QCD Coupling Research Articles

Bjorken polarised sum rule with IR-finite QCD coupling

We evaluate the Bjorken polarised sum rule (BSR) Γ‾1p−n(Q2) with truncated Operator Product Expansion (OPE) up to the dimension D=4 terms; the leading-twist (D=0) contribution is evaluated with a renormalon motivated resummation, where we use the IR-finite running coupling free of Landau singularities. The free residue parameters at the D=2 and D=4 terms are then extracted by fits to the experimental BSR data. In comparison to the case when perturbative QCD coupling is used in this approach (cf. Refs. [1,2]), many advantages become manifest in the present case: (a) no regularisation in the resummation integral is needed; (b) the Q2-interval in the fit can be significantly extended to lower Q2-values; (c) the extracted residue parameter values are more stable, this being reflected in the significantly reduced experimental uncertainties of these values and the suppressed (almost negligible) central extracted value of the D=4 residue parameter (μ6).

Ladder top-quark condensation imprints in supercooled electroweak phase transition

The electroweak (EW) phase transition in the early Universe might be supercooled due to the presence of the classical scale invariance involving Beyond the Standard Model (BSM) sectors and the supercooling could persist down till a later epoch around which the QCD chiral phase transition is supposed to take place. Since this supercooling period keeps masslessness for all the six SM quarks, it has simply been argued that the QCD phase transition is the first order, and so is the EW one. However, not only the QCD coupling but also the top Yukawa and the Higgs quartic couplings get strong at around the QCD scale due to the renormalization group running, hence this scenario is potentially subject to a rigorous nonperturbative analysis. In this work, we employ the ladder Schwinger-Dyson (LSD) analysis based on the Cornwall-Jackiw-Tomboulis formalism at the two-loop level in such a gauge-Higgs-Yukawa system. We show that the chiral broken QCD vacuum emerges with the nonperturbative top condensate and the lightness of all six quarks is guaranteed due to the accidental U(1) axial symmetry presented in the top-Higgs sector. We employ a quark-meson model-like description in the mean field approximation to address the impact on the EW phase transition arising due to the top quark condensation at the QCD phase transition epoch. In the model, the LSD results are encoded to constrain the model parameter space. We then observe the cosmological phase transition of the first-order type and discuss the induced gravitational wave (GW) productions. We find that in addition to the conventional GW signals sourced from an expected BSM at around or over the TeV scale, the dynamical topponium-Higgs system can yield another power spectrum sensitive to the BBO, LISA, and DECIGO, etc.

Analytical Inverse QCD Coupling Constant Approach and Its Result for αs

We propose a model for the QCD running coupling constant based on the analytical inverse QCD coupling constant concept with an additional regularization in the low momentum region. Analyticity in the q2-complex plane, where q is the four-momentum transfer, is imposed by methods of the Analytic Perturbation Theory. The model incorporates a peculiar low-momentum behavior for αs(q2) as a divergence at q2=0 to retrieve color confinement, without spoiling its correct high-momentum behavior. This was achieved by means of a two-parameter regularization function, for which we considered three possible analytic expressions. In fact, within the framework of the Analytic Perturbation Theory, αs(q2) assumes a finite value for q2=0, at all perturbative orders (infrared stability), hence the infrared divergence cannot be implemented. For this reason, we found it more straightforward to work with its reciprocal, namely, εs(q2)=1/αs(q2), imposing its vanishing at the origin of the q2-complex plane via the multiplication of the aforementioned regularizing functions and the spectral density. Once the two free parameters of the regularization functions were settled by fitting to the experimental values of αs(q2) at the momenta where these data were available and reliable, the model could reproduce the QCD running coupling constant at any other momentum transferred.

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.

Magnetic corrections to the QCD coupling: Strong field approximation

We compute the one-loop vertex function of the QCD coupling in the presence of an ultraintense magnetic field. From the vertex function, we extract the effective coupling and show that it grows with increasing magnetic field. We consider the quark-gluon vertex and the three-gluon vertex, accounting for the propagators of charged particles within the loops using the lowest Landau level approximation in order to satisfy the condition where the magnetic field is the largest energy scale. Under this approximation, we find that the contribution from the three-gluon vertex vanishes. Therefore, this result arises from the competition between the color charge associated to gluons and to quarks as well, with the former being larger than the latter. The behavior of the QCD coupling as a function of the magnetic field strength is analogous to that exhibited by the light-quark condensate, indicating the magnetic catalysis occurs. This increasing behavior stems from the dominant contribution of color charge associated to gluons in the vertex function. Published by the American Physical Society 2024

Baryonic screening masses in QCD at high temperature

We compute the baryonic screening masses of the nucleon and of its negative parity partner in thermal QCD with Nf=3 massless quarks for a wide range of temperatures, from T∼1 GeV up to ∼160 GeV. The computation is performed by Monte Carlo simulations of lattice QCD with O(a)-improved Wilson fermions by exploiting a recently proposed strategy to study non-perturbatively QCD at very high temperature. Very large spatial extensions are considered in order to have negligible finite volume effects. For each temperature we have simulated 3 or 4 values of the lattice spacing, so as to perform the continuum limit extrapolation with confidence at a few permille accuracy. The degeneracy of the positive and negative parity-state screening masses, expected from Ward identities associated to non-singlet axial transformations, provides further evidence for the restoration of chiral symmetry in the high temperature regime of QCD. In the entire range of temperatures explored, the baryonic masses deviate from the free theory result, 3πT, by 4–8%. The contribution due to the interactions is clearly visible up to the highest temperature considered, and cannot be explained by the expected leading behavior in the QCD coupling constant g over the entire range of temperatures explored.

Binned top quark spin correlation and polarization observables for the LHC at 13.6 TeV

We consider top-antitop quark (tt¯) production at the Large Hadron Collider (LHC) with subsequent decays into dileptonic final states. We use and investigate a set of leptonic angular correlations and distributions with which all the independent coefficient functions of the top-spin-dependent parts of the tt¯ production spin density matrices can be experimentally probed. We compute these observables for the LHC center-of-mass energy 13.6 TeV within the Standard Model at next-to-leading order in the QCD coupling including the mixed QCD weak corrections. We determine also the tt¯ charge asymmetry where we take in addition also the mixed QCD-QED corrections into account. In addition we analyze and compute possible new physics (NP) effects on these observables within effective field theory in terms of a gauge-invariant effective Lagrangian that contains the operators up to mass dimension six that are relevant for hadronic tt¯ production. First, we compute our observables inclusive in phase space. Then, in order to investigate which region in phase space has, for a specific observable, a high NP sensitivity, we determine our observables also in two-dimensional (Mtt¯,cosθt*) bins, where Mtt¯ denotes the tt¯-invariant mass and θt* is the top quark scattering angle in the tt¯ zero-momentum frame. Published by the American Physical Society 2024

Leptogenesis in parity solutions to the strong CP problem and Standard Model parameters

We study the simplest theories with exact spacetime parity that solve the strong CP problem and successfully generate the cosmological baryon asymmetry via decays of right-handed neutrinos. Lower bounds are derived for the masses of the right-handed neutrinos and for the scale of spontaneous parity breaking, vR. For generic thermal leptogenesis, vR ≳ 1012 GeV, unless the small observed neutrino masses arise from fine-tuning. We compute vR in terms of the top quark mass, the QCD coupling, and the Higgs boson mass and find this bound is consistent with current data at 1σ. Future precision measurements of these parameters may provide support for the theory or, if vR is determined to be below 1012 GeV, force modifications. However, modified cosmologies do not easily allow reductions in vR — no reduction is possible if leptogenesis occurs in the collisions of domain walls formed at parity breaking, and at most a factor 10 reduction is possible with non-thermal leptogenesis. Standard Model parameters that yield low values for vR can only be accommodated by having a high degree of degeneracy among the right-handed neutrinos involved in leptogenesis. If future precision measurements determine vR to be above 1012 GeV, it is likely that higher-dimensional operators of the theory will yield a neutron electric dipole moment accessible to ongoing experiments. This is especially true in a simple UV completion of the neutrino sector, involving gauge singlet fermions, where the bound from successful leptogenesis is strengthened to vR ≳ 1013 GeV.

Radiative corrections for factorized jet observables in heavy ion collisions

I look at the renormalization of the medium structure function and a medium induced jet function in a factorized cross section for jet substructure observables in Heavy Ion collisions. This is based on the formalism developed in [1], which uses an Open quantum system approach combined with the Effective Field Theory (EFT) for forward scattering to derive a factorization formula for jet observables which work as hard probes of a long lived dilute Quark Gluon Plasma (QGP) medium. I show that the universal medium structure function that captures the observable independent physics of the QGP has both rapidity and UV anomalous dimensions that appear due to medium induced Bremsstrahlung. The resulting Renormalization Group (RG) equations correspond to the BFKL equation and the running of the QCD coupling respectively. I present the first results for the numerical impact of resummation using these RG equations on the mean free path of the jet in the medium. I also briefly discuss the prospects of extending this formalism for a short lived dense medium.

QCD corrections to the Golden decay channel of the Higgs boson

Future colliders aim to provide highly precise experimental measurements of the properties of the Higgs boson. In order to benefit from these precision machines, theoretical errors in the Higgs sector observables have to match at least the experimental uncertainties. The theoretical uncertainties in the Higgs sector observables can be reduced by including missing higher-order terms in their perturbative calculations. In this direction, we compute the mixed QCD-electroweak corrections at \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{O}\\left({\\alpha \\alpha }_{s}\\right)$$\\end{document} to the Higgs decay into four charged leptons by considering the golden decay channel, H → e+e−μ+μ−. Due to color conservation, these corrections receive contributions only from the two-loop virtual diagrams. In the complex mass scheme, we find that the mixed QCD-electroweak corrections to the partial decay width, relative to the leading order predictions, are positive and about 0.27% for αs(MZ). Relative to the next-to-leading order electroweak corrections, the mixed QCD-electroweak corrections are found to be approximately 18% for αs(MZ). With respect to the leading order, we observe a flat effect of the mixed QCD-electroweak corrections on the invariant mass distribution of the lepton pairs with fixed QCD coupling. The ϕ distribution, due to the mixed QCD-electroweak corrections, follows a (1 − cos ϕ) dependence.

Evaluation of Bjorken polarised sum rule with a renormalon-motivated approach

We use the known renormalon structure of Bjorken polarised sum rule (BSR) Γ‾1p−n(Q2) to evaluate the leading-twist part of that quantity. In addition, we include D=2 and D=4 Operator Product Expansion (OPE) terms and fit this expression to available experimental data for inelastic BSR. Since we use perturbative QCD (pQCD) coupling, which fails at low squared spacelike momenta Q2≲1GeV2 due to Landau singularities, the fit is performed for Q2≥Qmin2 where Qmin2≈(1.7±0.3)GeV2. Due to large BSR experimental uncertainties, the extracted value of the pQCD coupling has very large uncertainties, especially when Qmin2 is varied. However, when we fix the pQCD coupling to the known world average values, the D=2 and D=4 residue parameters can be determined within large but reasonable uncertainties.

Soft-gluon effective coupling: perturbative results and the large-nF limit to all orders

We consider extensions of the soft-gluon effective coupling that generalize the Catani-Marchesini-Webber (CMW) coupling in the context of soft-gluon resummation beyond the next-to-leading logarithmic accuracy. Starting from the probability density of correlated soft emission in d dimensions we introduce a class of soft couplings relevant for resummed QCD calculations of hard-scattering observables. We show that at the conformal point, where the d-dimensional QCD β function vanishes, all these effective couplings are equal and they are also equal to the cusp anomalous dimension. We present explicit results in d dimensions for the soft-emission probability density and the soft couplings at the second-order in the QCD coupling αS. In d = 4 dimensions we obtain the explicit relation between the soft couplings at O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(αS3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\alpha}_{\ extrm{S}}^3 $$\\end{document}). Finally, we study the structure of the soft coupling in the large-nF limit and we present explicit expressions to all orders in perturbation theory. We also check that, at the conformal point, our large-nF results agree with the known result of the cusp anomalous dimension.

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.

QCD parameters and SM-high precisions from e+e−→ Hadrons

Using the PDG 22 compilation of the e+e−→ Hadrons ⊕ the recent CMD3 data for the pion form factor and the value of gluon condensate 〈αsG2〉 from heavy quarkonia, we extract the value of the four-quark condensate: ραs〈ψ¯ψ〉2=(5.98±0.64)×10−4 GeV6 and the dimension eight condensate: d8=(4.3±3.0)×10−2 GeV8 from the ratio R10 of Laplace sum rules to order αs4. We show the inconsistency in using at the same time the standard SVZ value of the gluon and the vacuum saturation of the four-quark condensates. Using the previous values of the four-quark and d8 condensates, we re-extract 〈αsG2〉 from R10 to be: (6.12±0.61)×10−2 GeV4 in perfect agreement with the one from heavy quarkonia. We also use the lowest τ-like decay moment Rτee to extract the value of the QCD coupling. We obtain to O(αs4) the mean of FO (fixed order) and CI (contour improved) PT series within the standard OPE: αs(Mτ)=0.3385(50)(136)syst where the last error is an added conservative systematic from the distance of the mean to the FO and CI central values. Assuming that the αs-coefficients of the PT series grow geometrically as observed in the calculated case, we obtain to O(αs5): αs(Mτ)=0.3262(37)(78)syst. These results lead to: αs(MZ)=0.1207(17)(3) [resp. 0.1193(11)(3)] to order αs4 [resp. αs5]. The corresponding value of the sum of the non-perturbative contribution at Mτ is: δNPV(Mτ)=(2.3±0.2)×10−2. Reciprocally, using αs(Mτ), 〈αsG2〉 and d8 as inputs, we test the stability of the value of the four-quark condensate obtained from the lowest τ-like moment. We complete our analysis by updating our previous determinations of the lowest order hadronic vacuum polarization contributions to the lepton anomalies and to α(MZ2). We obtain in Table 3: aμ|l.ohvp=(7036.5±38.9)×10−11, aτ|l.ohvp=(3494.8±24.7)×10−9 and α(5)(MZ)|had=(2766.3±4.5)×10−5. This new value of aμ leads to: Δaμ≡aμexp−aμth=(142±42th±41exp)×10−11 which reduces the tension between the SM prediction and experiment.

Novel method to reliably determine the QCD coupling from Ruds measurements and its effects to muon g − 2 and alpha left({M}_Z^2right) within the tau-charm energy region

We present a novel method for precisely determining the QCD running coupling from Ruds measurements in electron-positron annihilation. When calculating the fixed-order perturbative QCD (pQCD) approximant of Ruds, its effective coupling constant {alpha}_sleft({Q}_{ast}^2right) is determined by using the principle of maximum conformality, a systematic scale-setting method for gauge theories, whose resultant pQCD series satisfies all the requirements of renormalization group. Contribution due to the uncalculated higher-order (UHO) terms is estimated by using the Bayesian analysis. Using Ruds data measured by the KEDR detector at 22 centre-of-mass energies between 1.84 GeV and 3.72 GeV, we obtain {alpha}_sleft({M}_Z^2right) = {0.1227}_{-0.0132}^{+0.0117}left(exp .right)pm 0.0016left(textrm{the}.right) , where the theoretical uncertainty (the.) is negligible compared to the experimental one (exp.). Numerical analyses confirm that the new method for calculating Ruds removes conventional renormalization scale ambiguity, and the residual scale dependence due to the UHO-terms will also be highly suppressed due to a more convergent pQCD series. This leads to a significant stabilization of the perturbative series, and a significant reduction of theoretical uncertainty. It thus provides a reliable theoretical basis for precise determination of the QCD running coupling from Ruds measurements at future Tau-Charm Facility. It can also be applied for the precise determination of the hadronic contributions to muon g − 2 and QED coupling alpha left({M}_Z^2right) within the tau-charm energy range.

Top and bottom quark forward-backward asymmetries at next-to-next-to-leading order QCD in (un)polarized electron positron collisions

We consider, at order {alpha}_s^2 in the QCD coupling, top-quark pair production in the continuum at various center-of-mass energies and b-quark pair production at the Z resonance by (un)polarized electron and positron beams. For top quarks we compute the forward-backward asymmetry with respect to the top-quark direction of flight, the associated polar angle distribution, and we analyze the effect of beam polarization on the QCD corrections to the leading-order asymmetry. We calculate also the polarized forward-backward asymmetry. For b-quark production at the Z peak we explore different definitions of AFB. In particular, we analyze b jets defined by the Durham and the flavor-kT clustering algorithms. We compute the inclusive b-jet and two-jet asymmetry with respect to the b-jet direction. For the latter asymmetry the QCD corrections to order {alpha}_s^2 are small. That predestines it to act as a precision observable.

Soft-parton contributions to heavy-quark production at low transverse momentum

We consider QCD radiative corrections to the production of a heavy-quark pair in hadronic collisions. We present the computation of the soft-parton contributions at low transverse momentum of the heavy-quark pair up to second order in the QCD coupling αS. These results complete the evaluation at the next-to-next-to-leading order (NNLO) of the transverse-momentum resummation formula for this process. Moreover, they give all the ingredients that are needed for the NNLO implementation of the qT subtraction formalism for heavy-quark production. We discuss the details of the computation and we provide a code that can be used to obtain the relevant results in numerical form.

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.