Heavy Meson Chiral Perturbation Theory Research Articles

Bpi excited-state contamination in lattice calculations of B-meson correlation functions

Multi-particle states with additional pions are expected to result in a difficult-to-control excited-state contamination in lattice simulations. We show that heavy meson chiral perturbation theory can be employed to estimate the contamination due to two-particle Bpi states in various B-meson observables, like the B-meson decay constant and the B^*Bpi coupling. We work in the static limit and to next-to-leading order in the chiral expansion, i.e. including textrm{O}(p). The Bpi states are found to typically lead to an overestimation of the observables at the few percent level. We determine two of the LECs from Brightarrow pi form factor computations of the KEK group (Colquhoun et al. in Phys. Rev. D 106:054502, 2022) and discuss ways to determine the others. In particular, one LEC which is associated with smeared interpolating fields seems to be easily accessible and thus opens up a way to systematically study the effect of smearing on excited-state effects.

Hadronic loop effects to excited scalar charmed mesons revisited

We re-examine the hadronic loop effects on the masses of and calculated in quark models in the framework of heavy meson chiral perturbation theory (HMCHPT). Unlike previous approaches, ours reproduces the observed scalar charm states reported by the Particle Data Group (PDG). We show why previous approaches of using HMCHPT in studying mass shift effects due to chiral loops gave unsatisfactory results.

Phase shifts of the light pseudoscalar meson and heavy meson scattering in heavy meson chiral perturbation theory

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 Dpi (I=1/2), DK(I=0), D{bar{K}}(I=0), D_s{bar{K}}, Deta and D_seta 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 well-known exotic state D_{s0}^{*}(2317). The DK(I=0) channel corresponds to the well-known exotic state D_{s0}^{*}(2317). The coupled-channel Dpi , Deta and D_s{bar{K}} scattering corresponds to D_{0}^{*}(2400). The coupled-channel Dpi , Deta and D_s{bar{K}} scattering corresponds to D_{0}^{*}(2400). We also predict the scattering lengths and scattering volumes and observe good convergence in the scattering volumes. Our calculations provide a possibility to accurately investigate the exotic state in the light pseudoscalar meson and heavy meson interactions.

Study of possible molecular states of Ds(*)Ds(*) and Bs(*)Bs(*)

Recently the LHCb collaboration reported a new exotic state $T^+_{cc}$ which is conjectured to be a molecular state of $D^0D^{*+}$ (or $D^{*0}D^{+}$) theoretically. Belle Collaboration also searched for tetraquark state $X_{ccss}$ in $D_sD_s (D^*_sD^*_s )$ final states but no significant signals were observed, which did not rule out the possibility of $X_{ccss}$ to be a molecular state of $D_sD_s (D^*_sD^*_s )$. Inspired by these experimental results on double charmed exotic state, in this paper we study whether the molecular bound states of $D_s^{(*)}D_s^{(*)}$ and $B_s^{(*)}B_s^{(*)}$ can exist with the Bethe-Salpeter (B-S) equation approach. We employ heavy meson chiral perturbation theory with one boson-exchange approximation to calculate the interaction kernels in the B-S equations. Our numerical results suggest that two $B_s^{*}$ mesons perhaps form a $0^+$ molecular state. Future experimental search for $X_{ccss}$ states in other decay channels may shed light on the structure of double charmed exotic state.

Light pseudoscalar meson and heavy meson scattering lengths to O(p4) in heavy meson chiral perturbation theory

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 obtained correctly in the iterated method. Based on the heavy diquark-antiquark symmetry, we also estimate the meson and doubly charmed (bottom) baryon scattering lengths, and find that the bound states can be generated with high probability in the channels $\bar{K}\Xi_{cc}(I=0)$ and $\bar{K}\Xi_{bb}(I=0)$. We strongly urge the LHCb Collaboration to look for the very narrow $\bar{K}\Xi_{cc}$ state with $IJ^P=0{1\over 2}^-$ through either the electromagnetic decay or the iso-spin violating strong decay $\Omega_{cc} \pi$.

Isospin violating decay Ds*→Dsπ0 in chiral perturbation theory

We systematically calculate the isospin violating decay, $D_s^*\to D_s\pi^0$, with the heavy meson chiral perturbation theory up to $\mathcal{O}(p^3)$ including the loop diagrams. The $\mathcal{O}(p^3)$ tree level amplitudes contain four undetermined LECs. We use two strategies to estimate them. With the nonanalytic dominance approximation, we get $\Gamma[D_s^\ast\to D_s\pi^0]=(3.38\pm0.12)$ eV. With the naturalness assumption, we give a possible range of the isospin violating decay width, $[1.11-6.88]$ eV. We find that the contribution of the $\mathcal{O}(p^3)$ corrections might be significant.

Resonant and non-resonant contributions of B → K∗(p1,𝜖1){Kπ,ππ,KK} decay modes

In this paper, the non-leptonic three-body decays [Formula: see text], [Formula: see text], [Formula: see text] are studied by introducing two-meson distribution amplitude for the [Formula: see text], [Formula: see text] and [Formula: see text] pairs in naive and QCD factorization (QCDF) approaches, such that the analysis is simplified into quasi-two body decays. By considering that the vector meson is being ejected in factorization, the resonant and non-resonant contributions are analyzed by using intermediate mesons in Breit–Wigner resonance formalism and the heavy meson chiral perturbation theory (HMChPT), respectively. The calculated values of the resonant and non-resonant branching ratio of [Formula: see text], [Formula: see text] and [Formula: see text] decay modes are compared with the experimental data. For [Formula: see text] and [Formula: see text], the non-resonant contributions are about 70–80% of experimental data, for which the total results by considering resonant contributions are in good agreement with the experiment.

Masses of scalar and axial-vector B mesons revisited

The SU(3) quark model encounters a great challenge in describing even-parity mesons. Specifically, the qbar{q} quark model has difficulties in understanding the light scalar mesons below 1 GeV, scalar and axial-vector charmed mesons and 1^+ charmonium-like state X(3872). A common wisdom for the resolution of these difficulties lies on the coupled channel effects which will distort the quark model calculations. In this work, we focus on the near mass degeneracy of scalar charmed mesons, D_{s0}^* and D_0^{*0}, and its implications. Within the framework of heavy meson chiral perturbation theory, we show that near degeneracy can be qualitatively understood as a consequence of self-energy effects due to strong coupled channels. Quantitatively, the closeness of D_{s0}^* and D_0^{*0} masses can be implemented by adjusting two relevant strong couplings and the renormalization scale appearing in the loop diagram. Then this in turn implies the mass similarity of B_{s0}^* and B_0^{*0} mesons. The P_0^* P'_1 interaction with the Goldstone boson is crucial for understanding the phenomenon of near degeneracy. Based on heavy quark symmetry in conjunction with corrections from QCD and 1/m_Q effects, we obtain the masses of B^*_{(s)0} and B'_{(s)1} mesons, for example, M_{B_{s0}^*}= (5715pm 1),mathrm{MeV}+delta Delta _S, M_{B'_{s1}}=(5763pm 1),mathrm{MeV}+delta Delta _S with delta Delta _S being 1/m_Q corrections. We find that the predicted mass difference of 48 MeV between B'_{s1} and B_{s0}^* is larger than that of 20–30 MeV inferred from the relativistic quark models, whereas the difference of 15 MeV between the central values of M_{B'_{s1}} and M_{B'_1} is much smaller than the quark model expectation of 60–100 MeV. Experimentally, it is important to have a precise mass measurement of D_0^* mesons, especially the neutral one, to see if the non-strange scalar charmed meson is heavier than the strange partner as suggested by the recent LHCb measurement of the D_0^{*pm }.

Direct CP violation in charmless three-body decays of B mesons

Direct CP violation in charmless three-body hadronic decays of $B$ mesons is studied within the framework of a simple model based on the factorization approach. Three-body decays of heavy mesons receive both resonant and nonresonant contributions. Dominant nonresonant contributions to tree-dominated and penguin-dominated three-body decays arise from the $b\to u$ tree transition and $b\to s$ penguin transition, respectively. The former can be evaluated in the framework of heavy meson chiral perturbation theory with some modification, while the latter is governed by the matrix element of the scalar density $\langle M_1M_2|\bar q_1 q_2|0\rangle$. Strong phases in this work reside in effective Wilson coefficients, propagators of resonances and the matrix element of scalar density. In order to accommodate the branching fraction and CP asymmetries observed in $B^-\to K^-\pi^+\pi^-$, the matrix element $\langle K\pi|\bar sq|0\rangle$ should have an additional strong phase, which might arise from some sort of power corrections such as final-state interactions. We calculate inclusive and regional CP asymmetries and find that nonresonant CP violation is usually much larger than the resonant one and that the interference effect is generally quite significant. If nonresonant contributions are turned off in the $K^+K^-K^-$ mode, the predicted CP asymmetries due to resonances will be wrong in sign when confronted with experiment. In our study of $B^-\to \pi^-\pi^+\pi^-$, we find that ${\cal A}_{C\!P}(\rho^0\pi^-)$ should be positive in order to account for CP asymmetries observed in this decay. However, all theories predict a large and negative CP violation in $B^-\to \rho^0\pi^-$. Measurements of CP-asymmetry Dalitz distributions put very stringent constraints on the theoretical models. We check the magnitude and the sign of violation in some (large) invariant mass regions to test our model.

Isospin violating decays of positive parity $$B_s$$ B s mesons in HM $$\chi $$ χ PT

Recent lattice QCD results suggest that the masses of the first two positive parity \(B_s\) mesons lie below the BK threshold, similar to the case of \(D^*_{s0}(2317)^+\) and \(D_{s1}(2460)^+\) mesons. The mass spectrum of \(B_s\) mesons seems to follow the pattern of a \(D_s\) mass spectrum. As in the case of charmed mesons, the structure of positive parity \(B_s\) mesons is very intriguing. To shed more light on this issue, we investigate the strong isospin violating decays \(B_{s0}^{*0} \rightarrow B_s^0 \pi ^0\), \(B_{s1}^{0} \rightarrow B_s^{*0} \pi ^0\), and \(B_{s1}^{0} \rightarrow B_s^0 \pi \pi \) within heavy meson chiral perturbation theory. The two-body decay amplitude arises at tree level and we show that the loop corrections give significant contributions. On the other hand, in the case of three-body decay \(B_{s1}^{0} \rightarrow B_s^0 \pi \pi \) the amplitude occurs only at loop level. We find that the decay widths for these decays are \(\Gamma (B_{s1}^{0} \rightarrow B_s^0 \pi \pi )\sim 10^{-3}\,\) keV, and \(\Gamma (B_{s0}^{*0} \rightarrow B_s^0 \pi ^0) \le 55\,\) keV, \(\Gamma (B_{s1}^{0} \rightarrow B_s^{*0} \pi ^0) \le 50\,\) keV. More precise knowledge of the coupling constant describing the interaction of positive and negative parity heavy mesons with light pseudo-scalar mesons would help to increase the accuracy of our calculation.

P-wave coupled-channel scattering ofBsπ,Bs*π,BK¯,B*K¯and the puzzlingX(5568)

The D0 Collaboration has recently reported a narrow peak structure in the $B_s^0\pi^\pm$ invariant-mass spectrum, that is called $X(5568)$. Its proposed quantum numbers $J^P=0^+/1^+$ are not determined unambiguously, and we show that one can fit the data assuming $J^P=1^-$ with the same mass and width for the resonance signal. The corresponding isovector $P$-wave coupled-channel scattering involving the states $B_s\pi$, $B_s^*\pi$, $B \overline{K}$ and $B^*\overline K$ is studied employing leading-order Heavy Meson Chiral Perturbation Theory, which is then unitarized making use of standard techniques from Unitary Chiral Perturbation Theory. The subtraction constants that appear in the unitarization process are determined by a $u$-channel crossing symmetry constraint or by naturalness arguments, being the numerical values obtained in both cases quite closed, and no further freedom is left in the model. A crucial point is that if the $X(5568)$ is $1^-$ and decaying into $B_s^0\pi^\pm$ then it should appear as a pole in the $T$-matrix elements. It finally turns out that no $X(5568)$ pole is found that can be qualified as dynamically generated from the isovector $P$-wave coupled-channel dynamics. This result disfavors the interpretation of the $X(5568)$ within a "molecular" picture.

$$D^*_{s0}(2317)$$ D s 0 ∗ ( 2317 ) and $$\textit{DK}$$ DK scattering in B decays from BaBar and LHCb data

We study the experimental $DK$ invariant mass spectra of the reactions $B^+ \to \bar{D}^0 D^0 K^+$, $B^0 \to D^- D^0 K^+$ (measured by the BaBar Collaboration) and $B_s \to \pi^+ \bar{D}^0 K^-$ (measured by the LHCb Collaboration), where an enhancement right above the threshold is seen. We show that this enhancement is due to the presence of $D^\ast_{s0}(2317)$, which is a $DK$ bound state in the $I(J^P) = 0(0^+)$ sector. We employ a unitarized amplitude with an interaction potential fixed by heavy meson chiral perturbation theory. We obtain a mass $M_{D^\ast_{s0}} = 2315^{+12}_{-17}\ ^{+10}_{-5}\ \text{MeV}$, and we also show, by means of the Weinberg compositeness condition, that the $DK$ component in the wave function of this state is $P_{DK} = 70^{+4}_{-6}\ ^{+4}_{-8} \%$, where the first (second) error is statistical (systematic).

Can X (5568) be described as a B s π ,BK¯resonant state?

The D0 Collaboration has recently seen a resonant-like peak in the $B_s\pi$ invariant mass spectrum, claimed to be a new state called $X(5568)$. Using a $B_s\pi$--$B\bar{K}$ coupled channel analysis, implementing unitarity, and with the interaction derived from Heavy Meson Chiral Perturbation Theory, we are able to reproduce the reported spectrum, with a pole that can be associated to the claimed $X(5568)$ state, and with mass and width in agreement with the ones reported in the experimental analysis. However, if the $T$-matrix regularization is performed by means of a momentum cutoff, the value for the latter needed to reproduce the spectrum is $\Lambda = 2.80 \pm 0.04\ \text{GeV}$, much larger than a "natural" value $\Lambda \simeq 1\ \text{GeV}$. In view of this, it is difficult to interpret the nature of this new state. This state would not qualify as a resonance dynamically generated by the unitarity loops. Assuming the observed peak to correspond to a physical state, we make predictions for partners in the $D$, $D^\ast$, and $B^\ast$ sectors. Their observation (or lack thereof) would shed light into this issue.

Hadronic three-body decays of B mesons

Hadronic three-body decays of B mesons receive both resonant and nonresonant contributions. Dominant nonresonant contributions to tree-dominated three-body decays arise from the b→u tree transition which can be evaluated using heavy meson chiral perturbation theory valid in the soft meson limit. For penguin-dominated decays, nonresonant signals come mainly from the penguin amplitude governed by the matrix elements of scalar densities 〈M1M2|q‾1q2|0〉. The intermediate vector meson contributions to three-body decays are identified through the vector current, while the scalar meson resonances are mainly associated with the scalar density. We discuss inclusive and regional direct CP asymmetries. In the low mass regions of the Dalitz plot, we find that the regional CP violation is indeed largely enhanced with respect to the inclusive one.

B*Bπcoupling using relativistic heavy quarks

We report on a calculation of the B*Bpi coupling in lattice QCD. The strong matrix element for a B* to Bpi transition is directly related to the leading order low-energy constant in heavy meson chiral perturbation theory (HMChPT) for B mesons. We carry out our calculation directly at the b-quark mass using a non-perturbatively tuned clover action that controls discretization effects of order pa and (ma)^n for all n. Our analysis is performed on RBC/UKQCD gauge configurations using domain-wall fermions and the Iwasaki gauge action at two lattice spacings of ainverse = 1.729(25) GeV, ainverse = 2.281(28) GeV, and unitary pion masses down to 290 MeV. We achieve good statistical precision and control all systematic uncertainties, giving a final result for the HMChPT coupling g_b = 0.56(3)stat(7)sys in the continuum and at the physical light-quark masses. This is the first calculation performed directly at the physical b-quark mass and lies in the region one would expect from carrying out an interpolation between previous results at the charm mass and at the static point.

Chiral loops in the isospin violating decays ofDs1(2460)+andDs0*(2317)+

Positive parity meson states D*_{s0}(2317) and D_{s1}(2460) have masses slightly below the DK threshold. Therefore, both states can strongly decay only into isospin violating decays D_{s1}(2460) --> Ds \pi \pi, D_{s1}(2460) --> Ds* \pi 0 and D*_{s0}(2317) --> Ds \pi 0. The pion states are having rather small energies, what makes these decays appropriate to study within heavy meson chiral perturbation theory and calculate loop contributions. The D_{s1}(2460) --> Ds \pi \pi decays occur only at the loop level. Amplitude is a result of chiral loop contributions, which then have to be finite. However, in the case of D_{s1}(2460)--> Ds* \pi 0 and D*_{s0}(2317)--> Ds \pi 0 decays, there is a tree level contribution. We find that chiral loop contributions might be important in both cases. The calculated amplitudes are sensitive on the coupling constant describing the interaction of positive and negative parity heavy meson multiplets with the light pseudoscalars. The counter-terms contributions are also present in the amplitudes D_{s1}(2460) --> Ds* \pi 0 and D*_{s0}(2317) --> Ds \pi 0. We explore experimentally known ratio of the decay widths for these two decay modes to estimate the size of counter-terms contributions. We determine decay widths for both decay modes to be Gamma (D_{s1}(2460) --> Ds \pi + \pi -) = 0.25 keV and Gamma (D_{s1}(2460) --> Ds + \pi 0 \pi 0 ) = 0.15 keV.

B -meson decay constants from 2+1 -flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks

We calculate the B-meson decay constants f_B, f_Bs, and their ratio in unquenched lattice QCD using domain-wall light quarks and relativistic b-quarks. We use gauge-field ensembles generated by the RBC and UKQCD collaborations using the domain-wall fermion action and Iwasaki gauge action with three flavors of light dynamical quarks. We analyze data at two lattice spacings of a ~ 0.11, 0.086 fm with unitary pion masses as light as M_pi ~ 290 MeV; this enables us to control the extrapolation to the physical light-quark masses and continuum. For the b-quarks we use the anisotropic clover action with the relativistic heavy-quark interpretation, such that discretization errors from the heavy-quark action are of the same size as from the light-quark sector. We renormalize the lattice heavy-light axial-vector current using a mostly nonperturbative method in which we compute the bulk of the matching factor nonperturbatively, with a small correction, that is close to unity, in lattice perturbation theory. We also improve the lattice heavy-light current through O(alpha_s a). We extrapolate our results to the physical light-quark masses and continuum using SU(2) heavy-meson chiral perturbation theory, and provide a complete systematic error budget. We obtain f_B0 = 199.5(12.6) MeV, f_B+ = 195.6(14.9) MeV, f_Bs = 235.4(12.2) MeV, f_Bs/f_B0 = 1.197(50), and f_Bs/f_B+ = 1.223(71), where the errors are statistical and total systematic added in quadrature. These results are in good agreement with other published results and provide an important independent cross check of other three-flavor determinations of $B$-meson decay constants using staggered light quarks.

Decay constants of pseudoscalar D-mesons in lattice QCD with domain-wall fermion

We present the first study of the masses and decay constants of the pseudoscalar D mesons in two flavors lattice QCD with domain-wall fermion. The gauge ensembles are generated on the 243×48 lattice with the extent Ns=16 in the fifth dimension, and the plaquette gauge action at β=6.10, for three sea-quark masses with corresponding pion masses in the range 260–475 MeV. We compute the point-to-point quark propagators, and measure the time-correlation functions of the pseudoscalar and vector mesons. The inverse lattice spacing is determined by the Wilson flow, while the strange and the charm quark masses by the masses of the vector mesons ϕ(1020) and J/ψ(3097) respectively. Using heavy meson chiral perturbation theory (HMChPT) to extrapolate to the physical pion mass, we obtain fD=202.3(2.2)(2.6) MeV and fDs=258.7(1.1)(2.9) MeV.

Near mass degeneracy in the scalar meson sector: Implications forB(s)0*andB(s)1′mesons

The empirical observation of near degeneracy of scalar mesons above 1 GeV, namely, the mass of the strange-flavor scalar meson is similar to that of the non-strange one, is at variance with the naive expectation of the quark model. Qualitatively, the approximate mass degeneracy can be understood as a consequence of self-energy effects due to strong coupled channels which will push down the mass of the heavy scalar meson in the strange sector more than that in the non-strange partner. However, it works in the conventional model without heavy quark expansion, but not in the approach of heavy meson chiral perturbation theory as mass degeneracy and the physical masses of $D_{s0}^*$ and $D_0^*$ cannot be accounted for simultaneously. In the heavy quark limit, near mass degeneracy observed in the scalar charm sector will imply the same phenomenon in the $B$ system. We have the prediction $M_{B_0^*}\approx M_{B_{s0}^*}\approx 5715\,{\rm MeV}+\delta\Delta_S$ based on heavy quark symmetry and the leading-order QCD correction, where $\delta\Delta_S$ arises from $1/m_Q$ corrections. A crude estimate indicates that $\delta\Delta_S$ is of order $-35$ MeV or less. We stress that the closeness of $B_{s0}^*$ and $B_0^*$ masses implied by heavy quark symmetry is not spoiled by $1/m_Q$ or QCD corrections. The mass-shift effect on $K_0^*(1430)$ is discussed.

Chiral perturbation theory and theB¯B¯strong interaction

We have calculated the potentials of the heavy (charmed or bottomed) pseudoscalar mesons up to $O(\epsilon^2)$ with the heavy meson chiral perturbation theory. We take into account the contributions from the football, triangle, box, and crossed diagrams with the 2$\phi$ exchange and one-loop corrections to the contact terms. We notice that the total 2$\phi$-exchange potential alone is attractive in the small momentum region in the channel ${\bar B \bar B}^{I=1}$, ${\bar B_s \bar B_s}^{I=0}$, or ${\bar B \bar B_s}^{I=1/2}$, while repulsive in the channel ${\bar B \bar B}^{I=0}$. Hopefully the analytical chiral structures of the potentials may be useful in the extrapolation of the heavy meson interaction from lattice QCD simulation.