Pseudoscalar Meson Masses Research Articles

End point of the first-order phase transition of QCD in the heavy quark region by reweighting from quenched QCD

We study the end point of the first-order deconfinement phase transition in two and 2+1 flavor QCD in the heavy quark region of the quark mass parameter space. We determine the location of critical point at which the first-order deconfinement phase transition changes to crossover, and calculate the pseudo-scalar meson mass at the critical point. Performing quenched QCD simulations on lattices with the temporal extents Nt=6 and 8, the effects of heavy quarks are determined using the reweighting method. We adopt the hopping parameter expansion to evaluate the quark determinants in the reweighting factor. We estimate the truncation error of the hopping parameter expansion by comparing the results of leading and next-to-leading order calculations, and study the lattice spacing dependence as well as the spatial volume dependence of the result for the critical point. The overlap problem of the reweighting method is also examined. Our results for Nt=4 and 6 suggest that the critical quark mass decreases as the lattice spacing decreases and increases as the spatial volume increases.

Kaons and antikaons in strong magnetic fields

The in-medium masses of the kaons and antikaons in strongly magnetized asymmetric nuclear matter are studied using a chiral SU(3) model. The medium modifications of the masses of these open strange pseudoscalar mesons arise due to their interactions with the nucleons and scalar mesons within the model. The proton, the charged nucleon, has effects from the Landau energy levels in the presence of the magnetic field. The anomalous magnetic moments (AMM) of the nucleons are taken into consideration in the present study and these are seen to be large at high magnetic fields and high densities. The isospin effects are appreciable at high densities. The density effects are observed to be the dominant medium effects, as compared to the effects from magnetic field and isospin asymmetry. ~

Lattice computation of the electromagnetic contributions to kaon and pion masses

We present a lattice calculation of the electromagnetic (EM) effects on the masses of light pseudoscalar mesons. The simulations employ $2+1$ dynamical flavors of asqtad QCD quarks and quenched photons. Lattice spacings vary from $\ensuremath{\approx}0.12\text{ }\text{ }\mathrm{fm}$ to $\ensuremath{\approx}0.045\text{ }\text{ }\mathrm{fm}$. We compute the quantity $\ensuremath{\epsilon}$, which parametrizes the corrections to Dashen's theorem for the ${K}^{+}$--${K}^{0}$ EM mass splitting, as well as ${\ensuremath{\epsilon}}_{{K}^{0}}$, which parametrizes the EM contribution to the mass of the ${K}^{0}$ itself. An extension of the nonperturbative EM renormalization scheme introduced by the BMW group is used in separating EM effects from isospin-violating quark mass effects. We correct for leading finite-volume effects in our realization of lattice electrodynamics in chiral perturbation theory, and remaining finite-volume errors are relatively small. While electroquenched effects are under control for $\ensuremath{\epsilon}$, they are estimated only qualitatively for ${\ensuremath{\epsilon}}_{{K}^{0}}$ and constitute one of the largest sources of uncertainty for that quantity. We find $\ensuremath{\epsilon}=0.78(1{)}_{\text{stat}}(\genfrac{}{}{0}{}{+8}{\ensuremath{-}11}{)}_{\text{syst}}$ and ${\ensuremath{\epsilon}}_{{K}^{0}}=0.035(3{)}_{\text{stat}}(20{)}_{\text{syst}}$. We then use these results on $2+1+1$ flavor pure QCD highly improved staggered quark (HISQ) ensembles and find ${m}_{u}/{m}_{d}=0.4529(48{)}_{\text{stat}}(\genfrac{}{}{0}{}{+150}{\ensuremath{-}67}{)}_{\text{syst}}$.

Finite size effect on pseudoscalar meson sector in 2+1 flavor QCD at the physical point

We investigate the finite size effect on pseudoscalar meson masses and decay constants using a subset of the "PACS10" configurations which are generated keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. We have tried two kinds of analyses, fixing $\kappa$ values or measured axial Ward identity quark masses. Comparing the results on (5.4 fm$)^4$ and (10.8 fm$)^4$ lattices, we have found a sizable finite size effect on the pseudoscalar meson sector in the former analysis: a 2.1(8)%, 4.8(1.6)%, and 0.36(31)% finite size effect on $m_\pi$, $m_{\rm ud}$, and $f_\pi$, respectively, on the (5.4 fm$)^4$ lattice. For the latter analysis, the finite size effect on the pseudoscalar meson decay constants is 0.66(33)% for $f_\pi$, 0.26(13)% for $f_K$, and 0.40(32)% for $f_K/f_\pi$. These values with two-sigma error bars are consistent with the predictions from the full one-loop SU(3) chiral perturbation theory, which are 0.20% for $f_\pi$, 0.08% for $f_K$, and 0.13% for $f_K/f_\pi$. The finite size effect on the pseudoscalar meson masses is hardly detected under the current statistical precision.

Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD

We calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from $a\ensuremath{\approx}0.15$ to 0.03 fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the $\overline{\mathrm{MS}}$-renormalized masses are ${m}_{u}(2\text{ }\text{ }\mathrm{GeV})=\phantom{\rule{0ex}{0ex}}2.130(41)\text{ }\text{ }\mathrm{MeV}$, ${m}_{d}(2\text{ }\text{ }\mathrm{GeV})=4.675(56)\text{ }\text{ }\mathrm{MeV}$, ${m}_{s}(2\text{ }\text{ }\mathrm{GeV})=92.47(69)\text{ }\text{ }\mathrm{MeV}$, ${m}_{c}(3\text{ }\text{ }\mathrm{GeV})=\phantom{\rule{0ex}{0ex}}983.7(5.6)\text{ }\text{ }\mathrm{MeV}$, and ${m}_{c}({m}_{c})=1273(10)\text{ }\text{ }\mathrm{MeV}$, with four active flavors; and ${m}_{b}({m}_{b})=4195(14)\text{ }\text{ }\mathrm{MeV}$ with five active flavors. We also obtain ratios of quark masses ${m}_{c}/{m}_{s}=11.783(25)$, ${m}_{b}/{m}_{s}=53.94(12)$, and ${m}_{b}/{m}_{c}=4.578(8)$. The result for ${m}_{c}$ matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of ${\ensuremath{\alpha}}_{s}^{4}$. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: ${\overline{\mathrm{\ensuremath{\Lambda}}}}_{\mathrm{MRS}}=555(31)\text{ }\text{ }\mathrm{MeV}$ in the minimal renormalon-subtracted (MRS) scheme, ${\ensuremath{\mu}}_{\ensuremath{\pi}}^{2}=0.05(22)\text{ }\text{ }{\mathrm{GeV}}^{2}$, and ${\ensuremath{\mu}}_{G}^{2}({m}_{b})=0.38(2)\text{ }\text{ }{\mathrm{GeV}}^{2}$. The MRS scheme [Phys. Rev. D 97, 034503 (2018)] is the key new aspect of our method.

Updated study of the η−η′ mixing and the thermal properties of light pseudoscalar mesons at low temperatures

Within the framework of the $U(3)$ chiral perturbation theory, we revisit the masses, decay constants and the mixing parameters of the light pseudoscalar mesons $\pi, K, \eta$ and $\eta'$. The low energy constants up to next-to-next-to-leading order are determined by including the light-quark mass dependences of the various quantities from different lattice QCD simulations and relevant phenomenological inputs. Then we study the finite-temperature behaviors of the masses of the light pseudoscalar mesons. The thermal behaviors of the $\eta$-$\eta'$ mixing angles in singlet-octet and quark-flavor bases are also explored. While the masses of the $\pi, K$, and $\eta$ are increased when increasing the temperatures, the mass of the $\eta'$ turns out to be slightly decreased in the low-temperature region.

Large-Nc masses of light mesons from QCD sum rules for nonlinear radial Regge trajectories

The large-[Formula: see text] masses of light vector, axial, scalar and pseudoscalar mesons are calculated from QCD spectral sum rules for a particular ansatz interpolating the radial Regge trajectories. The ansatz includes a linear part plus exponentially degreasing corrections to the meson masses and residues. The form of corrections was proposed some time ago for consistency with analytical structure of Operator Product Expansion of the two-point correlation functions. We revised that original analysis and found the second solution for the proposed sum rules. The given solution describes better the spectrum of vector and axial mesons.

Effects of nonequilibrated topological charge distributions on pseudoscalar meson masses and decay constants

We study the effects of failure to equilibrate the squared topological charge $Q^2$ on lattice calculations of pseudoscalar masses and decay constants. The analysis is based on chiral perturbation theory calculations of the dependence of these quantities on the QCD vacuum angle $\theta$. For the light-light partially quenched case, we rederive the known chiral perturbation theory results of Aoki and Fukaya, but using the nonperturbatively-valid chiral theory worked out by Golterman, Sharpe and Singleton, and by Sharpe and Shoresh. We then extend these calculations to heavy-light mesons. Results when staggered taste-violations are important are also presented. The derived $Q^2$ dependence is compared to that of simulations using the MILC collaboration's ensembles of lattices with four flavors of HISQ dynamical quarks. We find agreement, albeit with large statistical errors. These results can be used to correct for the leading effects of unequilibrated $Q^2$, or to make estimates of the systematic error coming from the failure to equilibrate $Q^2$. In an appendix, we show that the partially quenched chiral theory may be extended beyond a lower bound on valence masses discovered by Sharpe and Shoresh. Subtleties occurring when a sea-quark mass vanishes are discussed in another appendix.

Doubly magic nuclei from lattice QCD forces at MPS=469MeV/c2

We perform ab initio self-consistent Green's function calculations of the closed shell nuclei $^{\rm 4}$He, $^{\rm 16}$O and $^{\rm 40}$Ca, based on two-nucleon potentials derived from Lattice QCD simulations, in the flavor SU(3) limit and at the pseudo-scalar meson mass of 469~MeV/c$^{\rm 2}$. The nucleon-nucleon interaction is obtained using the HAL QCD method and its short-distance repulsion is treated by means of ladder resummations outside the model space. Our results show that this approach diagonalises ultraviolet degrees of freedom correctly. Therefore, ground state energies can be obtained from infrared extrapolations even for the relatively hard potentials of HAL QCD. Comparing to previous Brueckner Hartree-Fock calculations, the total binding energies are sensibly improved by the full account of many-body correlations. The results suggest an interesting possible behaviour in which nuclei are unbound at very large pion masses and islands of stability appear at first around the traditional doubly-magic numbers when the pion mass is lowered toward its physical value. The calculated one-nucleon spectral distributions are qualitatively close to those of real nuclei even for the pseudo-scalar meson mass considered here.

Leading isospin-breaking corrections to meson masses on the lattice

We present a study of the isospin-breaking (IB) corrections to pseudoscalar (PS) meson masses using the gauge configurations produced by the ETM Collaboration with Nf = 2+1+1 dynamical quarks at three lattice spacings varying from 0.089 to 0.062 fm. Our method is based on a combined expansion of the path integral in powers of the small parameters [see formula in PDF] and αem, where [see formula in PDF] is the renormalized quark mass and αem the renormalized fine structure constant. We obtain results for the pion, kaon and Dmeson mass splitting; for the Dashen’s theorem violation parameters ϵγ(MM, 2 GeV), ϵπ0 ϵK0(MS, 2 GeV) for the light quark masses [see formula in PDF] for the flavour symmetry breaking parameters R(MS, 2 GeV) and Q(MS, 2 GeV) and for the strong IB effects on the kaon decay constants.

HQE parameters from unquenched lattice data on pseudoscalar and vector heavy-light meson masses

We present a new lattice determination of some of the parameters appearing both in the Operator Product Expansion (OPE) analysis of the inclusive semileptonic B-meson decays and in the Heavy Quark Expansion (HQE) of the pseudoscalar (PS) and vector (V) heavy-light meson masses. We perform a lattice QCD (LQCD) computation of PS and V heavy-light meson masses for heavy-quark masses mh in the range from [see formula in PDF] to ≃ [see formula in PDF]. We employed the Nf = 2 + 1 + 1 gauge configurations of the European Twisted Mass Collaboration (ETMC) at three values of the lattice spacing a ≃ (0.062,0.082,0.089) fm with pion masses in the range Mπ ≃ (210 - 450) MeV. The heavy-quark mass is simulated directly on the lattice up to ≃ [see formula in PDF]. The interpolation to the physical [see formula in PDF] is performed using the ETMC ratio method and adopting the kinetic mass scheme. We obtain [see formula in PDF] (1 GeV) = 4.61(20) GeV (m̅b(m̅b) = 4.26(18) GeV in the MS scheme). The lattice data are analyzed in terms of the HQE and the matrix elements of dimension-4 and dimension-5 operators are extracted with good precision, namely: [see formula in PDF] and [see formula in PDF]. The data also allow for an estimate of the dimension-6 operator matrix elements.

A tmQCD mixed-action approach to flavour physics

We discuss a mixed-action approach in which sea quarks are regularised using non-perturbatively O(a) improved Wilson fermions, while a fully-twisted tmQCD action is used for valence quarks. In this setup, automatic O(a) improvement is preserved for valence observables, apart from small residual O(a) effects from the sea. A strategy for matching sea and valence is set up, and carried out for Nf = 2 + 1 CLS ensembles with open boundary conditions at several simulation points. The scaling of basic light-quark observables such as the pseudoscalar meson decay constant is studied, as well as the isospin splitting of pseudoscalar meson masses.

Critical point phase transition for finite temperature 3-flavor QCD with nonperturbatively O(a) improved Wilson fermions at Nt=10

We study the finite temperature phase structure for three-flavor QCD with a focus on locating the critical point which separates crossover and first order phase transition region in the chiral regime of the Columbia plot. In this study, we employ the Iwasaki gauge action and the non-perturvatively O($a$) improved Wilson-Clover fermion action. We discuss the finite size scaling analysis including the mixing of magnetization-like and energy-like observables. We carry out the continuum extrapolation of the critical point using newly generated data at $N_{\rm t}=8$, $10$ and estimate the upper bound of the critical pseudo-scalar meson mass $m_{\rm PS,E} \lesssim 170 {\rm MeV}$ and the critical temperature $T_{\rm E}=134(3){\rm MeV}$. Our estimate of the upper bound is derived from the existence of the critical point as an edge of the 1st order phase transition while that of the staggered-type fermions is based on its absence.

Extraction of heavy-quark-expansion parameters from unquenched lattice data on pseudoscalar and vector heavy-light meson masses

We present a precise lattice computation of pseudoscalar and vector heavy-light meson masses for heavy-quark masses ranging from the physical charm mass up to $\simeq 4$ times the physical b-quark mass. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range $M_\pi \simeq 210 - 450$ MeV. The heavy-quark mass is simulated directly on the lattice up to $\simeq 3$ times the physical charm mass. The interpolation to the physical $b$-quark mass is performed using the ETMC ratio method, based on ratios of the meson masses computed at nearby heavy-quark masses, and adopting the kinetic mass scheme. The extrapolation to the physical pion mass and to the continuum limit yields $m_b^{\rm kin}(1~\mbox{GeV}) = 4.61 (20)$ GeV, which corresponds to $\overline{m}_b(\overline{m}_b) = 4.26 (18)$ GeV in the $\overline{MS}$ scheme. The lattice data are analyzed in terms of the Heavy Quark Expansion (HQE) and the matrix elements of dimension-4 and dimension-5 operators are extracted with a good precision, namely: $\overline{\Lambda} = 0.552 (26)$ GeV, $\mu_\pi^2 = 0.321 (32)$ GeV$^2$ and $\mu_G^2(m_b) = 0.253 (25)$ GeV$^2$. The data also allow for a rough estimate of the dimension-6 operator matrix elements. As the HQE parameters play a crucial role in the inclusive determination of the Cabibbo-Kobayashi-Maskawa matrix elements $V_{ub}$ and $V_{cb}$, their precise determination on the lattice may eventually validate and improve the analyses based on fits to the semileptonic moments.

Simple chromatic properties of gradient flow

It has become customary to use a smoothing algorithm called "gradient flow" to fix the lattice spacing in a simulation, through a parameter called $t_0$. It is shown that in order to keep the length $t_0$ fixed with respect to mesonic or gluonic observables as the number of colors $N_c$ is varied, the fiducial point for the flow parameter must be scaled nearly linearly in $N_c$. In simulations with dynamical fermions, the dependence of $t_0$ on the pseudoscalar meson mass flattens as the number of colors rises, in a way which is consistent with large $N_c$ expectations.

Leading isospin-breaking corrections to pion, kaon, and charmed-meson masses with twisted-mass fermions

We present a lattice computation of the isospin-breaking corrections to pseudoscalar meson masses using the gauge configurations produced by the European Twisted Mass collaboration with $N_f = 2 + 1 + 1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082$ and $0.089$ fm) with pion masses in the range $M_\pi \simeq 210 - 450$ MeV. The strange and charm quark masses are tuned at their physical values. We adopt the RM123 method based on the combined expansion of the path integral in powers of the $d$- and $u$-quark mass difference ($\widehat{m}_d - \widehat{m}_u$) and of the electromagnetic coupling $\alpha_{em}$. Within the quenched QED approximation, which neglects the effects of the sea-quark charges, and after the extrapolations to the physical pion mass and to the continuum and infinite volume limits, we provide results for the pion, kaon and (for the first time) charmed-meson mass splittings, for the prescription-dependent parameters $\epsilon_{\pi^0}$, $\epsilon_\gamma(\overline{MS}, 2~\mbox{GeV})$, $\epsilon_{K^0}(\overline{MS}, 2~\mbox{GeV})$, related to the violations of the Dashen's theorem, and for the light quark mass difference $(\widehat{m}_d - \widehat{m}_u)(\overline{MS}, 2~\mbox{GeV})$.

Application of the light-front holographic wavefunction for heavy-light pseudoscalar meson in Bd,s → Dd,sP decays

In this paper we extend our analyses of the decay constant and distribution amplitude with an improved holographic wavefunction to the heavy-light pseudoscalar mesons. In the evaluations, the helicity-dependence of the holographic wavefunction is considered; and an independent mass scale parameter is employed to moderate the strong suppression induced by the heavy quark. Under the constraints from decay constants and masses of pseudoscalar mesons, the χ2-analyses for the holographic parameters exhibit a rough consistence with the results obtained by fitting the Regge trajectory. With the fitted parameters, the results for the decay constants and distribution amplitudes are presented. We then show their application in evaluating the Bd,s→Dd,sP decays, in which the power-suppressed spectator scattering and weak annihilation corrections are first estimated. Numerically, the spectator scattering and weak annihilation corrections present a negative shift of about 0.7% on the branching fractions; while, the predictions are still larger than the experimental data. Such small negative shift confirms the estimation based on the power counting rules.

η−γ and η′−γ transition form factors in a nonlocal NJL model

We study the $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ distribution amplitudes (DAs) in the context of a nonlocal ${\mathrm{SU}(3)}_{L}\ensuremath{\bigotimes}{\mathrm{SU}(3)}_{R}$ chiral quark model. The corresponding Lagrangian allows us to reproduce the phenomenological values of pseudoscalar meson masses and decay constants, as well as the momentum dependence of the quark propagator arising from lattice calculations. It is found that the obtained DAs have two symmetric maxima, which arise from new contributions generated by the nonlocal character of the interactions. These DAs are then applied to the calculation of the $\ensuremath{\eta}\text{\ensuremath{-}}\ensuremath{\gamma}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\text{\ensuremath{-}}\ensuremath{\gamma}$ transition form factors. Implications of our results regarding higher twist corrections and/or contributions to the transition form factors originated by gluon-gluon components in the $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ mesons are discussed.

π0−η−η′mixing in a generalized multiquark interaction scheme

We investigate the isospin symmetry breaking effects within a recently derived Nambu-Jona-Lasinio related model by fitting the measured pseudoscalar meson masses and weak decay couplings $f_\pi$, $f_K$. Our model contains the next to leading order terms in the $1/N_c$ expansion of the effective multi-quark Lagrangian, including the ones that break the chiral symmetry explicitly. We show the important phenomenological role of these interactions: (1) they lead to an accurate fit of the low-lying pseudoscalar nonet characteristics; (2) they account for a very good agreement of the current quark masses with the present PDG values; (3) they reduce by $40\%$ the ratio $\epsilon/\epsilon'$ of the $\pi_0-\eta$ and $\pi_0-\eta'$ mixing angles, as compared to the case that contemplates explicit breaking only in the leading order, bringing it in consonance with the quoted values in the literature. The conventional NJL-type models fail in the joint description of these parameters.

QED effects in the pseudoscalar meson sector

We present results on the pseudoscalar meson masses from a fully dynamical simulation of QCD+QED. We concentrate particularly on violations of isospin symmetry. We calculate the $\pi^+$-$\pi^0$ splitting and also look at other isospin violating mass differences. We have presented results for these isospin splittings in arXiv:1508.06401 [hep-lat]. In this paper we give more details of the techniques employed, discussing in particular the question of how much of the symmetry violation is due to QCD, arising from the different masses of the $u$ and $d$ quarks, and how much is due to QED, arising from the different charges of the quarks. This decomposition is not unique, it depends on the renormalisation scheme and scale. We suggest a renormalisation scheme in which Dashen's theorem for neutral mesons holds, so that the electromagnetic self-energies of the neutral mesons are zero, and discuss how the self-energies change when we transform to a scheme such as $\bar{MS}$, in which Dashen's theorem for neutral mesons is violated.