Wilson Line Correlators Research Articles

Multiparton Cwebs at five loops

Scattering amplitudes involving multiple partons are plagued with infrared singularities. The soft singularities of the amplitude are captured by the soft function which is defined as the vacuum expectation value of Wilson line correlators. Renormalization properties of soft function allows us to write it as an exponential of the finite soft anomalous dimension. An efficient way to study the soft function is through a set of Feynman diagrams known as Cwebs (webs). We present the mixing matrices and exponentiated colour factors (ECFs) for the Cwebs at five loops that connect six Wilson lines, except those that are related by relabeling of Wilson lines. Further, we express these ECFs in terms of 29 basis colour factors. We also find that this basis can be categorized into two colour structures. Our results are the first key ingredients for the calculation of the soft anomalous dimension at five loops.

T-matrix analysis of static Wilson line correlators from lattice QCD at finite temperature

T-matrix analysis of static Wilson line correlators from lattice QCD at finite temperature

Analysis of static Wilson line correlators from lattice QCD at finite temperature with T-matrix approach

The thermodynamic T-matrix approach is used to study Wilson line correlators (WLCs) for a static quark-antiquark pair in the quark-gluon plasma (QGP). Selfconsistent results that incorporate constraints from the QGP equation of state can approximately reproduce WLCs computed in 2+1-flavor lattice-QCD (lQCD), provided the input potential exhibits less screening than in previous studies. Utilizing the updated potential to calculate pertinent heavylight T-matrices we evaluate thermal relaxation rates of heavy quarks in the QGP. We find a more pronounced temperature dependence for low-momentum quarks than in our previous results (with larger screening), which turns into a weaker temperature dependence of the (temperature-scaled) spatial diffusion coefficient, in fair agreement with the most recent lQCD data.

Small x physics beyond eikonal approximation: an effective Hamiltonian approach

Understanding the spin structure of hadrons in the small x regime is an important direction to unravel the spin puzzle in hadronic physics. To include spin degrees of freedom in the small x regime requires going beyond the usual eikonal approximation in high energy QCD. We developed an effective Hamiltonian approach to study spin related observables in the small x regime using the shockwave formalism. The small-x effective Hamiltonian incorporates both quark and gluon propagators in the background fields and the background field induced interaction vertices up to next-to-eikonal order. A novel feature of sub-eikonal interactions is the background gluon field induced gluon radiation inside the shockwave. Its relation to chromo-electrically polarized Wilson line correlator is established both in small x helicity evolution and in longitudinal double-spin asymmetry for gluon production.

$T\bar{T}$ in JT Gravity and BF Gauge Theory

JT gravity has a first-order formulation as a two-dimensional BF theory, which can be viewed as the dimensional reduction of the Chern-Simons description of 3d3d gravity. We consider {T\overbar{T}}TT¯-type deformations of the (0+1)(0+1)-dimensional dual to this 2d2d BF theory and interpret the deformation as a modification of the BF theory boundary conditions. The fundamental observables in this deformed BF theory, and in its 3d3d Chern-Simons lift, are Wilson lines and loops. In the 3d3d Chern-Simons setting, we study modifications to correlators involving boundary-anchored Wilson lines which are induced by a {T\overbar{T}}TT¯ deformation on the 2d2d boundary; results are presented at both the classical level (using modified boundary conditions) and the quantum-mechanical level (using conformal perturbation theory). Finally, we calculate the analogous deformed Wilson line correlators in 2d2d BF theory below the Hagedorn temperature where the principal series dominates over the discrete series.

Static quark-antiquark interactions at nonzero temperature from lattice QCD

We study the interactions of a static quark-antiquark pair at nonzero temperature using realistic $2+1$ flavor lattice QCD calculations. The study consists of two parts. The first investigates the properties of Wilson line correlators in Coulomb gauge and compares to predictions of hard-thermal loop perturbation theory. As a second step we extract the spectral functions underlying the correlators using four conceptually different methods: spectral function fits, a hard-thermal-loop-inspired fit for the correlation function, Pad\'e rational approximation and the Bayesian reconstruction. We find that our high-statistics Euclidean lattice data are amenable to different hypotheses for the shapes of the spectral function and we compare the implications of each analysis method for the existence and properties of a well-defined ground state spectral peak.

Static quark anti-quark interactions at non-zero temperature from lattice QCD

We present results on the in-medium interactions of static quark antiquark pairs using realistic 2+1 HISQ flavor lattice QCD. Focus is put on the extraction of spectral information from Wilson line correlators in Coulomb gauge using four complementary methods. Our results indicate that on HISQ lattices, the position of the dominant spectral peak associated with the real-part of the interquark potential remains unaffected by temperature. This is in contrast to prior work in quenched QCD and we present follow up comparisons to newly generated quenched ensembles.

Wilson line correlators beyond the large-Nc

We study hard 1 → 2 final-state parton splittings in the medium, and put special emphasis on calculating the Wilson line correlators that appear in these calculations. As partons go through the medium their color continuously rotates, an effect that is encapsulated in a Wilson line along their trajectory. When calculating observables, one typically has to calculate traces of two or more medium-averaged Wilson lines. These are usually dealt with in the literature by invoking the large-Nc limit, but exact calculations have been lacking in many cases. In our work, we show how correlators of multiple Wilson lines appear, and develop a method to calculate them numerically to all orders in Nc. Initially, we focus on the trace of four Wilson lines, which we develop a differential equation for. We will then generalize this calculation to a product of an arbitrary number of Wilson lines, and show how to do the exact calculation numerically, and even analytically in the large-Nc limit. Color sub-leading corrections, that are suppressed with a factor {N}_c^{-2} relative to the leading scaling, are calculated explicitly for the four-point correlator and we discuss how to extend this method to the general case. These results are relevant for high-pT jet processes and initial stage physics at the LHC.

Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate

We compute the next-to-leading order impact factor for inclusive dijet production in deeply inelastic electron-nucleus scattering at small xBj. Our computation, performed in the framework of the Color Glass Condensate effective field theory, includes all real and virtual contributions in the gluon shock wave background of all-twist lightlike Wilson line correlators. We demonstrate explicitly that the rapidity evolution of these correlators, to leading logarithmic accuracy, is described by the JIMWLK Hamiltonian. When combined with the next-to-leading order JIMWLK Hamiltonian, our results for the impact factor improve the accuracy of the inclusive dijet cross-section to mathcal{O} ( {alpha}_s^2 ln(xf/xBj)), where xf is a rapidity factorization scale. These results are an essential ingredient in assessing the discovery potential of inclusive dijets to uncover the physics of gluon saturation at the Electron-Ion Collider.

NLO impact factor for inclusive photon+dijet production in e+A DIS at small x

We compute the next-to-leading order (NLO) impact factor for inclusive photon $+$dijet production in electron-nucleus (e+A) deeply inelastic scattering (DIS) at small $x$. An important ingredient in our computation is the simple structure of ``shock wave" fermion and gluon propagators. This allows one to employ standard momentum space Feynman diagram techniques for higher order computations in the Regge limit of fixed $Q^2\gg \Lambda_{\rm QCD}^2$ and $x\rightarrow 0$. Our computations in the Color Glass Condensate (CGC) effective field theory include the resummation of all-twist power corrections $Q_s^2/Q^2$, where $Q_s$ is the saturation scale in the nucleus. We discuss the structure of ultraviolet, collinear and soft divergences in the CGC, and extract the leading logs in $x$; the structure of the corresponding rapidity divergences gives a nontrivial first principles derivation of the JIMWLK renormalization group evolution equation for multiparton lightlike Wilson line correlators. Explicit expressions are given for the $x$-independent $O(\alpha_s)$ contributions that constitute the NLO impact factor. These results, combined with extant results on NLO JIMWLK evolution, provide the ingredients to compute the inclusive photon $+$ dijet cross-section at small $x$ to $O(\alpha_s^3 \ln(x))$. First results for the NLO impact factor in inclusive dijet production are recovered in the soft photon limit. A byproduct of our computation is the LO photon+ 3 jet (quark-antiquark-gluon) cross-section.

Relating amplitude and PDF factorisation through Wilson-line geometries

We study long-distance singularities governing different physical quantities involving massless partons in perturbative QCD by using factorisation in terms of Wilson-line correlators. By isolating the process-independent hard-collinear singularities from quark and gluon form factors, and identifying these with the ones governing the elastic limit of the perturbative Parton Distribution Functions (PDFs) — δ(1 − x) in the large-x limit of DGLAP splitting functions — we extract the anomalous dimension controlling soft sin- gularities of the PDFs, verifying that it admits Casimir scaling. We then perform an independent diagrammatic computation of the latter using its definition in terms of Wil- son lines, confirming explicitly the above result through two loops. By comparing our eikonal PDF calculation to that of the eikonal form factor by Erdogan and Sterman and the classical computation of the closed parallelogram by Korchemsky and Korchemskaya, a consistent picture emerges whereby all singularities emerge in diagrammatic configurations localised at the cusps or along lightlike lines, but where distinct contributions to the anomalous dimensions are associated with finite (closed) lightlike segments as compared to infinite (open) ones. Both are relevant for resumming large logarithms in physical quantities, notably the anomalous dimension controlling Drell-Yan or Higgs production near threshold on the one hand, and the gluon Regge trajectory controlling the high-energy limit of partonic scattering on the other.

Small- x evolution of 2n -tuple Wilson line correlator revisited: The nonsingular kernels

JIMWLK equation tells how gauge invariant higher order Wilson line correlators would evolve at high energy. In this article we present a convenient integro-differential form of this equation, for 2n-tuple correlator, where all real and virtual terms are explicit. The `real' terms correspond to splitting (say at position z) of this 2n-tuple correlator to various pairs of 2m-tuple and (2n+2-2m)-tuple correlators whereas `virtual' terms correspond to splitting into pairs of 2m-tuple and (2n-2m)-tuple correlators. Kernels of virtual terms with m=0 (no splitting) and of real terms with m=1 (splitting with atleast one dipole) have poles and when integrated over z they do generate ultraviolet logarithmic divergences, separately for real and virtual terms. Except these two cases in all other terms the corresponding kernels, separately for real and virtual terms, have rather soften ultraviolet singularity and when integrated over z do not generate ultraviolet logarithmic divergences. We went on to study the solution of the JIMWLK equation for the 2n-tuple Wilson line correlator in the strong scattering regime where all transverse distances are much larger than inverse saturation momentum and shown that it also exhibits geometric scaling like color dipole deep inside saturation region.

Realistic in-medium heavy-quark potential from high statistics lattice QCD simulations

We present our first results on a direct computation of the complex in-medium heavy quark potential from realistic lattice QCD simulations. Ensembles with Nτ = 12 from the HotQCD and TUMQCD collaboration offer unprecedented high statistics, those with Nτ = 16 unprecedented time resolution, making possible a robust extraction of the real part from the spectral functions of Wilson line correlators. To this end we deploy a combination of a Bayesian reconstruction (BR method), as well as a Padé-like approximation. We corroborate findings made on less realistic lattices that Re[V] smoothly transitions from a confining to a screened behavior at high temperatures and its values lie close to the color singlet free energies. A finite value of the Im[V] is observed in the quark-gluon-plasma phase.

The Schwarzian theory \u2014 a Wilson line perspective

We provide a holographic perspective on correlation functions in Schwarzian quantum mechanics, as boundary-anchored Wilson line correlators in Jackiw-Teitelboim gravity. We first study compact groups and identify the diagrammatic representation of bilocal correlators of the particle-on-a-group model as Wilson line correlators in its 2d holographic BF description. We generalize to the Hamiltonian reduction of SL+(2, ℝ) and derive the Schwarzian correlation functions. Out-of-time ordered correlators are determined by crossing Wilson lines, giving a 6j-symbol, in agreement with 2d CFT results.

Inclusive prompt photon production in electron-nucleus scattering at small x

We compute the differential cross-section for inclusive prompt photon production in deeply inelastic scattering (DIS) of electrons on nuclei at small x in the framework of the Color Glass Condensate (CGC) effective theory. The leading order (LO) computation in this framework resums leading logarithms in x as well as power corrections to all orders in Qs, A2/Q2, where Qs,A(x) is the nuclear saturation scale. This LO result is proportional to universal dipole and quadrupole Wilson line correlators in the nucleus. In the soft photon limit, the Low-Burnett-Kroll theorem allows us to recover existing results on inclusive DIS dijet production. The k⊥ and collinearly factorized expressions for prompt photon production in DIS are also recovered in a leading twist approximation to our result. In the latter case, our result corresponds to the dominant next-to-leading order (NLO) perturbative QCD contribution at small x. We next discuss the computation of the NLO corrections to inclusive prompt photon production in the CGC framework. In particular, we emphasize the advantages for higher order computations in inclusive photon production, and for fully inclusive DIS, arising from the simple momentum space structure of the dressed quark and gluon “shock wave” propagators in the “wrong” light cone gauge A− = 0 for a nucleus moving with PN+ → ∞.

Inclusive Prompt Photons from the Color Glass Condensate at NLO

The cross-section for photons radiated by quarks in proton-nucleus collisions at collider energies was obtained using the Color Glass Condensate framework, in the dense-dilute kinematics regime. We observe that the inclusive photon cross-section is proportional to all-twist Wilson line correlators in the nucleus. These correlators also appear in quark-pair production; unlike the latter, photon production is insensitive to hadronization uncertainties and therefore more sensitive to multi-parton correlations in the gluon saturation regime of QCD.

Parton model description of multiparticle azimuthal correlations in pA collisions

In arXiv:1705.00745, an initial state "parton model" of quarks scattering off a dense nuclear target was shown to qualitatively reproduce the systematics of multiparticle azimuthal anisotropy cumulants measured in proton/deuteron-nucleus ($pA$) collisions at RHIC and the LHC. The systematics included i) the behavior of the four-particle cumulant $c_2\{4\}$, which generates a real four-particle second Fourier harmonic $v_2\{4\}$, ii) the ordering $v_2\{2\}>v_2\{4\}\approx v_2\{6\}\approx v_2\{8\}$ for two-, four-, six-, and eight-particle Fourier harmonics, iii) the behavior of so-called symmetric cumulants $\text{SC}(2,3)$ and $\text{SC}(2,4)$. These features of azimuthal multiparticle cumulants were previously interpreted as a signature of hydrodynamic flow; our results challenge this interpretation. We expand here upon our previous study and present further details and novel results on the saturation scale and transverse momentum ($p_\perp$) dependence of multiparticle azimuthal correlations. We find that the dependence of $v_2\{2\}$ and $v_2\{4\}$ on the number of color domains in the target varies with the $p_\perp$ window explored. We extend our prior discussion of symmetric cumulants and compute as yet unmeasured symmetric cumulants. We investigate the $N_c$ dependence of $v_2\{2\}$ and $v_2\{4\}$. We contrast our results, which include multiple scatterings of each quark off the target, to the Glasma graph approximation, where each quark suffers at most two gluon exchanges with the target. We find that coherent multiple scattering is essential to obtain a positive definite $v_2\{4\}$. We provide an algorithm to compute expectation values of arbitrary products of the "dipole" lightlike Wilson line correlators.

Linearly polarized small- x gluons in forward heavy-quark pair production

We use the Color Glass Condensate (CGC) framework to study the production of forward heavy quark-antiquark pairs in unpolarized proton-nucleus or proton-proton collisions in the small-x regime. In the limit of nearly back-to-back jets, the CGC result simplifies into the transverse-momentum dependent (TMD) factorization approach. For massless quarks, the TMD factorization formula involves three unpolarized gluon TMDs: the Weizs\"{a}cker-Williams gluon distribution, the adjoint-dipole gluon distribution, and an additional one. When quark masses are kept non-zero, three new gluon TMDs appear -- each partnered to one of the aforementioned distributions -- which describe the distribution of linearly-polarized gluons in the unpolarized small-x target. We show how these six gluon TMDs emerge from the CGC formulation and we determine their expressions in terms of Wilson line correlators. We calculate them analytically in the McLerran-Venugopalan model, and further evolve them towards smaller values of x using a numerical implementation of JIMWLK evolution.

General formulae for dipole Wilson line correlators with the Color Glass Condensate

We present general formulae to compute Wilson line correlators with the Color Glass Condensate described by the McLerran-Venugopalan model. We explicitly construct a complete and non-orthogonal set of color-singlet bases and write matrix elements down, so that the exponential of the matrix leads to the Wilson line correlators. We further develop a systematic perturbative expansion of dipole Wilson line correlators in terms of 1/Nc where Nc is the color number. As a phenomenological application we calculate the flow harmonics vn{m} in the dipole model and discuss the Nc scaling.

Probing gluon saturation with next-to-leading order photon production at central rapidities in proton-nucleus collisions

We compute the cross section for photons emitted from sea quarks in proton-nucleus collisions at collider energies. The computation is performed within the dilute-dense kinematics of the Color Glass Condensate (CGC) effective field theory. Albeit the result obtained is formally at next-to-leading order in the CGC power counting, it provides the dominant contribution for central rapidities. We observe that the inclusive photon cross section is proportional to all-twist Wilson line correlators in the nucleus. These correlators also appear in quark-pair production; unlike the latter, photon production is insensitive to hadronization uncertainties and therefore more sensitive to multi-parton correlations in the gluon saturation regime of QCD. We demonstrate that k⊥ and collinear factorized expressions for inclusive photon production are obtained as leading twist approximations to our result. In particular, the collinearly factorized expression is directly sensitive to the nuclear gluon distribution at small x. Other results of interest include the realization of the Low-Burnett-Kroll soft photon theorem in the CGC framework and a comparative study of how the photon amplitude is obtained in Lorenz and light-cone gauges.