Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD
Gunnar S. Bali, Vladimir M. Braun, Simon Bürger, Meinulf Göckeler, Michael Gruber, Fabian Hutzler, Piotr Korcyl, Andreas Schäfer, André Sternbeck, Philipp Wein
We present the first lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes with full control of all errors. The calculation is carried out on 35 different CLS ensembles with $N_f=2+1$ flavors of dynamical Wilson-clover fermions. These cover a multitude of pion and kaon mass combinations (including the physical point) and 5 different lattice spacings down to $a=0.039\,$fm. The momentum smearing technique and a new operator basis are employed to reduce statistical fluctuations and to improve the overlap with the ground states. The results are obtained from a combined chiral and continuum limit extrapolation that includes three separate trajectories in the quark mass plane.
The present arXiv version (v3) includes an Addendum where we update the results using the recently calculated three-loop matching factors for the conversion from the RI'/SMOM to the $\overline{\text{MS}}$ scheme. We find $a_2^π=0.116^{+19}_{-20}$ for the pion, $a_1^K=0.0525^{+31}_{-33}$ and $a_2^K=0.106^{+15}_{-16}$ for the kaon. We also include the previous values, which were obtained with two-loop matching.
We study the scattering of the light-flavor pseudoscalar mesons ($π, K, η$) off the ground-state charmed mesons ($D,D_s$) within chiral effective field theory. The recent lattice simulation results on various scattering lengths and the finite-volume spectra both in the moving and center-of-mass frames, most of which are obtained at unphysical meson masses, are used to constrain the free parameters in our theory. Explicit formulas to include the $S$- and $P$-wave mixing to determine the finite-volume energy levels are provided. After a successful reproduction of the lattice data, we perform a c…
This paper presents a first study of the decay constants of the charged, or flavor-off-diagonal, pseudoscalar mesons to two loops for three flavors of sea quarks, in Partially Quenched Chiral Perturbation Theory (PQ$χ$PT). Explicit analytical expressions up to ${\cal O}(p^6)$ in the momentum expansion are given. The calculations have been performed within the supersymmetric formulation of PQ$χ$PT. We also present some numerical results to indicate the size of the corrections.
We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We first apply chiral perturbation theory in the p-regime and calculate the corrections for masses, decay constants, pseudoscalar coupling constants and form factors at next-to-leading order. We show that the Feynman-Hellmann theorem and the relevant Ward-Takahashi identity are satisfied. We then derive asymptotic formulae a la Luscher for twisted boundary conditions. We show that chiral Ward identities for masses and decay constants are satisfied by the asymptotic formulae in finite volume a…
We consider a scenario (supported by some lattice results) in which a U(1)-breaking condensate survives across the chiral transition in QCD. This scenario has important consequences for the pseudoscalar-meson sector, which can be studied using an effective Lagrangian model. In particular, generalizing the results obtained in two previous papers, where the effects on the radiative decays eta,eta' --> gamma gamma were studied, in this paper we study the effects of the U(1) chiral condensate on the strong decays of the "light" pseudoscalar mesons, i.e., eta,eta' --> 3pi^0; eta,eta' --> pi^+ pi^- …
We discuss the recent experimental observation which suggested that the mass difference between the scalar and pseudoscalar heavy-light mesons is larger for the non-strange states than for the strange ones. After computing the chiral corrections in the heavy quark limit we show that, contrary to experiment, the mass difference in the non-strange case should be smaller.
We measure correlations appropriate for favour-singlet mesons using dynamical quark configurations from UKQCD. Improved methods of evaluating the disconnected quark diagrams are presented. The scalar and pseudoscalar meson channels are explored, with special reference to the mixing of scalar mesons with scalar glueballs.
We have calculated the scattering lengths between the pseudoscalar meson and charmed triplet, sextet, and excited sextet baryon to the third order with the heavy baryon chiral perturbation theory. The chiral expansion of the pion channels converges well.
Goldstone modes are the only pseudoscalar mesons to possess a nonzero leptonic decay constant in the chiral limit when chiral symmetry is dynamically broken. The decay constants of their radial excitations vanish. These features and aspects of their impact on the meson spectrum are illustrated using a manifestly covariant and symmetry preserving model of the kernels in the gap and Bethe-Salpeter equations.
This paper presents a first study of the pseudoscalar meson masses to two loops, or NNLO, within the supersymmetric formulation of partially quenched chiral perturbation theory (PQ$χ$PT). The expression for the pseudoscalar meson mass in the case of three valence and three sea quarks with equal masses, but different from each other, is given to ${\cal O}(p^6)$, along with a numerical analysis.
We present a study of the pseudoscalar and vector meson form factors, calculated using the Fat-Link Irrelevant Clover (FLIC) action in the framework of Quenched Lattice QCD. Of particular interest is the determination of a negative quadrupole moment, indicating that the $ρ$ meson is not spherically symmetric.
The strong coupling constants are basic quantities that carry information of the strong interactions among the baryon and meson multiplets as well as information on the natures and internal structures of the involved hadrons. These parameters enter to the transition matrix elements of various decays as main inputs and they play key roles in analyses of the experimental data including various hadrons. We determine the strong coupling constants among the doubly heavy spin-$ 3/2 $ baryons, $Ξ^*_{QQ'} $ and $Ω^*_{QQ'}$, and light pseudoscalar mesons, $π$, $K$ and $η$, using the light-cone QCD. The…
We present results for the first two moments of the distribution amplitudes of pseudoscalar mesons. Using two flavors of non-perturbatively improved clover fermions and non-perturbative renormalization of the matrix elements we perform both chiral and continuum extrapolations and compare with recent results from models and experiments.
I discuss the results of a recent quenched lattice calculation of the two independent form factors parametrizing the semileptonic decays between heavy-light pseudoscalar mesons. The differential decay rate of the process B --> D l nu has been calculated at non vanishing momentum transfer both in the case of the light leptons, l=e,mu, and in the case of a non vanishing lepton mass, l=tau.
We extend our calculations with the second-order tree-level and tadpole improved next-nearest-neighbor action to meson-meson systems. Correlation matrices built from interpolating fields representing two pseudoscalar mesons (pion-pion) with relative momenta p are diagonalized, and the mass spectrum is extracted. Link variable fuzzing and operator smearing at both sinks and sources is employed. Calculations are presented for two values of the hopping parameter. The spectrum is used to discuss the residual interaction in the meson-meson system.
We present the first 2+1 flavour lattice QCD calculations of pseudoscalar flavour-singlet propagators using improved staggered fermions. We explore the relevant techniques and discuss prospects for the larger scale studies now in progress. The disconnected correlator is shown to have a highly non-Gaussian distribution and reliable estimates of the errors require care.
We study the chiral condensates and the eta^prime meson correlators of the massive Schwinger model in non-zero theta vacuum. Our data suggest that the pseudoscalar operator does condense in a fixed topological sector and gives long range correlations of the eta^prime meson. We find that this is well understood from the clustering decomposition and statistical picture. Our result also indicates that even in theta=0 case, the long range correlation of eta^prime meson receives non-zero contributions from all the topological sectors and that their cancellation is non-trivial and requires accurate …
The results of a high-statistics study of scalar and pseudoscalar meson propagators in quenched lattice QCD are presented. For two values of lattice spacing, $β=5.7$ ($a \approx .18$ fm) and 5.9 ($a \approx .12$ fm), we probe the light quark mass region using clover improved Wilson fermions with the MQA pole-shifting ansatz to treat the exceptional configuration problem. The quenched chiral loop parameters $m_0$ and $α_Φ$ are determined from a study of the pseudoscalar hairpin correlator. From a global fit to the meson correlators, estimates are obtained for the relevant chiral Lagrangian para…
We have performed a systematical calculation of the pion ($π, K, η$) and heavy pseudoscalar meson S-wave scattering lengths up to ${\cal O}(p^3)$ in the chiral perturbation theory in the heavy quark symmetry limit. With the three scattering lengths from the lattice simulations as input we estimate the unknown low-energy constants. Then we predict all the other unmeasured scattering lengths. The analytical expressions and predictions may be helpful to future investigations. Especially we note that the DK scattering length is positive. Therefore their interaction is attractive, which helps to lo…
We present the results of a calculation of semileptonic form factors of D and B mesons. The calculation uses nonperturbatively order a improved quenched lattice QCD and two values of the coupling. Results for charm mesons show reasonable agreement with experiment. The lattice results for B -> rho l nu are compared with high q^2 experimental results.
We calculate the complete $T$ matrices of the elastic light pseudoscalar meson and heavy meson scattering to the third order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting the phase shifts and scattering lengths from lattice QCD simulations simultaneously and predict the phase shifts at the physical meson masses. The phase shifts in the $Dπ(I=1/2)$, $DK(I=0)$, $D\bar{K}(I=0)$, $D_s\bar{K}$, $Dη$ and $D_sη$ $S$ waves are so strong that bound states or resonances may be generated dynamically in all these channels. The $DK(I=0)$ channel corresponds to …
The chiral properties of the pseudoscalar mesons are studied numerically on a quenched $20^4$ lattice with the overlap fermion. We elucidate the role of the zero modes in the meson propagators, particularly that of the pseudoscalar meson. The non-perturbative renormalization constant $Z_A$ is determined from the axial Ward identity and is found to be almost independent of the quark mass for the range of quark masses we study; this implies that the $O(a^2)$ error is small. The pion decay constant, $f_π$, is calculated from which we determine the lattice spacing to be 0.148 fm. We look for quenc…
We present results of a high-statistics study of scalar and pseudoscalar meson propagators in quenched QCD at two values of lattice spacing, beta = 5.7 and 5.9, with clover-improved Wilson fermions. The study of the chiral limit is facilitated by the pole-shifting ansatz of the modified quenched approximation. Pseudoscalar masses and decay constants are determined as a function of quark mass and quenched chiral log effects are estimated. A study of the flavor singlet eta prime hairpin diagram yields a precise determination of the eta prime mass insertion. The corresponding value of the quenche…
This paper presents a first study of the masses and decay constants of the charged, or flavor-off-diagonal, pseudoscalar mesons to two loops for two flavors of sea-quarks, in Partially Quenched Chiral Perturbation Theory (PQ$χ$PT). Explicit analytical expressions up to ${\cal O}(p^6)$ in the momentum expansion are given. The calculations have been performed within the supersymmetric formulation of PQ$χ$PT. A numerical analysis is done to indicate the size of the corrections.
The axial-vector Ward-Takahashi identity places constraints on particular properties of every pseudoscalar meson. For example, in the chiral limit all pseudoscalar mesons, except the Goldstone mode, decouple from the axial-vector current. Nevertheless, all neutral pseudoscalar mesons couple to two photons. The strength of the π_n^0 γγcoupling, where n=0 denotes the Goldstone mode, is affected by the Abelian anomaly's continuum contribution. The effect is material for n \neq 0. The γ* π_n γ* transition form factor, T_{π_n}(Q^2), is nonzero for all n, and T_{π_n}(Q^2) \approx (4π^2/3) (f_{π_n}/Q…
