Coupling Αs Research Articles

Non-perturbative renormalization by decoupling

We propose a new strategy for the determination of the QCD coupling. It relies on a coupling computed in QCD with Nf≥3 degenerate heavy quarks at a low energy scale μdec, together with a non-perturbative determination of the ratio Λ/μdec in the pure gauge theory. We explore this idea using a finite volume renormalization scheme for the case of Nf=3 QCD, demonstrating that a precise value of the strong coupling αs can be obtained. The idea is quite general and can be applied to solve other renormalization problems, using finite or infinite volume intermediate renormalization schemes.

Precise determination of \u03b1s from relativistic quarkonium sum rules

We determine the strong coupling αs(mZ ) from dimensionless ratios of roots of moments of the charm- and bottom-quark vector and charm pseudo-scalar correlators, dubbed {R}_q^{X,n}equiv left({M}_q^{X,n}right)frac{1}{n}/{left({M}_q^{X,n+1}right)}^{frac{1}{n+1}}, with X = V, P , as well as from the 0-th moment of the charm pseudo-scalar correlator, {M}_c^{P,0}. In the quantities we use, the mass dependence is very weak, entering only logarithmically, starting at \U0001d4aa left({alpha}_s^2right). We carefully study all sources of uncertainties, paying special attention to truncation errors, and making sure that order-by-order convergence is maintained by our choice of renormalization scale variation. In the computation of the experimental uncertainty for the moment ratios, the correlations among individual moments are properly taken into account. Additionally, in the perturbative contributions to experimental vector-current moments, αs(mZ) is kept as a free parameter such that our extraction of the strong coupling is unbiased and based only on experimental data. The most precise extraction of αs from vector correlators comes from the ratio of the charm-quark moments {R}_c^{V,2} and reads αs(mZ) = 0.1168±0.0019, as we have recently discussed in a companion letter. From bottom moments, using the ratio {R}_c^{V,2} , we find αs (mZ) = 0.1186±0.0048. Our results from the lattice pseudo-scalar charm correlator agree with the central values of previous determinations, but have larger uncertainties due to our more conservative study of the perturbative error. Averaging the results obtained from various lattice inputs for the n = 0 moment we find αs(mZ) = 0.1177±0.0020. Combining experimental and lattice information on charm correlators into a single fit we obtain αs(mZ) = 0.1170±0.0014, which is the main result of this article.

QCD parameters, [formula omitted] and [formula omitted] from relativistic heavy quark sum rules

We report results of our recent works [S. Narison, Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison. Addendum: Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison, Phys. Lett. B802 (2020) 135221.] where the correlations between the c,b-quark running masses m‾c,b, the gluon condensate 〈αsG2〉 and the QCD coupling αs in the MS‾-scheme from an analysis of the charmonium and bottomium spectra and the Bc-meson mass. We use optimized ratios of relativistic Laplace sum rules (LSR) evaluated at the μ-subtraction stability point where higher orders PT and D≤6−8-dimensions nonperturbative condensates corrections are included. We obtain [S. Narison, Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison. Addendum: Int. J. Mod. Phys. A33 (2018) no. 10, 1850045.] αs(2.85)=0.262(9) and αs(9.50)=0.180(8) from the (pseudo)scalar Mχ0c(0b)−Mηc(b) mass-splittings at μ=2.85(9.50) GeV. The most precise result from the charm channel leads to αs(Mτ)=0.318(15) and αs(MZ)=0.1183(19)(3) in excellent agreement with the world average: αs(MZ)=0.1181(11) [For a review, see e.g: S. Bethke, Nucl. Part. Phys. Proc. 282–284 (2017)149; C. Patrignani et al. (Particle Data Group), Chin. Phys. C40, 100001 (2016) and 2017 update.]. Updated results from a global fit of the (axial-)vector and (pseudo)scalar channels using Laplace and Moments sum rules @ N2LO [S. Narison, Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison. Addendum: Int. J. Mod. Phys. A33 (2018) no. 10, 1850045.] combined with the one from MBc [S. Narison, Phys. Lett. B802 (2020) 135221.] lead to the new tentative QCD spetral sum rules (QSSR) average:m‾c(m‾c)|average=1266(6) MeV and m‾b(m‾b)|average=4196(8) MeV. The values of the gluon condensate 〈αsG2〉 from the (axial)-vector charmonium channels combined with previous determinations in Table 1, leads to the new QSSR average: [S. Narison, Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison. Addendum: Int. J. Mod. Phys. A33 (2018) no. 10, 1850045.] 〈αsG2〉|average=(6.35±0.35)×10−2 Ge4. Our results clarify the (apparent) discrepancies between different estimates of 〈αsG2〉 from J/ψ sum rule but also shows the sensitivity of the sum rules on the choice of the μ-subtraction scale. As a biproduct, we deduce the Bc-decay constants fBc=371(17) MeV and fBc(2S)≤139(6) MeV.

Polarization Control of the Interface Ferromagnetic to Antiferromagnetic Phase Transition in Co/Pb(Zr,Ti)O3

Based on first-principles calculations, we predict the polarization control of the interfacial magnetic phase and a giant electronically driven magnetoelectric coupling (MEC) in Co/PbZr0.25Ti0.75O3 (PZT)(001). The effect of Co oxidation at the interface shared with (Zr,Ti)O2-terminated PZTis evidenced. The magnetic phase of the oxidized Co interface layer is electrically switched from the ferromagnetic to the antiferromagnetic state by reversing the PZT polarization from upward to downward, respectively. A comparative study between oxidized and unoxidized Co/PZT interfaces shows that in oxidized Co/PZT bilayers, the variation of the interface spin moment upon polarization reversal exceeds that of unoxidized Co/PZT bilayers by about 1 order of magnitude. We define a surface MEC constant αS taking into account the polarization dependence of both the spin and orbital moments. In unoxidized Co/PZT bilayers, we obtain αS ≈ 2 × 10-10 G cm2 V-1, while a giant surface coupling αS ≈ 12 × 10-10 G cm2 V-1 is found in the case of oxidized Co/PZT. We demonstrate that the polarization control of the magnetocrystalline anisotropy via spin-orbit coupling is not only effective at the interface but it extends to the Co film despite the interface origin of the MEC. This study shows that tailoring the nature of atomic bonding and electron occupancies allows for improving the performance of functional interfaces, enabling an efficient electric field control of spin-orbit interactions. Moreover, the nonlocal character of this effect holds promising perspectives for the application of electronically driven interface MEC in spin-orbitronic devices.

Five-loop contributions to low-N non-singlet anomalous dimensions in QCD

We present the first calculations of next-to-next-to-next-to-next-to-leading order (N4LO) contributions to anomalous dimensions of spin-N twist-2 operators in perturbative QCD. Specifically, we have obtained the respective non-singlet quark–quark anomalous dimensions at N=2 and N=3 to the fifth order in the strong coupling αs. These results set the scale for the N4LO contributions to the evolution of the non-singlet quark distributions of hadrons outside the small-x region, and facilitate a first approximate determination of the five-loop cusp anomalous dimension. While the N4LO coefficients are larger than expected from the lower-order results, their inclusion stabilizes the perturbative expansions for three or more light flavours at a sub-percent accuracy for αs<0.3.

Formula omitted], 〈αsG2〉 and αs from Heavy Quarkonia

Explicit studies [S. Narison, Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison, addendum (to appear in Int. J. Mod. Phys. A).] of the correlations between the c, b-quark running masses m‾c,b, the gluon condensate 〈αsG2〉 and the QCD coupling αs in the MS‾-scheme from a global fit of charmonium and bottomium spectra are reviewed. We use optimized ratios of relativistic Laplace sum rules (LSR) evaluated at the μ-subtraction stability point where higher orders PT and D≤6−8-dimensions non-perturbative condensates corrections are included. Our results clarify the (apparent) discrepancies between different estimates of 〈αsG2〉 from J/ψ sum rule but also shows the sensitivity of the sum rules on the choice of the μ-subtraction scale which does not permit a high-precision estimate of m‾c,b from the alone vector channel. Updated results from a global fit of the (axial-)vector and (pseudo)scalar channels using Laplace and Moments sum rules @ N2LO lead to: m‾c(m‾c)|average=1264(6)MeV and m‾b(m‾b)|average=4190(8)MeV. The values of the gluon condensate 〈αsG2〉 from the (axial)-vector charmonium channels combined with previous determinations in Table 1, leads to the new sum rule average: 〈αsG2〉|average=(6.35±0.35)×10−2GeV4. The (pseudo)scalar mass-splittings Mχ0c(0b)−Mηc(b) allow to predict the QCD coupling αs at two different scales: αs(2.85)=0.262(9) for the charm and αs(9.50)=0.180(8) for the bottom. The strongest one from Mχ0c−Mηc leads to: αs(Mτ)=0.318(15)⇝αs(MZ)=0.1183(19)(3) in good agreement with the world average: αs(MZ)=0.1181(11) [For a review, see e.g: S. Bethke, Nucl. Part. Phys. Proc. 282–284 (2017) 149; PDG, C. Patrignani et al. (Particle Data Group), Chin. Phys. C40, 100001 (2016) and 2017 update.].

Determination of PDFs and the strong coupling based on four different schemes

In this article, we present a Next-to-Leading Order (NLO) QCD analysis to determine of Parton Distribution Functions (PDFs) and the strong coupling αs(MZ2) based on four different, Thorne-Roberts (TR or RT), Thorne-Roberts Fast (RT FAST), Thorne-Roberts Optimal (RTOPT) and Thorne-Roberts Optimal Fast (RTOPT FAST) heavy-quark schemes and compare the central values of PDFs, fit quality and numerical values of the strong coupling with each other. We show the best fit quality is corresponding to RTOPT FAST heavy-quark scheme with χTotal2/dof=1.077 and the best improvement in the uncertainty of the strong coupling is corresponding again to RTOPT FAST scheme with αs(MZ2)=0.1184±0.0030.

Analytic inclusion of the scale dependence of the anomalous dimension matrix in Standard Model Effective Theory

The renormalization group equations (RGEs) in Standard Model effective theory are usually either solved analytically, neglecting the scale dependence of gauge and Yukawa couplings, or numerically without such approximations. We present analytic solutions of RGEs that take into account the dominant scale dependence of the anomalous-dimension matrix due to the running of the QCD coupling αs and of the top-Yukawa coupling. We consider first the case for which a given operator is generated directly through mixing with the parent operator whose Wilson coefficient is non-vanishing at the new physics scale. Subsequently we consider the case of two-step running, in which two operators do not mix directly, but only via a third mediator operator. We generalize these solutions to an arbitrary number of operators and show how even in this case analytic solutions can be obtained.

Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra

The QCD light-front Hamiltonian equation HLFΨ=M2Ψ derived from quantization at fixed LF time τ=t + z/c provides a causal, frame-independent method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. The QCD Lagrangian with zero quark mass has no explicit mass scale. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color-confining potential κ4ζ2 for mesons, where ζ2 is the LF radial variable conjugate to the qq¯ invariant mass squared. The same result, including spin terms, is obtained using light-front holography, the duality between light-front dynamics and AdS5, if one modifies the AdS5 action by the dilaton eκ2z2 in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions provide a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons and a universal Regge slope. The pion qq¯ eigenstate has zero mass at mq=0. The superconformal relations also can be extended to heavy-light quark mesons and baryons. This approach also leads to insights into the physics underlying hadronization at the amplitude level. I will also discuss the remarkable features of the Poincaré invariant, causal vacuum defined by light-front quantization and its impact on the interpretation of the cosmological constant. AdS/QCD also predicts the analytic form of the nonperturbative running coupling αs(Q2)∝e-Q2/4κ2. The mass scale κ underlying hadron masses can be connected to the parameter ΛMS¯ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling αs(Q2) defined at all momenta. One obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. Finally, I address the interesting question of whether the momentum sum rule is valid for nuclear structure functions.

Hard and precision QCD measurements at HERA

Recent results on the combination of open charm and beauty production data in deep-inelastic scattering and their mparison to perturbative QCD calculations at next-to-leading order and approximate next-to-next-to-leading order are presented. The combined data are used to extract the masses of the charm and beauty quarks at next-to-leading order. Inclusive jet and dijet cross sections in deep-inelastic scattering are used to extract the strong coupling αs(mZ) at next-to-next-to-leading order for the first time. Finally, further new observables measured for the description of prompt photons plus jet production in deep-inelastic scattering and their comparison to perturbative QCD calculations are shown.

Soft-gluon resolution scale in QCD evolution equations

QCD evolution equations can be recast in terms of parton branching processes. We present a new numerical solution of the equations. We show that this parton-branching solution can be applied to analyze infrared contributions to evolution, order-by-order in the strong coupling αs, as a function of the soft-gluon resolution scale parameter. We examine the cases of transverse-momentum ordering and angular ordering. We illustrate that this approach can be used to treat distributions which depend both on longitudinal and on transverse momenta.

New Insights into Color Confinement, Hadron Dynamics, Spectroscopy, and Jet Hadronization from Light-Front Holography and Superconformal Algebra

A fundamental problem in hadron physics is to obtain a relativistic color-confining, first approximation to QCD which can predict both hadron spectroscopy and the frame-independent light-front (LF) wavefunctions underlying hadron dynamics. The QCD Lagrangian with zero quark mass has no explicit mass scale; the classical theory is conformally invariant. Thus, a fundamental problem is to understand how the mass gap and ratios of masses – such as m ρ/m p – can arise in chiral QCD. De Alfaro, Fubini, and Furlan have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator and rescales the time variable. If one applies the same procedure to the light-front Hamiltonian, it leads uniquely to a confinement potential κ 4 ζ 2 for mesons, where ζ 2 is the LF radial variable conjugate to the $$ q\overline{q} $$ invariant mass squared. The same result, including spin terms, is obtained using light-front holography – the duality between light-front dynamics and AdS5, the space of isometries of the conformal group if one modifies the action of AdS5 by the dilaton $$ {e}^{\kappa^2}{z}^2 $$ in the fifth dimension z . When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions predict unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons of the same parity. One also predicts observables such as hadron structure functions, transverse momentum distributions, and the distribution amplitudes defined from the hadronic light-front wavefunctions. The mass scale κ underlying confinement and hadron masses can be connected to the parameter $$ {\Lambda}_{\overline{MS}} $$ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling α s (Q 2) defined at all momenta. The matching of the high and low momentum transfer regimes also determines a scale Q0 which sets the interface between perturbative and nonperturbative hadron dynamics.

Radiative distortion of kinematic edges in cascade decays

Kinematic edges of cascade decays of new particles produced in high-energy collisions may provide important constraints on the involved particles' masses. For the exemplary case of gluino decay g˜→qq¯χ˜ into a pair of quarks and a neutralino through a squark resonance, we study the hadronic invariant mass distribution in the vicinity of the kinematic edge. We perform a next-to-leading order calculation in the strong coupling αs and the ratio of squark width and squark mass Γq˜/mq˜, based on a systematic expansion in Γq˜/mq˜. The separation into hard, collinear and soft contributions elucidates the process-dependent and universal features of distributions in the edge region, represented by on-shell decay matrix elements, universal jet functions and a soft function that depends on the resonance propagator and soft Wilson lines.

αs 2016

An update of measurements of the strong coupling αs and the determination of the world average value of αs(MZ2) is presented, resulting inαs(MZ2)=0.1181±0.0011.

Uncertainties on the determination of the strong coupling αs from the energy evolution of jet fragmentation functions at low z

The QCD coupling αs is determined at NLO*+NMLLA accuracy from the comparison of experimental jet data to theoretical predictions of the energy-evolution of the parton-to-hadron fragmentation function moments (multiplicity, peak, width, skewness) at low fractional hadron momentum z. From the existing e+e− and e±p jet data, we obtain αs(mZ2)=0.1195±0.0021(exp)−0.0+0.0015(scale) at the Z mass. The uncertainties of the extracted αs value are discussed.

Transverse energy-energy correlations at next-to-leading order in αs at the LHC

We compute the transverse energy-energy correlation (EEC) and its asymmetry (AEEC) at next-to-leading order (NLO) in αs in pp collisions at the LHC for the nominal center-of-mass energies of 7, 8 and 13 TeV. We show that the transverse EEC and the AEEC distributions have small sensitivity to the QCD factorisation and renormalisation scales and are almost insensitive to the structure functions of the proton. Hence, they can be used to precisely test QCD in hadron colliders and determine the strong coupling αs.

αs from the updated ALEPH data for hadronic τ decays

We extract the strong coupling αs(mτ2) from the recently updated ALEPH non-strange spectral functions obtained from hadronic τ decays. We apply a self-consistent analysis method, first tested in the analysis of OPAL data, to extract αs(mτ2) and non-perturbative contributions. The analysis yields αsFO(mτ2)=0.296±0.010, using Fixed Order Perturbation Theory (FOPT), and αsCI(mτ2)=0.310±0.014, using Contour Improved Perturbation Theory (CIPT). The weighted average of these results with those previously obtained from OPAL data give αsFO(mτ2)=0.303±0.009 and αsCI(mτ2)=0.319±0.012, which gives, after evolution to the Z boson mass scale, αsFO(mZ2)=0.1165±0.0012 and αsCI(mZ2)=0.1185±0.0015, respectively. We observe that non-perturbative effects limit the accuracy with which αs can be extracted from τ decay data.

Shear viscosity η to electric conductivity σel ratio for the quark–gluon plasma

The transport coefficients of strongly interacting matter are currently subject of intense theoretical and phenomenological studies due to their relevance for the characterization of the quark–gluon plasma produced in ultra-relativistic heavy-ion collisions (uRHIC). We discuss the connection between the shear viscosity to entropy density ratio, η/s, and the electric conductivity, σel. Once the relaxation time is tuned to have a minimum value of η/s=1/4π near the critical temperature Tc, one simultaneously predicts σel/T very close to recent lQCD data. More generally, we discuss why the ratio of (η/s)/(σel/T) supplies a measure of the quark to gluon scattering rates whose knowledge would allow to significantly advance in the understanding of the QGP phase. We also predict that (η/s)/(σel/T), independently on the running coupling αs(T), should increase up to about ∼20 for T→Tc, while it goes down to a nearly flat behavior around ≃4 for T≥4Tc. Therefore we in general predict a stronger T dependence of σel/T with respect to η/s that in a quasi-particle approach is constrained by lQCD thermodynamics. A conformal theory, instead, predicts a similar T dependence of η/s and σel/T.

Measurement of strong coupling αs in e + e − annihilation using jet rate and event shape

The hadronic events from the AMY data at 60 GeV center-of-mass energy are studied. We measure the coupling constant α s first by using the three-jet rate method. From the event shape, we also extract the strong coupling constant, based on next-to-next leading order. Our results are consistent with the running of α s expected from quantum chromodynamics predictions at next-to-next leading order corrections.

Using a Classical Gluon Cascade to study the Equilibration of a Gluon-Plasma

Using a classical gluon cascade, we study the thermalisation of a gluon-plasma in a homogeneous box by considering the time evolution of the entropy, and in particular how the thermalisation time depends on the strong coupling αs. We then partition the volume into cells with a linearly increasing temperature gradient in one direction, and homogeneous/isotropic in the the other two directions. We allow the gluons to stream in one direction in order to study how they then evolve spatially. We examine cases with and without collisions. We study the entropy as well as the flow-velocity in the z-direction and find that the system initially has a flow which dissipates over time as the gluons become distributed homogeneously throughout the box.