QCD with Analytic Coupling: Recent Results
This work provides an overview of recent results obtained in the framework of QCD with analytic coupling. Applications to the polarized Bjorken and Gross-Llewellyn Smith sum rules are considered.
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arXiv subjects
A. V. Kotikov
Publications and source records attributed to A. V. Kotikov.
Analytic QCD: Recent Results
We present a brief overview of analytical QCD, focusing primarily on a less common form of the analytical coupling A_{\rm MA}(Q^2), which is particularly convenient for Q^2\simΛ^2. This form has been extensively used in recent studies of the (polarized) Bjorken sum rule and the Gross-Llewellyn Smith sum rule.
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QCD analytic coupling
A brief overview of QCD analytic coupling is presented, mainly following the results obtained in [1]. An application to the pion-photon transition form factor is demonstrated.
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Pion-photon transition form factor with analytic coupling
We investigate the pion-photon transition form factor within the framework of analytic QCD. A comparison is performed between experimental data and perturbative QCD based on conventional and analytic versions of perturbation theory with the ``massive'' form of the twist-four contribution. We show that conventional perturbation theory fails to reproduce the data, while the analytic version demonstrates good agreement with experiment.
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Non-perturbative effects and soft-gluon dynamics in low-$p_T$ Drell-Yan production
The transverse-momentum spectrum of Drell--Yan lepton pairs at small \ptll\ probes non-perturbative QCD effects, including intrinsic partonic transverse momentum and initial-state soft-gluon radiation. The novel \pythiaPB\ approach, which implements the Parton Branching (\PB ) framework in \pythia\ while employing the same evolution ingredients, is used to study this spectrum in the low-\ptll\ region. This framework is particularly well suited for such investigations, as it allows for a systematic treatment of the dominant non-perturbative effects and their interplay. We examine in detail the implementation of primordial transverse momentum in \pythiaPB . With an improved recoil treatment, we determine the width of the intrinsic-\kt\ distribution and find a \sqrts\ dependence that is steeper than in \PB , but much flatter than in \pythia . We identify the origin of these differences. Furthermore, different treatments of the strong coupling at low scales are investigated and confronted with available experimental data. We find that, at the highest centre-of-mass energy considered, the low-\ptll\ Drell--Yan spectrum becomes sensitive to the transition between the perturbative and non-perturbative regimes.
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Testing the nuclear TMD gluon densities with heavy flavor production in proton-lead collisions at LHC
We employ a simple model for nuclear modification of ordinary parton densities in a proton to evaluate the Transverse Momentum Dependent gluon and quark distributions in nuclei (nTMDs) within the popular Kimber-Martin-Ryskin/Watt-Martin-Ryskin approach. The model is based on a global analysis of available deep inelastic scattering data for different nuclear targets within the rescaling model, incorporating Fermi motion effects. The derived nTMDs are tested with latest CMS data on inclusive $b$-jet and $B^+$ meson production in proton-lead collisions collected at $\sqrt s = 5.02$ and $8.16$~TeV using the High Energy Factorization framework. We predict the corresponding nuclear medium modification factors to be about of $0.8 - 1.2$ in the probed kinematical region, which is consistent with other estimations. Specially we highlight a possibility to investigate the nuclear modification of parton densities by applying different cuts on the final states in such processes.
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Gross-Llewellyn Smith sum rule with analytic coupling
We investigate the Gross-Llewellyn Smith sum rule within the framework of analytic QCD. A comparison is performed between experimental data, lattice calculations, and perturbative QCD based on conventional and analytic versions of perturbation theory with different parametrizations for the twist-four contribution. We show that conventional perturbation theory fails to reproduce the data, while the analytic version demonstrates good agreement with experiment and lattice calculations. We also discuss the relation between the Gross-Llewellyn Smith sum rule and the Bjorken sum rule.
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A simple model for PDFs and nPDFs
We present the main results of our recent papers, where we derived an analytical solution of the QCD evolution equations for parton distribution functions. The valence and non-singlet quark components satisfy the Gross-Llewellyn-Smith and Gottfried sum rules, respectively, while momentum conservation is maintained for the singlet quark and gluon densities. Several phenomenological parameters were extracted from a combined fit to precision data on the proton structure function $F_2(x,Q^2)$ collected by the BCDMS, H1, and ZEUS Collaborations, comprising a total of 933 points from 5 datasets. We proposed a model for nuclear medium modifications of parton densities. The approach is based on a global analysis of available deep inelastic scattering data for different nuclear targets within the rescaling model, incorporating Fermi motion effects. By fitting the rescaling parameters to experimental data on the ratio $F_2^A(x,Q^2)/F_2^{D}(x,Q^2)$ for several nuclear targets $A$, we obtained predictions for nuclear parton distribution functions.
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Transverse momentum dependent gluon density in a proton at low $x$ in the Laplace transform method
We investigate the gluon distribution in a proton at very low $x$, both integrated and transverse momentum dependent, using the Laplace transform technique. By accounting for leading and main next-to-leading contributions, we derive compact analytical expressions for the gluon densities valid in the asymptotic limit $x \to 0$. Our results closely match those from other analytical and numerical approaches, with the main advantage being the simplicity of the expressions, which capture the essential features of more complex calculations.
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A simple model for nuclear modification of parton distribution functions
A model for nuclear medium modification of parton densities is presented. The approach is based on the global analysis of available deep inelastic scattering data for different nuclear targets within the rescaling model combined with taking into account the effects of Fermi motion. The scale dependence is implemented into the DGLAP-evolved quark and gluon densities in a proton derived analytically at the leading order of QCD coupling. By fitting the rescaling parameters to experimental data on the ratio $F_2^A(x,Q^2)/F_2^{A^\prime}(x,Q^2)$ for several nuclear targets $A$ and $A^\prime$, we obtain redictions for nuclear parton distributions, even for unmeasured nuclei. The effects of nuclear modifications are investigated with respect to the mass number $A$. Our results highlight distinct shadowing and antishadowing behaviors for gluons and quarks.
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Updating TMD parton densities in a proton within the Kimber-Martin-Ryskin approach
We present analytical expressions for the Transverse Momentum Dependent (TMD, or unintegrated) gluon and quark densities in a proton derived at leading order of QCD running coupling and valid at both small and large x. The calculations are performed using the Kimber-Martin-Ryskin/Watt-Martin-Ryskin prescription (in both differential and integral formulations) with different treatment of kinematical constraint, which reflects the angular and strong ordering conditions for parton emissions. As an input, analytical solution of QCD evolution equations for conventional (collinear) parton distributions is applied, where the valence and non-singlet quark parts obey the Gross-Llewellyn-Smith and Gottfried sum rules and momentum conservation for the singlet quark and gluon densities is taken into account. Several phenomenological parameters are extracted from combined fit to precision data on the proton structure function $F_2(x,Q^2)$ collected by the BCDMS, H1 and ZEUS Collaborations, comprising a total of 933 points from 5 data sets. Comparison with the numerical results obtained by other groups is presented and phenomenological application to the inclusive b-jet production at the LHC is given.
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On Bjorken sum rule: heavy quarks and analytic coupling
We present the results of [1], where good agreement was obtained between calculations within the framework of analytic QCD and experimental data on polarized Bjorken sum rule. The heavy quark contributions are taken into account.
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The strong coupling constant: State of the art and the decade ahead
Theoretical predictions for particle production cross sections and decays at colliders rely heavily on perturbative Quantum Chromodynamics (QCD) calculations, expressed as an expansion in powers of the strong coupling constant $α_s$. The current $\mathcal{O}(1\%)$ uncertainty of the QCD coupling evaluated at the reference Z boson mass, $α_s(m_Z) = 0.1179 \pm 0.0009$, is one of the limiting factors to more precisely describe multiple processes at current and future colliders. A reduction of this uncertainty is thus a prerequisite to perform precision tests of the Standard Model as well as searches for new physics. This report provides a comprehensive summary of the state-of-the-art, challenges, and prospects in the experimental and theoretical study of the strong coupling. The current $α_s(m_Z)$ world average is derived from a combination of seven categories of observables: (i) lattice QCD, (ii) hadronic $τ$ decays, (iii) deep-inelastic scattering and parton distribution functions fits, (iv) electroweak boson decays, hadronic final-states in (v) $e^+e^-$, (vi) e-p, and (vii) p-p collisions, and (viii) quarkonia decays and masses. We review the current status of each of these seven $α_s(m_Z)$ extraction methods, discuss novel $α_s$ determinations, and examine the averaging method used to obtain the world-average value. Each of the methods discussed provides a ``wish list'' of experimental and theoretical developments required in order to achieve the goal of a per-mille precision on $α_s(m_Z)$ within the next decade.
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Heavy quark contributions in Bjorken sum rule with analytic coupling
We consider heavy quark contributions to the polarized Bjorken sum rule. We found good agreement between the experimental data and the predictions of analytic QCD. To satisfy the limit of photoproduction, we use new representation of the perturbative part of the polarized Bjorken sum rule, proposed recently.
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On Bjorken sum rule with analytic coupling
We present the results of [1], where good agreement was obtained between calculations within the framework of analytic QCD and experimental data on polarized Bjorken sum rule. The photoproduction limit was also considered and a new representation of the perturbative contribution to the polarized Bjorken sum rule was obtained.
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On anomalous dimension in 3D ABJM model
Anomalous dimension of the shortest single-trace operator is calculated in a simple form for the fishnet limit of the twisted ABJM model in 3D.
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Shadowing and antishadowing in the rescaling model
Nuclear deep inelastic structure functions F_2^A(x,Q^2) as well as parton distribution functions in a nuclei are investigated in the framework of rescaling model. Our analysis is based on analytical expressions for quark and gluon densities in a proton derived at the leading order of QCD coupling. By fitting the rescaling parameters from the experimental data on F_2^A(x,Q^2)/F_2^D(x,Q^2) ratio for several nuclear targets, we derive predictions for corresponding nuclear parton distributions and, thus, for shadowing and antishadowing effects.
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Bjorken sum rule with analytic coupling
We found good agreement between the experimental data obtained for the polarized Bjorken sum rule and the predictions of analytic QCD, as well as a strong difference between these data and the results obtained in the framework of perturbative QCD. To satisfy the limit of photoproduction and take into account Gerasimov-Drell-Hearn and Burkhardt-Cottingham sum rules, we develope new representation of the perturbative part of the polarized Bjorken sum rule.
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