Pseudoscalar Decay Constants Research Articles

Ground state spectra, decay properties of B and D mesons in a relativistic square root potential

We look at the mass spectra of the [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] mesons using a relativistic square root potential. Before looking at the mass spectra, we have to figure out the model parameters, which are [Formula: see text][Formula: see text]GeV and [Formula: see text][Formula: see text]GeV. The calculated result of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], findings of this study exhibit a notable concurrence with the experimental observations and pertinent theoretical projections. We estimate the decay constant, leptonic decay width, semileptonic decay width, and branching fractions of pseudoscalar and vector mesons, specifically B and D mesons, while keeping the model parameters unchanged. The pseudoscalar decay constants and partial decay widths of “B and D-mesons” reasonably agree with the theoretical predictions, lattice quantum chromodynamics (LQCD) calculations, and experimental data. Moreover, we have efficiently found the values for these mesons’ leptonic decay width and branching fraction, matching the experimental findings and theoretical forecasts. The calculated values of semileptonic decays are [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text], the proximity of the observed results to experimental and certain theoretical models is evident.

Pseudoscalar meson decay constants and distribution amplitudes up to the twist-4 in the light-front quark model

Pseudoscalar meson decay constants and distribution amplitudes up to the twist-4 in the light-front quark model

Independence of current components, polarization vectors, and reference frames in the light-front quark model analysis of meson decay constants

The issue of resulting in the same physical observables with different current components, in particular from the minus current, has been challenging in the light-front quark model (LFQM) even for the computation of the two-point functions such as meson decay constants. At the level of one-body current matrix element computation, we show the uniqueness of pseudoscalar and vector meson decay constants using all available components including the minus component of the current in the LFQM consistent with the Bakamjian-Thomas construction. Regardless of the current components, the polarization vectors, and the reference frames, the meson decay constants are uniquely determined in the noninteracting constituent quark and antiquark basis while the interactions of the constituents are added to the meson mass operator in the LFQM.

Bottomonium spectroscopy using Coulomb plus linear (Cornell) potential

The Coulomb plus linear (Cornell) potential is used to investigate the mass spectrum of bottomonium. Gaussian wave function is used in position and momentum space to estimate values of potential and kinetic energies, respectively. Based on our calculations, we study newly observed $${\varUpsilon {(10860)}}$$ as an admixture of $$4^{3}S_{1}$$ with $$4^{3}D_{1}$$ and $${\varUpsilon {(10753)}}$$ as an admixture of $$6^{3}S_{1}$$ with $$4^{3}D_{1}$$ ; also, we try to assign $${{\varvec{\Upsilon }}{(11020)}}$$ as a pure $$4^{3}D_{1}$$ bottomonium state. We also study the Regge trajectories in the $$(J,M^{2})$$ and $$(n_r,M^{2})$$ planes to help prove our association. We estimate the pseudoscalar and vector decay constants, the radiative (electric and magnetic dipole) transition rates, and the annihilation decay width for bottomonium states.

Meson spectrum in the large N limit

We present the result of our computation of the lowest lying meson masses for SU(N) gauge theory in the large N limit (with Nf /N → 0). The final values are given in units of the square root of the string tension, and with errors which account for both statistical and systematic errors. By using 4 different values of the lattice spacing we have seen that our results scale properly. We have studied various values of N (169, 289 and 361) to monitor the N-dependence of the most sensitive quantities. Our methodology is based upon a first principles approach (lattice gauge theory) combined with large N volume independence. We employed both Wilson fermions and twisted mass fermions with maximal twist. In addition to masses in the pseudoscalar, vector, scalar and axial vector channels, we also give results on the pseudoscalar decay constant and various remormalization factors.

Light- and strange-quark mass dependence of the \u03c1(770) meson revisited

Recent lattice data on ππ-scattering phase shifts in the vector-isovector channel, pseudoscalar meson masses and decay constants for strange-quark masses smaller or equal to the physical value allow us to study the strangeness dependence of these observables for the first time. We perform a global analysis on two kind of lattice trajectories depending on whether the sum of quark masses or the strange-quark mass is kept fixed to the physical point. The quark mass dependence of these observables is extracted from unitarized coupled-channel one-loop Chiral Perturbation Theory. This analysis guides new predictions on the ρ(770) meson properties over trajectories where the strange-quark mass is lighter than the physical mass, as well as on the SU(3) symmetric line. As a result, the light- and strange-quark mass dependence of the ρ(770) meson parameters are discussed and precise values of the Low Energy Constants present in unitarized one-loop Chiral Perturbation Theory are given. Finally, the current discrepancy between two- and three-flavor lattice results for the ρ(770) meson is studied.

Radiative contribution to the composite-Higgs potential in a two-representation lattice model

Working in a two-representation lattice gauge theory that is close to a composite Higgs model, we calculate the low-energy constant CLR which controls the contribution of the electroweak gauge bosons to the Higgs potential. In QCD, the corresponding low-energy constant governs the mass splitting of the pion multiplet. Taking the continuum and chiral limits, we find that CLR, in units of the pseudoscalar decay constant, is roughly of the same size as its QCD counterpart.

Mesons in a soft-wall AdS-Schwarzschild approach at low temperature

We derive a holographic soft-wall approach in five dimensional AdS-Schwarzschild space for the description of mesons at finite temperature. In this first application we consider the small temperature limit and derive analytical expression for the mass spectrum of mesons with adjustable quantum numbers $n$ (radial number), $L$ (angular orbital momentum) and $J$ (total angular momentum). We explicitly separate the contribution at zero temperature and the leading order temperature correction. The temperature corrections arise from the temperature dependence of the dilaton parameter (which is the parameter of spontaneous breaking of chiral symmetry related to the pseudoscalar meson decay constant) and the warping of the AdS metric due to temperature. We extend our results to any hadron with integer spin (tetraquarks, dibaryons, etc.). We present numerical analysis for the temperature dependence of meson masses and form factors.

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.

Simulating twisted mass fermions at physical light, strange, and charm quark masses

We present the QCD simulation of the first gauge ensemble of two degenerate light quarks, a strange and a charm quark with all quark masses tuned to their physical values within the twisted mass fermion formulation. Results for the pseudoscalar masses and decay constants confirm that the produced ensemble is indeed at the physical parameters of the theory. This conclusion is corroborated by a complementary analysis in the baryon sector. We examine cutoff and isospin breaking effects and demonstrate that they are suppressed through the presence of a clover term in the action.

Spectroscopy and decay properties of charmonium

The mass spectra of charmonium are investigated using a Coulomb plus linear (Cornell) potential. Gaussian wave functions in position space as well as in momentum space are employed to calculate the expectation values of potential and kinetic energy respectively. Various experimental states (X(4660)(53S1), X(3872)(23P1), X(3900)(21P1), X(3915)(23P0) and X(4274)(33P1) etc.) are assigned as charmonium states. We also study the Regge trajectories, pseudoscalar and vector decay constants, electric and magnetic dipole transition rates, and annihilation decay widths for charmonium states.

Spectroscopy of SU(4) composite Higgs theory with two distinct fermion representations

We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. Such theories arise naturally in the context of composite Higgs models that include a partially composite top quark. We describe the low-lying meson spectrum of the theory and fit the pseudoscalar masses and decay constants to chiral perturbation theory. We infer as well the mass and decay constant of the Goldstone boson corresponding to the nonanomalous U(1) symmetry of the model. Our results are broadly consistent with large-${N}_{c}$ scaling and vector-meson dominance.

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.

Constraints on low energy QCD parameters from eta rightarrow 3pi and pi pi scattering

The eta ,rightarrow ,3pi decays are a valuable source of information on low energy QCD. Yet they were not used for an extraction of the three flavor chiral symmetry breaking order parameters until now. We use a Bayesian approach in the framework of resummed chiral perturbation theory to obtain constraints on the quark condensate and pseudoscalar decay constant in the chiral limit. We compare our results with recent CHPT and lattice QCD fits and find some tension, as the eta ,rightarrow ,3pi data seem to prefer a larger ratio of the chiral order parameters. The results also disfavor a very large value of the pseudoscalar decay constant in the chiral limit, which was found by some recent work. In addition, we present results of a combined analysis including eta ,rightarrow ,3pi decays and pi pi scattering and though the picture does not changed appreciably, we find some tension between the data we use. We also try to extract information on the mass difference of the light quarks, but the uncertainties prove to be large.

Individual eigenvalue distributions of crossover chiral random matrices and low-energy constants of SU(2) × U(1) lattice gauge theory

We compute individual distributions of low-lying eigenvalues of a chiral random matrix ensemble interpolating symplectic and unitary symmetry classes by the Nystr\"om-type method of evaluating the Fredholm Pfaffian and resolvents of the quaternion kernel. The one-parameter family of these distributions are shown to fit excellently the Dirac spectra of SU(2) lattice gauge theory with a constant U(1) background or dynamically fluctuating U(1) gauge field, which weakly breaks the pseudo-reality of the unperturbed SU(2) Dirac operator. Observed linear dependence of the crossover parameter with the strength of U(1) perturbations leads to precise determination of the pseudo-scalar decay constant, as well as the chiral condensate in the effective chiral Lagrangian of AI class.

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.

Masses and decay constants of D(s)* and B(s)* mesons with Nf=2+1+1 twisted mass fermions

We present a lattice calculation of the decay constants and masses of $D_{(s)}^*$ and $B_{(s)}^*$ mesons using the gauge configurations produced by the European Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ dynamical quarks and at three values of the lattice spacing $a \sim 0.06 - 0.09$ fm. Pion masses are simulated in the range $m_{\pi} \sim 210 - 450$ MeV, while the strange and charm quark masses are close to their physical values. We computed the ratios of vector to pseudoscalar decay constants or masses for various values of the heavy-quark mass $m_h$ in the range $0.7 m_c^{phys} \lesssim m_h \lesssim 3 m_c^{phys}$. In order to reach the physical b-quark mass, we exploited the HQET prediction that, in the static limit of infinite heavy-quark mass, all the considered ratios are equal to one. We obtain: $ f_{D^*}/f_{D} = 1.078(36),$ $m_{D^*}/m_{D} = 1.0769(79)$, $f_{D^*_{s}}/f_{D_{s}} = 1.087(20)$, $m_{D^*_{s}}m_{D_{s}} = 1.0751(56)$, $f_{B^*}/f_{B} = 0.958(22)$, $m_{B^*}/m_{B} = 1.0078(15)$, $f_{B^*_{s}}/f_{B_{s}} = 0.974(10)$ and $m_{B^*_{s}}/m_{B_{s}} = 1.0083(10)$. Combining them with the corresponding experimental masses from the PDG and the pseudoscalar decay constants calculated by ETMC, we get: $f_{D^*} = 223.5(8.4)~\mathrm{MeV}$, $m_{D^*} = 2013(14)~\mathrm{MeV}$, $f_{D^*_{s}} = 268.8(6.6)~\mathrm{MeV}$, $ m_{D^*_{s}} = 2116(11)~\mathrm{MeV}$, $f_{B^*} = 185.9(7.2)~\mathrm{MeV}$, $m_{B^*} = 5320.5(7.6)~\mathrm{MeV}$, $f_{B^*_{s}} = 223.1(5.4)~\mathrm{MeV}$ and $m_{B^*_{s}}= 5411.36(5.3)~\mathrm{MeV}$.

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.

Flavour breaking effects in the pseudoscalar meson decay constants

The SU(3) flavour symmetry breaking expansion in up, down and strange quark masses is extended from hadron masses to meson decay constants. This allows a determination of the ratio of kaon to pion decay constants in QCD. Furthermore when using partially quenched valence quarks the expansion is such that SU(2) isospin breaking effects can also be determined. It is found that the lowest order SU(3) flavour symmetry breaking expansion (or Gell-Mann–Okubo expansion) works very well. Simulations are performed for 2+1 flavours of clover fermions at four lattice spacings.

SU(2) gauge theory with two fundamental flavors: A minimal template for model building

We investigate the continuum spectrum of the SU(2) gauge theory with $N_f=2$ flavours of fermions in the fundamental representation. This model provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics that range from composite (Goldstone) Higgs theories to several intriguing types of dark matter candidates, such as the SIMPs. We improve our previous lattice analysis [1] by adding more data at light quark masses, at two additional lattice spacings, by determining the lattice cutoff via a Wilson flow measure of the $w_0$ parameter, and by measuring the relevant renormalisation constants non-perturbatively in the RI'-MOM scheme. Our results for the lightest isovector states in the vector and axial channels, in units of the pseudoscalar decay constant, are $m_V/F_{\rm{PS}}\sim 13.1(2.2)$ and $m_A/F_{\rm{PS}}\sim 14.5(3.6)$ (combining statistical and systematic errors). In the context of the composite (Goldstone) Higgs models, our result for the spin-one resonances are $m_V > 3.2(5)$ TeV and $m_A > 3.6(9)$ TeV, which are above the current LHC constraints. In the context of dark matter models, for the SIMP case our results indicate the occurrence of a compressed spectrum at the required large dark pion mass, which implies the need to include the effects of spin-one resonances in phenomenological estimates.