Decay Constants Of Pseudoscalar Mesons Research Articles

Determination of theη-η′mixing angle

We extract $\eta$-$\eta^\prime$ mixing angle and the ratios of decay constants of light pseudoscalar mesons $\pi^0$, $\eta$ and $\eta^\prime$ using recently available BaBar measurements on $\eta$-photon and $\eta^\prime$-photon transition form factors and more accurate experimental data for the masses and two-photon decay widths of the light pseduoscalar mesons.

Decay constants of heavy pseudoscalar mesons from QCD sum rules

We revisit the sum-rule extraction of the decay constants of the D, Ds, B and Bs mesons from the two-point correlator of heavy–light pseudoscalar currents. We use the operator product expansion of this correlator expressed in terms of the heavy-quark mass for which the perturbative expansion exhibits a reasonable convergence. Our main emphasis is laid on the control over the uncertainties in the decay constants, related both to the input quantum chromodynamics (QCD) parameters and to the limited intrinsic accuracy of the method of QCD sum rules. This becomes possible due to the application of our procedure of extracting hadron observables that involves as novel feature dual thresholds depending on the Borel parameter. For charmed mesons, we find the decay constants and . For beauty mesons, the decay constants turn out to be extremely sensitive to the precise value of . By requiring our sum-rule estimate to match the average of the lattice results for fB, a very accurate value is extracted, leading to fB = (193.4 ± 12.3(OPE) ± 4.3(syst)) MeV and .

POWER COUNTING OF VARIOUS DIRAC COVARIANTS IN HADRONIC BETHE–SALPETER WAVE FUNCTIONS FOR PSEUDOSCALAR MESON DECAYS

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.

Scaling studies of QCD with the dynamical highly improved staggered quark action

We study the lattice spacing dependence, or scaling, of physical quantities using the highly improved staggered quark (HISQ) action introduced by the HPQCD/UKQCD collaboration, comparing our results to similar simulations with the asqtad fermion action. Results are based on calculations with lattice spacings approximately 0.15, 0.12 and 0.09 fm, using four flavors of dynamical HISQ quarks. The strange and charm quark masses are near their physical values, and the light-quark mass is set to 0.2 times the strange-quark mass. We look at the lattice spacing dependence of hadron masses, pseudoscalar meson decay constants, and the topological susceptibility. In addition to the commonly used determination of the lattice spacing through the static quark potential, we examine a determination proposed by the HPQCD collaboration that uses the decay constant of a fictitious "unmixed s bar s" pseudoscalar meson. We find that the lattice artifacts in the HISQ simulations are much smaller than those in the asqtad simulations at the same lattice spacings and quark masses.

η–[formula omitted] mixing angle from vector meson radiative decays

The octet–singlet η–η′ mixing mass term could have a derivative O(p2) term as found in recent analysis of the η–η′ system. This term gives rise to an additional momentum-dependent pole contribution which is suppressed by a factor mη2/mη′2 for η relative to the η′ amplitude. The processes with η meson can then be described, to a good approximation, by the momentum-independent mixing mass term which gives rise to a new η–η′ mixing angle θP, like the old η–η′ mixing angle used in the past, but a momentum-dependent mixing term d, like sin(θ0−θ8) in the two-angle mixing scheme used in the parametrization of the pseudo-scalar meson decay constants in the current literature, is needed to describe the amplitudes with η′. In this Letter, we obtain sum rules relating θP and d to the physical vector meson radiative decays with η and η′, as done in our previous work for η meson two-photon decay, and with nonet symmetry for the η′ amplitude, we obtain a mixing angle θP=−(18.76±3.4)°, d=0.10±0.03 from ρ→ηγ and η′→ργ decays, for ω, θP=−(15.81±3.1)°, d=0.02±0.03, and for ϕ, θP=−(13.83±2.1)°, d=0.08±0.03. A larger value of 0.06±0.02 for d is obtained directly from the nonet symmetry expression for the η′→ωγ amplitude. This indicates that more precise vector meson radiative decay measured branching ratios and higher order SU(3) breaking effects could bring these values for θP closer and allows a better determination of d.

Analyses of decay constants and light-cone distribution amplitudes fors-wave heavy meson

In this paper, a study of light-cone distribution amplitudes (LCDAs) for $s$-wave heavy meson are presented in both general and heavy quark frameworks. Within the light-front approach, the leading twist light-cone distribution amplitudes, ${\ensuremath{\phi}}_{M}(u)$, and their relevant decay constants of heavy pseudoscalar and vector mesons, ${f}_{M}$, have simple relations. These relations can be further simplified when the heavy quark limit is taken into consideration. After fixing the parameters that appear in both Gaussian and power-law wave functions, the corresponding decay constants are calculated and compared with those of other theoretical approaches. The curves and the first six $\ensuremath{\xi}$-moments of ${\ensuremath{\phi}}_{M}(u)$ are plotted and estimated. A conclusion is drawn from these results: Even though the values of the decay constants of the distinct mesons are almost equal, the curves of their LCDAs may have quite large differences, and vice versa. Additionally, in the heavy quark limit, the leading twist LCDAs, ${\ensuremath{\Phi}}_{Qq}(\ensuremath{\omega})$ and ${\ensuremath{\Phi}}_{Qq}(\ensuremath{\omega})$, are compared with the $B$-meson LCDAs, ${\ensuremath{\psi}}_{+}(\ensuremath{\omega})$, suggested by the other theoretical groups.

Nonperturbative QCD simulations with2+1flavors of improved staggered quarks

Dramatic progress has been made over the last decade in the numerical study of quantum chromodynamics (QCD) through the use of improved formulations of QCD on the lattice (improved actions), the development of new algorithms, and the rapid increase in computing power available to lattice gauge theorists. In this article simulations of full QCD are described using the improved staggered quark formalism, ``asqtad'' fermions. These simulations were carried out with two degenerate flavors of light quarks (up and down) and with one heavier flavor, the strange quark. Several light quark masses, down to about three times the physical light quark mass, and six lattice spacings have been used. These enable controlled continuum and chiral extrapolations of many low energy QCD observables. The improved staggered formalism is reviewed, emphasizing both advantages and drawbacks. In particular, the procedure for removing unwanted staggered species in the continuum limit is reviewed. Then the asqtad lattice ensembles created by the MILC Collaboration are described. All MILC lattice ensembles are publicly available, and they have been used extensively by a number of lattice gauge theory groups. The physics results obtained with them are reviewed, and the impact of these results on phenomenology is discussed. Topics include the heavy quark potential, spectrum of light hadrons, quark masses, decay constants of light and heavy-light pseudoscalar mesons, semileptonic form factors, nucleon structure, scattering lengths, and more.

Physical point simulation in2+1flavor lattice QCD

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.

Pseudoscalar decay constants of kaon andD-mesons fromNf= 2 twisted mass Lattice QCD

We present the results of a lattice QCD calculation of the pseudoscalar meson decay constants fpi, fK, fD and fDs, performed with Nf=2 dynamical fermions. The simulation is carried out with the tree-level improved Symanzik gauge action and with the twisted mass fermionic action at maximal twist. We have considered for the final analysis three values of the lattice spacing, a~0.10 fm, 0.09 fm and 0.07 fm, with pion masses down to mpi~270 MeV. Our results for the light meson decay constants are fK=158.1(2.4) MeV and fK/fpi=1.210(18). From the latter ratio, by using the experimental determination of Gamma(K-->mu nu_mu (gamma))/ Gamma(pi--> mu nu_mu (gamma)) and the average value of |Vud| from nuclear beta decays, we obtain |Vus|=0.2222(34), in good agreement with the determination from semileptonic Kl3 decays and the unitarity constraint. For the D and Ds meson decay constants we obtain fD=197(9) MeV, fDs=244(8) MeV and fDs/fD=1.24(3). Our result for fD is in good agreement with the CLEO experimental measurement. For fDs our determination is smaller than the PDG 2008 experimental average but in agreement with a recent improved measurement by CLEO at the 1.4 sigma level.

Physical results from2+1flavor domain wall QCD and SU(2) chiral perturbation theory

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 $m_{s}^{\bar{\rm MS}}(2 {\rm GeV}) = 107.3(4.4)_{\rm stat}(9.7)_{\rm ren}(4.9)_{\rm syst} {\rm MeV}$.

Heavy-strange meson decay constants in the continuum limit of quenched QCD

We improve a previous quenched result for heavy-light pseudoscalar meson decay constants with the light quark taken to be the strange quark. A finer lattice resolution (a ? 0.05 fm) in the continuum limit extrapolation of the data computed in the static approximation is included. We also give further details concerning the techniques used in order to keep the statistical and systematic errors at large lattice sizes L/a under control. Our final result, obtained by combining these data with determinations of the decay constant for pseudoscalar mesons around the Ds, follows nicely the qualitative expectation of the 1/m-expansion with a (relative) 1/m-term of about ?0.5GeV/mPS. At the physical b-quark mass we obtain FBs = 193(7)MeV, where all errors apart from the quenched approximation are included.

Heavy-light quark pseudoscalar and vector mesons at finite temperature

The temperature dependence of the mass, leptonic decay constant, and width of heavy-light quark peseudoscalar and vector mesons is obtained in the framework of thermal Hilbert moment QCD sum rules. The leptonic decay constant of both pseudoscalar and vector mesons decreases with increasing T, and vanishes at a critical temperature Tc, while the mesons develop a width which increases dramatically and diverges at Tc, where Tc is the temperature for chiral-symmetry restoration/quark-gluon deconfinement. These results indicate the disappearance of hadrons from the spectral function, which then becomes a smooth function of the energy. This is interpreted as a signal for deconfinement at T = Tc. In contrast, the masses show little dependence on the temperature, except very close to Tc, where the pseudoscalar meson masses increase slightly by 10-20%, and the vector meson masses decrease by some 20-30%.

First results from2+1-flavor domain wall QCD: Mass spectrum, topology change, and chiral symmetry withLs=8

We present results for the static interquark potential, light meson and baryon masses, and light pseudoscalar meson decay constants obtained from simulations of domain wall QCD with one dynamical flavour approximating the s quark, and two degenerate dynamical flavours with input bare masses ranging from m{sub s} to m{sub s}/4 approximating the u and d quarks. We compare these quantities obtained using the Iwasaki and DBW2 improved gauge actions, and actions with larger rectangle coefficients, on 16{sup 3}x32 lattices. We seek parameter values at which both the chiral symmetry breaking residual mass due to the finite lattice extent in the fifth dimension and the Monte Carlo time history for topological charge are acceptable for this set of quark masses at lattice spacings above 0.1 fm. We find that the Iwasaki gauge action is best, demonstrating the feasibility of using QCDOC to generate ensembles which are good representations of the QCD path integral on lattices of up to 3 fm in spatial extent with lattice spacings in the range 0.09-0.13 fm. Despite large residual masses and a limited number of sea quark-mass values with which to perform chiral extrapolations, our results for light hadronic physics scale and agree with experimental measurementsmore » within our statistical uncertainties.« less

Decay constants and radiative decays of heavy mesons in light-front quark model

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.

First nonperturbative test of a relativistic heavy quark action in quenched lattice QCD

We perform a numerical test of a relativistic heavy quark(RHQ) action, recently proposed by Tsukuba group, in quenched lattice QCD at $a\simeq 0.1$ fm. With the use of the improvement parameters previously determined at one-loop level for the RHQ action, we investigate a restoration of rotational symmetry for heavy-heavy and heavy-light meson systems around the charm quark mass. We focused on two quantities, the meson dispersion relation and the pseudo-scalar meson decay constants. It is shown that the RHQ action significantly reduces the discretization errors due to the charm quark mass. We also calculate the S-state hyperfine splittings for the charmonium and charmed-strange mesons and the $D_s$ meson decay constant. The remaining discretization errors in the physical quantities are discussed.

The decay constant of the first excited pion from lattice QCD

We review the theory that predicts that the decay constant of the excited light pseudo-scalar mesons are suppressed in the chiral limit relative to the pion decay constant. We compute the decay constant of the first excited pion (π′) using unquenched QCD at a fixed lattice spacing with sea quarks of mass as low as a third the mass of the strange quark. The final result is very sensitive to the improvement conditions. We obtain fπ′/fπ=0.078(93) in the chiral limit.

Twisted mass lattice QCD with non-degenerate quark masses

Quantum Chromodynamics on a lattice with Wilson fermions and a chirally twisted mass term is considered in the framework of chiral perturbation theory. For two and three numbers of quark flavours, respectively, with non-degenerate quark masses the pseudoscalar meson masses and decay constants are calculated in next-to-leading order including lattice effects quadratic in the lattice spacing a.

Strange quarks in quenched twisted mass lattice QCD

Two twisted doublets, one containing the up and down quarks and the other containing the strange quark with an $SU(2)$-flavor partner, are used for studies in the meson sector. The relevant chiral perturbation theory is presented, and quenched QCD simulations (where the partner of the strange quark is not active) are performed. Pseudoscalar meson masses and decay constants are computed; the vector and scalar mesons are also discussed. A comparison is made to the case of an untwisted strange quark, and some effects due to quenching, discretization, and the definition of maximal twist are explored.

Three-flavor partially quenched chiral perturbation theory at NNLO for meson masses and decay constants

We discuss Partially Quenched Chiral Perturbation Theory (PQ$\chi$PT) and possible fitting strategies to Lattice QCD data at next-to-next-to-leading order (NNLO) in the mesonic sector. We also present a complete calculation of the masses of the charged pseudoscalar mesons, in the supersymmetric formulation of PQ$\chi$PT. Explicit analytical results are given for up to three nondegenerate sea quark flavors, along with the previously unpublished expression for the pseudoscalar meson decay constant for three nondegenerate sea quark flavors. The numerical analysis in this paper demonstrates that the corrections at NNLO are sizable, as expected from earlier work.

Pseudoscalar meson decay constants and couplings, the Witten–Veneziano formula beyond large [formula omitted], and the topological susceptibility

The QCD formulae for the radiative decays η , η ′ → γ γ , and the corresponding Dashen–Gell-Mann–Oakes–Renner relations, differ from conventional PCAC results due to the gluonic U ( 1 ) A axial anomaly. This introduces a critical dependence on the gluon topological susceptibility. In this paper, we revisit our earlier theoretical analysis of radiative pseudoscalar decays and the DGMOR relations and extract explicit experimental values for the decay constants. This is our main result. The flavour singlet DGMOR relation is the generalisation of the Witten–Veneziano formula beyond large N c , so we are able to give a quantitative assessment of the realisation of the 1 / N c expansion in the U ( 1 ) A sector of QCD. Applications to other aspects of η ′ physics, including the relation with the first moment sum rule for the polarised photon structure function g 1 γ , are highlighted. The U ( 1 ) A Goldberger–Treiman relation is extended to accommodate SU ( 3 ) flavour breaking and the implications of a more precise measurement of the η and η ′ -nucleon couplings are discussed. A comparison with the existing literature on pseudoscalar meson decay constants using large- N c chiral Lagrangians is also made.