CGC formalism with two sources

In this work we extend the JIMWLK formalism to the two-source problem. The S-matrix for the forward scattering can be written in a double functional integral representation which involves the usual functional integral for the gluon field and the spin path integral for the external color sources. Modifications needed in the light-cone gauge are discussed. Using our source term we compute the produced gluon field and discuss the duality of the high energy evolution kernel in the pA collision.     

Singular and regular gauges in soft–collinear effective theory: The introduction of the new Wilson line T

Gauge invariance in soft–collinear effective theory (SCET) is discussed in regular (covariant) and singular (light-cone) gauges. It is argued that SCET, as it stands, is not capable to define in a gauge invariant way certain non-perturbative matrix elements that are an integral part of many factorization theorems. Those matrix elements involve two quark or gluon fields separated not only in light-cone direction but also in the transverse one. This observation limits the range of applicability of SCET. To remedy this we argue that one needs to introduce a new Wilson line as part of SCET formalism, that we call T. This Wilson line depends only on the transverse component of the gluon field. As such it is a new feature to the SCET formalism and it guarantees gauge invariance of the non-perturbative matrix elements in both classes of gauges.     

One-loopN-point functions in the light-cone gauge

We consider, in the light-cone gauge, the possible structure of the counterterms arising in the solution to the renormalization equation. Using the structure of these counterterms and the noncovariant formalism of the integrals as guidelines, we also examine to one-loop order the divergence and nonlocality of theN-point gluon vertex functions forN≧5.     

Radiative Parton Energy Loss and Baryon Stopping in AA Collisions

JETP Letters - We study the radiative energy loss contribution to proton stopping in AA collisions. The analyses is performed within the light-cone path integral approach to induced gluon emission....     

QCD calculations in the light-cone gauge

The non-singlet quark structure function is calculated in the leading logarithm approximation in an axial gauge with n² = 0, the light-cone gauge. The choice n² = 0 leads to a simple identity for loop integrals involving the extra n · k denominators. We compare the results graph by graph with both Feynman gauge QCD and a scalar gluon theory. The leading diagrams are the same “rainbow” diagrams as for the case of the scalar theory.The techniques are also applied to quark-quark scattering at large transverse momentum. The leading diagrams have the same dressed ladder-form factor structure.     

Infrared properties of the glue propagator in non-abelian gauge theories

In a pure Yang-Mills theory, the Dyson equation for the gluon propagator is studied in the infrared regime, under the assumption that, as in QED, only those parts of the proper gluon vertex functions determined by the Ward identities are relevant. The calculations are all carried out in the axial gauge. With a number of simplifying assumptions the resulting integral equation for the gluon propagator can be solved in the IR regime. The solution displays a power singularity in the IR for the renormalized coupling constant g(q²).     

Classical initial conditions in high energy nucleus-nucleus collisions

An iterative proceedure is proposed to compute the classical gauge field produced in the collision of two heavy nuclei. The leading order is obtained by linearizing the Yang-Mills equations in the light-cone gauge, and provides a simple formula for gluon production in nucleus-nucleus collisions. At this order k_t–factorization breaks down.     

Gluon polarization in nucleons

In QCD the gauge-invariant gluon polarization in a nucleon can be defined either in a non-local way as the integral over the Ioffe-time distribution of polarized gluons, or in light-cone gauge as the forward matrix element of the local topological current. We have investigated both possibilities within the framework of QCD sum rules. Although the topological current is built from local fields, we have found that its matrix element retains sensitivity to large longitudinal distances. Because QCD sum rules produce artificial oscillations of the Ioffe-time distribution of polarized glue at moderate and large light-like distances, the calculation of the matrix element of the topological current results in a small value of . In a more consistent approach QCD sum rules are used to describe the polarized gluon distribution only at small light-like distances. Assuming that significant contributions to arise only from longitudinal length scales not larger than the nucleon size leads to . Received: 19 August 1997 / Published online: 20 February 1998     

Adjoint QCD1 + 1 in light-cone gauge, quantized at equal time

SU (2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with “twisted” boundary conditions, periodic for one color component (the diagonal 3-component) and antiperiodic for the other two. The focus of the study is on the non-trivial vacuum structure and the fermion condensate. It is shown that the indefinite-metric quantization of free gauge bosons is not compatible with the residual gauge symmetry of the interacting theory. A suitable quantization of the unphysical modes of the gauge field is necessary in order to guarantee the consistency of the subsidiary condition and allow the quantum representation of the residual gauge symmetry of the classical Lagrangian: the 3-color component of the gauge field must be quantized in a space with an indefinite metric while the other two components require a positive-definite metric. The contribution of the latter to the free Hamiltonian becomes highly pathological in this representation, but a larger portion of the interacting Hamiltonian can be diagonalized, thus allowing perturbative calculations to be performed. The vacuum is evaluated through second order in perturbation theory and this result is used for an approximate determination of the fermion condensate.     

Infrared properties of two-loop,initial state spectator interactions in the Drell-Yan process

We use the light-cone axial gauge of proper-time ordered perturbation theory and study the soft-IR properties of the two-loop virtuals' diagrams considered by Bodwin, Brodsky and Lepage for ππ → μ⁺μ^- + X. It is shown that although the systematic summation over all possible spectator interactions removes the outside soft-IR divergences in the non-overlapping ladder Glauber diagrams, unphysical inside soft-IR divergences persist. So, in the light-cone axial gauge the on-shell Glauber region is not a gauge invariant concept which can be physically isolated from radiative corrections which non-trivially involve other diagrammatic regions. Due to gauge invariance it can be potentially misleading in eikonal phenomenologies based on perturbative QCD to assume an ad hoc inside soft-IR cutoff in analyzing possible non-abelian effects in multiple scatterings involving spectators.     

Can extra dimensions accessible to the SM explain the recent measurement of anomalous magnetic moment of the muon?

We investigate whether models with flat extra dimensions in which SM fields propagate can give a significant contribution to the anomalous magnetic moment of the muon (MMM). In models with only SM gauge and Higgs fields in the bulk, the contribution to the MMM from Kaluza–Klein (KK) excitations of gauge bosons is very small. This is due to the constraint on the size of the extra dimensions from tree-level effects of KK excitations of gauge bosons on precision electroweak observables such as Fermi constant. If the quarks and leptons are also allowed to propagate in the (same) bulk (“universal” extra dimensions), then there are no contributions to precision electroweak observables at tree-level. However, in this case, the constraint from one-loop contribution of KK excitations of (mainly) the top quark to T parameter again implies that the contribution to the MMM is small. We show that in models with leptons, electroweak gauge and Higgs fields propagating in the (same) bulk, but with quarks and gluon propagating in a sub-space of this bulk, both the above constraints can be relaxed. However, with only one Higgs doublet, the constraint from the process b→sγ requires the contribution to the MMM to be smaller than the SM electroweak correction. This constraint can be relaxed in models with more than one Higgs doublet.     

Path integral approach to the large-N expansion of the two-dimensional U(N) QCD

We use path integral method for the large-N expansion of the two-dimensional U(N) QCD in the light-cone gauge. We derive the 't Hooft equation for the quark-antiquark bound states from the quadratic part of the expansion. We also derive the effective interactions of the mesons from the higher-order terms of the expansion.