During the last years, the ALPHA collaboration has been developing and implementing a method based on Heavy Quark Effective Theory (HQET) to compute B-mesons observables through lattice simulations. Thanks to a non-perturbative matching to QCD, the theory is renormalizable at any order of the heavy quark mass expansion. In order to extract precisely the relevant matrix elements and masses, we use all-to-all propagators and solve an generalized eigenvalue problem (GEVP). We have shown in the quenched approximation that quantities like the b-quark mass mb, the heavy-light decay constant(s) or the B-meson spectrum can be computed precisely beyond the static approximation (including the first corrections in 1/\mb). More recently, we have started to include the sea quark effects, by working with Nf=2 light flavors of dynamical fermions[1]. The computation of the matching parameters is almost finished, but concerning the extraction of the hadronic quantities for which we use some CLS ensembles[2], only one lattice spacing has been analyzed so far. In this proceeding we report on the status of this project and present some preliminary results.
The pseudoscalar and vector heavy meson masses are calculated in the ε-regime of Heavy Meson Chiral Perturbation Theory to order ε^4. The results of this calculation will allow the determination of low-energy coefficients (LECs) directly from Lattice QCD calculations of the heavy mesons masses for lattices that satisfy the ε-regime criteria. In particular, the LECs that parametrize the NLO volume dependance of the heavy meson masses are necessary for evaluating the light pseudoscalar meson (π, K, η) and heavy meson ({D^0, D^+, D^+_s}, {B^-,\bar{B}^0,\bar{B}^0_s}) scattering phase shifts.
We study the finite-size scaling of heavy-light mesons in the static limit. We compute two-point functions of chiral current densities as well as pseudoscalar densities in the epsilon-regime of heavy meson Chiral Perturbation Theory (HMChPT). As expected, finite volume dependence turns out to be significant in this regime and can be predicted in the effective theory in terms of the infinite-volume low-energy couplings. These results might be relevant for extraction of heavy-meson properties from lattice simulations.
In highly improved staggered quark (HISQ) simulations by the HPQCD, MILC, and Fermilab Lattice collaborations, both the light quarks and the charm quark are staggered. We extend chiral perturbation theory for staggered quarks to include such all-staggered heavy-light mesons. We assume that the heavy quark action is sufficiently improved that we may take $a m_Q <<1$ (where $m_Q$ is the heavy quark mass), but also that $m_Q>>Λ_{QCD}$ so that a continuum heavy quark expansion is appropriate. We develop this effective chiral theory through next-to-leading order, and use it to study the pattern of …
In HISQ simulations by the MILC and Fermilab Lattice collaborations, both the light quarks and the charm quark are staggered. We extend staggered chiral perturbation theory (\schpt) to include such all-staggered heavy-light mesons. We assume that the heavy quark action is sufficiently improved that we may take $a m_Q <<1$ (where $m_Q$ is the heavy quark mass), but also that $m_Q>>Λ_{QCD}$ so that a continuum heavy quark expansion is appropriate. Using this \schpt, the leptonic decay constant of the heavy-light meson is calculated at next-to-leading-order. The pattern of taste splittings in the…
We consider effective theory treatment for the lowest-lying $S$- and $P$-wave states of charmed mesons. In our analysis, quantum corrections and contributions from leading chiral and heavy quark symmetry breakings are taken into account. The heavy meson mass expressions have abundance parameters, low-energy constants, in comparison to the measured charmed mesons masses. The experimental and lattice QCD data on charmed meson spectroscopy are used to extract, for the first time, the numerical values of the full set of low-energy constants of the effective chiral Lagrangian. Our results on these …
We present non-perturbative first-principle results for quark-, gluon- and meson $1$PI correlation functions of two-flavour Landau-gauge QCD in the vacuum. These correlation functions carry the full information about the theory. They are obtained by solving their Functional Renormalisation Group equations in a systematic vertex expansion, aiming at apparent convergence. This work represents a crucial prerequisite for quantitative first-principle studies of the QCD phase diagram and the hadron spectrum within this framework. In particular, we have computed the gluon, ghost, quark and scalar-pse…
The QCD string model is employed to evaluate the masses of orbitally and radially excited heavy-light mesons and lightest hybrids in the spectrum of charmonium and bottomonium. The number of parameters of the model is reduced to only seven which are the string tension, the two values of the strong coupling constant (one for heavy-light and $\bar{c}c$ mesons and one for $\bar{b}b$ mesons), and the four overall spectrum shift constants which depend on the quark contents of the particular meson or hybrid family. A few well-established states in the spectrum of heavy-light and heavy-heavy mesons a…
Compared with lattice QCD, isospin breaking of heavy-meson decay constants from QCD sum rules agrees for $D$ mesons but disagrees (by a factor of four) for $B$ mesons.
We construct a holographic model of heavy-light mesons by extending the AdS/QCD to incorporate the behavior of the heavy quark limit. In that limit, the QCD dynamics is governed by the light quark and the heavy quark simply plays the role of a static color source. The heavy quark spin symmetry can be treated as a global symmetry in the AdS bulk. As a consequence, the heavy-light mesons are mapped to "fermions" in the AdS theory. The light flavor chiral symmetry is naturally built in by this construction, and its breaking produces the splitting of the parity-doubled heavy-light meson states. Th…
QCD sum rules for decay constants of heavy mesons with $u$ or $d$ quark yield for $B$ mesons much less isospin breaking than lattice QCD but good agreement for $D$ mesons.
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 …
We calculate the threshold $T$ matrices of the light pseudoscalar meson and heavy meson scattering to fourth order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting to the lattice QCD data points through both the perturbative and iterated methods and obtain the physical scattering lengths in both formalisms. The values of the scattering lengths tend to be convergent at fourth order for most of the channels in the perturbative method. The value of the scattering length for the channel $DK (I=0)$, which involves the bound state $D_{s0}^{*}(2317)$, is obt…
Recent lattice QCD simulations of the scattering lengths of Nambu-Goldstone bosons off the $D$ mesons are studied using unitary chiral perturbation theory. We show that the Lattice QCD data are better described in the covariant formulation than in the heavy-meson formulation. The $D^*_{s0}(2317)$ can be dynamically generated from the coupled-channels $DK$ interaction without \textit{a priori} assumption of its existence. A new renormalization scheme is proposed which manifestly satisfies chiral power counting rules and has well-defined behavior in the infinite heavy-quark mass limit. Using thi…
Slight sophistications of the QCD sum-rule formalism may have great impact on the reliability of predicted hadron observables, as exemplified for the case of heavy-meson decay constants.
We derive the $k_T$ resummation for doubly heavy-flavored $B_c$ meson decays by including the charm quark mass effect into the known formula for a heavy-light system. The resultant Sudakov factor is employed in the perutrbative QCD study of the "golden channel" $B_c^+ \to J/ψπ^+$. With a reasonable model for the $B_c$ meson distribution amplitude, which maintains approximate on-shell conditions of both the partonic bottom and charm quarks, it is observed that the imaginary piece of the $B_c \to J/ψ$ transition form factor appears to be power suppressed, and the $B_c^+ \to J/ψπ^+$ branching rat…
