Soft gluon fields and anomalous magnetic moment of muon

An impact of nonperturbatively treated soft gluon modes on the value of anomalous magnetic moment of muon a_µ is studied within the mean-field approach to QCD vacuum and hadronization. It is shown that radial excitations of vector mesons strongly enhance contribution of hadronic vacuum polarization to a_µ, doubling the contribution of one-meson processes compared to the result for ground state mesons. The mean field also strongly influences the hadronic light-by-light scattering contribution due to the Wilson line in quark propagators.

Higher order RG flow on the Wilson line in $$ \mathcal{N} $$ = 4 SYM

Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling ζ in a generalized Wilson loop operator of the $$ \mathcal{N} $$ N = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for ζ has fixed points at ζ = ±1 and ζ = 0, corresponding respectively to the supersymmetric Wilson-Maldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. We also find a subset of higher-loop contributions (with highest powers of ζ at each order in ‘t Hooft coupling λ) coming from the scalar ladder graphs determining the corresponding terms in the five-loop beta-function. We discuss the related structure of the circular Wilson loop expectation value commenting, in particular, on consistency with a 1d defect version of the F-theorem. We also compute (to two loops in the planar ladder model approximation) the two-point correlators of scalars inserted on the Wilson line.

Boomerang webs up to three-loop order

Webs are sets of Feynman diagrams which manifest soft gluon exponentiation in gauge theory scattering amplitudes: individual webs contribute to the logarithm of the amplitude and their ultraviolet renormalization encodes its infrared structure. In this paper, we consider the particular class of boomerang webs, consisting of multiple gluon exchanges, but where at least one gluon has both of its endpoints on the same Wilson line. First, we use the replica trick to prove that diagrams involving self-energy insertions along the Wilson line do not contribute to the web, i.e. their exponentiated colour factor vanishes. Consequently boomerang webs effectively involve only integrals where boomerang gluons straddle one or more gluons that connect to other Wilson lines. Next we classify and calculate all boomerang webs involving semi-infinite non-lightlike Wilson lines up to three-loop order, including a detailed discussion of how to regulate and renormalize them. Furthermore, we show that they can be written using a basis of specific harmonic polylogarithms, that has been conjectured to be sufficient for expressing all multiple gluon exchange webs. However, boomerang webs differ from other gluon-exchange webs by featuring a lower and non-uniform transcendental weight. We cross-check our results by showing how certain boomerang webs can be determined by the so-called collinear reduction of previously calculated webs. Our results are a necessary ingredient of the soft anomalous dimension for non-lightlike Wilson lines at three loops.

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 $$ \mathcal{O} $$ O ($$ {\alpha}_s^2 $$ α 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.

Towards high-precision parton distributions from lattice QCD via distillation

We apply the Distillation spatial smearing program to the extraction of the unpolarized isovector valence PDF of the nucleon. The improved volume sampling and control of excited-states afforded by distillation leads to a dramatically improved determination of the requisite Ioffe-time Pseudo-distribution (pITD). The impact of higher-twist effects is subsequently explored by extending the Wilson line length present in our non-local operators to one half the spatial extent of the lattice ensemble considered. The valence PDF is extracted by analyzing both the matched Ioffe-time Distribution (ITD), as well as a direct matching of the pITD to the PDF. Through development of a novel prescription to obtain the PDF from the pITD, we establish a concerning deviation of the pITD from the expected DGLAP evolution of the pseudo-PDF. The presence of DGLAP evolution is observed once more following introduction of a discretization term into the PDF extractions. Observance and correction of this discrepancy further highlights the utility of distillation in such structure studies.

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 $$ {N}_c^{-2} $$ 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.

Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution

We apply the formalism developed earlier [1, 2] for studying transverse momentum dependent parton distribution functions (TMDs) at small Bjorken x to construct the small-x asymptotics of the quark Sivers function. First, we explicitly construct the complete fundamental “polarized Wilson line” operator to sub-sub-eikonal order: this object can be used to study a variety of quark TMDs at small x. We then express the quark Sivers function in terms of dipole scattering amplitudes containing various components of the “polarized Wilson line” and show that the dominant (eikonal) term which contributes to the quark Sivers function at small x is the spin-dependent odderon, confirming the re- cent results of Dong, Zheng and Zhou [3]. Our conclusion is also similar to the case of the gluon Sivers function derived by Boer, Echevarria, Mulders and Zhou [4] (see also [5]). We also analyze the sub-eikonal corrections to the quark Sivers function using the constructed “polarized Wilson line” operator. We derive new small-x evolution equations re-summing double-logarithmic powers of αs ln2(1/x) with αs the strong coupling constant. We solve the corresponding novel evolution equations in the large-Nc limit, obtaining a sub-eikonal correction to the spin-dependent odderon contribution. We conclude that the quark Sivers function at small x receives contributions from two terms and is given by$$ {f}_{1T}^{\perp q}\left(x,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left({k}_T^2\right){\left(\frac{1}{x}\right)}^0+\cdots $$ f 1 T ⊥ q x k T 2 = C O x k T 2 1 x + C 1 k T 2 1 x 0 + ⋯ with the function CO(x,$$ {k}_T^2 $$ k T 2 ) varying slowly with x and the ellipsis denoting the subasymptotic and sub-sub-eikonal (order-x) corrections.

On the geometry of operator mixing in massless QCD-like theories

We revisit the operator mixing in massless QCD-like theories. In particular, we address the problem of determining under which conditions a renormalization scheme exists where the renormalized mixing matrix in the coordinate representation, $$Z(x, \mu )$$ Z ( x , μ ) , is diagonalizable to all perturbative orders. As a key step, we provide a differential-geometric interpretation of renormalization that allows us to apply the Poincaré-Dulac theorem to the problem above: We interpret a change of renormalization scheme as a (formal) holomorphic gauge transformation, $$-\frac{\gamma (g)}{\beta (g)}$$ - γ ( g ) β ( g ) as a (formal) meromorphic connection with a Fuchsian singularity at $$g=0$$ g = 0 , and $$Z(x,\mu )$$ Z ( x , μ ) as a Wilson line, with $$\gamma (g)=\gamma _0 g^2 + \cdots $$ γ ( g ) = γ 0 g 2 + ⋯ the matrix of the anomalous dimensions and $$\beta (g)=-\beta _0 g^3 +\cdots $$ β ( g ) = - β 0 g 3 + ⋯ the beta function. As a consequence of the Poincaré-Dulac theorem, if the eigenvalues $$\lambda _1, \lambda _2, \ldots $$ λ 1 , λ 2 , … of the matrix $$\frac{\gamma _0}{\beta _0}$$ γ 0 β 0 , in nonincreasing order $$\lambda _1 \ge \lambda _2 \ge \cdots $$ λ 1 ≥ λ 2 ≥ ⋯ , satisfy the nonresonant condition $$\lambda _i -\lambda _j -2k \ne 0$$ λ i - λ j - 2 k ≠ 0 for $$i\le j$$ i ≤ j and k a positive integer, then a renormalization scheme exists where $$-\frac{\gamma (g)}{\beta (g)} = \frac{\gamma _0}{\beta _0} \frac{1}{g}$$ - γ ( g ) β ( g ) = γ 0 β 0 1 g is one-loop exact to all perturbative orders. If in addition $$\frac{\gamma _0}{\beta _0}$$ γ 0 β 0 is diagonalizable, $$Z(x, \mu )$$ Z ( x , μ ) is diagonalizable as well, and the mixing reduces essentially to the multiplicatively renormalizable case. We also classify the remaining cases of operator mixing by the Poincaré–Dulac theorem.

Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.