Flavour breaking effects in the pseudoscalar meson decay constants

We have simulated QCD using 2+1 flavors of domain wall quarks on a $(2.74 {\rm fm})^3$ volume with an inverse lattice scale of $a^{-1} = 1.729(28)$ GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617 and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter $B_K$ and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulae from both approaches fit our data for light quarks, we find the higher order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the $\Omega$ baryon, and the $\pi$ and $K$ mesons to set the lattice scale and determine the quark masses. We then find $f_\pi = 124.1(3.6)_{\rm stat}(6.9)_{\rm syst} {\rm MeV}$, $f_K = 149.6(3.6)_{\rm stat}(6.3)_{\rm syst} {\rm MeV}$ and $f_K/f_\pi = 1.205(0.018)_{\rm stat}(0.062)_{\rm syst}$. Using non-perturbative renormalization to relate lattice regularized quark masses to RI-MOM masses, and perturbation theory to relate these to $\bar{\rm MS}$ we find $ m_{ud}^{\bar{\rm MS}}(2 {\rm GeV}) = 3.72(0.16)_{\rm stat}(0.33)_{\rm ren}(0.18)_{\rm syst} {\rm MeV}$ and $m_{s}^{\bar{\rm MS}}(2 {\rm GeV}) = 107.3(4.4)_{\rm stat}(9.7)_{\rm ren}(4.9)_{\rm syst} {\rm MeV}$.

Partially quenched chiral perturbation theory and numerical simulations

We present the results of the physical point simulation in 2+1 flavor lattice QCD with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $\beta=1.9$ on a $32^3 \times 64$ lattice. The physical quark masses together with the lattice spacing is determined with $m_\pi$, $m_K$ and $m_\Omega$ as physical inputs. There are two key algorithmic ingredients to make possible the direct simulation at the physical point: One is the mass-preconditioned domain-decomposed HMC algorithm to reduce the computational cost. The other is the reweighting technique to adjust the hopping parameters exactly to the physical point. The physics results include the hadron spectrum, the quark masses and the pseudoscalar meson decay constants. The renormalization factors are nonperturbatively evaluated with the Schr{\"o}dinger functional method. The results are compared with the previous ones obtained by the chiral extrapolation method.

Light quenched hadron spectrum and decay constants on different lattices

We have employed the framework of Bethe–Salpeter equation under covariant instantaneous ansatz to calculate leptonic decay constants of unequal mass pseudoscalar mesons like π±, K, D, DS and B, and radiative decay constants of neutral pseudoscalar mesons like π0 and ηc into two photons. In the Dirac structure of hadronic Bethe–Salpeter wave function, the covariants are incorporated from their complete set in accordance with a recently proposed power counting rule. The contribution of both leading order and next-to-leading order Dirac covariants to decay constants are studied. The results are found to improve and hence validating the power counting rule which provides a practical means of incorporating Dirac covariants in the Bethe–Salpeter wave function for a hadron.

We determine masses and decay constants of heavy-heavy and heavy-charm pseudoscalar mesons as a function of heavy quark mass using a fully relativistic formalism known as highly improved staggered quarks for the heavy quark. We are able to cover the region from the charm quark mass to the bottom quark mass using MILC ensembles with lattice spacing values from 0.15 fm down to 0.044 fm. We obtain ${f}_{{B}_{c}}=0.427(6)\text{ }\text{ }\mathrm{GeV}$; ${m}_{{B}_{c}}=6.285(10)\text{ }\text{ }\mathrm{GeV}$ and ${f}_{{\ensuremath{\eta}}_{b}}=0.667(6)\text{ }\text{ }\mathrm{GeV}$. Our value for ${f}_{{\ensuremath{\eta}}_{b}}$ is within a few percent of ${f}_{\ensuremath{\Upsilon}}$, confirming that spin effects are surprisingly small for heavyonium decay constants. Our value for ${f}_{{B}_{c}}$ is significantly lower than potential model values being used to estimate production rates at the LHC. We discuss the changing physical heavy-quark mass dependence of decay constants from heavy-heavy through heavy-charm to heavy-strange mesons. A comparison between the three different systems confirms that the ${B}_{c}$ system behaves in some ways more like a heavy-light system than a heavy-heavy one. Finally we summarize current results on decay constants of gold-plated mesons.

We calculate the decay constants of light and heavy-light pseudoscalar and vector mesons with improved soft-wall holographic wavefuntions, which take into account the effects of both quark masses and dynamical spins. We find that the predicted decay constants, especially for the ratio fV/fP, based on light-front holographic QCD, can be significantly improved, once the dynamical spin effects are taken into account by introducing the helicity-dependent wavefunctions. We also perform detailed χ2 analyses for the holographic parameters (i.e. the mass-scale parameter κ and the quark masses), by confronting our predictions with the data for the charged-meson decay constants and the meson spectra. The fitted values for these parameters are generally in agreement with those obtained by fitting to the Regge trajectories. At the same time, most of our results for the decay constants and their ratios agree with the data as well as the predictions based on lattice QCD and QCD sum rule approaches, with only a few exceptions observed.

The QCD sum-rules of Shifman et al. for n-th order moments are applied to the determination of the decay constants of pseudoscalar mesons containing a heavy quark (c or b). The general case when Q/sup 2/, the squared momentum transfer, is non-zero is considered. The stability of the sum-rules against variations in both Q/sup 2/ and n is discussed.

We update our determinations of f D + , f D s , f K , and quark mass ratios from simulations with four flavors of HISQ dynamical quarks.The availability of ensembles with light quarks near their physical mass means that we can extract physical results with only small corrections for valence-and sea-quark mass mistunings instead of a chiral extrapolation.The adjusted valencequark masses and lattice spacings may be determined from an ensemble-by-ensemble analysis, and the results for the quark mass ratios then extrapolated to the continuum limit.Our central values of the charmed meson decay constants, however, come from an alternative analysis, which uses staggered chiral perturbation theory for the heavy-light mesons, and allows us to incorporate data at unphysical quark masses where statistical errors are often smaller.A jackknife analysis propagated through all of these steps takes account of the correlations among all the quantities used in the analysis.Systematic errors from the finite spatial size and EM effects are estimated by varying the parameters in the analysis, and systematic errors from the assumptions in the continuum extrapolation are estimated from the spread of values from different extrapolations.

Mixing and decay constants of pseudoscalar mesons: the sequel

Decay constants of heavy mesons from a QCD relativistic potential model

We generate $2+1$ flavor QCD configurations near the physical point on a $96^4$ lattice employing the 6-APE stout smeared Wilson clover action with a nonperturbative $c_{\rm SW}$ and the Iwasaki gauge action at $\beta=1.82$. The physical point is estimated based on the chiral perturbation theory using several data points generated by the reweighting technique from the simulation point, wherer $m_\pi$,$m_K$ and $m_\Omega$ are used as physical inputs. The physics results include the quark masses, the hadron spectrum, the pseudoscalar meson decay constants and nucleon sigma terms, using the nonperturbative renormalization factors evaluated with the Schrodinger functional method.

We study the pseudoscalar and vector B mesons decay constants within the framework of the light cone quark model (LCQM). LCQM deals with the wave function defined on the four-dimensional space-time plane defined by $x^+ = x^0 +x^3$ and includes the important relativistic effects that are neglected in the traditional constituent quark model. With the help of known values of constituent quark masses and the scale parameter $\beta$, we calculate the values of B mesons decay constants, respectively. The decay constants of pseudoscalar and vector mesons are useful for controlling the meson semileptonic decay widths, hadronic couplings and form factors.

We investigate the magnetic dipole decays $V\ensuremath{\rightarrow}P\ensuremath{\gamma}$ of various heavy-flavored mesons such as $(D,{D}^{*},{D}_{s},{D}_{s}^{*},{\ensuremath{\eta}}_{c},J/\ensuremath{\psi})$ and $(B,{B}^{*},{B}_{s},{B}_{s}^{*},{\ensuremath{\eta}}_{b},\ensuremath{\Upsilon})$ using the light-front quark model constrained by the variational principle for the QCD-motivated effective Hamiltonian. The momentum dependent form factors ${F}_{VP}({q}^{2})$ for $V\ensuremath{\rightarrow}P{\ensuremath{\gamma}}^{*}$ decays are obtained in the ${q}^{+}=0$ frame and then analytically continued to the timelike region by changing ${\mathbf{q}}_{\ensuremath{\perp}}$ to $i{\mathbf{q}}_{\ensuremath{\perp}}$ in the form factors. The coupling constant ${g}_{VP\ensuremath{\gamma}}$ for real photon case is then obtained in the limit as ${q}^{2}\ensuremath{\rightarrow}0$, i.e. ${g}_{VP\ensuremath{\gamma}}={F}_{VP}({q}^{2}=0)$. The weak decay constants of heavy pseudoscalar and vector mesons are also calculated. Our numerical results for the decay constants and radiative decay widths for the heavy-flavored mesons are overall in good agreement with the available experimental data as well as other theoretical model calculations.

We make an analysis of three -loop effects of the strong coupling constant in the study of masses and decay constants of the heavy-flavour pseudo-scalar mesons (PSM) D, D_s , B, B_s,B_c, eta _c and eta _b in a non-relativistic QCD potential model using Dalgarno’s perturbation theory (DPT). The first order mesonic wavefunction is obtained using Dalgarno’s perturbation theory. The three-loop effects of strong coupling constant are included in the wave function in co-ordinate space and then used to examine the static and dynamic properties of the heavy-flavour mesons for 2S and 3S higher states. The results are compared with the other models available and are found to be compatible with available experimental values. In V-scheme, the three-loop effects on masses and decay constants of heavy-flavour mesons show a significant result.