We study dijet production in pA collisions at forward rapidities at next-to-eikonal accuracy. We restrict ourselves to the next-to-eikonal corrections that are induced by the quark background field of the target. We consider all possible channels, compute scattering amplitudes both in general kinematics and in the back-to-back limit. By using these results, we compute the back-to-back production cross section and obtain a factorized expression with a quark TMD times associated hard factor for each channel.

Poland

Tolga Altinoluk

Guillaume Beuf

Etienne Blanco

Swaleha Mulani

Quark TMDs from back-to-back dijet production at forward rapidities in pA collisions beyond eikonal accuracy in the CGC

<p>We derive the full next-to-eikonal (NEik) corrections to the gluon propagator from before to after traversing a highly boosted gluon background field, including corrections both beyond the shockwave limit and beyond the static limit in particular. After summarizing the results of the full NEik corrections to the before-to-after quark propagator computed in our earlier works, we also derive the before-to-inside, inside-to-inside, and inside-to-after quark and gluon propagators, which are building blocks to calculate high-energy scattering processes at NEik order. Using these results and also including the NEik corrections that stem from interactions with the target via t-channel quark exchanges, we compute inclusive cross sections for quark and gluon production at forward rapidities in quark-nucleus and gluon-nucleus scatterings at NEik accuracy.</p>

Forward parton-nucleus scattering at next-to-eikonal accuracy in the color glass condensate

We consider dijet production in deep inelastic scattering at small <math><mi>x</mi></math>, on a purely gluonic unpolarized target. Starting from earlier results obtained at next-to-eikonal accuracy in the high-energy limit, we perform the expansion in the back-to-back dijet limit, at next-to-leading power accuracy. We rewrite our results in the language of transverse-momentum-dependent (TMD) factorization, in terms of twist-2 and twist-3 TMD gluon distributions (gluon TMDs). Among the next-to-eikonal corrections, we find in particular twist-2 contributions corresponding to the <math><mi>x</mi></math> dependent phase of the twist-2 gluon TMDs. We also find two types of twist-3 unpolarized gluon TMDs, as well as correlators of three gluon field strength tensors.

Alina Czajka

France

Cyrille Marquet

Back-to-back dijet production in DIS at next-to-eikonal accuracy and twist-3 gluon TMDs

We investigate the high <math><msup><mi>Q</mi><mn>2</mn></msup></math> (photon virtuality) limit of single-inclusive hadron production in deep inelastic scattering at small <math><mi>x</mi></math>, using the color glass condensate formalism at next-to-leading order. We focus on the <math><msubsup><mi>Λ</mi><mrow><mi>QCD</mi></mrow><mn>2</mn></msubsup><mo>≪</mo><msubsup><mi>p</mi><mi>h</mi><mn>2</mn></msubsup><mo>≪</mo><msup><mi>Q</mi><mn>2</mn></msup></math> kinematic regime, where <math><msub><mi>p</mi><mi>h</mi></msub></math> is the produced hadron transverse momentum, and extract the Sudakov double logarithms. We further argue that compatibility between the color glass condensate calculation and transverse momentum dependent distribution factorization at one-loop order can only be achieved if the small-x evolution is kinematically constrained.

CERN

United States

Jamal Jalilian-Marian

Sudakov double logs in single-inclusive hadron production in DIS at small <math><mi>x</mi></math> from the color glass condensate formalism

We analyze the effects of next-to-eikonal corrections on dijet production in Deep Inelastic Scattering off nuclear targets in the framework of the Color Glass Condensate. They require the knowledge of correlators of fields in the target beyond those computed in the standard McLerran-Venugopalan model, specifically those between transverse and boost-enhanced components, and of the recoil of the fields. We neglect the latter, while for the former we develop a linear model valid for large nuclei. We considered the unpolarized cross sections for dijet production in the approximation of a homogenous dilute nucleus, obtaining simple analytic expressions for the cross sections at next-to-eikonal accuracy, valid in the limit of total dijet momentum and dijet momentum imbalance larger than the saturation scale of the nucleus. We perform a numerical study of the results at energies of the Electron Ion Collider, finding   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (10%) effects in the cross sections at large total momentum. We also analyze the azimuthal asymmetries between total momentum and imbalance, finding that non-eikonal corrections induce odd azimuthal harmonics for the situation of jets with equal momentum fractions from the virtual photon, where they are absent in the eikonal approximation. Finally, in the eikonal approximation we have compared the results of our analytic expansion valid in the dilute limit of the target, and the full Color Glass Condensate results in the McLerran-Venugopalan model and their correlation limit. Our analytic expressions match the correlation limit ones in the region where both should be simultaneously valid and reproduce very well the full Color Glass Condensate results in its validity region.

Spain

Pedro Agostini

Néstor Armesto

Next-to-eikonal corrections to dijet production in Deep Inelastic Scattering in the dilute limit of the Color Glass Condensate

Various conventional running coupling prescriptions reproducing β 0-dependent terms of NLO JIMWLK are reviewed and found to be theoretically inconsistent: the JIMWLK evolution Hamiltonian with running coupling violates the requirement of positive semidefiniteness. This requirement appears to be tightly related to the possibility of having a Langevin formulation for the evolution.

Israel

Michael Lublinsky

Vladimir Skokov

On running coupling in the JIMWLK evolution and its Langevin formulation

We study the production, in deep inelastic scattering at high energy, of a quark-gluon dijet induced by <math><mi>t</mi></math>-channel quark exchange with the target, which goes beyond the eikonal approximation. Throughout this study we follow the color glass condensate approach, keep full dependence on the quark mass and consider the target to be unpolarized. We focus on the correlation limit in which the produced jets fly almost back-to-back and find a factorized expression for the cross section, for both longitudinal and transverse photons, involving the unpolarized quark transverse momentum dependent distribution. Quark-gluon dijets can be distinguished from other types of dijets at least in the heavy quark case, thanks to heavy flavor tagging. In that case, the dominant background is expected to come from the eikonal production of a quark-antiquark-gluon system. We propose experimental cuts to suppress that background contribution, making the process of quark-gluon dijet production in deep inelastic scattering a new method to probe the quark transverse momentum dependent distribution at the Electron Ion Collider.

Probing quark transverse momentum distributions in the color glass condensate: Quark-gluon dijets in deep inelastic scattering at next-to-eikonal accuracy

We revisit the calculation of the cross section for forward inclusive single hadron production in <math><mi>p</mi><mi>A</mi></math> collisions within the hybrid approach. We show that the proper framework to perform this calculation beyond leading order is not the collinear factorization, as has been assumed so far, but the transverse momentum dependent (TMD) factorized framework. Within the TMD factorized approach we show that all the large transverse logarithms appearing in the fixed order calculation are resummed into the evolution of the TMD parton distribution functions and TMD fragmentation functions with factorization scale. The resulting expressions, when written in terms of TMDs evolved to the appropriate, physically well understood factorization scale, contain no additional large logarithms. The absence of any large logarithms in the resummed result should ensure positivity of the cross section and eradicate the persistent problem that has plagued the previous attempts at calculating this observable in the hybrid approach.

Alexander Kovner

Single inclusive particle production at next-to-leading order in proton-nucleus collisions at forward rapidities: Hybrid approach meets TMD factorization

We perform a numerical analysis of the two particle azimuthal correlations at central rapidities generated in pA collisions within the framework of the Color Glass Condensate. We extend the standard computations to include the subeikonal corrections which stem from considering the finite longitudinal width of the dense target. For practical reasons, we only consider the next-to-next-to-eikonal corrections instead of using the all-order expressions for the inclusive two gluon production cross section. We show that the subeikonal terms that we account for in the two gluon yields contribute to both even and odd harmonics, the latter being absent in the standard Color Glass Condensate calculations performed at eikonal accuracy. Our analysis confirms the vanishing of the subeikonal effects with increasing collision energy and when going to forward rapidities, as expected.

Finite width effects on the azimuthal asymmetry in proton-nucleus collisions in the Color Glass Condensate

We compute dijet production in deep inelastic scattering at low <math><mi>x</mi></math> in the dipole formalism at next-to-eikonal accuracy. We calculate the contributions induced by single photon exchange of either longitudinal or transverse polarization. We include all types of corrections to the eikonal approximation in the gluon background field: (i) finite longitudinal width of the target, (ii) interaction of the quark-antiquark pair with the subleading (transverse) component of the background field, and (iii) dynamics of the target which is encoded in the <math><msup><mi>z</mi><mo>−</mo></msup></math>-coordinate dependence of the background field. The final expressions for the dijet cross section are written as the sum of a “generalized eikonal” contribution (where the longitudinal momentum <math><msup><mi>p</mi><mo>+</mo></msup></math> exchange between the target and the incoming quark-antiquark pair is allowed since the average <math><msup><mi>z</mi><mo>−</mo></msup></math> dependence of the background field is kept) and explicit next-to-eikonal corrections that involve decorated dipole and quadrupole operators.