Charm Quark Mass Research Articles

Three-loop contributions to b → sγ associated with the current-current operators

In a recent work, we calculated all three-loop diagrams contributing to the decay amplitude for b → sγ where none of the gluons touch the b-leg. In the present paper, we complete the calculation by working out all remaining three-loop diagrams (of order αs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\alpha}_s^2 $$\\end{document}) associated with the current-current operators O1 and O2 at the physical value of the charm-quark mass mc. Using the programs AMFlow and DiffExp to solve the differential equations for the master integrals, we obtained precise numerical results at 23 values for z=mc2/mb2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ z={m}_c^2/{m}_b^2 $$\\end{document}, ranging from z = 1/1000 to z = 1/5, along with asymptotic expansions around z = 0. For certain diagrams, the asymptotic expansion breaks down in the physical z-range, necessitating a Taylor expansion (which we do around z = 1/10). In all expansions, we retained power terms up to z20 and included the accompanying log(z) terms to all powers for asymptotic expansions. Numerical results for the sum of all diagrams (including those calculated in the previous paper) are presented in tabular form, while the mentioned expansions of individual diagram classes are provided electronically. We note that our results for the asymptotic expansions around z = 0 are in good agreement with those recently published by Fael et al. and Czaja et al.

Heavy quark mass near the phase transition

Abstract Assuming that the number densities of heavy flavor in hadron gas and in QGP are same at $T_c$, we obtain the effective mass of heavy quark at $T_c$ from the comparison with the hadron resonance gas model which well describes particle yield in heavy-ion collisions. We find that charm quark mass at vanishing baryon chemical potential is around 1.8 GeV which is much heavier than QCD bare mass and close to $D$ meson mass. The mass slightly increases with increasing baryon chemical potential and then decreases.
On the other hand, anticharm quark mass constantly decreases with increasing baryon chemical potential. Bottom quark mass has a similar pattern. Extending the hadron resonance gas model to a bit higher temperature beyond $T_c$, the effective masses of charm and bottom quarks decrease with increasing temperature.

Strong Coupling from Inclusive Semi-leptonic Decay of Charmed Mesons

Abstract Employing the heavy quark expansion model with the kinetic scheme, we evaluate αS(mc 2), the strong coupling constant at the charm quark mass mc with data on inclusive semileptonic decays of charmed mesons. Using the experimental values of semileptonic decay widths of the D0 and the D+, the value of αS(mc 2) is determined to be 0.445±0.009±0.114, where the first uncertainty is experimental and the second systematic. This reported αS(mc 2) is in good agreement with the value of αS(mc 2) calculated by running αS(mZ 2) at the Z0 boson mass mZ with the renormalization group evolution equation. In addition, values of αS(mc 2) obtained individually from each of the D0, D+, and D+ s mesons are found to be consistent being of the same origin.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Nonleptonic B-meson decays to next-to-next-to-leading order

We compute next-to-next-to-leading order QCD corrections to the partonic processes b → cu¯d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ c\\overline{u}d $$\\end{document} and b → cc¯s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ c\\overline{c}s $$\\end{document}, which constitute the dominant decay channels in standard model predictions for B-meson lifetimes within the heavy quark expansion. We consider the contribution from the four-quark operators O1 and O2 in the ∆B = 1 effective Hamiltonian. The decay rates are obtained from the imaginary parts of four-loop propagator-type diagrams. We compute the corresponding master integrals using the “expand and match” approach which provides semi-analytic results for the physical charm and bottom quark masses. We show that the dependence of the decay rate on the renormalization scale is significantly reduced after including the next-to-next-to-leading order corrections. Furthermore, we compute next-to-next-to-leading order corrections to the Cabibbo-Kobayashi-Maskawa-suppressed decay channels b → uc¯s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ u\\overline{c}s $$\\end{document} and b → uu¯d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ u\\overline{u}d $$\\end{document}.

Absorbing discretization effects with a massive renormalization scheme: The charm-quark mass

We present the first numerical implementation of the massive symmetric-momentum-subtraction (mSMOM) renormalization scheme and use it to calculate the charm-quark mass. Based on ensembles with three flavors of dynamical domain-wall fermions with lattice spacings in the range 0.11–0.08 fm, we demonstrate that the mass scale which defines the mSMOM scheme can be chosen such that the extrapolation has significantly smaller discretization effects than the SMOM scheme. Converting our results to the MS¯ scheme we obtain m¯c(3 GeV)=1.008(13) GeV and m¯c(m¯c)=1.292(12) GeV. Published by the American Physical Society 2024

Pseudoscalar heavy quarkonium production in heavy ion ultraperipheral collision

The inclusive production of pseudoscalar heavy quarkonia (ηc, ηb, and Bc) via photon-photon fusion in heavy ion ultraperipheral collision (UPC) are calculated to QCD next-to-leading order in the framework of nonrelativistic QCD (NRQCD). The total cross section of ηc produced in Pb-Pb UPC is 194 nb and 1275 nb at nucleon-nucleon c.m. energies SNN=5.52 TeV and 39.4 TeV, respectively. The cross sections for ηb and Bc mesons are more than two to three orders of magnitude smaller. We make a detailed phenomenological analysis on the ηc production; the uncertainties caused by the renormalization scale and the charm quark mass, the cross sections in other ultraperipheral nucleon-nucleon colliding systems, and the transverse momentum distribution are discussed. At the coming HL-LHC and future FCC, the heavy ion UPC opens another door of the study on the production of heavy quarkonium. Published by the American Physical Society 2024

B meson mixing at NNLO: technical aspects

We provide details to several technical aspects which are important for the calculation of next-to-next-to-leading order corrections to the mixing of neutral B mesons. This includes the computation of the master integrals for finite charm and bottom quark masses, projectors for products of up to 22 γ matrices and tensor integrals with up to rank 11.

Effect of charm quark on chiral phase transition in Nf=2+1+1 holographic QCD

We investigate the effect of the charm quark on the chiral phase transition of light quarks at finite temperature based on the four-flavor soft-wall holographic QCD model. In the massless limit, we find that the thermal chiral phase transition is of the second order in the four-quark-flavor system. In the case with the massive charm quark and the massless light and strange quarks, the order of the phase transition changes to the first order. This is due to the quark-flavor symmetry breaking which is associated with the violation of the U(1) axial symmetry. Once the light and strange quarks get massive, the explicit chiral symmetry breaking becomes eminent, and then the crossover phase transition is realized at the physical quark masses. We also map the order of the phase transition on a phase diagram in the quark-mass plane where the light- and strange-quark masses are degenerate but differ from the value of the charm-quark mass. This phase diagram is an extension of the conventional Columbia plot to the four-quark-flavor system. The critical exponents related to the chiral phase transition are also addressed. Published by the American Physical Society 2024

Study of weak radiative decays of D0→Vγ

The weak radiative decay of D0→Vγ with V=K¯0, and ϕ, ρ0, and ω, is systematically studied in the vector meson dominance model. It allows us to distinguish the short-distance mechanisms which can be described by the tree-level transitions in the nonrelativistic constituent quark model, and the long-distance mechanisms which are related to the final-state interactions (FSIs). We find that the FSI effects play a crucial role in D0→Vγ and the SU(3) flavor symmetry can provide a natural constraint on the relative phase between the short and long-distance transition amplitudes. Our analysis suggests that the D-meson weak radiative decays can serve as a good case for investigating the nonperturbative QCD mechanisms at the charm quark mass region. Published by the American Physical Society 2024

Toward the quark mass dependence of Tcc+ from lattice QCD

The DD* scattering phase shifts in the Tcc+=ccu¯d¯ channel are extracted from lattice QCD for five different charm quark masses and a fixed light-quark mass corresponding to mπ≃280 MeV. The phase shifts are analyzed employing two approaches: effective range expansion and Lippmann-Schwinger equation derived in the effective field theory. In the latter case, the results imply an attraction at short range parametrized by contact terms and a slight repulsion at long range mediated by one-pion exchange with mπ>mD*−mD. The poles in the amplitude across the complex energy plane are extracted and their trajectories are discussed as the charm quark mass is varied. Two complex conjugate poles corresponding to a resonance below threshold are found for mc close to the physical value. They turn into a pair of virtual states at the largest mc studied. With further increasing mc, one virtual pole representing Tcc+ is expected to move towards the two-body threshold and turn into a bound state. The light-quark mass dependence of the Tcc+ pole is briefly discussed using the data on DD* scattering from other lattice collaborations. Published by the American Physical Society 2024

Hadronic physics from a Wilson fermion mixed-action approach: charm quark mass and D(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{(s)}$$\\end{document} meson decay constants

We present our first set of results for charm physics, using the mixed-action setup introduced in a companion paper [1]. Maximally twisted Wilson valence fermions are used on a sea of non-perturbatively O(a)-improved Wilson fermions, made up by CLS Nf=2+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_\\mathrm {\\scriptstyle f}=2+1$$\\end{document} ensembles. Our charm-sector observables are free from O(amc)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(am_c)$$\\end{document} discretisation effects, without need of tuning any improvement coefficient, and show continuum-limit scaling properties consistent with leading cutoff effects of O(a2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(a^2)$$\\end{document}. We consider a subset of CLS ensembles – including four values of the lattice spacing and pion masses down to 200 MeV – allowing to take the continuum limit and extrapolate to the physical pion mass. A number of techniques are incorporated in the analysis in order to estimate the systematic uncertainties of our results for the charm quark mass and the D(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{(s)}$$\\end{document}-meson decay constants. This first study of observables in the charm sector, where the emphasis has been on the control of the methodology, demonstrates the potential of our setup to achieve high-precision results.

Extraction of nonperturbative parameters for D(*) mesons from lattice data

Recent data for the masses of D and D* mesons determined using methods of lattice QCD for several values of the charm quark mass different from its physical mass are analyzed in heavy quark effective theory. Nonperturbative parameters are extracted that arise at order O(1/mc) in the heavy quark mass expansion of a heavy-light meson mass. The determined parameters are used to establish the charm quark masses corresponding to the employed lattice sets. Published by the American Physical Society 2024

Relativistic corrections to prompt double charmonium hadroproduction near threshold

We calculate the relativistic corrections to prompt J/ψ pair and J/ψ+ψ(2S) hadroproduction through the color singlet channel within the framework of nonrelativistic-QCD (NRQCD) factorization. The short-distance coefficients are obtained by matching full-QCD and NRQCD calculations at the partonic level, in which both squared amplitude and phase space are expanded in v2. We find that such an expansion of the phase space spoils the convergence of NRQCD factorization near the production threshold. To fix this problem, we propose to modify the matching between full QCD and NRQCD by adopting the physical phase space. In this modified approach, the theoretical uncertainties due to the choice of charm quark mass mc are largely reduced and the overall agreement of our predictions with LHC data is significantly improved, both for total and differential cross sections. Published by the American Physical Society 2024

B→D*ℓνℓ semileptonic form factors from lattice QCD with Möbius domain-wall quarks

We calculate the form factors for the B→D*ℓνℓ decay in 2+1 flavor lattice QCD. For all quark flavors, we employ the Möbius domain-wall action, which preserves chiral symmetry to a good precision. Our gauge ensembles are generated at three lattice cutoffs a−1∼2.5, 3.6, and 4.5 GeV with pion masses as low as Mπ∼230 MeV. The physical lattice size L satisfies the condition MπL≥4 to control finite volume effects (FVEs), while we simulate a smaller size at the smallest Mπ to directly examine FVEs. The bottom quark masses are chosen in a range from the physical charm quark mass to 0.7a−1 to control discretization effects. We extrapolate the form factors to the continuum limit and physical quark masses based on heavy meson chiral perturbation theory at next-to-leading order. Then the recoil parameter dependence is parametrized using a model independent form leading to our estimate of the decay rate ratio between the tau (ℓ=τ) and light lepton (ℓ=e, μ) channels R(D*)=0.252(22) in the Standard Model. A simultaneous fit with recent data from the Belle experiment yields |Vcb|=39.19(91)×10−3, which is consistent with previous exclusive determinations, and shows good consistency in the kinematical distribution of the differential decay rate between the lattice and experimental data. Published by the American Physical Society 2024

Long-distance contribution to εK from lattice QCD

A lattice QCD approach to the calculation of the long-distance contributions to εK is presented. This parameter describes indirect CP violation in K→ππ decay. While the short-distance contribution to εK can be accurately calculated in terms of standard model parameters and a single hadronic matrix element, BK, there is a long-distance part which is estimated to be approximately 5% of the total and is more difficult to determine. A method for determining this small but phenomenologically important contribution to εK using lattice QCD is proposed and a complete exploratory calculation of the contribution is presented. This exploratory calculation uses an unphysical light quark mass corresponding to a 339 MeV pion mass and an unphysical charm quark mass of 968 MeV, expressed in the MS¯ scheme at 2 GeV. This calculation demonstrates that future work should be able to determine this long-distance contribution from first principles with a controlled error of 10% or less. Published by the American Physical Society 2024

Heavy quarks in polarised deep-inelastic scattering at the electron-ion collider

We extend the FONLL general-mass variable-flavour-number scheme to the case of longitudinally polarised DIS structure functions, accounting for perturbative corrections up to Oαs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \\alpha _s^2\\right) $$\\end{document}. We quantify the impact of charm quark mass and higher-order perturbative corrections on projected measurements of inclusive and charm-tagged longitudinal asymmetries at the Electron-Ion Collider (EIC) and at the Electron-ion collider in China (EicC). We demonstrate how the inclusion of these corrections is essential to compute predictions with an accuracy that matches the projected precision of the measurements. The computation is made publicly available through the open-source EKO and YADISM programs.

Selected lattice QCD results on hadron structure

We present recent results on hadron structure using lattice QCD simulations with physical values of the light, strange and charm quark masses. We overview progress on quantities that probe the three-dimensional structure of the nucleon focusing on recent results on Mellin moments and the direct computation of the x-dependence of parton distribution functions employing mainly the quasi-parton distribution approach within the large momentum effective theory.

First-principle calculation of the [formula omitted] decay width from lattice QCD

We perform a lattice QCD calculation of the ηc→2γ decay width using a model-independent method that requires no momentum extrapolation of the off-shell form factors. This method also provides a straightforward and simple way to examine the finite-volume effects. The calculation is accomplished using Nf=2 twisted mass fermion ensembles. The statistically significant excited-state effects are observed and eliminated using a multi-state fit. The impact of fine-tuning the charm quark mass is also examined and confirmed to be well-controlled. Finally, using three lattice spacings for the continuum extrapolation, we obtain the decay width Γηcγγ=6.67(16)stat(6)syst keV, which differs significantly from the Particle Data Group’s reported value of Γηcγγ=5.4(4) keV (2.9σ tension). We provide insight into the comparison between our findings, previous theoretical predictions, and experimental measurements.

Quark mass dependence of the low-lying charmed mesons at one loop in HHχPT

We study the light and heavy quark mass dependence of the low-lying charmed mesons in the framework of one-loop HHχPT. The low energy constants are determined by analyzing the available lattice data from different LQCD simulations. Model selection tools are implemented to determine the relevant parameters as required by data with a higher precision. Discretization and other effects due to the charm quark mass setting are discussed.

Specific three-loop contributions to b → sγ associated with the current-current operators

We work out a specific class of three-loop diagrams (of order {alpha}_s^2 ) contributing to the decay amplitude for b → sγ associated with the current-current operators O1 and O2 at the physical value of the charm-quark mass mc. For many of the considered diagrams we were able to solve the master integrals using differential equations in the canonical form. For some diagrams we did not find a transformation to canonical form and therefore calculated the corresponding master integrals directly as an expansion around z={m}_c^2/{m}_b^2=0 , retaining power terms up to z10 and keeping the accompanying log(z) terms to all powers. The results for the sum of all considered diagrams are given in tabular form, while contributions of individual diagrams (or combinations thereof) are given in electronic form.