In this work, we will present the first complete calculation of the one-loop longitudinal photon-to-quark-antiquark light cone wave function, with massive quarks. The quark masses are renormalized in the pole mass scheme. The result is used to calculate the next-to-leading order correction to the high energy Deep Inelastic Scattering longitudinal structure function on a dense target in the dipole factorization framework. For massless quarks the next-to-leading order correction was already known to be sizeable, and our result makes it possible to evaluate it also for massive quarks.
We use a factorization scheme analogous to one proposed for single inclusive forward hadron production to factorize the soft gluon divergence present in the deep inelastic scattering cross sections in the dipole picture at next-to-leading order (NLO). We show numerically that in this carefully constructed scheme it is possible to obtain meaningful results for the DIS cross sections at NLO, and so we are able to quantitatively study the recently derived NLO corrections to the DIS cross sections. We find that the NLO corrections can be significant and sensitive to the details of the factorizatio…
In the hybrid kT-factorization formula, one initial-state parton momentum is space-like and carries non-vanishing transverse components, while the other is on-shell. We promote this factorization formula to next-to-leading order. Studying the partonic cross section, we identify all soft and collinear divergencies in the real and virtual contribution, and recognize that all non-cancelling ones can be attributed to PDF evolution, evolution kernel, and target impact factors. In result, we construct a framework that may be used to compute NLO impact factors in general. In particular, we recover kn…
Single inclusive particle production cross sections in high energy hadron collisions at forward rapidity are an important benchmark process for the CGC picture of small x QCD. Recent calculations of this process have not led to a stable perturbative expansion for this quantity at high transverse momenta. We consider the quark channel production cross section using the new rapidity factorization procedure proposed by Iancu et al. We show that for fixed coupling one does indeed obtain a physically meaningful cross section which is positive and reduces in a controlled way to previous leading orde…
Investigation of the factorization scheme dependence of finite order perturbative QCD calculations: searching for approximately ZERO factorization scheme
The one-loop QCD corrections to the light-front wave-function for the quark-antiquark Fock state inside a transverse or longitudinal off-shell photon are explicitly calculated, both in full momentum space and in mixed space (a.k.a. dipole space). These results provide one of the main contributions to virtual NLO corrections to many DIS observables (inclusive or not) in the dipole factorization formalism at low Bjorken x. In a follow-up article, these one-loop corrections are combined with earlier results on the wave-function for the quark-antiquark-gluon Fock state, in order to get the full se…
In this paper we firstly demonstrate step by step that the factorization hypothesis is valid at the next-to-leading order (NLO) for the exclusive process $ργ^{\star} \to ρ$ by employing the collinear factorization approach, and then extend this proof to the case of the $k_T$ factorization by taking into account the transversal momentum of the light external quark (anti-quark) lines in the $ρ$ meson. At the NLO level, we then show that the soft divergences from different sub-diagrams will be canceled each other in the quark level, while the remaining collinear divergences can be absorbed into t…
In this paper, we investigate the factorization hypothesis step by step for the exclusive process $B \to ρ$ at next-to-leading order (NLO) with the collinear factorization approach, and then we extend our results to the $k_T$ factorization frame. We show that the soft divergence from the specific NLO diagrams will cancel each other at the quark level, while the remaining collinear divergence can be absorbed into the NLO wave functions. The full NLO amplitudes can be factorized into two parts: the NLO $B$ and $ρ$ meson wave functions containing the collinear divergence and the leading order (LO…
We calculate large mass diphoton exclusive photoproduction in the framework of collinear QCD factorization at next to leading order in αs and at leading twist. Collinear divergences of the coefficient function are absorbed by the evolution of the generalized parton distributions (GPDs). This result enlarges the existing factorization proofs to 2 -> 3 processes, opening new reactions to a trustable extraction of GPDs.
The NLO corrections to the DIS structure functions $F_2$ and $F_L$ (or equivalently the photon-target cross sections $σ^{γ^*}_{T}$ and $σ^{γ^*}_{L}$) at low $x_{Bj}$ are obtained, as a generalization of the dipole factorization formula. For the first time, the contributions of both the $q\bar{q}$ and the $q\bar{q}g$ Fock states in the photon are directly calculated, using earlier results for the $q\bar{q}$ light-front wave-functions at one loop inside a dressed virtual photon. Both the $q\bar{q}$ and the $q\bar{q}g$ contributions have UV divergences, which are shown to cancel each other, using…
The perturbatively-stable scheme of Next-to-Leading order (NLO) calculations of cross-sections for multi-scale hard-processes in DIS-like kinematics is developed in the framework of High-Energy Factorization. The evolution equation for unintegrated PDF, which resums $\log 1/z$-corrections to the coefficient function in the Leading Logarithmic approximation together with a certain subset of Next-to-Leading Logarithmic and Next-to-Leading Power corrections, necessary for the perturbative stability of the formalism, is formulated and solved in the Doubly-Logarithmic approximation. An example of D…
In this paper we calculate the next-to-leading-order (NLO) corrections to $ρ$-meson electromagnetic form factors by employing the $k_T$ factorization approach. We find that the NLO correction to $F_i (Q^2)(i=LT,TL)$ is around $30\%$ of the leading-order (LO) contributionin the region $Q^2>2GeV^2$. The NLO correction to $F_{LL}(Q^2)$ is close to $20\%$ of the LO one in the region $Q^2>3GeV^2$. The NLO radiative corrections to the electric, magnetic, and quadruple form factors $F_j(Q^2) (j=1,2,3)$ are sizeable in magnitude and agree with those from other approaches.
Single inclusive forward hadron production in high-energy hadron collisions can provide an important test of the Color Glass Condensate picture at small $x$. Recent studies of this process at next-to-leading order have led to problematic results, with cross sections becoming negative at large transverse momenta. We study a new formulation of this quantity proposed recently by Iancu et al. We show that it leads to physical results up to large transverse momenta at fixed coupling. Taking into account running coupling effects in a way that is consistent with existing DIS calculations still poses …
We calculate the light cone wave functions for the QCD Fock components in a transverse virtual photon necessary for applications at next-to-leading order in the QCD coupling, including quark masses. We present a detailed calculation of both the one loop wave function for the quark-antiquark Fock component and the tree level wave function for the quark-antiquark-gluon Fock component. The quark masses are renormalized in the pole mass scheme, satisfying constraints from the requirement of Lorentz invariance. In particular the quark Pauli form factor at NLO is recovered from the on-shell limit of…
Within the Color Glass Condensate effective theory, we reconsider the next-to-leading order (NLO) calculation of the single inclusive particle production at forward rapidities in proton-nucleus collisions at high energy. Focusing on quark production for definiteness, we establish a new factorization scheme, perturbatively correct through NLO, in which there is no `rapidity subtraction'. That is, the NLO correction to the impact factor is not explicitly separated from the high-energy evolution. Our construction exploits the skeleton structure of the (NLO) Balitsky-Kovchegov equation, in which t…
The factorisation scheme (FS) abbreviated as KRK FS including a new definition of the PDFs for initial hadrons was formulated while developing KrkNLO scheme of matching QCD NLO corrections for the hard process with the parton shower heavy boson production in hadron-hadron collision and for deep inelastic lepton-hadron scattering. KRK FS (originally called Monte Carlo FS) can be regarded as a variant of the $\overline{MS}$ system. It is therefore trivially universal, that is process independent. The question of its universality is formulated differently: As the basic role of KRK FS is to simpli…
We compute the next-leading-order cross-sections for diffractive electro- or photoproduction of a pair of hadrons with large $p_T$, out of a nucleus or a nucleon. A hybrid factorization is used, mixing collinear and small-$x$ factorizations, more precisely shockwave formalism. We demonstrate the cancellation of divergences and extract the finite parts of the differential cross-section in general kinematics.
Recently, the ATLAS data of isolated three-photon production showed that the next-to-leading order (NLO) collinear factorization is not enough to describe experimental data. Therefore, one needs to calculate the cross section beyond the NLO, and as showed later, these data can be well described by the NNLO calculation within the collinear factorization framework. However, it is shown that the $k_t$-factorization can be quite successful in describing exclusive and high energy collision processes, henceforth we decided to calculate isolated three-photon production within this framework. In this …
We study single inclusive forward hadron production in high energy proton-nucleus collisions at next-to-leading order in the Color Glass Condensate framework. Recent studies have shown that the next-to-leading order corrections to this process are large and negative at large transverse momentum, leading to negative cross sections. We propose to overcome this difficulty by introducing an explicit rapidity factorization scale when subtracting the rapidity divergence into the evolution of the target.
The twist-3 collinear factorization framework has drawn much attention in recent decades as a successful approach in describing the data for single spin asymmetries (SSAs). Many SSAs data have been experimentally accumulated in a variety of energies since the first measurement was done in late 70s and it is expected that the future experiments like Electron-Ion collider will provide us with more data. In order to perform a consistent and precise description of the data taken in different kinematic regimes, the scale evolution of the collinear twist-3 functions and the perturbative higher order…
The next-to-leading order (NLO) ($\mathcal{O}(α_s^3)$) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in ${^{3}\hspace{-0.6mm}P_{J}^{[1,8]}}$ states are calculated within the NRQCD factorization. We use integration-by-parts reduction and differential equations to semi-analytically calculate fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergence…
By employing the perturbative QCD (PQCD) factorization approach, we calculated the branching ratios, CP-violating asymmetries, the longitudinal and transverse polarization fractions and other physical observables of the thirteen charmless hadronic $\bar{B}^0_s \to V V $ decays with the inclusion of all currently known next-to-leading order (NLO) contributions. We focused on the examination of the effects of all those currently known NLO contributions and found that: (a) for the measured decays $\bar{ B}_s^0 \to ϕϕ, K^{*0} ϕ,\bar K^{*0} K^{*0}$ and $ρ^0 ϕ$, the NLO contributions can provide $\s…
