Running Quark Masses Research Articles

Precise determination of the top-quark on-shell mass via its scale- invariant perturbative relation to the top-quark mass * *Supported in part by the National Natural Science Foundation of China (12247129, 12175025, 12347101) and the Graduate Research and Innovation Foundation of Chongqing, China (ydstd1912)

The principle of maximum conformality (PMC) provides a systematic approach to solve the conventional renormalization scheme and scale ambiguities. Scale-fixed predictions of physical observables using the PMC are independent of the choice of renormalization scheme – a key requirement for renormalization group invariance. In this paper, we derive new degeneracy relations based on the renormalization group equations that involve both the usual β-function and the quark mass anomalous dimension -function. These new degeneracy relations enable improved PMC scale-setting procedures for correct magnitudes of the strong coupling constant and -running quark mass to be determined simultaneously. By using these improved PMC scale-setting procedures, the renormalization scale dependence of the -on-shell quark mass relation can be eliminated systematically. Consequently, the top-quark on-shell (or ) mass can be determined without conventional renormalization scale ambiguity. Taking the top-quark mass GeV as the input, we obtain GeV. Here, the uncertainties arise from errors combined with those from and the approximate uncertainty resulting from the uncalculated five-loop terms predicted through the Padé approximation approach.

Higgs boson decays to Bc meson in the fragmentation-function approach

In the paper, we present a calculation of the decay widths for the Higgs boson decays to the $B_c$, $B_c^*$, $B_c(2^1S_0)$ and $B_c^*(2^3S_1)$ mesons using the fragmentation-function approach. In the calculation, the fragmentation functions up to order $\alpha_s^3$ based on the nonrelativistic QCD factorization theory are used, and the decay widths for $H\to Q+X$ and $H \to g+X$ at the partonic level are calculated up to order $\alpha_s$. The large logarithms of $m_H^2/m_{Bc}^2$ are resummed up to next-to-leading logarithmic accuracy by solving the evolution equations for the running quark masses and the fragmentation functions. Compared to the leading-order decay widths based on the nonrelativistic QCD approach, the decay widths based on the fragmentation-function approach that include the higher-order QCD corrections are reduced significantly. Our numerical results show that there are about $1.2\times 10^5$ $B_c$ events via the Higgs decays to be produced at the HL-LHC with $3ab^{-1}$, and about $1.6\times 10^6$ $B_c$ events via the Higgs decays to be produced at the HE-LHC with $15ab^{-1}$.

Pion model with the Nakanishi integral representation

In the present work, we describe a model for the pion based on an analytic expression for the Bethe-Salpeter (BSA) amplitude, combined with some ingredients from Lattice QCD calculations. The running quark mass function M(p2), used here, reproduces well the results of Lattice QCD calculations. The analytical form of the running quark mass function contains a single time-like pole, which implies in time-like poles of the dressed quark propagator. Such a form allows to build the weight functions, Gi(γ, z), for the Nakanishi integral representation of each scalar function, χi(k, p), appearing in the decomposition of the Bethe-Salpeter amplitude in terms of Dirac operators. Such scalar amplitudes can also be used to obtain the pion valence light-front wave function.

Precise values of running quark and lepton masses in the standard model

The precise values of the running quark and lepton masses $m^{}_f(\mu)$, which are defined in the modified minimal subtraction scheme ($\overline{\rm MS}$) with $\mu$ being the renormalization scale and the subscript $f$ referring to all the charged fermions in the Standard Model (SM), are very useful for the model building of fermion masses and flavor mixing and for the precision calculations in the SM or its new-physics extensions. In this paper, we calculate the running fermion masses by taking account of the up-to-date experimental results collected by Particle Data Group and the latest theoretical higher-order calculations of relevant renormalization-group equations and matching conditions in the literature. The emphasis is placed on the quantitative estimation of current uncertainties on the running fermion masses, and the linear error propagation method is adopted to quantify the uncertainties, which has been justified by the Monte-Carlo simulations. We identify two main sources of uncertainties, i.e., one from the experimental inputs and the other from the truncations at finite-order loops. The correlations among the uncertainties of running parameters can be remarkable in some cases. The final results of running fermion masses at several representative energy scales are tabulated for further applications.

Nonintegrable threshold singularities of two-point functions in perturbation theory

In perturbation theory, the spectral densities of two-point functions develop non-integrable threshold singularities at higher orders. In QCD, such singularities emerge when calculating the diagrams in terms of the pole quark mass, and they become stronger when one rearranges the perturbative expansion in terms of the running quark mass. In this paper we discuss the proper way to handle such singularities.

Finite temperature Landau gauge lattice quark propagator

The quark propagator at finite temperature is investigated using quenched gauge configurations. The propagator form factors are investigated for temperatures above and below the gluon deconfinement temperature T_c and for the various Matsubara frequencies. Significant differences between the functional behaviour below and above T_c are observed both for the quark wave function and the running quark mass. The results for the running quark mass indicate a link between gluon dynamics, the mechanism for chiral symmetry breaking and the deconfinement mechanism. For temperatures above T_c and for low momenta, our results support also a description of quarks as free quasiparticles.

Constraining quark-hadron interface tension in the multimessenger era

We study the interface effects of quark-hadron mixed phase in compact stars. The properties of nuclear matter are obtained based on the relativistic-mean-field model. For the quark phase, we adopt perturbation model with running quark masses and coupling constant. At certain choices of parameter sets, it is found that varying the quark-hadron interface tension will have sizable effects on the radii ($\Delta R \approx 600$ m) and tidal deformabilities ($\Delta \Lambda/\Lambda \approx 50\%$) of hybrid stars. These provide possibilities for us to constrain the quark-hadron interface tension with future gravitational wave observations as well as the ongoing NICER mission.

Updating [formula omitted] from SVZ-moments and their ratios

Using recent values of αs, the gluon condensates 〈αsG2〉 and 〈g3fabcG3〉 and the new data on the ψ/ϒ-families, we update our determinations of the MS‾ running quark masses m‾c,b(m‾c,b) from the SVZ-moments Mn(Q2) and their ratios [1,2] by including higher order perturbative (PT) corrections, non-perturbative (NPT) terms up to dimension d=8 and using the degree n-stability criteria of the (ratios of) moments. Optimal results from different (ratios of) moments converge to the accurate mean values: m‾c(m‾c)=1264(6)MeV and m‾b(m‾b)=4188(8)MeV in Table 4, which improve and confirm our previous findings [1,2] and the recent ones from Laplace sum rules [3]. Comments on some other determinations of m‾c(m‾c) and 〈αsG2〉 from the SVZ-(ratios of) moments in the vector channel are given in Section 5.

On the relation between pole and running heavy quark masses beyond the four-loop approximation

The effective charges motivated method is applied to the relation between pole and M̅S̅-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running quark masses. The non-calculated five- and six-loop perturbative QCD coefficients are estimated. This approach predicts for these terms the sign-alternating expansion in powers of number of lighter flavors nl, while the analyzed recently infrared renormalon asymptotic expressions do not reproduce the same behavior. We emphasize that coefficients of the quark mass relation contain proportional to π2 effects, which result from analytical continuation from the Euclidean region, where the scales of the running masses and QCD coupling constant are initially fixed, to the Minkowskian region, where the pole masses and the running QCD parameters are determined. For the t-quark the asymptotic nature of the non-resummed PT mass relation does not manifest itself at six-loops, while for the b-quark the minimal PT term appears at the probed by direct calculations four-loop level. The recent infrared renormalon based studies support these conclusions.

Understanding the internal structures of X(4140), X(4274), X(4500) and X(4700)

We investigate the newly observed X(4500) and X(4700) based on the diquark–antidiquark configuration within the framework of QCD sum rules. Both of them may be interpreted as the D-wave csbar{c}bar{s} tetraquark states of J^P = 0^+, but with opposite color structures, which is remarkably similar to the result obtained in Chen and Zhu (Phys Rev D 83:034010, 2011) that X(4140) and X(4274) can be both interpreted as the S-wave csbar{c}bar{s} tetraquark states of J^P = 1^+, also with opposite color structures. However, the extracted masses and these suggested assignments to these X states do depend on these running quark masses where m_s (2,text{ GeV }) = 95 pm 5 MeV and m_c (m_c) = 1.23 pm 0.09 GeV. As a byproduct, the masses of the hidden-bottom partner states of X(4500) and X(4700) are extracted to be both around 10.64 GeV, which can be searched for in the Upsilon phi invariant mass distribution.

Stable strange quark matter objects with running masses and coupling constant

We improve our recently proposed unified description for strange quark matter (SQM) objects, in the way that analytical expressions are derived and used to calculate the distribution of particles inside an SQM object. In the improved model, the computational time is greatly reduced without losing accuracy. The properties of SQM objects are then investigated by adopting perturbative quantum chromodynamics (pQCD) with running quark masses and coupling constant. Aside from the increase of masses and radii of strange stars, it is found that the perturbative interactions also make the electric field on the surface stronger and extends deeper into the core, while small SQM objects become less compact and more positively charged. These may affect the experimental searches of SQM.

Minkowski space pion model inspired by lattice QCD running quark mass

Abstract The pion structure in Minkowski space is described in terms of an analytic model of the Bethe–Salpeter amplitude combined with Euclidean Lattice QCD results. The model is physically motivated to take into account the running quark mass, which is fitted to Lattice QCD data. The pion pseudoscalar vertex is associated to the quark mass function, as dictated by dynamical chiral symmetry breaking requirements in the limit of vanishing current quark mass. The quark propagator is analyzed in terms of a spectral representation, and it shows a violation of the positivity constraints. The integral representation of the pion Bethe–Salpeter amplitude is also built. The pion space-like electromagnetic form factor is calculated with a quark electromagnetic current, which satisfies the Ward–Takahashi identity to ensure current conservation. The results for the form factor and weak decay constant are found to be consistent with the experimental data.

Spectrum and Structure of Excited Baryons with CLAS*

In this contribution we discuss recent results in light quark baryon spectroscopy involving CLAS data and higher level analysis results from the partial wave analysis by the Bonn-Gatchina group. New baryon states were discovered largely based on the open strangeness production channels $\gamma p \to K^+ \Lambda$ and $\gamma p \to K^+ \Sigma^0$. The data illustrate the great potential of the kaon-hyperon channel in the discovery of higher mass baryon resonances in s-channel production. Other channels with discovery potential, such as $\gamma p \to p \omega$ and $\gamma p \to \phi p$ are also discussed. In the second part I will demonstrate on data the sensitivity of meson electroproduction to expose the active degrees of freedom underlying resonance transitions as a function of the probed distance scale. For several of the prominent excited states in the lower mass range the short distance behavior is described by a core of three dressed-quarks with running quark mass, and meson-baryon contributions make up significant parts of the excitation strength at large distances. Finally, an outlook is given of baryon resonance physics at the 12 GeV CEBAF electron accelerator.

On the flavour dependence of the $O(\alpha_{s}^{4})$ correction to the relation between running and pole heavy quark masses

Recently the four-loop perturbative QCD contributions to the relations between pole and running masses of charm, bottom and top quarks were evaluated in the $ \overline{MS}$ scheme with identical numerical error bars. In this work the flavour dependence of the $O(\alpha_{s}^{4})$ correction to these asymptotic series is obtained in the semi-analytical form with the help of the least squares method. The numerical structure of the corresponding asymptotic perturbative relations between pole and running c -, b - and t -quark masses is considered and the theoretical errors of the $O(\alpha_{s}^{4})$ contributions are discussed. The explicit dependence for these relations on the renormalization scale $ \mu^{2}$ and the flavour number nl is presented.

Explorations of two empirical formulas for fermion masses

Two empirical formulas for the lepton and quark masses (i.e. Kartavtsev’s extended Koide formulas), $$K_l=(\sum _l m_l)/(\sum _l\sqrt{m_l})^2=2/3$$ and $$K_q=(\sum _q m_q)/(\sum _q\sqrt{m_q})^2=2/3$$ , are explored in this paper. For the lepton sector, we show that $$K_l=2/3$$ , only if the uncertainty of the tauon mass is relaxed to about $$2\sigma $$ confidence level, and the neutrino masses can consequently be extracted with the current experimental data. For the quark sector, the extended Koide formula should only be applied to the running quark masses, and $$K_q$$ is found to be rather insensitive to the renormalization effects in a large range of energy scales from GeV to $$10^{12}$$ GeV. We find that $$K_q$$ is always slightly larger than 2/3, but the discrepancy is merely about 5 %.

Analytical determination of the QCD quark masses

The current status of determinations of the QCD running quark masses is reviewed. Emphasis is on recent progress on analytical precision determinations based on finite energy QCD sum rules. A critical discussion of the merits of this approach over other alternative QCD sum rules is provided. Systematic uncertainties from both the hadronic and the QCD sector have been recently identified and dealt with successfully, thus leading to values of the quark masses with unprecedented accuracy. Results currently rival in precision with lattice QCD determinations.

Improved light quark masses from pseudoscalar sum rules

Using ratios of the inverse Laplace transform sum rules within stability criteria for the subtraction point μ in addition to the ones of the usual τ spectral sum rule variable and continuum threshold tc, we extract the π(1300) and K(1460) decay constants to order αs4 of perturbative QCD by including power corrections up to dimension-six condensates, tachyonic gluon mass for an estimate of large order PT terms, instanton and finite width corrections. Using these inputs with enlarged generous errors, we extract, in a model-independent and conservative ways, the sum of the scale-independent renormalization group invariant (RGI) quark masses (mˆu+mˆq):q≡d,s and the corresponding running masses (m¯u+m¯q) evaluated at 2 GeV. By giving the value of the ratio mu/md, we deduce the running quark masses m¯u,d,s and condensate 〈u¯u¯〉 and the scale-independent mass ratios: 2ms/(mu+md) and ms/md. Using the positivity of the QCD continuum contribution to the spectral function, we also deduce, from the inverse Laplace transform sum rules, for the first time to order αs4, new lower bounds on the RGI masses which are translated into the running masses at 2 GeV and into upper bounds on the running quark condensate 〈u¯u¯〉. Our results summarized in Table 3 and compared with our previous results and with recent lattice averages suggest that precise phenomenological determinations of the sum of light quark masses require improved experimental measurements of the π(1.3) and K(1.46) hadronic widths and/or decay constants which are the dominant sources of errors in the analysis.

Summary on [formula omitted] and precise [formula omitted] from heavy-light QCD spectral sum rules

We summarize recent results obtained in [S. Narison, arXiv:1209.2023 (2012).] on the running m¯c,b(m¯c,b) in the MS¯ scheme and fD(s),B(s) using QCD spectral sum rules (QSSR) known to N2LO PT series, including all dimension-six NP condensate contributions in the full QCD theory, an estimate of the N3LO terms based on the geomteric growth of the PT series and using the most recent values of the QCD input parameters given in Table 1. The study of the effects of the subtraction scale μ on “different QSSR data” and the use (for the first time) of the Renormalization Group Invariant (RGI) scale independent quark masses in the analysis are emphasized. The estimates [rigourous model-independent upper bounds within the SVZ framework] reported in Table 2: fD/fπ=1.56(5)[⩽1.68(1)], fB/fπ=1.58(5)[⩽1.80(3)] and fDs/fK=1.58(4)[⩽1.63(1)], fBs/fK=1.50(3)[⩽1.61(3.5)], improve previous QSSR estimates. The remarkable agreements with some of the experimental data on fD,Ds and with lattice simulations within dynamical quarks confirm both the success of the QSSR semi-approximate approach based on the OPE in terms of the quark and gluon condensates and of the Minimal Duality Ansatz (MDA) for parametrizing the hadronic spectral function which we have tested from the complete data of the J/ψ and ϒ systems. The running quark masses m¯c(mc)=1286(66)MeV and m¯b(mb)=4236(69)MeV from MD,B are in good agreement though less accurate than the ones from recent J/ψ and ϒ sum rules.

A fresh look into [formula omitted] and precise [formula omitted] from heavy–light QCD spectral sum rules

Using recent values of the QCD (non-)perturbative parameters given in Table 1 and an estimate of the N3LO QCD perturbative contributions based on the geometric growth of the PT series, we re-use QCD spectral sum rules (QSSR) known to N2LO PT series and including all dimension-six NP condensate contributions in the full QCD theory, for improving the existing estimates of m¯c,b and fD(s),B(s) from the open charm and beauty systems. We especially study the effects of the subtraction point on “different QSSR data” and use (for the first time) the Renormalization Group Invariant (RGI) scale-independent quark masses in the analysis. The estimates [rigourous model-independent upper bounds within the SVZ framework] reported in Table 8: fD/fπ=1.56(5)[⩽1.68(1)], fB/fπ=1.58(5)[⩽1.80(3)] and fDs/fK=1.58(4)[⩽1.63(1)], fBs/fK=1.50(3)[⩽1.61(3.5)], which improve previous QSSR estimates, are in perfect agreement (in values and precisions) with some of the experimental data on fD,Ds and on recent lattice simulations within dynamical quarks. These remarkable agreements confirm both the success of the QSSR semi-approximate approach based on the OPE in terms of the quark and gluon condensates and of the Minimal Duality Ansatz (MDA) for parametrizing the hadronic spectral function which we have tested from the complete data of the J/ψ and ϒ systems. The values of the running quark masses m¯c(mc)=1286(66) MeV and m¯b(mb)=4236(69) MeV from MD,B are in good agreement though less accurate than the ones from recent J/ψ and ϒ sum rules.

Gluon condensates and precise [formula omitted] from QCD-moments and their ratios to order [formula omitted] and [formula omitted

We reconsider the extraction of the gluon condensates 〈αsG2〉, 〈g3fabcG3〉 and the MS¯ running quark masses m¯c,b from different Mn(Q2) moments and their ratios by including PT corrections to order αs3, NPT terms up to 〈G4〉 and using stability criteria of the results versus the degree n (number of Q2-derivative). We explicitly show that the spectral part of the lowest moment M1(0) depends strongly (as expected) on its high-energy (continuum) contribution, which is minimized for Mn⩾3−4(0). Using higher moments and the correlations of 〈αsG2〉 with 〈g3fabcG3〉 and 〈G4〉, we obtain 〈αsG2〉=(7.0±1.3)×10−2 GeV4 and 〈g3fabcG3〉=(8.8±5.5) GeV2×〈αsG2〉, while our analysis favours a modified precise factorisation for 〈G4〉. Using the previous results, we re-determine m¯c(m¯c) and find that the commonly used M1(0) lowest moment tends to overestimate its value compared to the ones from higher moments where stable values of m¯c(m¯c) versus the variations of n and the continuum models are reached. These features can indicate that the quoted errors of m¯c,b from M1(0) may have been underestimated. Our best results from different high-n moments and their ratios are: m¯c(m¯c)=1261(16) MeV and m¯b(m¯b)=4171(14) MeV, in excellent agreement with results obtained in Narison (2010) [1] using some judicious choices of ratios of moments.