gluon limit at next-to-next-to-leading log. The resummed results show controlled scale-variation uncertainty within the range of momentum fraction x ∈ [0.25, 0.75] at the largest pion momentum Pz ≈ 1.85 GeV. In addition, we apply the same analysis to quasi-DAs from a highly-improved-staggered-quark ensemble at physical pion mass and a = 0.076 fm. By comparison we find with 2σ confidence level that the DA obtained from chiral fermions is flatter and lower near x = 0.5.

Ghost-gluon vertex in the presence of the Gribov horizon: General kinematics

Correlation functions are important probes for the behavior of quantum field theories. Already at tree-level, the refined Gribov-Zwanziger (RGZ) effective action for Yang-Mills theories provides a good approximation for the gluon propagator, as compared to that calculated by nonperturbative methods such as lattice field theory and Dyson-Schwinger equations. However, the study of higher correlation functions of the RGZ theory is still at its beginning. In this work we evaluate the ghost-gluon vertex function in Landau gauge at one-loop level, in d=4 space-time dimensions for the gauge groups SU(2) and SU(3). More precisely, we extend the analysis conducted in [1] for the soft-gluon limit to an arbitrary kinematic configuration. We introduce renormalization group effects by means of a toy model for the running coupling and investigate the impact of such a model in the ultraviolet tails of our results. We find that RGZ results match fairly closely those from lattice simulations, Schwinger-Dyson equations and the Curci-Ferrari model for three different kinematic configurations. This is compatible with RGZ being a feasible theory for the strong interaction in the infrared regime. Published by the American Physical Society 2024

Exploring smoking-gun signals of the Schwinger mechanism in QCD

In Quantum Chromodynamics, the Schwinger mechanism endows the gluons with an effective mass through the dynamical formation of massless bound-state poles that are longitudinally coupled. The presence of these poles affects profoundly the infrared properties of the interaction vertices, inducing crucial modifications to their fundamental Ward identities. Within this general framework, we present a detailed derivation of the non-Abelian Ward identity obeyed by the pole-free part of the three-gluon vertex in the soft-gluon limit, and determine the smoking-gun displacement that the onset of the Schwinger mechanism produces to the standard result. Quite importantly, the quantity that describes this distinctive feature coincides formally with the bound-state wave function that controls the massless pole formation. Consequently, this signal may be computed in two independent ways: by solving an approximate version of the pertinent Bethe-Salpeter integral equation, or by appropriately combining the elements that enter in the aforementioned Ward identity. For the implementation of both methods we employ two- and three-point correlation functions obtained from recent lattice simulations, and a partial derivative of the ghost-gluon kernel, which is computed from the corresponding Schwinger-Dyson equation. Our analysis reveals an excellent coincidence between the results obtained through either method, providing a highly nontrivial self-consistency check for the entire approach. When compared to the null hypothesis, where the Schwinger mechanism is assumed to be inactive, the statistical significance of the resulting signal is estimated to be 3 standard deviations.

Ghost dynamics in the soft gluon limit

We present a detailed study of the dynamics associated with the ghost sector of quenched QCD in the Landau gauge, where the relevant dynamical equations are supplemented with key inputs originating from large-volume lattice simulations. In particular, we solve the coupled system of Schwinger-Dyson equations that governs the evolution of the ghost dressing function and the ghost-gluon vertex, using as input for the gluon propagator lattice data that have been cured from volume and discretization artifacts. In addition, we explore the soft gluon limit of the same system, employing recent lattice data for the three-gluon vertex that enters in one of the diagrams defining the Schwinger-Dyson equation of the ghost-gluon vertex. The results obtained from the numerical treatment of these equations are in excellent agreement with lattice data for the ghost dressing function, once the latter have undergone the appropriate scale-setting and artifact elimination refinements. Moreover, the coincidence observed between the ghost-gluon vertex in general kinematics and in the soft gluon limit reveals an outstanding consistency of physical concepts and computational schemes.

Numerical resummation at subleading color in the strongly ordered soft gluon limit

We present a Monte Carlo approach to soft-gluon resummation at subleading color which can be used to improve existing parton shower algorithms. At the single-emission level, soft-collinear enhancements of the splitting functions are explicitly linked to quadratic Casimir operators, while wide angle single-soft enhancements are connected to nontrivial color correlators. We focus on a numerically stable implementation of color matrix element corrections to all orders and approximate the virtual corrections by requiring unitarity at the single-emission level. We provide a proof-of-concept implementation to compute nonglobal event shapes at lepton colliders.

Medium-induced cascade in expanding media

Detailed insight into the interplay between parton energy loss and the way deconfined medium created in heavy-ion collisions expands is of great importance for improving the understanding of the jet quenching phenomenon. In this paper we study the impact of the expansion of deconfined medium on the single-gluon emission spectrum, its resummation and the jet suppression factor (QAA) within the BDMPS-Z formalism. We calculate these quantities for three types of expansion scenarios, namely static, exponentially decaying and Bjorken expanding media. The distribution of medium-induced gluons is calculated using an evolution equation with splitting kernels derived from the gluon emission spectra. A universal behavior of splitting kernels is derived in the regime of soft gluon emissions when evaluated at a common effective evolution time τeff. Novel scaling features of the resulting gluon distribution and jet QAA are discussed. For realistic spectra valid beyond the soft-gluon emission limit, where the results are obtained by a numerical solution of the evolution equation, these features are partially replaced by a scaling expected from considering an averaged jet quenching parameter along the trajectory of propagation. Further we show that differences arising from different types of the medium expansion can be to a large extent scaled out by appropriate choice of the quenching parameter. Sizable differences among the values of the quenching parameter for different types of medium expansion point to the importance of the medium expansion for precise modeling of the jet quenching phenomenon.

The soft-gluon limit and the infrared enhancement of the quark-gluon vertex

The Schwinger–Dyson quark equation (SDE) combined with results from lattice simulation for the propagators are used to obtain information on the quark-gluon vertex, taking into account the recent full QCD lattice results for the soft-gluon limit. Its inclusion leads to a clear enhancement of the infrared quark-gluon vertex. We also find that the relative contribution of the quark-ghost kernel to the quark-gluon vertex in the infrared region does not follow the rules from the perturbative analysis of the ultraviolet region. This shows that for QCD the intuition based on perturbation theory does not apply to the full momentum range. The framework developed in the current work provides analytical expressions for all the longitudinal components of vertex taken into account.

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.

Medium-induced gluon emission via transverse and longitudinal scattering in dense nuclear matter

We study the medium-induced gluon emission from a hard quark jet traversing the dense nuclear matter within the framework of deep inelastic scattering off a large nucleus. We extend the previous work and compute the single gluon emission spectrum including both transverse and longitudinal momentum exchanges between the hard jet parton and the medium constituents. On the other hand, with only transverse scattering and using static scattering centers for the traversed medium, our induced gluon emission spectrum in the soft gluon limit reduces to the Gyulassy-Levai-Vitev one-rescattering-one-emission formula.

Exploring the quark-gluon vertex with Slavnov\u2013Taylor identities and lattice simulations

The soft gluon limit of the longitudinal part of the quark-gluon vertex is studied by resorting to non-perturbative approaches to quantum chromodynamics (QCD). Based on a Slavnov–Taylor identity (STI), the longitudinal form factors is expressed in terms of the quark-ghost kernel, the quark self energy and the quark wave function. An exact relation between the non-vanishing longitudinal form factors is derived for the soft gluon limit and explored to understand the behaviour of the vertex. Within a Ball–Chiu vertex, the form factor lambda _1 was analysed using recent lattice simulations for full QCD for the soft gluon limit. The lattice data shows that the gluon propagator resumes the momentum dependence of such component of the vertex. This connection is understood via a fully dressed one-loop Bethe–Salpeter equation. The behaviour of the remaining longitudinal form factors lambda _2(p^2) and lambda _3(p^2) is investigated combining both the information of lattice simulations and the derived relations based on the STI.

Lattice Landau Gauge Quark Propagator and the Quark--Gluon Vertex

We report preliminary results of our ongoing lattice computation of the Landau gauge quark propagator and the soft gluon limit of the quark-gluon vertex with 2 flavors of dynamical O(a) improved Wilson fermions.

On p ⊥-broadening of high energy partons associated with the LPM effect in a finite-volume QCD medium

We study the contributions from radiation to p ⊥-broadening of a high energy parton traversing a QCD medium with a finite length L. The interaction between the parton and the medium is described by decorrelated static multiple scattering. Amplitudes of medium-induced gluon emission and parton self-energy diagrams are evaluated in the soft gluon limit in the BDMPS formalism. We find both the double-logarithmic correction from incoherent scattering, which is parametrically the same as that in single scattering, and the logarithmic correction from the LPM effect. Therefore, we expect a parametrically large correction from radiation to the medium-induced p ⊥-broadening in perturbative QCD.

Analytical results forO(αs)radiative corrections toe+e−→tt¯↑up to a given gluon energy cut

We determine the O({alpha}{sub s}) radiative corrections to polarized top quark pair production in e{sup +}e{sup -} annihilations with a specified gluon energy cut. We write down fully analytical results for the unpolarized and polarized O({alpha}{sub s}) cross sections e{sup +}e{sup -}{yields}tt(G) and e{sup +}e{sup -}{yields}tt{sup {up_arrow}}(G) including their polar orientation dependence relative to the beam direction. In the soft-gluon limit we recover the usual factorizing form known from the soft-gluon approximation. In the limit when the gluon energy cut takes its maximum value we recover the totally inclusive unpolarized and polarized cross sections calculated previously. We provide some numerical results on the cutoff dependence of the various polarized and unpolarized cross sections and discuss how the exact results numerically differ from the approximate soft-gluon results.

Multigluon scattering in open superstring theory

We discuss the amplitudes describing $N$-gluon scattering in type I superstring theory, on a disk world sheet. After reviewing the general structure of amplitudes and the complications created by the presence of a large number of vertices at the boundary, we focus on the most promising case of maximally helicity violating (MHV) configurations because in this case, the zero Regge slope limit (${\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\rightarrow}0$) is particularly simple. We obtain the full-fledged MHV disk amplitudes for $N=4$, 5, and $N=6$ gluons, expressed in terms of one, two and six functions of kinematic invariants, respectively. These functions represent certain boundary integrals---generalized Euler integrals---which for $N\ensuremath{\ge}6$ correspond to multiple hypergeometric series (generalized Kamp\'e de F\'eriet functions). Their ${\ensuremath{\alpha}}^{\ensuremath{'}}$ expansions lead to Euler-Zagier sums. For arbitrary $N$, we show that the leading string corrections to the Yang-Mills amplitude, of order $\mathcal{O}({\ensuremath{\alpha}}^{\ensuremath{'}2})$, originate from the well-known ${\ensuremath{\alpha}}^{\ensuremath{'}2}\text{ }\mathrm{Tr}{F}^{4}$ effective interactions of four gauge field strength tensors. By using iteration based on the soft gluon limit, we derive a simple formula valid to that order for arbitrary $N$. We argue that such a procedure can be extended to all orders in ${\ensuremath{\alpha}}^{\ensuremath{'}}$. If nature gracefully picked a sufficiently low string mass scale, our results would be important for studying string effects in multijet production at the Large Hadron Collider (LHC).

Gluon interference effects intt¯production at the Next Linear Collider

We study the effects of gluon interference in the production and semi-leptonic decay of a t-tbar pair above threshold at the Next Linear Collider (NLC). We calculate all matrix elements to next-to-leading order and use the resulting expressions for the development of a Monte Carlo event generator. Our results show effects at the level of 10% in differential cross-sections. We thus extend previous results obtained by analytical means in the soft-gluon limit.

Covariant off-shell model for dynamical quark confinement

A model for quark propagation is developed in which quarks cannot go on-shell and thus are confined dynamically. The approach is based on a recently proposed time-ordered formulation of the relativistic many-body problem made manifestly covariant by an off-shell modification of Lorentz transformations. It is argued that the present off-shell formalism is better suited for studies of dynamical confinement since it provides a straightforward off-shell extension of the Dirac equation. In the usual Lorentz-covariant formulation, by contrast, spinor solutions do not exist for quarks which cannot go on-shell. Defining the quark propagator by a nonlinear time-ordered one-gluon-loop expansion, similar to a Dyson-Schwinger equation, an energy-dependent quark mass is determined by a nonlinear self-consistency condition. The corresponding time-ordered propagator is found to possess no poles for real energies, thus ensuring confinement. Evidence is given that it is analytic in the entire upper half of the complex energy plane as required by causality. In the model, the self-energy integral exists without regularization, with the convergence being provided by the chiral limit of the quark mass itself. The self-consistency condition exhibits the scaling behavior of the renormalization group and provides an eigenvalue condition for the low-energy value of the quark-gluon coupling constant. Its numerically determined value of g 2/4π= 4.712 can actually be derived in the soft-gluon limit as g 2/4π=3/2π. Implications of these findings and possible further applications are discussed.

Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross sections of multi-parton processes

We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method by calculating the singular part of the one-loop helicity amplitudes of all 2 → 3 parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all 2 → 4 parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporated in existing Monte Carlo simulation programs.

?Pure monojet? events at hadron colliders: supersymmetry or the standard model?

The matrix elements squared of processes\(q\bar q \to g\tilde \gamma \tilde \gamma , qg \to q\tilde \gamma \tilde \gamma \) are calculated and a factorization in the soft gluon limit is obtained. Three-body phase space corresponding to experimental cuts is analysed. It is shown that the detection of SUSY particles at the UNK and the SSC in “pure monojet” events, generated by these processes, is possible only in the case of a light scalar neutrino.

Radiative corrections to the effective W approximation

We derive the O( α s) corrections to the W and Z gauge boson distribution functions in the effective W approximation. The QCD radiative corrections are calculated in the soft gluon limit which correctly gives the terms of O( α s π). We compare the radiatively corrected rates for Higgs production from vector boson fusion and for the background from the q q → W + W − subprocess. In the soft gluon limit, the Higgs signal is unchanged by O( α s) corrections, while the calculation of Barger, Lopez, and Putikka finds that the background from q q → W + W − is increased by a factor of 1+ 8 9 α sπ .

Duality and multi-gluon scattering

For the six-gluon scattering process we give explicit and simple expressions for the amplitude and its square. To achieve this we use an analogy with string theories to identify a unique procedure for writing the multi-gluon scattering amplitudes in terms of a sum of gauge invariant dual sub-amplitudes multiplied by an appropriate color (Chan-Paton) factor. The sub-amplitudes defined in this way are invariant under cyclic permutations, satisfy powerful identities which relate different non-cyclic permutations and factorize in the soft gluon limit, the two-gluon collinear limit and on multi-gluon poles. Also, to leading order in the number of colors these sub-amplitudes sum incoherently in the square of the full matrix element. The results contained here are important for Monte Carlo studies of multi-processes at hadron colliders as well as for understanding the general structure of QCD.