Light Quark Masses Research Articles

Study of the isoscalar scalar bcu¯d¯ tetraquark Tbc with lattice QCD

We present a lattice QCD study of the elastic S-wave DB¯ scattering in search of tetraquark candidates with explicitly exotic flavor content bcu¯d¯ in the isospin I=0 and JP=0+ channel. We use four lattice QCD ensembles with dynamical u/d, s, and c quark fields generated by the MILC collaboration. A nonrelativistic QCD Hamiltonian, including improvement coefficients up to O(αsv4), is utilized for the bottom quarks. For the rest of the valence quarks we employ a relativistic overlap action. Five different valence quark masses are utilized to study the light quark mass dependence of the DB¯ scattering amplitude. The finite volume energy spectra are extracted following a variational approach. The elastic DB¯ scattering amplitudes are extracted employing Lüscher’s prescription. The light quark mass dependence of the continuum extrapolated amplitudes suggests an attractive interaction between the B¯ and D mesons. At the physical pseudoscalar meson mass (Mps=Mπ) the DB¯ scattering amplitude has a subthreshold pole corresponding to a binding energy of −39(−6+4)(−18+8) MeV with respect to the DB¯ threshold. The critical Mps at which the DB¯ scattering length diverges and the system becomes unbound corresponds to Mps*=2.94(15)(5) GeV. This result can hold significant experimental relevance in the search for a bound scalar Tbc tetraquark, which could well be the next “doubly heavy” bound tetraquark to be discovered with only weak decay modes. Published by the American Physical Society 2024

Ratios of the light quark masses: Cubic curve versus ellipse

The bounds on the light quark masses are obtained by fitting the squares of pseudoscalar meson masses mπ2 and mK2 to second order in 1/Nc expansion. The result is an algebraic cubic curve whose coefficients are the known Weinberg values for the quark mass ratios mu/md and ms/md. Additional restrictions arise when using the ratio ms/mud=27.23(10) quoted by FLAG for lattice simulations with four quark flavors. This provides a tight constraint on the ratio mu/md=0.455(8). Published by the American Physical Society 2024

QCD bounds on leading-order hadronic vacuum polarization contributions to the muon anomalous magnetic moment

QCD bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon [aμHVP,LO, aμ=(g−2)μ/2] are determined by imposing Hölder inequalities and related inequality constraints on systems of finite-energy QCD sum rules. This novel methodology is complementary to lattice QCD and data-driven approaches to determining aμHVP,LO. For the light-quark (u, d, s) contributions up to five-loop order in perturbation theory in the chiral limit, LO in light-quark mass corrections, next-to-leading order in dimension-four QCD condensates, and to LO in dimension-six QCD condensates, we find that (657.0±34.8)×10−10≤aμHVP,LO≤(788.4±41.8)×10−10, bridging the range between lattice QCD and data-driven values. Published by the American Physical Society 2024

D and Ds decay constants in Nf = 2 + 1 QCD with Wilson fermions

We present results for the leptonic decay constants of the D and Ds mesons from Nf = 2 + 1 lattice QCD. We employ a set of 49 high statistics gauge ensembles generated by the Coordinated Lattice Simulations (CLS) effort utilising non-perturbatively improved Wilson fermions and the tree-level Symanzik improved gauge action at six values of the lattice spacing in the range a = 0.098 fm down to a = 0.039 fm, with pion masses varying from around 420 MeV down to below the physical point. The ensembles lie on three trajectories in the quark mass plane, two trajectories intersecting close to the physical quark mass point and the third one approaching the SU(3) chiral limit, enabling tight control of the light and strange quark mass dependence. We obtain fDs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {f}_{{\ extrm{D}}_{\ extrm{s}}} $$\\end{document} = 246.8(1.3) MeV, fD = 208.4(1.5) MeV and fDs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {f}_{{\ extrm{D}}_{\ extrm{s}}} $$\\end{document}/fD = 1.1842(36), where the precision of our results is mostly limited by the determination of the scale.

Chiral analysis of the nucleon mass and sigma commutator

Schemes for describing the light quark mass dependence of the nucleon mass calculated in lattice QCD are compared. The three schemes in consideration include a fully relativistic and Lorentz covariant scheme, one that is fully relativistic but not Lorentz covariant, and a semirelativistic scheme utilizing the heavy baryon approximation. Calculations of observables involving pseudoscalar meson loop diagrams generate nonanalytic terms proportional to square roots and logarithms of the quark mass. The three schemes all yield the correct model-independent leading and next-to-leading nonanalytic terms of the chiral expansion of the baryon mass. Results for the masses of the other members of the octet are also presented. Here, low-energy coefficients of the analytic terms of the expansion for the nucleon and hyperons are constrained by lattice QCD results and are demonstrated to be independent of the renormalization scheme used. The differences in the leading coefficient of the chiral expansions are found to be consistent with strange quark counting. Using the schemes examined herein, we report results for the pion-nucleon sigma commutator based upon recent lattice results from the CLS Collaboration. We find σπN=51.7±3.2±1.4 MeV, where the uncertainties are statistical and systematic, respectively. Published by the American Physical Society 2024

Light-quark mass dependence of the Λ(1405) resonance

We present the light-quark mass dependence of the Λ(1405) resonance at leading order in a renormalizable framework of covariant chiral effective field theory. The meson-baryon scattering amplitudes, which are obtained by solving the scattering equation within time-ordered perturbation theory, follow the quark mass trajectory of the Coordinated Lattice Simulations consortium. At Mπ≈200 MeV and MK≈487 MeV, our parameter-free prediction of Λ(1405) poles is consistent with the recent lattice results of BaSc Collaboration [Phys. Rev. Lett. 132, 051901 (2024)]. Varying the pion mass from 135 MeV to 400 MeV, we present the evolution of double-pole positions of Λ(1405): the higher pole remains a resonance around the K¯N threshold; whereas the lower pole undergoes a transition from resonance to a virtual state, and ultimately to a bound state of the πΣ system, which could be verified by the forthcoming lattice QCD simulations.

Charmonium χc0 and χc2 resonances in coupled-channel scattering from lattice QCD

In order to explore the spectrum of hidden-charm scalar and tensor resonances, we study meson-meson scattering with JPC=0++,2++ in the charmonium energy region using lattice QCD. Employing a light-quark mass corresponding to mπ≈391 MeV, we determine coupled-channel scattering amplitudes up to around 4100 MeV considering all kinematically relevant channels consisting of a pair of open-charm mesons or a charmonium meson with a light meson. A single isolated scalar resonance near 4000 MeV is found with large couplings to DD¯, DsD¯s and the kinematically closed D*D¯* channel. A single tensor resonance at a similar mass couples strongly to DD¯, DD¯* and D*D¯*. We compare the extracted resonances to contemporary experimental candidate states, previous lattice results and theoretical modeling. In contrast to several other studies, we do not find any significant feature in the scalar amplitudes between the ground state χc0(1P) and the resonance found around 4000 MeV. 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

Trace anomaly form factors from lattice QCD

The hadron mass can be obtained through the calculation of the trace of the energy-momentum tensor in the hadron which includes the trace anomaly and sigma terms. The anomaly due to conformal symmetry breaking is believed to be an important ingredient for hadron mass generation and confinement. In this work, we will present the calculation of the glue part of the trace anomaly form factors of the pion up to Q2∼4.3 GeV2 and the nucleon up to Q2∼1 GeV2. The calculations are performed on a domain wall fermion ensemble with overlap valence quarks at seven valence pion masses varying from ∼250 to ∼540 MeV, including the unitary point ∼340 MeV. We calculate the radius of the glue trace anomaly for the pion and the nucleon from the z expansion. By performing a two-dimensional Fourier transform on the glue trace anomaly form factors in the infinite momentum frame with no energy transfer, we also obtain their spatial distributions for several valence quark masses. The results are qualitatively extrapolated to the physical valence pion mass with systematic errors from the unphysical sea quark mass, discretization effects in the renormalization sum rule, and finite-volume effects to be addressed in the future. We find the pion’s form factor changes sign, as does its spatial distribution, for light quark masses. This explains how the trace anomaly contribution to the pion mass approaches zero toward the chiral limit. Published by the American Physical Society 2024

Nonperturbative Collins-Soper kernel from chiral quarks with physical masses

We present a lattice QCD calculation of the rapidity anomalous dimension of quark transverse-momentum-dependent distributions, i.e., the Collins-Soper (CS) kernel, up to transverse separations of about 1 fm. This unitary lattice calculation is conducted, for the first time, employing the chiral-symmetry-preserving domain wall fermion discretization and physical values of light and strange quark masses. The CS kernel is extracted from the ratios of pion quasi-transverse-momentum-dependent wave functions (quasi-TMDWFs) at next-to-leading logarithmic perturbative accuracy. Also for the first time, we utilize the recently proposed Coulomb-gauge-fixed quasi-TMDWF correlator without a Wilson line. We observe significantly slower signal decay with increasing quark separations compared to the established gauge-invariant method with a staple-shaped Wilson line. This enables us to determine the CS kernel at large nonperturbative transverse separations and find its near-linear dependence on the latter. Our result is consistent with the recent lattice calculation using gauge-invariant quasi-TMDWFs, and agrees with various recent phenomenological parametrizations of experimental data.

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

Light Roberge-Weiss tricritical endpoint at imaginary isospin and baryon chemical potential

Imaginary chemical potentials serve as a useful tool to constrain the QCD phase diagram and to gain insight into the thermodynamics of strongly interacting matter. In this study, we report on the first determination of the phase diagram for arbitrary imaginary baryon and isospin chemical potentials at high temperature using one-loop perturbation theory, revealing a nontrivial structure of Roberge-Weiss (RW) phase transitions in this plane. Subsequently, this system is simulated numerically with Nf=2 unimproved staggered quarks on Nτ=4 lattices at a range of temperatures at one of the RW phase transitions. We establish a lower bound for the light quark mass, where the first-order transition line terminates in a tricritical point. It is found that this tricritical mass is increased as compared to the case of purely baryonic imaginary chemical potentials, indicating that our setup is more advantageous for identifying critical behavior toward the chiral limit. Finally, the dynamics of local Polyakov loop clusters is also studied in conjunction with the RW phase transition. Published by the American Physical Society 2024

Determination of crossing-symmetric ππ scattering amplitudes and the quark mass evolution of the σ constrained by lattice QCD

Lattice QCD spectra can be used to constrain partial-wave scattering amplitudes that, while satisfying unitarity, do not have to respect crossing symmetry and analyticity. This becomes a particular problem when extrapolated far from real energies, e.g. in the case of broad resonances like the σ, leading to large systematic uncertainties in the pole position. In this manuscript, we will show how dispersion relations can implement the additional constraints, using as input lattice-determined ππ partial-wave scattering amplitudes with isospin–0,1,2. We will show that only certain combinations of amplitude parametrizations satisfy all constraints, and that when we restrict to these, the σ pole position is determined with minimal systematic uncertainty. The evolution of the now well-constrained σ pole with varying light quark mass is presented, showing how it transitions from a bound-state to a broad resonance. Published by the American Physical Society 2024

Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Axial-vector case

Recently, we made significant advancements in improving the computational efficiency of lattice QCD calculations for generalized parton distributions (GPDs). This progress was achieved by adopting calculations of matrix elements in asymmetric frames, deviating from the computationally-expensive symmetric frame typically used, and allowing freedom in the choice for the distribution of the momentum transfer between the initial and final states. A crucial aspect of this approach involves the adoption of a Lorentz covariant parametrization for the matrix elements, introducing Lorentz-invariant amplitudes. This approach also allows us to propose an alternative definition of quasi-GPDs, ensuring frame independence and potentially reduce power corrections in matching to light cone GPDs. In our previous work, we presented lattice QCD results for twist-2 unpolarized GPDs (H and E) of quarks obtained from calculations performed in asymmetric frames at zero skewness. Building upon this work, we now introduce a novel Lorentz covariant parametrization for the axial-vector matrix elements. We employ this parametrization to compute the axial-vector GPD H˜ at zero skewness, using an Nf=2+1+1 ensemble of twisted mass fermions with clover improvement. The light-quark masses employed in our calculations correspond to a pion mass of approximately 260 MeV. Published by the American Physical Society 2024

Quark mass dependence of D*s0 (2317) and Ds1(2460) states

Abstract. We investigate the dependence of both light and heavy quark masses on the properties of low-lying charmed mesons within the framework of one-loop HHX PT. Determination of the low energy constants is accomplished through an analysis of lattice data obtained from various Lattice Quantum Chro-modynamics (LQCD) simulations. Model selection tools are employed to identify the pertinent parameters needed to achieve higher precision alignment with the data. Our study extends to the analysis of HSC energy levels for DK scattering in I = 0, considering different boosts and two pion masses. A comprehensive global fit is performed, incorporating HSC energy levels along with those from DK and D* K scattering obtained from RQCD and Prelovsek et al. Finally, we extract the dependence of D*s0(2317) and Ds1(2460) resonances on the pion mass.

Microscopic origin of criticality at macroscale in QCD chiral phase transition

We reveal that the criticality of the chiral phase transition in QCD at the macroscale arises from the microscopic energy levels of its fundamental constituents, the quarks. We establish a novel relation between cumulants of the chiral order parameter (i.e., chiral condensate) and correlations among the energy levels of quarks (i.e., eigenspectra of the massless Dirac operator), which naturally leads to a generalization of the Banks-Casher relation. Based on this novel relation and through (2+1)-flavor lattice QCD calculations using the HISQ action with varying light quark masses in the vicinity of the chiral phase transition, we demonstrate that the correlations among the infrared part of the Dirac eigenspectra exhibit same universal scaling behaviors as expected of the cumulants of the chiral condensate. We find that these universal scaling behaviors extend up to the physical values of the up and down quark masses.

Dynamical origin of universal two-pole structures and their light quark mass evolution

Two-pole structures refer to the fact that two dynamically generated states are located close to each other between two coupled channels and have a mass difference smaller than the sum of their widths. Thus, the two poles overlap in the invariant mass distribution of their decay products, creating the impression that only one state exists. This phenomenon was first noticed for the Λ(1405) and the K1(1270), and then for several other states. This report explicitly shows how the two-pole structures emerge from the underlying universal chiral dynamics describing the coupled-channel interactions between a heavy matter particle and a pseudo-Nambu-Goldstone boson. Furthermore, we predict similar two-pole structures in other systems dictated by chiral symmetry, such as the isospin 1/2 K¯∑c − πΞ′c coupled channel, awaiting experimental discoveries.

Light quark mass dependence of nucleon electromagnetic form factors in dispersively modified chiral perturbation theory

Light quark mass dependence of nucleon electromagnetic form factors in dispersively modified chiral perturbation theory

Regge trajectories for the light diquarks

We attempt to present an unified description of the light meson spectra and the light diquark spectra by applying the Regge trajectory approach. However, we find that the direct application of the linear Regge trajectory formula for the light mesons and baryons fails. To address this issue, we fit the experimental data of light meson spectra and the light diquark spectra obtained by other theoretical approaches. By considering the light quark mass and the parameter C in the Cornell potential, we provide a provisional Regge trajectory formula. We also crudely estimate the masses of the light diquarks (ud), (us), and (ss), and find that they agree with other theoretical results. The diquark Regge trajectory not only becomes a new and very simple approach for estimating the spectra of the light diquarks, but also can explicitly show the behavior of the masses with respect to l or nr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_r$$\\end{document}. Moreover, it is expected that the diquark Regge trajectory can provide a simple method for investigating the ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document}-mode excitations of baryons, tetraquarks and pentaquarks containing diquarks.

Open charm mesons and charmonium states in magnetized strange hadronic medium at finite temperature

In this paper, we investigate the masses of the pseudoscalar ([Formula: see text]([Formula: see text], [Formula: see text]), [Formula: see text]([Formula: see text], [Formula: see text]) and vector open charm mesons ([Formula: see text]([Formula: see text], [Formula: see text]), [Formula: see text]([Formula: see text], [Formula: see text]) as well as the pseudoscalar ([Formula: see text], [Formula: see text]) and the vector charmonium states ([Formula: see text], [Formula: see text], [Formula: see text]) in the asymmetric hot strange hadronic medium in the presence of strong magnetic fields. In the magnetized medium, the mass modification of open charm mesons due to their interactions with baryons and the scalar fields ([Formula: see text], [Formula: see text], and [Formula: see text]) is investigated in a chiral effective model. Moreover, the charged pseudoscalar meson ([Formula: see text]), as well as the longitudinal component of charged vector meson ([Formula: see text]), experience additional positive mass modifications in the magnetic field due to Landau quantization. The effect of the modification of gluon condensates simulated by the medium change of dilaton field [Formula: see text] on the masses of the charmonia is also calculated in the chiral effective model. The contribution of masses of light quarks is also considered in the modification of gluon condensates. At high temperatures, the magnetically induced modifications of scalar fields significantly reduce the in-medium masses of mesons. The effects of magnetically induced spin mixing between the pseudoscalar and the corresponding vector mesons are incorporated in our study through a phenomenological effective Lagrangian interaction. The spin mixing result in a positive mass shift for the longitudinal component of the vector mesons and a negative mass shift for the pseudoscalar mesons in the presence of the magnetic field. From the obtained in-medium masses of charmonia and open charm mesons, we have also calculated the partial decay widths of [Formula: see text] to [Formula: see text], using a light quark pair creation model, namely, the [Formula: see text] model.