Physical Quark Masses Research Articles

Dirac spectral density in Nf=2+1 QCD at T=230 MeV

We compute the renormalized Dirac spectral density in Nf=2+1 QCD at physical quark masses, temperature T=230 MeV, and system size Ls=3.4 fm. To that end, we perform a pointwise continuum limit of the staggered density in lattice QCD with staggered quarks. We find, for the first time, that a clear infrared structure (IR peak) emerges in the density of the Dirac operator describing dynamical quarks. We also provide numerical evidence that a component of this peak, which becomes dominant in the thermodynamic limit, is due to a nontrivial accumulation of near-zero modes. Features of this structure are consistent with those previously attributed to the recently proposed IR phase of thermal QCD. Our results (i) provide the only complete first-principles evidence that these IR features exist and are physical, (ii) improve the upper bound for IR phase transition temperature TIR so that the new window is 200<TIR<230 MeV, and (iii) are consistent with the nonrestoration of anomalous UA(1) symmetry (chiral limit) below T=230 MeV. Published by the American Physical Society 2024

Coupled-channel J−− meson resonances from lattice QCD

We extend an earlier calculation within lattice QCD of excited light meson resonances with JPC=1−−,2−−,3−− at the SU(3) flavor point in the representation, by considering the representation. In this case the resonances appear in coupled-channel amplitudes, which we determine, establishing the relative strength of pseudoscalar-pseudoscalar to pseudoscalar-vector decays. Combining the new octet results with the prior results for the singlet, we perform a plausible extrapolation to the physical quark mass, and compare to experimental ρJ⋆,KJ⋆,ωJ⋆ and ϕJ⋆ resonances. Published by the American Physical Society 2024

Kaon mixing beyond the standard model with physical masses

We present nonperturbative results for beyond the standard model kaon mixing matrix elements in the isospin symmetric limit (mu=md) of QCD, including a complete estimate of all dominant sources of systematic error. Our results are obtained from numerical simulations of lattice QCD with Nf=2+1 flavors of dynamical domain wall fermions. For the first time, these quantities are simulated directly at the physical pion mass mπ∼139 MeV for two different lattice spacings. We include data at three lattice spacings in the range a=0.11–0.07 fm and with pion masses ranging from the physical value up to 450 MeV. Compared to our earlier work, we have added both direct calculations at physical quark masses and a third lattice spacing making the removal of discretization effects significantly more precise and eliminating the need for any significant mass extrapolation beyond the range of simulated data. We renormalize the lattice operators nonperturbatively using RI-SMOM off-shell schemes. These schemes eliminate the need to model and subtract nonperturbative pion poles that arises in the RI-MOM scheme and, since the calculations are performed with domain wall fermions, the unphysical mixing between chirality sectors is suppressed. Our results for the bag parameters in the MS¯ scheme at 3 GeV are BK≡B1=0.5240(17)(54), B2=0.4794(25)(35), B3=0.746(13)(17), B4=0.897(02)(10) and B5=0.6882(78)(94), where the first error is from lattice uncertainties and the second is the uncertainty due to the perturbative matching to MS¯. Published by the American Physical Society 2024

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

Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass

We present a direct lattice QCD calculation of the x-dependence of the pion distribution amplitude (DA), which is performed using the quasi-DA in large momentum effective theory on a domain-wall fermion ensemble at physical quark masses and spacing a ≈ 0.084 fm. The bare quais-DA matrix elements are renormalized in the hybrid scheme and matched to MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{MS}} $$\\end{document} with a subtraction of the leading renormalon in the Wilson-line mass. For the first time, we include threshold resummation in the perturbative matching onto the light-cone DA, which resums the large logarithms in the soft gluon limit at next-to-next-to-leading log. The resummed results show controlled scale-variation uncertainty within the range of momentum fraction x ∈ [0.25, 0.75] at the largest pion momentum Pz ≈ 1.85 GeV. In addition, we apply the same analysis to quasi-DAs from a highly-improved-staggered-quark ensemble at physical pion mass and a = 0.076 fm. By comparison we find with 2σ confidence level that the DA obtained from chiral fermions is flatter and lower near x = 0.5.

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.

B→D* and Bs→Ds* vector, axial-vector and tensor form factors for the full q2 range from lattice QCD

We compute the complete set of Standard Model (SM) and tensor B→D*ℓν¯ and Bs→Ds*ℓν¯ semileptonic form factors across the full kinematic range of the decays using second generation MILC nf=2+1+1 highly improved staggered quark (HISQ) gluon field configurations and HISQ valence quarks, with the method. Lattice spacings range from 0.09 to 0.044 fm with pion masses from ≈300 MeV down to the physical value and heavy quark masses ranging between ≈1.5mc and 4.1mc≈0.9mb; currents are normalized nonperturbatively. Using the recent untagged B→D*ℓν¯ℓ data from Belle and Bs→Ds*μν¯μ from LHCb together with our form factors, we determine a model independent value of Vcb=39.03(56)exp(67)latt×10−3, in agreement with previous exclusive determinations and in tension with the most recent inclusive result at the level of 3.6σ. We also observe a ≈1σ tension between the shape of the differential decay rates computed using our form factors and those measured by Belle. We compute a purely theoretical Standard Model value for the ratio of semitauonic and semimuonic decay rates, R(D*)=0.273(15), which we find to be closer to the recent Belle measurement and heavy flavor averaging group average than theory predictions using fits to experimental differential rate data for B→D*ℓν¯ℓ. Determining Vcb from our form factors and the experimental total rate for B→D*ℓν also gives a value in agreement with inclusive results. We also compute the longitudinal polarization fraction for the semitauonic mode, FLD*=0.395(24), which is in tension at the level of 2.2σ with the recent Belle measurement. Our calculation combines B→D* and Bs→Ds* lattice results in a simultaneous chiral continuum extrapolation, maintaining correlations between both modes. We then give results for both B→D* and Bs→Ds*, with the Bs→Ds* results superseding our previous lattice computation. We also give the chiral perturbation theory needed to analyze the tensor form factors. Published by the American Physical Society 2024

Nucleon form factors in Nf=2+1 lattice QCD at the physical point: Finite lattice spacing effect on the root-mean-square radii

We present results for the nucleon form factors: electric (GE), magnetic (GM), axial (FA), induced pseudoscalar (FP), and pseudoscalar (GP) form factors, using the second PACS10 ensemble that is one of three sets of 2+1 flavor lattice QCD configurations at physical quark masses in large spatial volumes [exceeding (10 fm)3]. The second PACS10 gauge configurations are generated by the PACS Collaboration with the six stout-smeared O(a) improved Wilson quark action and Iwasaki gauge action at the second gauge coupling β=2.00 corresponding to the lattice spacing of a=0.063 fm. We determine the isovector electric, magnetic and axial radii, and magnetic moment from the corresponding form factors, as well as the axial-vector coupling gA. Combining our previous results for the coarser lattice spacing [E. Shintani , ; ], the finite lattice spacing effects on the isovector radii, magnetic moment, and axial-vector coupling are investigated using the difference between the two results. It was found that the effect on gA is kept smaller than the statistical error of 2% while the effect on the isovector radii was observed as a possible discretization error of about 10%, regardless of the channel. We also report the partially conserved axial-vector current relation using a set of nucleon three-point correlation functions in order to verify the effect by O(a) improvement of the axial-vector current. 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

Two-body double pole and three-body bound states: Physical and unphysical quark masses

We solve the Faddeev bound-state equations for three particles with simple two-body nonlocal, separable potentials that yield a scattering length twice as large as a positive effective range, as indicated by some lattice QCD simulations. Neglecting shape parameters, the two-body bound state is a double pole. For bosons we obtain a correlation between three- and two-body energies. For nucleons, this correlation depends additionally on the ratio of the effective ranges for the two-body S-wave channels. When this ratio takes the value suggested by lattice QCD, our three-body energy agrees well with a direct lattice determination. When this ratio takes the experimental value, we find a three-body bound state with energy close to that of the physical triton. We suggest that results could be improved systematically with distorted-wave perturbation theory around a separable potential whose form factor is an inverse square root of momentum squared.

Cold and dense perturbative QCD in a very strong magnetic background

We compute the pressure from first principles within perturbative QCD at finite baryon density and very high magnetic fields up to two-loops and with physical quark masses. The region of validity for our framework is given by ms≪μq≪eB, where ms is the strange quark mass, μq is the quark chemical potential, e is the fundamental electric charge, and B is the magnetic field strength. We include the effects of the renormalization scale in the running coupling, αs(μq,eB), and running strange quark mass. We also discuss the simplifications that come about in the chiral limit. The effectively negligible contribution of the exchange diagram allows for building a simple analytic model for the equation of state for pure quark magnetars and computing their mass and radius at very large values of B. These results provide constraints on the behavior of the maximum mass and associated radius from perturbative QCD. We also discuss the magnetic bag model for extreme magnetic fields. Published by the American Physical Society 2024

Transversity PDFs of the proton from lattice QCD with physical quark masses

We present a lattice QCD calculation of the transversity isovector- and isoscalar-quark parton distribution functions (PDFs) of the proton utilizing a perturbative matching at next-to-leading-order (NLO) accuracy. Additionally, we determine the isovector and isoscalar tensor charges for the proton. In both calculations, the disconnected contributions to the isoscalar matrix elements have been ignored. The calculations are performed using a single ensemble of Nf=2+1 highly improved staggered quarks simulated with physical-mass quarks and a lattice spacing of a=0.076 fm. The Wilson-clover action, with physical quark masses and smeared gauge links obtained from one iteration of hypercubic smearing, is used in the valence sector. Using the NLO operator product expansion, we extract the lowest four to six Mellin moments and the PDFs via a neural network from the matrix elements in the pseudo-PDF approach. In addition, we calculate the PDFs in the quasi-PDF approach with hybrid-scheme renormalization and the recently developed leading-renormalon resummation technique, at NLO with the resummation of leading small-x logarithms. Published by the American Physical Society 2024

Approaches to inclusive semileptonic B(s)-meson decays from Lattice QCD

We address the nonperturbative calculation of the inclusive decay rate of semileptonic B(s)-meson decays from lattice QCD. Precise Standard-Model predictions are key ingredients in searches for new physics, and this type of computation may eventually provide new insight into the long-standing tension between the inclusive and exclusive determinations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements |Vcb| and |Vub|. We present results from a pilot lattice computation for Bs → Xclνl, where the initial b quark described by the relativistic-heavy-quark (RHQ) formalism on the lattice and the other valence quarks discretised with domain-wall fermions are simulated approximately at their physical quark masses. We compare two different methods for computing the decay rate from lattice data of Euclidean n-point functions, namely Chebyshev and Backus-Gilbert approaches. We further study how much the ground-state meson dominates the inclusive decay rate and indicate our strategy towards a computation with a more comprehensive systematic error budget.

Study of Quarkonium in QGP from Unquenched Lattice QCD

This paper discusses the charmonium and bottomonium correlators in the pseudoscalar channel and the corresponding spectral reconstruction on the lattice. The absence of a transport peak in the pseudoscalar channel spectral function allows for an easier study of the in-medium modification of bound states. However, extracting spectral information from Euclidean correlators is still a numerically ill-posed problem. To constrain the spectral reconstruction, we use an ansatz motivated from perturbation theory. The perturbative model spectral function has two main contributions: a thermal part around the threshold obtained from pNRQCD and the vacuum part well above the threshold. These two regions are matched continuously, and the model spectral function is obtained by introducing parameters that control the overall thermal shift of the peak and the overall amplitude. The lattice correlator data is computed using clover-improved Wilson valence fermions on large and fine gauge field configurations generated using N_f=2+1 flavors Highly Improved Staggered Quark action with physical strange quark mass m_s, and slightly heavy degenerate up and down quark masses m_l=m_s/5 that correspond to m_pi simeq 320 MeV. Our results obtained at T=220 MeV and T=251 MeV suggest that no resonance peaks are needed to describe the charmonium lattice data at these temperatures, while for bottomonium thermally broadened resonance peaks persists.

Exclusive semileptonic Bs→Kℓν decays on the lattice

Semileptonic $B_s \to K \ell \nu$ decays provide an alternative $b$-decay channel to determine the CKM matrix element $|V_{ub}|$, and to obtain a $R$-ratio to investigate lepton-flavor-universality violations. Results for the CKM matrix element may also shed light on the discrepancies seen between analyses of inclusive or exclusive decays. We calculate the decay form factors using lattice QCD with domain-wall light quarks and a relativistic $b$-quark. We analyze data at three lattice spacings with unitary pion masses down to $268\,\mathrm{MeV}$. Our numerical results are interpolated/extrapolated to physical quark masses and to the continuum to obtain the vector and scalar form factors $f_+(q^2)$ and $f_0(q^2)$ with full error budgets at $q^2$ values spanning the range accessible in our simulations. We provide a possible explanation of tensions found between results for the form factor from different lattice collaborations. Model- and truncation-independent $z$-parameterization fits following a recently proposed Bayesian-inference approach extend our results to the entire allowed kinematic range. Our results can be combined with experimental measurements of $B_s \to D_s$ and $B_s\to K$ semileptonic decays to determine $|V_{ub}|=3.8(6)\times 10^{-3}$. The error is currently dominated by experiment. We compute differential branching fractions and two types of $R$ ratios, the one commonly used as well as a variant better suited to test lepton-flavor universality.

Scale setting and the light baryon spectrum in Nf = 2 + 1 QCD with Wilson fermions

We determine the light baryon spectrum on ensembles generated by the Coordinated Lattice Simulations (CLS) effort, employing Nf = 2 + 1 flavours of non-perturbatively improved Wilson fermions. The hadron masses are interpolated and extrapolated within the quark mass plane, utilizing three distinct trajectories, two of which intersect close to the physical quark mass point and the third one approaching the SU(3) chiral limit. The results are extrapolated to the continuum limit, utilizing six different lattice spacings ranging from a ≈ 0.10 fm down to below 0.04 fm. The light pion mass varies from Mπ ≈ 429 MeV down to 127 MeV. In general, the spatial extent is kept larger than four times the inverse pion mass and larger than 2.3 fm, with additional small and large volume ensembles to investigate finite size effects. We determine the Wilson flow scales sqrt{t_{0,textrm{ph}}}={0.1449}_{(9)}^{(7)}textrm{fm} [1] and {t}_0^{ast}approx {t}_{0,textrm{ph}} [2] from the octet cascade (Ξ baryon). Determining the light baryon spectrum in the continuum limit, we find the nucleon mass {m}_N={941.7}_{(7.6)}^{(6.5)} MeV and the other stable baryon masses to agree with their experimental values within sub-percent level uncertainties. Moreover, we determine SU(3) and SU(2) chiral perturbation theory low energy constants, including the octet and the Ω baryon sigma terms σπN = 43.9(4.7) MeV, {sigma}_{pi Lambda}={28.2}_{(5.4)}^{(4.3)} MeV, {sigma}_{pi Sigma}={25.9}_{(6.1)}^{(3.8)} MeV, {sigma}_{pi Xi}={11.2}_{(6.4)}^{(4.5)} and {sigma}_{pi Omega}={6.9}_{(4.3)}^{(5.3)} MeV, as well as various parameters, renormalization factors and improvement coefficients that are relevant for simulations with our lattice action.

Unpolarized proton PDF at NNLO from lattice QCD with physical quark masses

Unpolarized proton PDF at NNLO from lattice QCD with physical quark masses

Static energy in ( 2+1+1 )-flavor lattice QCD: Scale setting and charm effects

We present results for the static energy in ($2+1+1$)-flavor QCD over a wide range of lattice spacings and several quark masses, including the physical quark mass, with ensembles of lattice-gauge-field configurations made available by the MILC Collaboration. We obtain results for the static energy out to distances of nearly $1$~fm, allowing us to perform a simultaneous determination of the scales $r_{1}$ and $r_{0}$, as well as the string tension $\sigma$. For the smallest three lattice spacings we also determine the scale $r_{2}$. Our results for $r_{0}/r_{1}$ and $r_{0}\sqrt{\sigma}$ agree with published ($2+1$)-flavor results. However, our result for $r_{1}/r_{2}$ differs significantly from the value obtained in the ($2+1$)-flavor case, which is most likely due to the effect of the charm quark. We also report results for $r_{0}$, $r_{1}$, and $r_{2}$ in~fm, with the former two being slightly lower than published ($2+1$)-flavor results. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest two lattices with the previously published ($2+1$)-flavor QCD results at similar lattice spacing. We find that for $r > 0.2$~fm our results on the static energy agree with the ($2+1$)-flavor result, implying the decoupling of the charm quark for these distances. For smaller distances, on the other hand, we find that the effect of the dynamical charm quark is noticeable. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects. This is the first time that the decoupling of the charm quark is observed and quantitatively analyzed on lattice data of the static energy.

Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses

The decreasing uncertainties in theoretical predictions and experimental measurements of several hadronic observables related to weak processes, which in many cases are now smaller than O(1%), require theoretical calculations to include subleading corrections that were neglected so far. Precise determinations of leptonic and semi-leptonic decay rates, including QED and strong isospin-breaking effects, can play a central role in solving the current tensions in the first-row unitarity of the CKM matrix. In this work we present the first RBC/UKQCD lattice calculation of the isospin-breaking corrections to the ratio of leptonic decay rates of kaons and pions into muons and neutrinos. The calculation is performed at fixed lattice spacing (a−1 ≃ 1.730 GeV) on a 483× 96 volume with Nf = 2 + 1 dynamical quarks close to the physical point and domain wall fermions in the Möbius formulation are employed. Long-distance QED interactions are included according to the QEDL prescription and the crucial role of finite-volume electromagnetic corrections in the determination of leptonic decay rates, which produce a large systematic uncertainty, is extensively discussed. Finally, we study the different sources of uncertainty on |Vus|/|Vud| and observe that, if finite-volume systematics can be reduced, the error from isospin-breaking corrections is potentially sub-dominant in the final precision of the ratio of the CKM matrix elements.

Kaon semileptonic form factors at the physical quark masses on large volumes in Nf = 2 + 1 lattice QCD

We present our results for the kaon semileptonic form factors calculated by using two sets of the PACS10 configuration, whose physical volumes are more than (10 fm)4 at the physical light and strange quark masses in the Nf = 2+1 lattice QCD. The configurations were generated using the Iwasaki gauge action and Nf = 2 + 1 stout-smeared clover quark action. The form factors near zero momentum transfer q 2 can be calculated thanks to the large volume. Using our data, a q 2 interpolation and continuum extrapolation are carried out simultaneously. The value of |Vus | is determined using the result of the form factors at q 2 = 0 in the continuum limit. Our result of |Vus| is compared with the one determined from the CKM matrix unitarity and with those determined using recent lattice results.