Starting from the first renormalized factorization theorem for a process described at subleading power in soft-collinear effective theory, we discuss the resummation of Sudakov logarithms for such processes in renormalization-group improved perturbation theory. Endpoint divergences in convolution integrals, which arise generically beyond leading power, are regularized and removed by systematically rearranging the factorization formula. We study in detail the example of the $b$-quark induced $h\toγγ$ decay of the Higgs boson, for which we resum large logarithms of the ratio $M_h/m_b$ at next-to-leading logarithmic order. We also briefly discuss the related $gg\to h$ amplitude.
In this article we extract soft distribution functions for Drell-Yan and Higgs production processes using mass factorisation theorem and the perturbative results that are known upto three loop level. We find that they are maximally non-abelien. We show that these functions satisfy Sudakov type integro differential equations. The formal solutions to such equations and also to the mass factorisation kernel upto four loop level are presented. Using the soft distribution function extracted from Drell-Yan production, we show how the soft plus virtual cross section for the Higgs production can be ob…
We investigate the QCD resummation for the Higgs boson plus a high $P_T$ jet production with large rapidity separations in proton-proton collisions at the LHC. The relevant Balitsky-Fadin-Kuraev-Lipatov (BFKL) and Sudakov logs are identified and resummed. In particular, we apply recent developments of the transverse momentum dependent factorization formalism in the impact factors, which provides a systematic framework to incorporate both the BFKL and Sudakov resummations.
The Leding-Logarithmic (LL) gluon Sudakov formfactor is derived from rapidity-ordered BFKL evolution with longitudinal-momentum conservation. This derivation further clarifies the relation between High-Energy and TMD-factorizations and can be extended beyond LL-approximation as well.
We apply the strategy of regions within dimensional regularization to find functions involved in evolution equations which govern the asymptotic dynamics of the Abelian form factor and four-fermion amplitude in the SU(N) gauge theory in the Sudakov limit up to the next-to-leading logarithmic approximation. The results are used for the analysis of the dominant electroweak corrections to the fermion-antifermion pair production in the $e^+e^-$ annihilation at high energy.
Recent results for the asymptotic behavior of fermion scattering amplitudes in the Sudakov limit are presented including next-to-leading logarithmic corrections. These are used for the analysis of the dominant electroweak corrections to the fermion-antifermion pair production in $e^+e^-$ annihilation at high energy.
A complete description of W and Z boson production at high-energy hadron colliders requires the resummation of large Sudakov double logarithms which dominate the transverse momentum (q_T) distribution at small q_T. We compare different prescriptions for performing this resummation, in particular implicit impact parameter space resummation versus explicit transverse momentum space resummation. We argue that the latter method can be formulated so as to retain the advantages of the former, while at the same time allowing a smooth transition to finite order dominance at high q_T.
We present the general expressions for the resummation, up to next-to-leading logarithmic accuracy, of Sudakov-type logarithms in processes with an arbirtrary number of hard-scattering partons. These results document the formulae used by the authors in several previous phenomenological studies. The resummation formulae presented here, which are valid for phase-space factorizable observables, determine the resummation correction in a process-independent fashion. All process dependence is encoded in the colour and flavour structure of the leading order and virtual one-loop amplitudes, and in Sud…
We investigate the scale dependence of transverse momentum dependent(TMD) gluon distribution in saturation regime. We found that in the Collins-2011 scheme, the scale dependence of small x gluon TMD is governed by the same renormalization group(RG) equation that holds at moderate or large $x$. Following the standard procedure, one then can resum both double leading logarithm and single leading logarithm in saturation regime by jointly solving the Collins-Soper equation and the RG equation.
Future colliders will probe the electroweak theory at energies much larger than the gauge boson masses. Large double (DL) and single (SL) logarithmic virtual electroweak Sudakov corrections lead to significant effects for observable cross sections. Recently, leading and subleading universal corrections for external fermions and transverse gauge boson lines were resummed by employing the infrared evolution equation method. The results were confirmed at the DL level by explicit two loop calculations with the physical Standard Model (SM) fields. Also for longitudinal degrees of freedom the approa…
We present a unified derivation of the resummation of Sudakov logarithms, directly from the factorization properties of cross sections in which they occur. We rederive in this manner the well-known exponentiation of leading and nonleading logarithmic enhancements near the edge of phase space for cross sections such as deeply inelastic scattering, which are induced by an electroweak hard scattering. For QCD hard-scattering processes, such as heavy-quark production, we show that the resummation of nonleading logarithms requires in general mixing in the space of the color tensors of the hard scat…
We derive and solve renormalization group equations that allow for the resummation of subleading power rapidity logarithms. Our equations involve operator mixing into a new class of operators, which we term the "rapidity identity operators", that will generically appear at subleading power in problems involving both rapidity and virtuality scales. To illustrate our formalism, we analytically solve these equations to resum the power suppressed logarithms appearing in the back-to-back (double light cone) limit of the Energy-Energy Correlator (EEC) in $\mathcal{N}$=4 super-Yang-Mills. These logar…
When the allowed range of an observable grows order-by-order in perturbation theory, its perturbative expansion can have discontinuities (as in the $C$ parameter) or discontinuities in its derivatives (as in thrust or heavy jet mass) called Sudakov shoulders. We explore the origin of these logarithms using both perturbation theory and effective field theory. We show that for thrust and heavy jet mass, the logarithms arise from kinematic configurations with narrow jets and deduce the next-to-leading logarithmic series. The left-shoulder logarithms in heavy jet mass ($ρ$) of the form $r\ α_s^n \…
The dispersive approach to power corrections is given a precise implementation, valid beyond single gluon exchange, in the framework of Sudakov resummation for deep inelastic scattering and the Drell-Yan process. It is shown that the assumption of infrared finite Sudakov effective couplings implies the universality of the corresponding infrared fixed points. This property is closely tied to the universality of the virtual contributions to space-like and time-like processes, encapsulated in the second logarithmic derivative of the quark form factor.
Through an explicit calculation of massive scalar particle (e.g., Higgs boson) production in high energy pA collisions up to one-loop order, we demonstrate that the Sudakov-type logarithms in hard processes in small-x saturation formalism can be systematically separated from the typical small-x logarithms. The generic feature of the Sudakov logarithms and all order resummation is derived. We further comment on the phenomenological implications and extension to other hard processes in the small-x calculations.
A complete description of W and Z boson production at high-energy colliders requires the resummation of large Sudakov logarithms which dominate the production at small transverse momentum. Currently there are two techniques for performing this resummation: impact parameter space and transverse momentum space. We argue that the latter can be formulated in a way which retains the advantages of the former, while at the same time allowing a smooth transition to finite order dominance at high transverse momentum.
We present a general all-order formulation of Sudakov resummation in QCD in terms of dispersion integrals. We show that the Sudakov exponent can be written as a dispersion integral over spectral density functions, weighted by characteristic functions that encode information on power corrections. The characteristic functions are defined and computed analytically in the large-beta_0 limit. The spectral density functions encapsulate the non-Abelian nature of the interaction. They are defined by the time-like discontinuity of specific effective charges (couplings) that are directly related to the …
New arguments are presented in favor of the infrared finite coupling approach to power corrections in the context of Sudakov resummation. The more regular infrared behavior of some peculiar combinations of Sudakov anomalous dimensions, free of Landau singularities at large Nf, is pointed out. A general conflict between the infrared finite coupling and infrared renormalon approaches to power corrections is explained, and a possible resolution is proposed, which makes use of the arbitrariness of the choice of constant terms in the Sudakov exponent. A simple ansatz for a `universal' non-perturbat…
The leading and next-to-leading threshold logarithms of the QCD corrections to electroproduction of heavy quarks in single-particle inclusive kinematics are resummed to all orders in perturbation theory. The resummed cross-section is used to derive the NLO and NNLO results near threshold and their numerical impact on the charm structure function is studied.
We claim that factorization implies that the evolution kernel, defined by the logarithmic derivative of the N-th moment of the structure function d ln F_2^N / d ln Q^2, receives logarithmically enhanced contributions (Sudakov logs) from a single source, namely the constrained invariant mass of the jet. Available results from fixed-order calculations facilitate Sudakov resummation up to the next-to-next-to-leading logarithmic accuracy. We use additional all-order information on the physical kernel from the large-beta_0 limit to model the behaviour of further subleading logs and explore the unce…
We apply Soft-Collinear Effective Theory to prove at leading power in Lambda_QCD/m_b a factorization formula for the radiative leptonic decay B -> gamma l nu. Large logarithms entering the hard-scattering kernel are systematically resummed by a two-step perturbative matching procedure.
We present the explicit expressions for the resummation of large-x Sudakov effects in the transverse-energy distribution of prompt-photons produced in hadronic collisions, to next-to-leading logarithmic (NLL) accuracy. Fragmentation processes do not contribute to the Sudakov resummation at NLL level. In Mellin space, the resummed radiative factor factorizes in the product of independent radiators for the two initial and the one final coloured partons appearing in the Born process, times a simple factor describing the soft-gluon interferences between initial and final states. The formulae are g…
I show that Sudakov resummation takes a transparent form if one deals with the second logarithmic derivative of the short distance coefficient functions for deep inelastic scattering and the Drell-Yan process. A uniquely defined Sudakov exponent emerges, and the constant terms not included in the exponent are conjectured to be given by the second logarithmic derivative of the massless quark form factor. The precise framework for the implementation of the dispersive approach to power corrections is set-up, yielding results in agreement with infrared renormalon expectations, but which are not ti…
In high energy hadron-hadron collisions, dijet production with large rapidity separation proposed by Mueller and Navelet, is one of the most interesting processes which can help us to directly access the well-known Balitsky-Fadin-Kuraev-Lipatov evolution dynamics. The objective of this work is to study the Sudakov resummation of Mueller-Navelet jets. Through the one-loop calculation, Sudakov type logarithms are obtained for this process when the produced dijets are almost back-to-back. These results could play an important role in the phenomenological study of dijet correlations with large rap…
We compute the effects of soft-gluon resummation, at the next-to-leading-logarithmic level, in the fixed-target hadroproduction cross section for prompt photons. We find in general that the corrections to the fixed next-to-leading-order results are large for large renormalization scales, and small for small scales. This leads to a significant reduction of the scale dependence of the results for most experimental configurations of interest. We compare our results to the recent measurements by the E706 and UA6 collaborations.
In this manuscript, we present a complete study of the Sudakov double logarithms resummation for various hard processes in eA and pA collisions in the small-x saturation formalism. We first employ a couple of slightly different formalisms to perform the one-loop analysis of the Higgs boson production process in pA collisions, and demonstrate that Sudakov-type logarithms arise as the leading correction and that they can be systematically resummed in addition to the usual small-x resummation. We further study the Sudakov double logarithms for other processes such as heavy quark pair production a…
We resum Sudakov threshold enhancements in heavy quark hadroproduction for single-heavy quark inclusive and pair-inclusive kinematics. We expand these resummed results and derive analytical finite-order cross sections through next-to-next-to-leading order. This involves the construction of next-to-leading order matching conditions in color space. For the scale dependent terms we derive exact results using renormalization group methods. We study the effects of scale variations, scheme and kinematics choice on the partonic and hadronic cross sections, and provide estimates for top and bottom qua…
We derive and analytically solve renormalization group (RG) equations of gauge invariant non-local Wilson line operators which resum logarithms for event shape observables $τ$ at subleading power in the $τ\ll 1$ expansion. These equations involve a class of universal jet and soft functions arising through operator mixing, which we call $θ$-jet and $θ$-soft functions. An illustrative example involving these operators is introduced which captures the generic features of subleading power resummation, allowing us to derive the structure of the RG to all orders in $α_s$, and provide field theory de…
We consider the higher-order resummation of Sudakov double logarithms in the presence of multiple coupled gauge interactions. The associated evolution equations depend on the coupled $β$ functions of two (or more) coupling constants $α_a$ and $α_b$, as well as anomalous dimensions that have joint perturbative series in $α_a$ and $α_b$. We discuss possible strategies for solving the system of evolution equations that arises. As an example, we obtain the complete three-loop (NNLL) QCD$\otimes$QED Sudakov evolution factor. Our results also readily apply to the joint higher-order resummation of el…
There has been recent interest in understanding the all loop structure of the subleading power soft and collinear limits, with the goal of achieving a systematic resummation of subleading power infrared logarithms. Most of this work has focused on subleading power corrections to soft gluon emission, whose form is strongly constrained by symmetries. In this paper we initiate a study of the all loop structure of soft fermion emission. In $\mathcal{N}=1$ QCD we perform an operator based factorization and resummation of the associated infrared logarithms, and prove that they exponentiate into a Su…
New arguments are presented to emphasize the interest of the infrared finite coupling approach to power corrections in the context of Sudakov resummation. The more regular infrared behavior of some peculiar combinations of Sudakov anomalous dimensions, free of Landau singularities at large Nf, is pointed out. A general conflict between the infrared finite coupling and infrared renormalon approaches to power corrections is explained, and a possible resolution is proposed, which makes use of the arbitrariness of the choice of exponentiated constant terms. A simple ansatz for a 'universal' non-pe…
We prove the all-order exponentiation of soft logarithmic corrections to prompt photon production in hadronic collisions, by generalizing an approach previously developed in the context of Drell-Yan production and deep-inelastic scattering. We show that all large logs in the soft limit can be expressed in terms of two dimensionful variables, and we use the renormalization group to resum them. The resummed results that we obtain are more general though less predictive than those proposed by other groups, in that they can accommodate for violations of Sudakov factorization.
I show that Sudakov resummation takes a particularly transparent form if one deals with the second logarithmic derivative of the short distance coefficient functions for deep inelastic scattering and the Drell-Yan process. A uniquely defined Sudakov exponent emerges, and I conjecture that the leftover constant terms not included in the exponent are given by the second logarithmic derivative of the massless quark form factor. The meaning of a previously obtained large $N_f$ evidence for an infrared finite perturbative Sudakov coupling is reconsidered. This coupling is reinterpreted as a Minkows…
In future collider experiments at the TeV scale, large logarithmic corrections originating from massive boson exchange can lead to significant corrections to observable cross sections. Recently double logarithms of the Sudakov-type were resummed for spontaneously broken gauge theories and found to exponentiate. In this paper we use the virtual contributions to the Altarelli-Parisi splitting functions to obtain the next to leading order kernel of the infrared evolution equation in the fixed angle scattering regime at high energies where particle masses can be neglected. In this regime the virtu…
The inclusive spectra of radiative and semi-leptonic B-meson decays near the endpoint is computed taking into account renormalons in the Sudakov exponent (Dressed Gluon Exponentiation). In this framework we demonstrate the factorization of decay spectra into hard, jet and soft functions and discuss the universality of the latter two. Going beyond perturbation theory the soft function, which we identify as the longitudinal momentum distribution in an on-shell b quark, is replaced by the b-quark distribution in the B meson. The two differ by power corrections. We show how the resummation of runn…
Using the known resummation of virtual corrections together with knowledge of the leading-log structure of real radiation in a parton shower, we derive analytic expressions for the resummed real radiation after they have been integrated over all of phase space. Performing a numerical analysis for both the 13 TeV LHC and a 100 TeV $pp$ collider, we show that resummation of the real corrections is at least as important as resummation of the virtual corrections, and that this resummation has a sizable effect for partonic center of mass energies exceeding $\sqrt{s} = {\cal O}$(few TeV). For parton…
I briefly review three topics of recent interest concerning power corrections, renormalons and Sudakov resummation: (a) $1/Q$ corrections to event shape observables in $e^+ e^-$ annihilation, (b) power corrections in Drell-Yan production and (c) factorial divergences that arise in resummation of large infrared (Sudakov) logarithms in moment or `real' space.
In this thesis we present an introduction to Soft-Collinear Effective Theory, which can be used to prove (or disprove) factorization theorems to all orders in the strong coupling constant for some B decays into light and energetic particles. Specifically, the factorizable amplitudes for inclusive B->X_u l nu and exclusive B->gamma l nu are calculated in renormalization-group improved perturbation theory to first non-trivial order. Form factors encoding the exclusive decay amplitudes for B->P l nu and B->V l nu (P=light pseudoscalar meson, V=light vector meson) are studied and proved to be domi…
The perturbation series for electroweak vector boson production at small transverse momentum is dominated by large double logarithms at each order in perturbation theory. An accurate theoretical prediction therefore requires a resummation of these logarithms. This can be performed either directly in transverse momentum space or in impact parameter (Fourier transform) space. While both approaches resum the same leading double logarithms, the subleading logarithms are, in general, treated differently. We comment on two recent approaches to this problem, emphasising the particular subleading loga…
The hard-scattering contributions to heavy-to-light form factors at large recoil are studied systematically in soft-collinear effective theory (SCET). Large logarithms arising from multiple energy scales are resummed by matching QCD onto SCET in two stages via an intermediate effective theory. Anomalous dimensions in the intermediate theory are computed, and their form is shown to be constrained by conformal symmetry. Renormalization-group evolution equations are solved to give a complete leading-order analysis of the hard-scattering contributions, in which all single and double logarithms are…
We summarize our recent results on the resummation of hard-scattering coefficient functions and on-shell form factors in massless perturbative QCD. The threshold resummation has been extended to the fourth logarithmic order for deep-inelastic scattering, Drell-Yan lepton pair production and Higgs production via gluon-gluon fusion. The leading six infrared pole terms have been derived to all orders in the strong coupling constant for the photon-quark-quark and the (heavy-top) Higgs-gluon-gluon form factors. These results have many implications, most notably they lead to a new best estimate for …
We present a Monte Carlo approach to soft-gluon resummation at subleading color which can be used to improve existing parton shower algorithms. At the single-emission level, soft-collinear enhancements of the splitting functions are explicitly linked to quadratic Casimir operators, while wide angle single-soft enhancements are connected to nontrivial color correlators. We focus on a numerically stable implementation of color matrix element corrections to all orders and approximate the virtual corrections by requiring unitarity at the single-emission level. We provide a proof-of-concept impleme…
Soft-collinear effective theory is used to prove factorization of the B->gamma+l+nu decay amplitude at leading power in Lambda/m_b, including a demonstration of the absence of non-valence Fock states and of the finiteness of the convolution integral in the factorization formula. Large logarithms entering the hard-scattering kernel are resummed by performing a two-step perturbative matching onto the low-energy effective theory, and by solving evolution equations derived from the renormalization properties of the leading-order B-meson light-cone distribution amplitude. As a byproduct, the evolut…
In this PhD thesis, we analyze and generalize the renormalization group approach to the resummation of large logarithms in the perturbative expansion due to soft and collinear multiparton emissions. In particular, we present a generalization of this approach to prompt photon production. It is interesting to see that also with the more intricate two-scale kinematics that characterizes prompt photon production in the soft limit, it remains true that resummation simply follows from general kinematic properties of the phase space. Also, this approach does not require a separate treatment of indivi…
For superpartner masses not much heavier than the weak scale $M=M_{\rm W}$, large logarithmic corrections of the Sudakov type arise at TeV energies. In this paper we discuss the general structure of electroweak supersymmetric (susy) Sudakov corrections in the framework of the infrared evolution equation method. We discuss Yukawa sector Ward-identities which lead to the exponentiation of the subleading (SL) logarithmic Yukawa enhanced Sudakov corrections in both the Standard Model (SM) as well as in softly broken supersymmetric extensions. The results are given to SL accuracy to all orders in p…
The QCD Trace Anomaly in Pion Gravitational Form Factors with Sudakov Resummation
Dipartimento di Matematica e Fisica, Università del Salento（萨伦托大学数学与物理系）；INFN Sezione di Lecce（意大利国家核物理研究所莱切分部）；National Centre for HPC, Big Data and Quantum Computing（高性能计算、大数据与量子计算国家中心）；CNR Nanotec（意大利国家研究委员会纳米技术研究所）
The soft radiation emitted in jet cross sections can resolve the directions and colors of individual hard partons, leading to a complicated pattern of logarithmically enhanced terms in the perturbative series. Starting from a factorization theorem and solving the renormalization group equations for its ingredients, these large logarithms can be resummed. In this paper, we extract the two-loop anomalous dimension governing the resummation of subleading logarithms in jet cross sections and other non-global observables. This anomalous dimension can be obtained by considering soft limits of hard a…
We begin a systematic investigation of the anomalous dimension of subleading power N-jet operators in view of resummation of logarithmically enhanced terms in partonic cross sections beyond leading power. We provide an explicit result at the one-loop order for fermion-number two N-jet operators at the second order in the power expansion parameter of soft-collinear effective theory.
The $B$-meson light-cone distribution amplitude is an important non-perturbative quantity arising in the factorization of the amplitudes for many exclusive decays of $B$ mesons, such as $B^-\toγ\,\ell^-\barν$. We reconsider the renormalization-group (RG) equation satisfied by this function and present its solution at next-to-leading order (NLO) in RG-improved perturbation theory in Laplace space and, for the first time, in momentum space and the so-called diagonal (or dual) space. Since the information needed to describe the $B$ decay processes at leading order in $Λ_{\rm QCD}/m_b$ is most dir…
We discuss the resummation of Sudakov effects in a cross section from the viewpoint of its underlying factorization near the edge of phase space. We perform the resummation of Sudakov threshold logarithms in Higgs (Standard Model and Minimal Supersymmetric SM) production at the LHC, using an evolution equation in the Higgs mass that is derived from this factorization. We extend the class of universal large terms that is resummed to include additional universal contributions, which, when included, help to reproduce the exact result to within a few percent for the full allowed range of Higgs bos…
At future linear $e^+e^-$ collider experiments in the TeV range, Sudakov double logarithms originating from massive boson exchange can lead to significant corrections to the cross sections of the observable processes. These effects are important for the high precision objectives of the Next Linear Collider. We use the infrared evolution equation, based on a gauge invariant dispersive method, to obtain double logarithmic asymptotics of scattering amplitudes and discuss how it can be applied, in the case of broken gauge symmetry, to the Standard Model of electroweak processes. We discuss the dou…
A simple ansatz is suggested for the structure of threshold resummation of the momentum space physical evolution kernels (`physical anomalous dimensions') at all orders in (1-x), taking as examples Deep Inelastic Scattering (F_2(x, Q^2) and F_L(x, Q^2)) and the Drell-Yan process. Each term in the expansion is associated to a distinct renormalization group and scheme invariant perturbative object (`physical Sudakov anomalous dimension') depending on a single momentum scale variable. Both logarithmically enhanced terms and constant terms are captured by the ansatz at any order in the expansion. …
The off-diagonal parton-scattering channels $g+γ^*$ and $q+ϕ^*$ in deep-inelastic scattering are power-suppressed near threshold $x\to 1$. We address the next-to-leading power (NLP) resummation of large double logarithms of $1-x$ to all orders in the strong coupling, which are present even in the off-diagonal DGLAP splitting kernels. The appearance of divergent convolutions prevents the application of factorization methods known from leading power resummation. Employing $d$-dimensional consistency relations from requiring $1/ε$ pole cancellations in dimensional regularization between momentum …
We consider the high energy behaviour of the amplitudes for pair production of charged leptons, quarks, Higgs bosons, sleptons, squarks and charginos at lepton colliders. We give the general expressions of the leading quadratic and subleading linear logarithms that appear at the one loop level, and derive the corresponding resummed expansions to \underline{subleading} logarithmic order accuracy. Under the assumption of a relatively light SUSY scenario and choosing the MSSM as a specific model, we compare the predictions of the one-loop and of the resummed expansions at variable energy. We show…
We discuss the Sudakov form factor in the framework of the soft-collinear effective theory. The running of the short distance coefficient function from high to low scale gives the summation of Sudakov logarithms to all orders. Our discussions concentrate on the factorization and derivation of the renormalization group equation from the effective theory point of view. The intuitive interpretation of the renormalization group method is discussed. We compared our method with other resummation approaches in the literatures.
We develop the first systematic theoretical approach to dijet asymmetries in hadron-hadron collisions based on the perturbative QCD (pQCD) expansion and the Sudakov resummation formalism. We find that the pQCD calculation at next-to-leading order is indispensable to describe the experimental data, while the Sudakov resummation formalism is vital near the end points where the pQCD expansion fails to converge due to the appearance of large Sudakov logarithms. Utilizing our resummation improved pQCD approach, we obtain good agreement with the most up-to-date fully corrected ATLAS data on dijet as…
We discuss recent results for the asymptotic behavior of fermion scattering amplitudes in the Sudakov limit. The results include next-to-next-to-leading logarithmic electroweak corrections and are used for the analysis of fermion-antifermion pair production in e+e- annihilation at high energy. The importance of the subleading logarithmic contributions is emphasized and the fermionic contributions to the Abelian form factor at two loops are discussed.
We discuss central-forward dijet production at LHC energies within the framework of high energy factorization. In our study, we profit from the recent progress on consistent merging of Sudakov resummation with small-$x$ effects, which allows us to compute two different gluon distributions which depend on longitudinal momentum, transverse momentum and the hard scale of the process: one for the quark channel and one for the gluon channel. The small-$x$ resummation is included by means of the BK equation supplemented with a kinematic constraint and subleading corrections. We test the new gluon di…
