Heavy Quark Symmetry Research Articles

Pseudoscalar and vector open-charm mesons at finite temperature

Vacuum and thermal properties of pseudoscalar and vector charm mesons are analyzed within a self-consistent many-body approach, employing a chiral effective field theory that incorporates heavy-quark spin symmetry. Upon unitarization of the vacuum interaction amplitudes for the scattering of charm mesons off light mesons in a fully coupled-channel basis, new dynamically generated states are searched. The imaginary-time formalism is employed to extend the calculation to finite temperatures up to $T=150$ MeV. Medium-modified spectral shapes of the $D$, $D^*$, $D_s$ and $D_s^*$ mesons are provided. The temperature dependence of the masses and decay widths of the nonstrange $D_0^*$ (2300) and $D_1^*$(2430) mesons, both showing a double-pole structure in the complex-energy plane, is also reported, as well as that of the $D_{s0}^*$(2317) and $D_{s1}^*$(2460) resonances and other states not yet identified experimentally. Being the first calculation incorporating open-charm vector mesons at finite temperature in a self-consistent fashion, it brings up the opportunity to discuss the medium effects on the open charm sector under the perspective of chiral and heavy-quark spin symmetries.

X0(2866) as a D*K¯* molecular state

Very recently the LHCb Collaboration reported the discovery of two open charm tetraquark states, $X_{0}(2866)$ and $X_{1}(2904)$. In the present work, we study the $D^{(\ast)}$ and $\bar{K}^{(\ast)}$ interaction in the one-boson exchange model and show that the $X_{0}(2866)$ can be understood as a $D^{\ast}\bar{K}^{\ast}$ molecule with $I(J^{P})=0(0^{+})$, or at least it has a large molecular component. On the other hand, the $X_{1}(2904)$ can not be interpreted as a molecular state. Inspired by the discovery of the $X_0(2866)$ and the fact that the $D^*\bar{K}^*$ interaction is strong enough to generate a bound state, we also discuss likely existence of other open charm molecules. In the meson-meson sector, two molecules near the mass thresholds of $DD^{\ast}$ and $D^{\ast}D^{\ast}$ with $I(J^{P})=0(1^{+})$ are obtained, and using the heavy quark flavor symmetry their $\bar{B}\bar{B}^{\ast}$ and $\bar{B}^{\ast}\bar{B}^{\ast}$ counterparts are also predicted. In the meson-baryon sector, 7 open charm molecules with $I=1/2$ near the mass thresholds of $D^{(\ast)}\Sigma_{c}^{(\ast)}$ naturally appear, as dictated by the heavy quark spin symmetry.

Open charm and bottom tetraquarks in an extended relativized quark model

In present work, we systematically calculate the mass spectra of open charm and bottom tetraquarks $q q\bar q \bar Q$ within an extended relativized quark model. The four-body relativized Hamiltonians including the Coulomb potential, confining potential, spin-spin interactions, and relativistic corrections are solved by using the variational method. It is found that the predicted masses of four $0^+$ $ud\bar s \bar c$ states are 2765, 3065, 3152, and 3396 MeV, which disfavor the assignment of the newly observed $X_0(2900)$ as a compact tetraquark. Moreover, the whole mass spectra of the open charm and bottom tetraquarks show quite similar patterns, which preserve the light flavor SU(3) symmetry and heavy quark symmetry well. In addition, our results suggest that the flavor exotic states $nn\bar s \bar c$, $nn\bar s \bar b$, $ss\bar n \bar c$, and $ss\bar n \bar b$ and their antiparticles can be searched in the heavy-light meson plus kaon final states by future experiments. More theoretical and experimental efforts are needed to investigate these singly heavy tetraquarks.

First branching fraction measurement of the suppressed decay Ξc0→π−Λc+

The $\Xi_c^0$ baryon is unstable and usually decays into charmless final states by the $c \to s u\overline{d}$ transition. It can, however, also disintegrate into a $\pi^-$ meson and a $\Lambda_c^+$ baryon via $s$ quark decay or via $cs\to d c$ weak scattering. The interplay between the latter two processes governs the size of the branching fraction ${\cal{B}}$$(\Xi_c^0\to \pi^-\Lambda_c^+)$, first measured here to be $(0.55\pm 0.02 \pm 0.18)$%, where the first uncertainty is statistical and second systematic. This result is compatible with the larger of the theoretical predictions that connect models of hyperon decays using partially conserved axial currents and SU(3) symmetry with those involving the heavy-quark expansion and heavy-quark symmetry. In addition, the branching fraction of the normalization channel, ${\cal{B}}(\Xi_c^+\to p K^- \pi^+) = (1.135 \pm 0.002 \pm 0.387)$% is measured.

Quadruply charmed dibaryons as heavy quark symmetry partners of the DDK bound state

Both unitary chiral theories and lattice QCD simulations show that the DK interaction is attractive and can form a bound state, namely, D^*_{s0}(2317). Assuming the validity of the heavy antiquark–diquark symmetry, the Xi _{cc}{bar{K}} interaction is the same as the DK interaction, which implies the existence of a Xi _{cc}{bar{K}} bound state with a binding energy of 49-64 MeV. In this work, we study whether a Xi _{cc}Xi _{cc}{bar{K}} three-body system binds. The Xi _{cc}Xi _{cc} interaction is described by exchanging pi , sigma , rho , and omega mesons, with the corresponding couplings related to those of the NN interaction via the quark model. We indeed find a Xi _{cc}Xi _{cc}{bar{K}} bound state, with quantum numbers J^P=0^-, I=frac{1}{2}, S=1 and C=4, and a binding energy of 80–118 MeV. With the same formalism, we find that the Xi _{cc}bar{Xi }_{cc}{bar{K}} system also binds, yielding a I(J^P)=frac{1}{2}(0^+) state and a frac{1}{2}(1^+) state with binding energies of 56–68 MeV and 56–67 MeV respectively. As a byproduct, we show the existence of a NN{bar{K}} state with a binding energy of 35–43 MeV, consistent with the results of other theoretical works and experimental data, which serves as a consistency check on the predicted Xi _{cc}Xi _{cc}{bar{K}} bound state.

From triply charmed dibaryons to pentaquark states: A model-independent way to determine the spins of the Pc(4440) and Pc(4457)

The LHCb collaboration has recently observed three narrow pentaquark states --- the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ ---that are located close to the $\bar{D} \Sigma_c$ and $\bar{D}^* \Sigma_c$ thresholds. Among the so-far proposed theoretical interpretations for these pentaquarks, the molecular hypothesis seems to be the preferred one. Nevertheless, in the molecular picture the spins of the $P_c(4440)$ and $P_c(4457)$ have not been unambiguously determined yet. In this letter we point out that heavy antiquark-diquark symmetry induces a model-independent relation between the spin-splitting in the masses of the $P_c(4440)$ and $P_c(4457)$ $\bar{D}^* \Sigma_c$ pentaquarks and the corresponding splitting for the $0^+$ and $1^+$ $\Xi_{cc} \Sigma_c$ triply charmed dibaryons. This is particularly relevant owing to a recent lattice QCD prediction of the $1^+$ triply charmed dibaryon, which suggests that a calculation of the mass of its $0^+$ partner might be within reach. This in turn would reveal the spins of the $P_c(4440)$ and $P_c(4457)$ pentaquarks, providing a highly nontrivial test of heavy-quark symmetry and the molecular nature of the pentaquarks. Furthermore, the molecular interpretation of the hidden-charm pentaquarks implies the existence of a total of ten triply charmed dibaryons as $\Xi_{cc}^{(*)} \Sigma_c^{(*)}$ molecules, which, if confirmed in the lattice, will largely expand our understanding of the non-perturbative strong interaction in the heavy-quark sector.

Nonrelativistic effective field theory for heavy exotic hadrons

We propose an effective field theory to describe hadrons with two heavy quarks without any assumption on the typical distance between the heavy quarks with respect to the typical hadronic scale. The construction is based on Non-Relativistic QCD and inspired in the strong coupling regime of Potential Non-Relativistic QCD. We construct the effective theory at leading and next-to-leading order in the inverse heavy-quark mass expansion for arbitrary quantum numbers of the light degrees of freedom. Hence our results hold for hybrids, tetraquarks, double heavy baryons and pentaquarks, for which we also present the corresponding operators at Non-Relativistic level. At leading order, the effective theory enjoys heavy quark spin symmetry and corresponds to the Born-Oppenheimer approximation. At next-to-leading order, spin and velocity dependent terms arise, which produce splittings in the heavy-quark spin symmetry multiplets. A concrete application to double heavy baryons is presented in an accompanying paper.

Heavy baryons in holographic QCD with higher dimensional degrees of freedom

We try to introduce heavy flavors to Sakai-Sugimoto model by regarding higher dimensional components of gauge fields as heavy mesons. Using the Forg\'acs and Manton approach, we obtain a theory composed of heavy mesons and the instanton of light flavors. Applying the collective coordinate quantization method, we derived a mass formula of heavy baryons. In the leading order of $1/m_{H}$ expansion ($m_{H}$ the mass of a heavy quark), we find singlet and doublet states in the heavy quark symmetry (HQS). Also, we obtain the degenerate Roper like and odd parity excitations. By virtue of heavy meson degrees of freedom, our mass formula reproduces the mass ordering of $\Sigma^*_c$ and $\Lambda_c^*$ correctly.

Spectra and decay constants of Bc-like and [formula omitted] mesons in QCD

Using the existing state of art of the QCD expressions of the two-point correlators into the Inverse Laplace sum rules (LSR) within stability criteria, we present a first analysis of the spectra and decay constants of Bc-like scalar (0++) and axial-vector (1++) mesons and revisit the ones of the Bc⁎(1−−) vector meson. Improved predictions are obtained by combining these LSR results with some mass-splittings from Heavy Quark Symmetry (HQS). We complete the analysis by revisiting the B0⁎(0++) mass which might be likely identified with the BJ⁎(5732) experimental candidate. The results for the spectra collected in Table 2 are compared with some recent lattice and potential models ones. New estimates of the decay constants are given in Table 3.

Pc pentaquarks with chiral tensor and quark dynamics

We investigate the hidden-charm pentaquarks as superpositions of $\Lambda_c \bar{D}^{(*)}$ and $\Sigma_c^{(*)} \bar{D}^{(*)}$ (isospin $I = 1/2$) meson-baryon channels coupled to a $uudc\bar{c}$ compact core by employing an interaction satisfying the heavy quark and chiral symmetries. Our model can consistently explain the masses and decay widths of $P_c^+(4312)$, $P_c^+(4440)$ and $P_c^+(4457)$ with the dominant components of $\Sigma_c \bar D$ and $\Sigma_c \bar D^\ast$ with spin parity assignments $J^P = 1/2^{-}, 3/2^{-}$ and $1/2^{-}$, respectively. We analyze basic properties of the $P_c$'s such as masses and decay widths, and find that the mass ordering is dominantly determined by the quark dynamics while the decay widths by the tensor force of the one-pion exchange.

Impact of a thermal medium on D mesons and their chiral partners

We study D and Ds mesons at finite temperature using an effective field theory based on chiral and heavy-quark spin-flavor symmetries within the imaginary-time formalism. Interactions with the light degrees of freedom are unitarized via a Bethe-Salpeter approach, and the D and Ds self-energies are calculated self-consistently. We generate dynamically the D0⁎(2300) and Ds(2317) states, and study their possible identification as the chiral partners of the D and Ds ground states, respectively. We show the evolution of their masses and decay widths as functions of temperature, and provide an analysis of the chiral-symmetry restoration in the heavy-flavor sector below the transition temperature. In particular, we analyse the very special case of the D-meson, for which the chiral partner is associated to the double-pole structure of the D0⁎(2300).

Recently observed Pc as molecular states and possible mixture of Pc(4457)

Recently observed spectrum of $P_c$ states exhibits a strong link to $\Sigma_c \bar{D}^{(*)}$ thresholds. In spite of successful molecular interpretations, we still push forward to wonder whether there exist finer structures. Utilizing the effecitve lagrangians respecting heavy quark symmetry and chiral symmetry, as well as instantaneous Bethe-Salpeter equations, we investigate the $\Sigma_c \bar{D}^{(*)}$ interactions and three $P_c$ states. We confirm that $P_c(4312)$ and $P_c(4440)$ are good candidates of $\Sigma_c \bar{D}$ and $\Sigma_c \bar{D}^{*}$ molecules with spin-$\frac12$, respectively. Unlike other molecular calculations, our results indicate $P_c(4457)$ signal might be a mixture of spin-$\frac32$ and spin-$\frac12$ $\Sigma_c \bar{D}^{*}$ molecules, where the latter one appears to be an excitation of $P_c(4440)$. Therefore we conclude that, confronting three LHCb $P_c$ signals, there may exist not three, but four molecular states.

Y(4626) as a molecular state from interaction {D}^*_s{bar{D}}_{s1}(2536)-{D}_s{bar{D}}_{s1}(2536)

Recently, a new structure Y(4626) was reported by the Belle Collaboration in the process e^+e^-rightarrow D_s^+D_{s1}(2536)^-. In this work, we propose an assignment of the Y(4626) as a {D}^*_s{bar{D}}_{s1}(2536) molecular state, which decays into the D_s^+D_{s1}(2536)^- channel through a coupling between {D}^*_s{bar{D}}_{s1}(2536) and {D}_s{bar{D}}_{s1}(2536) channels. With the help of the heavy quark symmetry, the potential of the interaction {D}^*_s{bar{D}}_{s1}(2536)-{D}_s{bar{D}}_{s1}(2536) is constructed within the one-boson-exchange model, and inserted into the quasipotential Bethe–Salpeter equation. The pole of obtained scattering amplitude is searched for in the complex-energy plane, which corresponds to a molecular state from the interaction {D}^*_s{bar{D}}_{s1}(2536)-{D}_s{bar{D}}_{s1}(2536). The results suggest that a pole is produced near the {D}^*_s{bar{D}}_{s1}(2536) threshold, which exhibits as a peak in the invariant mass spectrum of the {D}_s{bar{D}}_{s1}(2536) channel at about 4626 MeV. It obviously favors the Y(4626) as a {D}^*_s{bar{D}}_{s1}(2536) molecular state. In the same model, other molecular states from the interaction {D}^*_s{bar{D}}_{s1}(2536)-{D}_s{bar{D}}_{s1}(2536) are also predicted, which can be checked in future experiments.

Properties of heavy mesons at finite temperature

We study the properties of heavy mesons using a unitarized approach in a hot pionic medium, based on an effective hadronic theory. The interaction between the heavy mesons and pseudoscalar Goldstone bosons is described by a chiral Lagrangian at next-to-leading order in the chiral expansion and leading order in the heavy-quark mass expansion so as to satisfy heavy-quark spin symmetry. The meson-meson scattering problem in coupled channels with finite-temperature corrections is solved in a self-consistent manner. Our results show that the masses of the ground-state charmed mesons D(0^-)D(0−) and D_s(1^-)Ds(1−) decrease in a pionic environment at T\neq 0T≠0 and they acquire a substantial width. As a consequence, the behaviour of excited mesonic states (D_{s0}^*(2317)^\pmDs0*(2317)± and D_0^*(2300)^{0,\pm}D0*(2300)0,±), generated dynamically in our heavy-light molecular model, is also modified at T\neq 0T≠0. The aim is to test our results against Lattice QCD calculations in the future.

Precision model-independent bounds from a global analysis of b→cℓν form factors

We present a model-independent global analysis of hadronic form factors for the semileptonic decays $b\rightarrow c\ell\nu$ that exploits lattice-QCD data, dispersion relations, and heavy-quark symmetries. The analysis yields predictions for the relevant form factors, within quantifiable bounds. These form factors are used to compute the semileptonic ratios $R(H_c)$ and various decay-product polarizations. In particular, we find $R(D_s^*)=0.20(3)$ and $R(J/\psi)=0.25(3)$, predictions that can be compared to results of upcoming LHCb measurements. In developing this treatment, we obtain leading-order NRQCD results for the nonzero-recoil relations between the $B_c^+ \rightarrow \{J/\psi , \eta_c \}$ form factors.

Hidden-charm and hidden-bottom molecular pentaquarks in chiral effective field theory

The newly observed Pc(4312), Pc(4440) and Pc(4457) at the LHCb experiment are very close to the {varSigma}_coverline{D} and {varSigma}_c{overline{D}}^{ast } thresholds. In this work, we perform a systematic study and give a complete picture on the interactions between the {varSigma}_c^{left(ast right)} and {overline{D}}^{left(ast right)} systems in the framework of heavy hadron chiral effective field theory, where the short-range contact interaction, long-range one-pion-exchange contribution, and intermediate-range two-pion-exchange loop diagrams are all considered. We first investigate the three Pc states without and with considering the Λc contribution in the loop diagrams. It is difficult to simultaneously reproduce the three Pcs unless the Λc is included. The coupling between the {varSigma}_c^{left(ast right)}{overline{D}}^{left(ast right)} and {Lambda}_c{overline{D}}^{left(ast right)} channels is crucial for the formation of these Pcs. Our calculation supports the Pc(4312), Pc(4440) and Pc(4457) to be the S-wave hidden-charm {left[{varSigma}_coverline{D}right]}_{J=1/2}^{I=1/2},{left[{varSigma}_c{overline{D}}^{ast}right]}_{J=1/2}^{I=1/2} and {left[{varSigma}_c{overline{D}}^{ast}right]}_{J=3/2}^{I=1/2} molecular pentaquarks, respectively. Our calculation disfavors the spin assignment {J}^P=frac{1^{-}}{2} for Pc(4457) and {J}^P=frac{3^{-}}{2} for Pc(4440), because the excessively enhanced spin-spin interaction is unreasonable in the present case. We obtain the complete mass spectra of the {left[{varSigma}_c^{left(ast right)}{overline{D}}^{left(ast right)}right]}_J systems with the fixed low energy constants. Our result indicates the existence of the {left[{varSigma}_c^{ast }{overline{D}}^{ast}right]}_Jleft(J=frac{1}{2},frac{3}{2},frac{5}{2}right) hadronic molecules. The previously reported Pc(4380) might be a deeper bound one. Additionally, we also study the hidden-bottom {varSigma}_b^{left(ast right)}{B}^{left(ast right)} systems, and predict seven bound molecular states, which could serve as a guidance for future experiments. Furthermore, we also examine the heavy quark symmetry breaking effect in the hidden-charm and hidden-bottom systems by taking into account the mass splittings in the propagators of the intermediate states. As expected, the heavy quark symmetry in the bottom cases is better than that in the charmed sectors. We notice that the heavy quark symmetry in the {varSigma}_coverline{D} and {varSigma}_c^{ast}overline{D} systems is much worse for some fortuitous reasons. The heavy quark symmetry breaking effect is nonnegligible in predicting the effective potentials between the charmed hadrons.

Molecular states from varSigma ^{(*)}_c{bar{D}}^{(*)}-varLambda _c{bar{D}}^{(*)} interaction

In this work, we systemically investigate the molecular states from the varSigma ^{(*)}_c{bar{D}}^{(*)}-varLambda _c{bar{D}}^{(*)} interaction with the help of the Lagrangians with heavy quark and chiral symmetries in a quasipotential Bethe–Salpeter equation (qBSE) approach. The molecular states are produced from isodoublet (I=1/2) varSigma _c{bar{D}} interaction with spin parity J^P=1/2^- and varSigma _c{bar{D}}^* interaction with 1/2^- and 3/2^-. Their masses and widths are consistent with the P_c(4312), P_c(4440) and P_c(4457) observed at LHCb. The states, varSigma _c^*{bar{D}}^*(1/2^-), varSigma _c^*{bar{D}}^*(3/2^-) and varSigma ^*_c{bar{D}}(3/2^-), are also produced with the same parameters. The isodoublet varSigma _c^*{bar{D}}^* interaction with 5/2^-, as well as the isoquartet (I=3/2) varSigma _c{bar{D}}^* interactions with 1/2^- and 3/2^-, varSigma _c^*{bar{D}}^* interaction with 3/2^- and 5/2^-, are also attractive while very large cutoff is required to produce a molecular state. We also investigate the origin of the widths of these molecular states in the same qBSE frame. The varLambda {bar{D}}^* channel is dominant in the decays of the states, varSigma _c{bar{D}}^*(1/2^-), varSigma _c{bar{D}}^*(3/2^-), varSigma _c^*{bar{D}}(3/2^-), and varSigma _c{bar{D}}(1/2^-). The varSigma ^*_c{bar{D}}^*(1/2^-) state has large coupling to varSigma _c{bar{D}} channel while the varSigma _c{bar{D}}^*, varSigma ^*_c{bar{D}} and varLambda _c{bar{D}}^* channels provide similar contributions to the width of the varSigma ^*_c{bar{D}}^*(3/2^-) state. These results will be helpful to understand the current LHCb experimental results, and the three predicted states and the decay pattern of these hidden-charmed molecular pentaquarks can be checked in future experiments.

Spin-isospin Kondo effects for Σc and Σc* baryons and D¯ and D¯* mesons

We study the Kondo effect for a $\Sigma_{c}$ ($\Sigma_{c}^{\ast}$) baryon in nuclear matter. In terms of the spin and isospin ($\mathrm{SU}(2)_{\mathrm{spin}} \times \mathrm{SU}(2)_{\mathrm{isospin}}$) symmetry, the heavy-quark spin symmetry and the S-wave interaction, we provide the general form of the Lagrangian for a $\Sigma_{c}$ ($\Sigma_{c}^{\ast}$) baryon and a nucleon. We analyze the renormalization equation at the one-loop level, and find that the coexistence of spin exchange and isospin exchange magnifies the Kondo effect in comparison with the case where the spin-exchange interaction and the isospin-exchange interaction exist separately. We demonstrate that the solution exists for the ideal sets of the coupling constants, including the $\mathrm{SU}(4)$ symmetry as an extension of the $\mathrm{SU}(2)_{\mathrm{spin}} \times \mathrm{SU}(2)_{\mathrm{isospin}}$ symmetry. We also conduct a similar analysis for the Kondo effect of a $\bar{D}$ ($\bar{D}^{\ast}$) meson in nuclear matter. On the basis of the obtained result, we conjecture that there could exist a "mapping" from the heavy meson (baryon) in vacuum onto the heavy baryon (meson) in nuclear matter.

Mass spectrum of the hidden-charm pentaquarks in the compact diquark model

The LHCb collaboration have recently updated their analysis of the resonant J/ \U0001d713 p mass spectrum in the decay {varLambda}_b^0 → J/\U0001d713 p K−, making use of their combined Run 1 and Run 2 data. In the updated analysis, three narrow states, Pc (4312)+, Pc (4440)+, and Pc (4457)+, are observed. The spin-parity assignments of these states are not yet known. We interpret these narrow resonances as compact hidden-charm diquark-diquark- antiquark pentaquarks. Using an effective Hamiltonian, based on constituent quarks and diquarks, we calculate the pentaquark mass spectrum for the complete SU (3) F lowest S- and P -wave multiplets, taking into account dominant spin-spin, spin-orbit, orbital and tensor interactions. The resulting spectrum is very rich and we work out the quark flavor compositions, masses, and JP quantum numbers of the pentaquarks. However, heavy quark symmetry restricts the observable states in Λb-baryon, as well as in the decays of the other weakly-decaying b-baryons, Ξb and Ωb. In addition, some of the pentaquark states are estimated to lie below the J/ \U0001d713 p threshold in Λb-decays (and corresponding thresholds in Ξb- and Ωb-decays). They decay via c overline{c} annihilation into light hadrons or a dilepton pair, and are expected to be narrower than the Pc-states observed. We anticipate their discovery, as well as of the other pentaquark states present in the spectrum at the LHC, and in the long-term future at a Tera-Z factory.

DK , DDK , and DDDK molecules–understanding the nature of the Ds0*(2317)

The $DK$ interaction is strong enough to form a bound state, the $D_{s0}^*(2317)$. This in turn begs the question of whether there are bound states composed of several charmed mesons and a kaon. Previous calculations indicate that the three-body $DDK$ system is probably bound, where the quantum numbers are $J^P = 0^{-}$, $I=\tfrac{1}{2}$, $S = 1$ and $C = 2$. The minimum quark content of this state is $cc\bar{q}\bar{s}$ with $q=u,d$, which means that, if discovered, it will be an explicitly exotic tetraquark. In the present work. we apply the Gaussian Expansion Method to study the $DDDK$ system and show that it binds as well. The existence of these three and four body states is rather robust with respect to the $DD$ interaction and subleading (chiral) corrections to the $DK$ interaction. If these states exist, it is quite likely that their heavy quark symmetry counterparts exist as well. These three-body $DDK$ and four-body $DDDK$ molecular states could be viewed as counterparts of atomic nuclei, which are clusters of nucleons bound by the residual strong force, or chemical molecules, which are clusters of atoms bound by the residual electromagnetic interaction.