V. Bertone, M. Botje, D. Britzger, S. Camarda, A. Cooper-Sarkar, F. Giuli, A. Glazov, A. Luszczak, F. Olness, R. Placakyte, V. Radescu, W. Słomiński, O. Zenaiev
备注：
6 pages, 7 figures.Presented at 25th International Workshop on Deep Inelastic Scattering and Related Topics, 3-7 April 2017, Birmingham, UK. PoS(DIS2017)203
xFitter is an open-source package that provides a framework for the determination of the parton distribution functions (PDFs) of the proton for many different kinds of analyses in Quantum Chromodynamics (QCD). xFitter version 2.0.0 has recently been released, and offers an expanded set of tools and options. It incorporates experimental data from a wide range of experiments including fixed-target, Tevatron, HERA, and LHC. xFitter can analyze this data up to next-to-next-to-leading-order (NNLO) in perturbation theory with a variety of theoretical calculations including numerous methodological options for carrying out PDF fits and plotting tools which help visualize the results. While primarily based on the collinear factorization foundation, xFitter also provides facilities for fits of dipole models and transverse-momentum dependent (TMD) PDFs. The package can be used to study the impact of new precise measurements from hadron colliders, and also assess the impact of future colliders. This paper provides a brief overview of xFitter with emphasis of the new version 2.0.0 features.
We investigate charm production in charged-current deep-inelastic scattering (DIS) using the xFitter program. xFitter is an open-source software framework for the determination of PDFs and the analysis of QCD physics, and has been used for a variety of LHC studies. The study of charged current DIS charm production provides an important perspective on the strange quark PDF, s(x). We make use of the xFitter tools to study the present s(x) constraints, and then use LHeC pseudodata to infer how these might improve. Furthermore, as xFitter implements both Fixed Flavor and Variable Flavor number sch…
We present the first open-source analysis of fragmentation functions (FFs) of charged pions (entitled IPM-xFitter) computed at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) accuracy in perturbative QCD using the xFitter framework. This study incorporates a comprehensive and up-to-date set of pion production data from single-inclusive annihilation (SIA) processes, as well as the most recent measurements of inclusive cross-sections of single pion by the BELLE collaboration. The determination of pion FFs along with their theoretical uncertainties is performed in the Zero-Ma…
We provide an overview of the xFitter open-source software package, review the general capabilities of the program, and highlight applications relevant to the Snowmass study. An updated version of the program (2.2.0) is available on CERN GitLab, a and this has been updated to a C++ codebase with enhanced and extended features. We also discuss some of the ongoing and future code developments that may be useful for precision studies. We survey recent analyses performed by the xFitter developers' team including: W and Z production, photon PDFs, Drell-Yan forward-backward asymmetry studies, resumm…
The xFitter project (former HERAFitter project) is an open-source package that provides a framework for the determination of the parton distribution functions (PDFs) of the proton for many different kinds of analyses in Quantum Chromodynamics (QCD). xFitter version 2.0.0 has recently been released, and offers an expanded set of tools and options. It incorporates experimental data from a wide range of experiments including fixed-target, Tevatron, HERA, and LHC. xFitter can analyze this data up to next-to-next-to-leading-order (NNLO) in perturbation theory with a variety of theoretical calculati…
We present the first open-source analysis of parton distribution functions (PDFs) of charged pions using xFitter, an open-source QCD fit framework to facilitate PDF extraction and analyses. Our calculations are implemented at next-to-leading order (NLO) using APPLgrids generated by MCFM generator. Using currently available Drell-Yan and photon production data, we find the valence distribution is well constrained; however, the considered data are not sensitive enough to unambiguously determine sea and gluon distributions. Fractions of momentum carried by the valence, sea and gluon components ar…
xFitter is an open-source package that provides a framework for the determination of the parton distribution functions (PDFs) of the proton for many different kinds of analyses in Quantum Chromodynamics (QCD). It incorporates experimental data from a wide range of experiments including fixed-target, Tevatron, HERA, and LHC. xFitter version 2.0.0 has recently been released, and offers an expanded set of tools and options. The new xFitter 2.0.0 program links to the APFEL code which has implemented generalized matching conditions that enable the switch from $N_F$ to $N_F+1$ active flavors at an a…
We present {\tt SKMHS22}, a new set of diffractive parton distribution functions (PDFs) and their uncertainties at next-to-leading-order accuracy in perturbative QCD within the {\tt xFitter} framework. We describe all available diffractive DIS data sets from HERA and the most recent high-precision H1/ZEUS combined measurements considering three different scenarios. First, we extract the diffractive PDFs considering the standard twist-2 contribution. Then, we include the twist-4 correction from the longitudinal virtual photons. Finally, the contribution of subleading Reggeon exchange to the str…
In this contribution, we review the results of the recent paper "The photon PDF from high-mass Drell Yan data at the LHC" (arXiv:1701.08553), where a determination of the photon PDF from fits to recent ATLAS measurements of high-mass Drell-Yan dilepton production at centre-of-mass energy of 8 TeV is presented.
Knowledge of parton distribution functions (PDFs) at large momentum fraction $ x $ is not only important to study the flavor and spin dynamics of quarks in the nucleon, but also to search for signals of new physics at collider experiments. It is well known now that the nonperturbative QCD effects generally play a more significant role at such kinematic regions. In this work, we present an open-source QCD analysis of PDFs considering target mass corrections (TMCs) and higher-twist (HT) effects which are necessary when the analysis includes also data points from deep inelastic scattering (DIS) w…
We present {\tt GKG18-DPDFs}, a next-to-leading order (NLO) QCD analysis of diffractive parton distribution functions (diffractive PDFs) and their uncertainties. This is the first global set of diffractive PDFs determined within the {\tt xFitter} framework. This analysis is motivated by all available and most up-to-date data on inclusive diffractive deep inelastic scattering (diffractive DIS). Heavy quark contributions are considered within the framework of the Thorne-Roberts (TR) general mass variable flavor number scheme (GM-VFNS). We form a mutually consistent set of diffractive PDFs due to…
In this contribution, I present a new QCD fit to final combined HERA deep-inelastic scattering cross-section data incorporating $\ln(1/x)$-resummation terms. This fit has been performed within the xFitter framework. The main effect of including such resummed terms results not only in a better description of the low-$x$ and low-$Q^{2}$ data, but also in a steeply rising gluon PDF at low x for low scales. Furthermore, the kinematic region where this resummation is important is delineated. This contribution is based on the results presented in arXiv:1802.00064.
A new QCD analysis for nuclear parton distribution functions (nPDFs) at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) is presented. The framework of the analysis, including the form of the parameterization as well as the included DIS data sets, are discussed. The results of this QCD analysis are compared to the existing nPDF sets and to the fitted data. The presented framework is based on an open-source tool, xFitter, which has been modified to be applicable also for a nuclear PDF analysis. The required modifications are covered as well. Finally, an outlook for the next …
We introduce a new parametrization for the parton distribution functions (PDFs) designed to be flexible in the small-x region. We implement it in the xFitter open-source PDF fitting tool, and compare it to the default xFitter parametrization, widely used for many PDF studies, and notably for the HERAPDF determination. We find that we can describe the combined inclusive HERA I+II data using NNLO theory with a significantly higher quality than HERAPDF2.0: the $χ^2$ is reduced by more than 60 units, having used only four more parameters. Our result highlights a significant parametrization bias in…
We present new sets of nuclear parton distribution functions (nPDFs) at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO). Our analyses are based on deeply inelastic scattering data with charged-lepton and neutrino beams on nuclear targets. In addition, a set of proton baseline PDFs is fitted within the same framework with the same theoretical assumptions. The results of this global QCD analysis are compared to existing nPDF sets and to the fitted cross sections. Also, the uncertainties resulting from the limited constraining power of the included experimental data are prese…
Fits to the final combined HERA deep-inelastic scattering cross-section data within the conventional DGLAP framework of QCD have shown some tension at low $x$ and low $Q^2$. A resolution of this tension incorporating $\ln(1/x)$-resummation terms into the HERAPDF fits is investigated using the xFitter program. The kinematic region where this resummation is important is delineated. Such high-energy resummation not only gives a better description of the data, particularly of the longitudinal structure function $F_L$, it also results in a gluon PDF which is steeply rising at low $x$ for low scales…
A new parametrization for the parton distribution functions with a higher flexibility in the small-$x$ region is presented. It has been implemented in the xFitter open-source PDF fitting tool, and compared to the default xFitter parametrization, used for the determination of the HERAPDF set. It has been found that the combined inclusive HERA I+II data can be described using NNLO theory with a significantly higher quality than HERAPDF2.0: the $χ^2$ is reduced by more than 60 units, having used only four more parameters. Our result highlights a significant parametrization bias in the default xFi…
I present a determination of the photon PDF from a fit to the recent ATLAS measurements of high-mass Drell-Yan lepton-pair production at $\sqrt{s} = 8$ TeV. This analysis is based on the {\tt xFitter} framework interfaced to the {\tt APFEL} program, that accounts for NLO QED effects, and to the {\tt aMCfast} code to account for the photon-initiated contributions within {\tt MadGraph5\_aMC@NLO}. The result is compared with other recent determinations of the photon PDF finding a general good agreement.
We present new sets of nuclear parton distribution functions (nPDFs) at next-to-leading order and next-to-next-to-leading order in perturbative QCD. Our analyses are based on deeply inelastic scattering data with charged-lepton and neutrino beams on nuclear targets, and experimental data from measurements of $W^{\pm},\,Z$ boson production in p+Pb collisions at the LHC. In addition, a set of proton baseline PDFs is fitted within the same framework and with the same theoretical assumptions. The results of our global QCD analysis are compared to existing nPDF sets and to the previous nPDF set TUJ…
Nuclear parton distribution functions (nPDFs) can be determined in a global QCD analysis using a wide range of experimental data. In addition to older fixed-target deep inelastic scattering and Drell-Yan (DY) dilepton production data, several analyses from p+Pb collisions at the LHC provide further constraints and extend the kinematic reach of applicable data. Here we present an update of our previous TUJU19 analysis where we now include also electroweak-boson production data recently measured by ATLAS and CMS. For the first time, LHC data are included in a nPDF analysis performed at next-to-n…
Simultaneous extraction of top quark mass, strong coupling, effective mixing angle, and proton PDFs using inclusive DIS and proton-proton collision data
Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；Bergische Universität Wuppertal（伍珀塔尔大学）；Lunds universitet（隆德大学）；University of Hamburg（汉堡大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
We describe new QCD fits to diffractive proton structure functions measured at HERA, and we use these parton densities to predict the shape of the dijet mass fraction at the Tevatron and look for the existence of exclusive events in the dijet channel.
NLO QCD fits using the DGLAP formalism have been made to the high precision ZEUS $e^+p$ reduced cross-section data and to fixed target structure function data, in order to detrmine parton distribution functions and the value of $α_s(M^2_Z)$, taking full account of correlated systematic errors. Preliminary results are reported.
We discuss the results obtained by fitting the lattice data of the gauge-invariant field strength correlators in QCD with some particular functions which are commonly used in the literature in some phenomenological approaches to high-energy hadron-hadron scattering. A comparison is done with the results obtained in the original fits to the lattice data.
Experimental data obtained for the polarized Bjorken sum rule (BSR) $Γ_1^{p-n}(Q^2)$ are fitted by using predictions derived within a truncated operator product expansion (OPE) approach to QCD. Four QCD versions are considered: perturbative QCD (pQCD) in the MSbar scheme, Analytic Perturbation Theory (APT), and 2$δ$ and 3$δ$ analytic QCD versions. In contrast to pQCD, these QCD variants do not have Landau singularities at low positive $Q^2$, which facilitates the fitting procedure significantly. The fitting procedure is applied first to the experimental data of the inelastic part of BSR, and t…
Preliminary results are presented on the gluon density obtained from a QCD analysis of ZEUS and NMC F2 structure function data. Also given is an estimate of the experimental error on the positron-proton NC Born cross-section at large x and Q2.
We present a preliminary account of a new global QCD analysis of DIS data, including recent $ν, \bar ν$ DIS measurements. The model-independent cross section reanalysis by CCFR allows a new determination of the strange sea asymmetry, whose first moment is found to be small. The impact on the NuTeV measurement of $\sin^2 θ_W$ is discussed.
We report the parton distribution functions (PDFs) determined from the NNLO QCD analysis of the world inclusive DIS data with account of the precise NNLO QCD corrections to the evolution equations kernel. The value of strong coupling constant α_s^{NNLO}(M_Z)=0.1141(14), in fair agreement with one obtained using the earlier approximate NNLO kernel by van Neerven-Vogt. The intermediate bosons rates calculated in the NNLO using obtained PDFs are in agreement to the latest Run II results.
The most recent H1 and ZEUS data for diffractive structure functions are analyzed under three different theoretical approaches. This includes the Pomeron Structure Function (PSF) framework, Bartels-Ellis-Kowalski-Wusthoff (BEKW) color dipole approach and the Golec-Biernat-Wusthoff (GBW) saturation model. The models are shown to successfully fit the set of combined data. Conceptual differences between the models are discussed and, as an example, the prediction for the longitudinal diffractive structure function is presented.
An NLO QCD analysis of the ZEUS data on $e^+ p$ deep inelastic scattering together with fixed-target data has been performed from which the gluon and quark densities of the proton and the value of the strong coupling parameter, $α_s(M_Z^2)$, have been extracted. The study includes a full treatment of the experimental systematic uncertainties, including point-to-point correlations. Different ways of incorporating correlated systematic uncertainties into the fit are discussed and compared.
In this paper polarized valon distribution is derived from unpolarized valon distribution. In driving polarized valon distribution some unknown parameters exist which must be determined by fitting to experimental data. Here we have used Bernstein polynomial method to fit QCD predictions for the moments of $g_1^p$ structure function, to suitably the constructed appropriate average quantities of the E143 and SMC experimental data. After calculating polarized valon distributions and all parton distributions in a valon, polarized parton density in a proton are available. The results are used to ev…
We discuss the influence of fixed target Drell-Yan data on the extraction of parton distribution functions at next-to-next-to-leading order (NNLO) in QCD. When used in a parton distribution fit, the Drell-Yan (DY) data constrain sea quark distributions at large values of Bjorken x. We find that not all available DY data are useful for improving the precision of parton distribution functions (PDFs) obtained from a fit to the deep inelastic scattering (DIS) data. In particular, some inconsistencies between DIS-based parton distribution functions and DY data for large values of dilepton rapidity …
The high-precision HERA data can be used as an input to a QCD analysis within the DGLAP formalism to obtain the detailed description of the proton structure in terms of the parton distribution functions (PDFs). However, when searching for Beyond Standard Model (BSM) contributions in the data one should take into account the possibility that the PDF set may already have been biased by partially or totally absorbing previously unrecognised new physics contributions. The ZEUS Collaboration has proposed a new approach to the BSM analysis of the inclusive $ep$ data based on the simultaneous QCD fit…
The combined HERA-I data set, of neutral and charged current inclusive cross-sections for $e^+p$ and $e^-p$ scattering, is used as the sole input for a next-to-leading order (NLO) QCD parton distribution function (PDF) fit. The consistent treatment of systematic uncertainties in the joint data set ensures that experimental uncertainties on the PDFs can be calculated without need for an increased $χ^2$ tolerance. This results in PDFs with greatly reduced experimental uncertainties compared to the separate analyses of the ZEUS and H1 experiments. Model uncertainties, including those arising from…
Extraction of the Pion Unpolarized Quark Generalized Parton Distribution at Zero Skewness from Charge Form Factors
Dr. B.R. Ambedkar National Institute of Technology（B.R. 安贝德卡尔博士国立理工学院）；Institute of Physics, Academia Sinica（中央研究院物理研究所）；Moscow Institute of Physics and Technology (MIPT)（莫斯科物理技术学院（MIPT））；Doaba College（多阿巴学院）
We present the results of our QCD analysis for non-singlet unpolarized quark distributions and structure function $F_2(x,Q^2)$ up to N$^3$LO. In this regards 4-loop anomalous dimension can be obtain from the Padé approximations. The analysis is based on the Jacobi polynomials expansion of the structure function. New parameterizations are derived for the non-singlet quark distributions for the kinematic wide range of $x$ and $Q^2$. Our calculations for non-singlet unpolarized quark distribution functions up to N$^3$LO are in good agreement with available theoretical models. The higher twist con…
We try a global fit of the experimental branching ratios and CP-asymmetries of the charmless $B\to PV$ decays according to QCD factorisation. We find it impossible to reach a satisfactory agreement, the confidence level (CL) of the best fit is smaller than .1 %. The main reason for this failure is the difficulty to accomodate several large experimental branching ratios of the strange channels. Furthermore, experiment was not able to exclude a large direct CP asymmetry in $\bar {B^0}\toρ^+ π^-$, which is predicted very small by QCD factorisation. Trying a fit with QCD factorisation complemented…
Trying a global fit of the experimental branching ratios and CP-asymmetries of the charmless $B\to PV$ decays according to QCD factorization, we find it impossible to reach a satisfactory agreement, the confidence level (CL) of the best fit is smaller than .1 %. This failure reflects the difficulty to accommodate several large experimental branching ratios of the strange channels. Furthermore, experiment was not able to exclude a large direct CP asymmetry in $\bar {B}^0\toρ^+ π^-$, which is predicted very small by QCD factorization. Proposing a fit with QCD factorization complemented by a char…
In this paper I show that it is possible to use Regge theory to constrain the initial parton distribution functions of a global DGLAP fit. In this approach, both quarks and gluons have the same high-energy behaviour which may also be used to describe soft interactions. More precisely, I show that, if we parametrise the parton distributions with a triple-pole pomeron, {\em i.e.} like $\log^2(1/x)$ at small $x$, at $Q^2=Q_0^2$ and evolve these distribution with the DGLAP equation, we can reproduce $F_2^p$, $F_2^d$, $F_2^n/F_2^p$, $F_2^{νN}$ and $xF_3^{νN}$ for $W^2\ge 12.5$ GeV$^2$. In this case…
We use QCD light-cone sum rules with holographic anti de Sitter/Chromodynamics (AdS/QCD) Distribution Amplitudes (DAs) for the $K^*$ meson in order to predict the full set of seven $B \to K^*$ transition form factors for intermediate-to-high recoil of the vector meson. We provide simple parametrizations for the form factors that fit our AdS/QCD predictions. We also provide parametrizations that fit both our AdS/QCD predictions and the most recent lattice data for low recoil. We use our form factors to predict the differential and total branching fraction of the rare dileptonic decay $B \to K^*…
We analyze the CP asymmetries of $B\to ϕK$ and $B\to η^{(\prime)} K$ modes in the QCD improved factorization framework. For our calculation we use the phenomenological parameters predetermined from the global fit for the available $B\to PP$ and $VP$ modes (without the quark-level subprocess $b\to s\bar s s$). We show that the large negative $\sin (2ϕ_1)_{ϕK_s}$ and the large branching ratio for $B^{\pm}\to η' K^{\pm}$ can be simultaneously explained in the context of supersymmetry (SUSY). The R-parity conserving SUGRA models are used and their parameter space is constrained with the observed d…
We directly fit the experimentally measured energy dependence of the average value of 1-Thrust, <1-T>, over the e^+e^- centre-of-mass energy range Q=14 - 172 GeV to the QCD expectation obtained by integrating up the evolution equation for d<1-T>/dlog Q in terms of <1-T>. We fit for Lambda_QCD, uncalculated O(alpha_S^3) and higher perturbative corrections parameterized by the scheme invariant rho_2, and the parameter lambda which characterizes the magnitude of the leading 1/Q power corrections anticipated for <1-T>. A 3-parameter fit yields Lambda_QCD=245^{+20}_{-17} MeV, rho_2=-16\pm 11 and la…
A global fit to the shape of the first QCD Laplace sum rule exhibiting sensitivity to pion-resonance [$Π(1300)$] parameters is performed, leading to predictions for the pion-resonance mass and decay constant. This fit leads to predictions of $M_π = 1.15 \pm 0.15 GeV$ for the pion-resonance mass, and $F_π^2=(4.5\pm 2.1).(f_π^2m_π^4/M_π^4)$ for the pion-resonance decay constant.
This contribution reviews the QCD analysis of the H1 inclusive DIS data. Flavor separated parton densities are extracted in a NLO QCD fit using neutral and charged current HERA I data. The results of a dedicated QCD analysis of the gluon and $α_s$ are also reviewed.
We reanalyze deep inelastic scattering data of BCDMS Collaboration by including proper cuts of ranges with large systematic errors. We perform also the fits of high statistic deep inelastic scattering data of BCDMS, SLAC, NM and BFP Collaborations taking the data separately and in combined way and find good agreement between these analyses. We extract the values of both the QCD coupling constant α_s(M^2_Z) up to NLO level and of the power corrections to the structure function F_2. The fits of the combined data for the nonsinglet part of the structure function F_2 predict the coupling constant …
We present fits to charmless hadronic B decay data from the BaBar, Belle and Cleo experiments using two theoretical models: (i) the QCD factorization model of Beneke et al. and (ii) QCD factorization complemented with the so-called charming penguins of Ciuchini et al. When we include the data from pseudoscalar-vector decays the results favor the incorporation of the charming penguin terms. We also fit results for the unitarity triangle parameters and the CP-violating asymmetries.
We report on the extension of the data fitting considering the QCD inspired model based on the summation of gluon ladders applied to the $ep$ scattering. In lines of a two Pomeron approach, the structure function $F_2$ has a hard piece given by the model and the remaining soft contribution: a soft Pomeron and non-singlet content. In this contribution, we carefully estimate the relative role of the hard and the soft pieces from a global fit in a large span of $x$ and $Q^2$.
We present a global fit of current available experimental results on $χ_c$ decays within next-to-leading-order perturbative QCD. The quality and reduced errors of recent data improve the agreement between theory and experiment.
The proton diffractive structure function $F_2^{D(3)}$ measured in the H1 and ZEUS experiments at HERA is analyzed in terms of both Regge phenomenology and perturbative QCD evolution. A new method determines the values of the Regge intercepts in ``hard'' diffraction, confirming a higher value of the Pomeron intercept than for soft physics. The data are well described by a QCD analysis in which point-like parton distributions, evolving according to the DGLAP equations, are assigned to the leading and sub-leading Regge exchanges. The gluon distributions are found to be quite different for H1 and…
We study the internal structure of the pion using a model inspired by the AdS/QCD correspondence. The holographic approach provides the light-front wave function (LFWF) for the leading Fock state component of the pion. We adopt two different forms for the LFWF derived from the AdS/QCD soft-wall model, with free parameters fitted to the available experimental information on the pion electromagnetic form factor and the leading-twist parton distribution function. The intrinsic scale of the model is taken as an additional fit parameter. Within this framework, we provide predictions for the unpolar…
HERAFitter is an open-source package that provides a framework for the determination of the parton distribution functions (PDFs) of the proton and for many different kinds of analyses in Quantum Chromodynamics (QCD). It encodes results from a wide range of experimental measurements in lepton-proton deep inelastic scattering and proton-proton (proton-antiproton) collisions at hadron colliders. These are complemented with a variety of theoretical options for calculating PDF-dependent cross section predictions corresponding to the measurements. The framework covers a large number of the existing …
We present the results of a QCD fit to global data on deep-inelastic polarised lepton-hadron scattering. We find that it is possible to fit the data with strongly broken SU(2) flavour for the polarised sea densities. This can easily be tested in $W$ production at polarised RHIC. The data fails to pin down polarised singlet sea quark and gluon densities. We explore the uncertainties in detail and show that improvement in statistics, achievable at polarised HERA for measurement of A_1 at moderately low values of x, have large payoffs in terms of the improvement in measurement of gluon and sea qu…
The recent measurements of the B_s meson mixing amplitude by CDF and of the leptonic branching fraction BR(B to tau nu) by Belle call for an upgraded analysis of the Unitarity Triangle in the Standard Model. Besides improving the previous constraints on the parameters of the CKM matrix, these new measurements, combined with the recent determinations of the angles alpha, beta and gamma from non-leptonic decays, allow, in the Standard Model, a quite accurate extraction of the values of the hadronic matrix elements relevant for K-Kbar and B_{s,d}-B_{s,d}bar mixing and of the leptonic decay consta…
Linear and non-linear QCD evolutions at high energy suffer from severe issues related to convergence, due to higher order corrections enhanced by large double and single transverse logarithms. We resum double logarithms to all orders by taking into account successive soft gluon emissions strongly ordered in lifetime. We further resum single logarithms generated by the first non-singular part of the splitting functions and by the one-loop running of the coupling. The resulting collinearly improved BK equation admits stable solutions, which are used to successfully fit the HERA data at small-x f…
