QCD Coupling Constant Research Articles

Not all that is β0 is β-function: the DGLAP resummation and the running coupling in NLO JIMWLK

We reanalyze the origin of the large transverse logarithms associated with the QCD one loop β function coefficient in the NLO JIMWLK Hamiltonian. We show that some of these terms are not associated with the running of the QCD coupling constant but rather with the DGLAP evolution. The DGLAP-like resummation of these logarithms is mandatory within the JIMWLK Hamiltonian, as long as the color correlation length in the projectile is larger than that in the target. This regime in fact covers the whole range of rapidities at which JIMWLK evolution is supposed to be applicable. We derive the RG equation that resums these logarithms to all orders in αs in the JIMWLK Hamiltonian. This is a nonlinear equation for the eikonal scattering matrix S(x). We solve this equation, and perform the DGLAP resummation in two simple cases: the dilute limit, where both the projectile and the target are far from saturation, and the saturated regime, where the target correlation length also determines its saturation momentum.

A new method that automatically regularizes scattering amplitudes

We present a new regularization procedure called autoregularization. The new procedure regularizes the divergences, encountered previously in a scattering process, using the intrinsic scale of the process. We use autoregularization to calculate the amplitudes of several scattering processes in QED and compare the calculations with experimental measurements over a broad range of center-of-momentum energies (≲MeV to ≳200 GeV). The calculated amplitudes are found to be in good agreement with experimental data. 1 1 Specifically, the O(α) correction to electron’s gyromagnetic ratio predicted by autoregularization agrees with experimental measurement to within 0.06% (Section ), which is to be compared to Schwinger’s O(α) correction which agrees with experimental measurement to within 0.15%; the O(α) estimate of the Lamb shift predicted by autoregularization agrees with the experimental measurements to within 0.33% (section ); the running fine structure constant predicted by autoregularization at O(α) agrees with the prediction of cutoff regularization to within 0.8% over one to four orders of magnitude above the electron’s mass scale (section ); the tree-level prediction of autoregularization for Compton scattering is in better agreement with experimental data than the prediction of the well-known Klein-Nishina formula by about 4.02% (section ); the tree-level predicition of autoregularization for pair annihilation at center-of-momentum energy of 206.671 GeV agrees with the experimental data about 0.67 % better than the prediction of the standard QED (section ). To test autoregularization in a non-Abelian gauge theory, we calculate the QCD coupling constant at 1-loop and show that, like the known regularization schemes, autoregularization also predicts asymptotic freedom in QCD. Finally, we show that the vacuum energy density of the free fields in the Standard Model, calculated using autoregularization, is smaller than the current estimate of the cosmic critical density.

Nonperturbative strong coupling at timelike momenta

We compute the strong coupling constant of Landau gauge QCD in the full complex momentum plane, both directly and via spectral reconstruction. In particular, we consider the Taylor coupling given by the product of ghost and gluon dressing functions. Assuming spectral representations for the latter, we first show that also the coupling obeys such a representation. The subsequent spectral reconstruction of the coupling data, obtained from 2+1 flavour lattice QCD results for the ghost and gluon, is based on a probabilistic inversion of this representation using Gaussian process regression with analytically enforced asymptotics. In contradistinction, our direct calculation relies on earlier reconstruction results for the ghost and gluon spectral functions themselves, as well as data obtained in functional QCD. Apart from its relevance for studies of resonances or scattering processes, the calculation also serves as a non-trivial benchmark of our reconstruction approach. The results show remarkable agreement, testifying to the reliability of the method.

Parton distribution functions and QCD coupling constant from LHC and non-LHC data

We present a new QCD analysis of parton distribution functions (PDFs) at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO). In the present paper, the role of special types of experimental measurements for extracting PDFs is investigated, and simultaneously the values of the strong coupling constant are determined. Essential elements of this QCD analysis are the HERA combined data as a base, heavy-quark cross-section measurement together with Tevatron data on jet production and H1 and ZEUS jet cross sections as ``non-LHC'' data, and especially the ``LHC'' dataset for top-quark and jet cross sections. These different datasets have allowed detailed information at low $x$, providing worthwhile information on the nucleon's flavor, and have played an important role for some PDFs at large-$x$ and strong coupling constant. Since the large-$x$ gluon PDF benefits from an accurate determination of quark PDFs, we have enough motivation to focus on the top-quark production and jet cross-section measurements from LHC to find the impact of these data on the gluon PDF and strong coupling constant. These experimental data have an impact on the relative uncertainties of PDF. The gluon PDF at large $x$ and the values of ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})$ are affected significantly. Although the main motivation of this paper is to focus on the gluon PDF and its uncertainty at large-$x$, giving notice to heavy PDF behavior in this region is also very important. We study the intrinsic charm (IC) using the BHPS model together with our extracted extrinsic charm PDF at large $x$, which can be very worthwhile for future experiments at the LHC.

Fractional analytic QCD beyond leading order

Fractional analytic QCD is constructed beyond leading order using the standard inverse logarithmic expansion. It is shown that, contrary to the usual QCD coupling constant, for which this expansion can be used only for large values of its argument, in the case of analytic QCD, the inverse logarithmic expansion is applicable for all values of the argument of the analytic coupling constant. We present four different views, two of which are based primarily on Polylogarithms and generalized Euler ζ-functions, and the other two are based on dispersion integrals. The results obtained up to the 5th order of perturbation theory, have a compact form and do not contain complex special functions that were used to solve this problem earlier. As an example, we apply our results to study the polarized Bjorken sum rule, which is currently measured very accurately.

New derivation of the twist-3 gluon fragmentation contribution to polarized hyperon production

A novel method of formulating the twist-3 gluon fragmentation function contribution to hyperon polarization in the proton-proton collision is presented. The method employs a covariant gauge and takes full advantage of the Ward-Takahashi identities before performing the collinear expansion. It provides a robust way of constructing the general cross section formula and also a clear understanding for the absence of the ghostlike terms in the twist-3 cross section in the leading order with respect to the QCD coupling constant.

NLO JIMWLK evolution with massive quarks

NLO evolution of the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) equation with massless quarks was derived a few years ago. We make a step further to compute the evolution kernels focusing on the effects due to finite quark masses. To this goal, the light-cone wave function of a fast moving dilute hadronic projectile is computed up to mathcal{O} (g3) in QCD coupling constant. Compared with the massless case, a new IR divergence emerges, which is eventually canceled by a mass dependent counter term. Our results extend the theoretical tools used in physics of gluon saturation and aim at improving precision in future phenomenological applications.

Transverse polarization of hyperons produced in semi-inclusive deep inelastic scattering

We study the transverse polarization of hyperons produced in semi-inclusive deep inelastic scattering, $ep\to e\Lambda^\uparrow X$, in the framework of the collinear twist-3 factorization. The cross section from the twist-3 distribution functions and the twist-3 quark fragmentation functions is computed in the leading order with respect to the QCD coupling constant. The constraint relations among the twist-3 FFs are taken into account to simplify the formula. The formula is relevant to large-$P_T$ hyperon production in the future Electron-Ion-Collider experiment.

Dilepton production in the SMEFT at O(1/Λ4)

We study the inclusion of $\mathcal O(1/\Lambda^4)$ effects in the Standard Model Effective Field Theory in fits to the current Drell-Yan data at the LHC. Our analysis includes the full set of dimension-6 and dimension-8 operators contributing to the dilepton process, and is performed to next-to-leading-order in the QCD coupling constant at both $\mathcal O(1/\Lambda^2)$ and $\mathcal O(1/\Lambda^4)$. We find that the inclusion of dimension-6 squared terms and certain dimension-8 operators has significant effects on fits to the current data. Neglecting them leads to bounds on dimension-6 operators off by large factors. We find that dimension-8 four-fermion operators can already be probed to the several-TeV level by LHC results, and that their inclusion significantly changes the limits found for dimension-6 operators. We discuss which dimension-8 operators should be included in fits to the LHC data. Only a manageable subset of two-derivative dimension-8 four-fermion operators need to be included at this stage given current LHC uncertainties.

Twist-3 gluon fragmentation contribution to polarized hyperon production in unpolarized proton-proton collision

Understanding the origin and mechanism of the transverse polarization of hyperons produced in unpolarized proton-proton collision, $pp\to \Lambda^\uparrow X$, has been one of the long-standing issues in high-energy spin physics. In the framework of the collinear factorization applicable to large-$p_T$ hadron productions, this phenomenon is a twist-3 observable which is caused by multi-parton correlations either in the initial protons or in the process of fragmentation into the hyperon. We derive the twist-3 gluon fragmentation function (FF) contribution to this process in the leading order (LO) with respect to the QCD coupling constant. Combined with the known results for the contribution from the twist-3 distribution function and the twist-3 quark FF, this completes the LO twist-3 cross section. We also found that the model independent relations among the twist-3 gluon FFs based on the QCD equation of motion and the Lorentz invariance property of the correlation functions guarantee the color gauge invariance and the frame-independence of the cross section.

Reanalysis of the top-quark pair hadroproduction and a precise determination of the top-quark pole mass at the LHC * *Supported in part by the Natural Science Foundation of China (11625520, 11705033, 11905056, 11947406), the Project of Guizhou Provincial Department (KY[2021]003) and the Department of Energy Contract (DE-AC02-76SF00515. SLAC-PUB-17567)

In this study, we calculate the pQCD production cross-section at the NNLO and determine the top-quark pole mass from recent measurements at the LHC at the center-of-mass energy TeV to a high precision by applying the principle of maximum conformality (PMC). The PMC provides a systematic method that rigorously eliminates QCD renormalization scale ambiguities by summing the nonconformal contributions into the QCD coupling constant. The PMC predictions satisfy the requirements of renormalization group invariance, including renormalization scheme independence, and the PMC scales accurately reflect the virtuality of the underlying production subprocesses. By using the PMC, an improved prediction for the production cross-section is obtained without scale ambiguities, which in turn provides a precise value for the top-quark pole mass. Moreover, the prediction of PMC calculations that the magnitudes of higher-order PMC predictions are well within the error bars predicted from the known lower-order has been demonstrated for the top-quark pair production. The resulting determination of the top-quark pole mass, GeV, from the LHC measurement at TeV agrees with the current world average cited by the Particle Data Group (PDG). The PMC prediction provides an important high-precision test of the consistency of pQCD and the SM at TeV with previous LHC measurements at lower CM energies.

The Debye length and the running coupling of QCD: A potential and phenomenological approach

In this paper, one uses a damped potential to present a description of the running coupling constant of QCD in the confinement phase. Based on a phenomenological perspective for the Debye screening length, one compares the running coupling obtained here with both the Brodsky–de Téramond–Deur and the Richardson approaches. The results seem to indicate the model introduced here corroborate the Richardson approach. Moreover, the Debye screening mass in the confinement phase depends on a small parameter, which tends to vanish in the nonconfinement phase of QCD.

The Monte Carlo Program KKMC, for the Lepton or Quark Pair Production at LEP/SLC Energies—Updates of electroweak calculations

Since the {\tt KKMC} program was published for the first time over 20 years ago, it has gained popularity and was exploited in a broad spectrum of applications. The core part of the program itself did not change much. In contrast, some of the libraries have evolved substantially. The aim of this publication is to archive four versions, alternative to the one published 20 years ago versions of the electroweak libraries (or just parameter initialization versions), which were instrumental for the precision Standard Model calculation from the end of LEP era till now and for the sake of the future applications/comparisons for the future electron-positron colliders, in particular for the FCC-ee related studies. These electroweak libraries are useful for the hadron collider applications as well, for instance for {\tt KKMC-hh} or {\tt TauSpinner} projects.

Chiral effective Lagrangian for heavy-light mesons from QCD

We derive the chiral effective Lagrangian for heavy-light mesons in the heavy quark limit from QCD under proper approximations. The low energy constants in the effective Lagrangian are expressed in terms of the light quark self-energy. With typical forms of the running coupling constant of QCD and the quark self-energy obtained from Dyson-Schwinger equations as well as lattice QCD, we estimate the low energy constants in the model and the strong decay widths. A comparison with data and some discussions of the numerical results are presented.

Renormalization scale setting for heavy quark pair production in e+e− annihilation near the threshold region

Heavy fermion pair production in $e^+e^-$ annihilation is a fundamental process in hadron physics and is of considerable interest for various phenomena. In this paper, we will apply the Principle of Maximum Conformality (PMC) to provide a comprehensive analysis of these processes. The PMC provides a systematic, unambiguous method for determining the renormalization scales of the QCD coupling constant for single-scale and multiple-scale applications. The resulting predictions eliminate any renormalization scheme-and-scale ambiguities, eliminate the factorial renormalon divergences, and are consistent with the requirements of the renormalization group. It is remarkable that two distinctly different scales are determined by using the PMC for heavy fermion pair production near the threshold region. One scale is the order of the fermion mass $m_f$, which enters the hard virtual corrections, and the other scale is of order $ v\,m_f$, where $v$ is the quark velocity, which enters the Coulomb rescattering amplitude. The PMC scales yield the correct physical behavior and reflect the virtuality of the propagating gluons (photons) for the QCD (QED) processes. Moreover, we demonstrate the consistency of PMC scale setting from QCD to QED. Perfect agreement between the Abelian unambiguous Gell-Mann-Low and the PMC scale-setting methods in the limit of zero number of colors is demonstrated.

The Odderon in QCD with running coupling

Starting from the leading Odderon solution of the three gluon system in perturbative QCD we introduce, as a first step towards the transition to the non-perturbative region, an infrared cutoff and use the running QCD coupling constant. In our numerical analysis we find that the fixed cut solution with intercept one persists, hinting at a physical Odderon with intercept one and a small t-slope.

Nonsinglet polarized nucleon structure function in infrared-safe QCD

The polarized nucleon structure function in the nonsinglet case is investigated here by a new insight rather than conventional perturbative QCD (pQCD). For this purpose we note that the solution of the evolution equations in moment space involves noninteger powers of the coupling constant. Therefore it is possible to employ a new approach which is called fractional analytical perturbation theory Consequently, it is possible to remove the Landau singularities of the renormalized coupling, i.e., at the scales $Q \sim \Lambda$, using this approach. This provides an opportunity to continue the desired calculations toward small values of energy scales even less than the $\Lambda$ scale. To modify the analytical perturbation theory, a newer approach is introduced, called 2$\delta$anQCD, in which the spectral function of the holomorphic coupling is parameterized in the low-energy region by two delta functions. This model gives us more reliable results for the considered QCD observables, even in the deep infrared region. We calculate the nonsinglet part of the polarized nucleon structure function, using the 2$\delta$anQCD model, and compare it with the result from the underlying pQCD where both are in a new defined scheme, called the Lambert scheme. For this purpose we employ the anQCD package in the \textit{Mathematica} environment to establish the analytic (holomorphic) coupling constant. The results at various energy scales are also compared with the available experimental data, and it turns out that there is a good consistency between them. The results show that the obtained nucleon structure function at small energy scales has smoother behavior when using the 2$\delta$anQCD model than the underlying pQCD. In fact the coupling constant in analytic QCD behaves moderately and it makes the result approach the available data in a better way.

Eta-nucleon and eta-prime-nucleon coupling constants in QCD and the role of gluons

Coupling constants of η and η′ mesons with nucleons have been calculated using the method of QCD sum rules. Starting from vacuum-to-meson correlation function of interpolating fields of two nucleons, its matrix element with respect to nucleon spinors has been considered. Coupling constants at the physical points have been estimated from extrapolation of results obtained at two other points. Anomalous glue has been found to give substantial contribution to the coupling constants and also accounts for a significant OZI-rule violation.

Heavy quark fragmentation function in the noncommutative Standard Model

The dominant mechanism to produce hadronic bound states with large transverse momentum is fragmentation. The hadronization processes are described by the fragmentation functions (FFs) which are universal and process-independent functions. In this paper, we study for the first time the noncommutative effects to the FF of a heavy quark to fragment into heavy mesons to leading order in the QCD coupling constant. As an example, we focus on the FF of a charm quark to split into the S-wave D-meson and compare our analytical results with both the experimental data and a well-known phenomenological model. Here, we compute the corrections of FFs induced by noncommutativity and find a bound on the energy scale where the noncommutative effects of the space-time will be relevant.

Proof of factorization of heavy quarkonium production in non-equilibrium QCD at RHIC and LHC

Recently we have proved the NRQCD factorization in heavy quarkonium production at high energy colliders at all orders in coupling constant. In this paper we extend this to non-equilibrium QCD and prove the NRQCD factorization in heavy quarkonium production at all orders in coupling constant in non-equilibrium QCD. This proof is necessary to study heavy quarkonium production from quark gluon plasma at RHIC and LHC.