Infinite Heavy Quark Mass Limit Research Articles

Is the Λc(2625)+ the heavy quark spin symmetry partner of the Λc(2595)+ ?

We use a $\mathcal{O}(\Lambda_\text{QCD}/m_c)$ heavy quark effective theory scheme, where only $\mathcal{O}(\Lambda_\text{QCD}/m_b)$ and perturbative QCD short distance corrections are neglected, to study the matrix elements of the scalar, pseudoscalar, vector, axial-vector and tensor currents between the $\Lambda_b$ ground state and the odd parity charm $\Lambda_c(2595)^+$ and $\Lambda_c(2625)^+$ resonances. We show that in the near-zero recoil regime, the scheme describes reasonably well, taking into account uncertainties, the results for the 24 form-factors obtained in lattice QCD (LQCD) just in terms of only 4 Isgur-Wise (IW) functions. We also find some support for the possibility that the $\Lambda_c(2595)^+$ and $\Lambda_c(2625)^+$ resonances might form a heavy-quark spin symmetry (HQSS) doublet. However, we argue that the available LQCD description of these two resonances is not accurate enough to disentangle the possible effects of the $\Sigma_c \pi$ and $\Sigma_c^*\pi$ thresholds, located only a few MeV above their position, and that it cannot be ruled out that these states are not HQSS partners. Finally, we study the ratio $\frac{d\Gamma[\Lambda_b\to \Lambda_{c,1/2^-}^* \ell \bar\nu_\ell]/dq^2}{d\Gamma[\Lambda_b\to \Lambda_{c,3/2^-}^*\ell \bar\nu_\ell]/dq^2}$ of the Standard Model differential semileptonic decay widths, with $q^\mu$ the momentum transferred between the initial and final hadrons. We provide a natural explanation for the existence of large deviations, near the zero recoil, of this ratio from 1/2 (value predicted in the infinite heavy quark mass limit, assuming that the $\Lambda_{c,1/2^-}^*$ and $\Lambda_{c,3/2^-}^*$ are the two members of a HQSS doublet) based on S-wave contributions to the $\Lambda_b\to \Lambda_{c,1/2^-}^*$ decay amplitude driven by a sub-leading IW function.

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 $m_{B^*_{s}}= 5411.36(5.3)~\mathrm{MeV}$.

A Potential Model Approach in the Study of Static and Dynamic Properties of Heavy-Light Quark-Antiquark Systems

We report some approximate analytic form of meson wave function constructed upon solving Schrodinger equation with linear plus Coulomb type Cornell potential. With this wave function, we study Isgur-Wise function and its derivatives for heavy-light mesons in the infinite heavy quark mass limit. We also explore the elastic form factors, charge radii and decay constants of pseudoscalar mesons in this QCD inspired quark model approach.

Scattering lengths of Nambu-Goldstone bosons offDmesons and dynamically generated heavy-light mesons

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 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 this scheme we predict the heavy-quark spin and flavor symmetry counterparts of the ${D}_{s0}^{*}(2317)$.

HYPERFINE MIXING IN b → c SEMILEPTONIC AND ELECTROMAGNETIC DECAYS OF DOUBLY HEAVY bc BARYONS

We show that semileptonic and electromagnetic decays involving spin-1/2 doubly heavy bc baryons are very sensitive to hyperfine mixing in their wave functions. We further show how heavy quark spin symmetry relations, obtained in the infinite heavy quark mass limit and near zero recoil, could be used to extract the admixtures in a model independent way from semileptonic decay data. On the other hand the infinite heavy quark mass limit gives wrong predictions in the electromagnetic case.

Exclusive c → s, d Semileptonic Decays of Spin-1/2 and Spin-3/2 cb Baryons

We present results for exclusive semileptonic decay widths of ground state spin-$1/2$ and spin-$3/2$ $cb$ baryons corresponding to a $c\to s, d$ transition at the quark level. The relevance of hyperfine mixing in spin-1/2 $cb$ baryons is shown. Our form factors are compatible with heavy quark spin symmetry constraints obtained in the infinite heavy quark mass limit.

Hyperfine mixing in electromagnetic decay of doubly heavy bc baryons

We investigate the role of hyperfine mixing in the electromagnetic decay of ground state doubly heavy bc baryons. As in the case of a previous calculation on b→c semileptonic decays of doubly heavy baryons, we find large corrections to the electromagnetic decay widths due to this mixing. Contrary to the weak case just mentioned, we find here that one cannot use electromagnetic width relations obtained in the infinite heavy quark mass limit to experimentally extract information on the admixtures in a model independent way.

Possible complex annihilation andB→KπdirectCPasymmetry

We point out that a strong phase from the penguin annihilation channel in $B$ meson decays is sensitive to the treatment of subleading terms with physical $b$ quark mass ${m}_{b}$. In the limit of infinite heavy-quark mass, both the soft-collinear effective theory and the perturbative QCD approach based on the ${k}_{T}$ factorization theorem agree that the strong phase is suppressed. For finite heavy-quark mass, the two approaches predict different results, which are related to the treatment of subleading terms. This is illustrated by taking a toy model for soft-collinear effective theory, in which a small quantity, suppressed by $O(\ensuremath{\Lambda}/{m}_{b})$, with $\ensuremath{\Lambda}$ being a hadronic scale, is kept in the denominators of internal particle propagators. This model can generate a sizable strong phase to accommodate the data of the ${B}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{\mp}}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ direct $CP$ asymmetry.

Static properties and semileptonic decays of doubly heavy baryons in a nonrelativistic quark model

We evaluate masses and semileptonic decay widths for the ground state of doubly heavy $\Xi$ and $\Omega$ baryons in the framework of a nonrelativistic quark model. We solve the three-body problem by means of a variational ansatz made possible by heavy-quark spin symmetry constraints. Our masses are comparable to the ones obtained in relativistic calculations and we get one of the best agreements with lattice data. Our simple wave functions are used to evaluate semileptonic decays of doubly heavy $\Xi, \Xi'(J=1/2)$ and $\Omega, \Omega'(J=1/2)$ baryons. Our results for the decay widths are in reasonable agreement with calculations done in a relativistic calculation in the quark-diquark approximation. We also check that our wave functions comply with what it is expected in the infinite heavy quark mass limit.

Study of semileptonic and nonleptonic decays of the Bc - meson

We evaluate semileptonic and two-meson nonleptonic decays of the B c − meson in the framework of a nonrelativistic quark model. The former are done in spectator approximation using one-body current operators at the quark level. Our model reproduces the constraints of heavy-quark spin symmetry obtained in the limit of infinite heavy-quark mass. For the two-meson nonleptonic decays we work in factorization approximation. We compare our results to the ones obtained in different relativistic approaches.

Lattice calculation of SU(3) flavor breaking ratios inB0−B¯0mixing

We present an unquenched lattice calculation for the SU(3) flavor breaking ratios of the heavy-light decay constants and the {delta}B=2 matrix elements. The calculation was performed on 16{sup 3}x32 lattices with two dynamical flavors of domain-wall quarks and inverse lattice spacing 1/a=1.69(5) GeV. Heavy quarks were implemented using an improved lattice formulation of the static approximation. In the infinite heavy-quark mass limit we obtain f{sub B{sub s}}/f{sub B{sub d}}=1.29(4)(6), B{sub B{sub s}}/B{sub B{sub d}}=1.06(6)(4), {xi}=1.33(8)(8) where the first error is statistical and the second systematic.

Analysis of the three-bodyB→D+D−π0decay

The decay process $B\to D^+ D^- \pi^0$ is an interesting channel for the investigation of CP violating effects in the $b-$ sector. We write down a decay amplitude constrained by a low-energy theorem, which also includes the contribution of resonant $S-$ and $P-$wave beauty and charmed mesons, and we determine the relevant matrix elements in the infinite heavy quark mass limit, assuming the factorization ansatz. We estimate the rate of the decay: ${\cal B}(B \to D^+ D^- \pi^0)\simeq 1 \times 10^{-3}$. We also analyze the time-independent and time-dependent differential decay distributions, concluding that a signal for this process should be observed at the B-factories. Finally, we give an estimate of the decay rate of the Cabibbo-favoured process $B\to D^+ D^- K_S$.

Semileptonic and rare B meson decays into a light pseudoscalar meson

In the framework of a QCD relativistic potential model we evaluate the form factors describing the exclusive decays B→ πℓ ν and B→ Kℓ +ℓ −. The present calculation extends a previous analysis of B meson decays into light vector mesons. We find results in agreement with the data, when available, and with the theoretical constraints imposed by the Callan-Treiman relation and the infinite heavy quark mass limit.

Universal Isgur-Wise form factors from QCD sum rules in HQET

We review the role of the universal Isgur-Wise functions parameterizing the B meson semileptonic matrix elements to excited charm states in the infinite heavy quark mass limit. We also discuss the determination of such form factors by QCD sum rules in the framework of the Heavy Quark Effective Theory.

QCD interactions of heavy mesons with pions by light-cone sum rules

Light-cone QCD sum rules are employed to compute the strong coupling constants: \(g_{B^* B^* \pi}\), \(g_{B_1 B_0 \pi}\) and \(g_{B_1 B^* \pi}\), where \((B,B^*)\) and \((B_0,B_1)\) are negative and positive parity \((0^-,1^-)\) and \((0^+,1^+)\)\(\bar q Q\) doublets. The couplings are calculated both for finite values of the heavy quark mass and in the infinite heavy quark mass limit, deriving sum rules for \(m_Q \to \infty\).

Isgur-Wise form factors of heavy baryons within a light-front constituent quark model

The space-like elastic form factors of baryons containing a heavy quark are investigated within a light-front constituent quark model in the limit of infinite heavy-quark mass, adopting a gaussian-like ansatz for the three-quark wave function. The results obtained for the Isgur-Wise form factors corresponding both to a spin-0 and a spin-1 light spectator pair are presented. It is found that the Isgur-Wise functions depend strongly on the baryon structure, being sharply different in case of diquark-like or collinear-type configurations in the three-quark system. It is also shown that the relativistic effects lead to a saturation property of the form factors as a function of the baryon size. Our results are compared with those of different models as well as with recent predictions from QCD sum rules and lattice QCD simulations; the latter ones seem to suggest the dominance of collinear-type configurations, in which the heavy-quark is sitting close to the center-of-mass of the light quark pair.

Electromagnetic mass difference of heavy mesons

Using the Cottingham formula, we give an estimate of the electromagnetic mass splitting of pseudoscalar heavy mesons in the beauty and charm sector. We include in the dispersion relation the Born term, the $1^-$ resonance and the positive parity $1^+$ resonance. We also evaluate the contribution to the mass difference from the isospin breaking quark mass differences. Our results: $m_{B^+}-m_{B^0} = - 0.83\pm 0.34 MeV$ and $m_{D^+}-m_{D^0} = + 4.33\pm 0.37 MeV$, are in agreement with the experimental measurements: $m_{B^+}-m_{B^0} = - 0.35\pm 0.29 MeV$ and $m_{D^+}-m_{D^0} = + 4.78\pm 0.10 MeV$. We also compute the mass differences in the infinite heavy quark mass limit, which show small deviations from the finite mass results for the B case and 30% effects in the charm case.

QCD interactions of heavy mesons with pions by light-cone sum rules

Light-cone QCD sum rules are employed to compute the strong coupling constants: g_{B^* B^* pi}, g_{B_1 B_0 pi} and g_{B_1 B^* pi}, where (B,B^*) and (B_0,B_1) are negative and positive parity (0^-,1^-) and (0^+,1^+) \bar qQ doublets. The couplings are calculated both for finite values of the heavy quark mass and in the infinite heavy quark mass limit, deriving sum rules for m_Q \to \infty.

Leptonic constant from B meson radiative decay

We propose a method to determine the leptonic decay constant f B ∗ in the infinite heavy quark mass limit from the analysis of the radiative decay mode B − → ℓ − ν ℓγ . The method relies on HQET symmetries and on experimental data from D ∗0 → D 0γ .

On the coupling of heavy mesons to pions in QCD

We compute the strong coupling constant g P∗Pπ , with P and P ∗ respectively pseudoscalar and vector heavy mesons by using the QCD sum rules approach. Our computation is based on the evaluation of the time ordered product of currents between the vacuum and the soft pion state. The so-called parasitic terms are taken into account and give a contribution to the sum rule of the same order of the lowest lying state, while higher dimension non perturbative terms have small numerical effects. The infinite heavy quark mass limit is also examined.