Heavy Quark Spin Symmetry Research Articles

Decays of Pc into J/ψN and ηcN with heavy quark spin symmetry

We investigate the consequences of heavy quark spin symmetry (HQSS) on hidden-charm pentaquark $P_c$ states. As has been proposed before, assuming the $P_c(4440)$ and the $P_c(4457)$ as $S$-wave $\bar{D}^*\Sigma_c$ molecules, seven hadronic molecular states composed of $\bar{D}\Sigma_c$, $\bar{D}\Sigma_c^*$, $\bar{D}^*\Sigma_c$, and $\bar{D}^*\Sigma_c^*$ can be obtained, with the $\bar{D}\Sigma_c$ molecule corresponding to the $P_c(4312)$. These seven states can decay into $J/\psi N$ and $\eta_c N$, and we use HQSS to predict ratios of partial widths of the $S$-wave decays. For the decays into $J/\psi N$, it is found that among all six $P_c$ molecules with spin $1/2$ or $3/2$, at least four states decay much more easily into the $J/\psi N$ than the $P_c(4312)$, and two of them couple dominantly to the $\bar D^*\Sigma_c^*$. While no significant peak around the $\bar{D}^*\Sigma_c^*$ threshold is found in the $J/\psi p$ distribution, these higher $P_c$ states either are produced with lower rates or some special production mechanism for the observed $P_c$ states might play an important role, such as an intricate interplay between the production of pentaquarks and triangle singularities.

Strong decays of the latest LHCb pentaquark candidates in hadronic molecule pictures

We investigate the observed pentaquark candidates $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ from the latest LHCb measurement, as well as four possible spin partners in the $\bar{D}^{(*)}\Sigma_c^*$ system predicted from the heavy quark spin symmetry with the hadronic molecule scenarios. Similar to the previous calculation on $P_c(4380)$ and $P_c(4450)$, the partial widths of all the allowed decay channels for these $P_c$ states are estimated with the effective Lagrangian method. The cutoff dependence of our numerical results are also presented. Comparing with the experimental widths, our results show that $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ can be described well with the spin-parity-$1/2^-$-$\bar{D}\Sigma_c$, $1/2^-$-$\bar{D}^*\Sigma_c$ and $3/2^-$-$\bar{D}^*\Sigma_c$ molecule pictures, respectively.

Some decay properties of hidden-charm pentaquarks as baryon-meson molecules

It is pointed out that the previously suggested interpretation of the hidden-charm pentaquarks $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ as molecular bound states of $\Sigma_c \bar D$ and $\Sigma_c \bar D^*$ baryon-meson pairs gives rise to specific relations for their decays. In particular, the heavy quark spin symmetry predicts ratios of rates of decays of each of the molecules to $J/\psi p$ and to $\eta_c p$ as well as of the decays to $\Lambda_c \bar D$ and to $\Lambda_c \bar D^*$. Experimental studies of these relations would thus provide an indicative probe of the molecular structure.

Hidden charm pentaquark states and ΣcD¯(*) interaction in chiral perturbation theory

In this work, we employ the heavy hadron chiral perturbation theory (HHChPT) to calculate the $\Sigma_c\bar{D}^{(*)}$ potentials to the next-to-leading order. The contact, the one-pion exchange and the two-pion exchange interactions are included. Besides, the mass splittings between the heavy quark spin symmetry (HQSS) multiplets are kept in calculations. Our result shows that neglecting the heavy quark symmetry (HQS) violation effect may be misleading to predict the potentials between the charmed hadrons. We perform numerical analysis with three scenarios. In the first scenario, we relate the low-energy constants (LECs) in the contact terms of $\Sigma_c\bar{D}^{(*)}$ to those of nucleon systems, and reproduce the $P_c(4312)$ and $P_c(4440)$ as loosely bound states. In the second scenario, we vary the unknown LECs and find a small parameter region in which $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ can coexist as molecular states. In the third scenario, we include the coupled-channel effect on the basis of scenario II, and notice that the three $P_c$ states can be reproduced as molecular states simultaneously in a large region of parameters. Our analytical results can be used for the chiral extrapolations in lattice QCD. With the lattice QCD results in the future as inputs, the identification of the $P_c$ states and predictions for other systems would be more reliable.

Heavy quark spin symmetric molecular states from D¯(*)Σc(*) and other coupled channels in the light of the recent LHCb pentaquarks

We consider the ${\bar D}^{(*)}\Sigma_c^{(*)}$ states, together with $J/\psi N$ and other coupled channels, and take an interaction consistent with heavy quark spin symmetry, with the dynamical input obtained from an extension of the local hidden gauge approach. By fitting only one parameter to the recent three pentaquark states reported by the LHCb collaboration, we can reproduce the three of them in base to the mass and the width, providing for them the quantum numbers and approximate molecular structure as $1/2^-$ $\bar{D} \Sigma_c$, $1/2^-$ $\bar{D}^* \Sigma_c$, and $3/2^-$ $\bar{D}^* \Sigma_c$, and isospin $I=1/2$. We find another state around 4374 MeV, of $3/2^-$ $\bar{D} \Sigma_c^*$ structure, for which indications appear in the experimental spectrum. Two other near degenerate states of $1/2^-$ $\bar{D}^* \Sigma_c^*$ and $3/2^-$ $\bar{D}^* \Sigma_c^*$ nature are also found around 4520 MeV, which although less clear, are not incompatible with the observed spectrum. In addition, a $5/2^-$ $\bar D^* \Sigma_c^*$ state at the same energy appears, which however does not couple to $J/\psi p$ in $S-$wave, and hence it is not expected to show up in the LHCb experiment.

Emergence of a Complete Heavy-Quark Spin Symmetry Multiplet: Seven Molecular Pentaquarks in Light of the Latest LHCb Analysis.

A recent analysis by the LHCb Collaboration suggests the existence of three narrow pentaquarklike states-the P_{c}(4312), P_{c}(4440), and P_{c}(4457)-instead of just one in the previous analysis [the P_{c}(4450)]. The closeness of the P_{c}(4312) to the D[over ¯]Σ_{c} threshold and the P_{c}(4440) and P_{c}(4457) to the D[over ¯]^{*}Σ_{c} threshold suggests a molecular interpretation of these resonances. We show that these three pentaquarklike resonances can be naturally accommodated in a contact-range effective field theory description that incorporates heavy-quark spin symmetry. This description leads to the prediction of all the seven possible S-wave heavy antimeson-baryon molecules [that is, there should be four additional molecular pentaquarks in addition to the P_{c}(4312), P_{c}(4440), and P_{c}(4457)], providing the first example of a heavy-quark spin symmetry molecular multiplet that is complete. If this is confirmed, it will not only give us an impressive example of the application of heavy-quark symmetries and effective field theories in hadron physics, it will also uncover a clear and powerful ordering principle for the molecular spectrum, reminiscent of the SU(3)-flavor multiplets to which the light hadron spectrum conforms.

Heavy-quark spin and flavor symmetry partners of the X(3872) revisited: What can we learn from the one boson exchange model?

Heavy-quark symmetry as applied to heavy hadron systems implies that their interactions are independent of their heavy-quark spin (heavy-quark spin symmetry) and heavy flavour contents (heavy flavour symmetry). In the molecular hypothesis the $X(3872)$ resonance is a $1^{++}$ $D^*\bar{D}$ bound state. If this is the case, the application of heavy-quark symmetry to a molecular $X(3872)$ suggests the existence of a series of partner states, the most obvious of which is a possible $2^{++}$ $D^*\bar{D}^*$ bound state for which the two-body potential is identical to that of the $1^{++}$ $D^*\bar{D}$ system, the reason being that these two heavy hadron-antihadron states have identical light-spin content. As already discussed in the literature this leads to the prediction of a partner state at $4012\,{\rm MeV}$, at least in the absence of other dynamical effects which might affect the location of this molecule. However the prediction of further heavy-quark symmetry partners cannot be done solely on the basis of symmetry and requires additional information. We propose to use the one boson exchange model to fill this gap, in which case we will be able to predict or discard the existence of other partner states. Besides the isoscalar $2^{++}$ $D^*\bar{D}^*$ bound state, we correctly reproduce the location and quantum numbers of the isovector hidden-bottom $Z_b(10610)$ and $Z_b(10650)$ molecular candidates. We also predict the hidden-bottom $1^{++}$ $B^*\bar{B}^*$ and $2^{++}$ $B^*\bar{B}^*$ partners of the $X(3872)$, in agreement with previous theoretical speculations, plus a series of other states. The isoscalar, doubly charmed $1^+$ $D D^*$ and $D^* D^*$ molecules and their doubly bottomed counterparts are likely to bind, providing a few instances of explicitly exotic systems.

Lambda _b decays into Lambda _c^*ell bar{nu }_ell and Lambda _c^*pi ^-[Lambda _c^*=Lambda _c(2595) and Lambda _c(2625)] and heavy quark spin symmetry

We study the implications for Lambda _b rightarrow Lambda _c^*ell bar{nu }_ell and Lambda _b rightarrow Lambda _c^*pi ^-[Lambda _c^*=Lambda _c(2595) and Lambda _c(2625)] decays that can be deduced from heavy quark spin symmetry (HQSS). Identifying the odd parity Lambda _c(2595) and Lambda _c(2625) resonances as HQSS partners, with total angular momentum–parity j_q^P=1^- for the light degrees of freedom, we find that the ratios Gamma (Lambda _brightarrow Lambda _c(2595)pi ^-)/Gamma (Lambda _brightarrow Lambda _c(2625)pi ^-) and Gamma (Lambda _brightarrow Lambda _c(2595) ell bar{nu }_ell )/ Gamma (Lambda _brightarrow Lambda _c(2625) ell bar{nu }_ell ) agree, within errors, with the experimental values given in the Review of Particle Physics. We discuss how future, and more precise, measurements of the above branching fractions could be used to shed light into the inner HQSS structure of the narrow Lambda _c(2595) odd-parity resonance. Namely, we show that such studies would constrain the existence of a sizable j^P_q=0^- component in its wave-function, and/or of a two-pole pattern, in analogy to the case of the similar Lambda (1405) resonance in the strange sector, as suggested by most of the approaches that describe the Lambda _c(2595) as a hadron molecule. We also investigate the lepton flavor universality ratios R[Lambda _c^*] = mathcal{B}(Lambda _b rightarrow Lambda _c^* tau ,bar{nu }_tau )/mathcal{B}(Lambda _b rightarrow Lambda _c^* mu ,bar{nu }_mu ), and discuss how R[Lambda _c(2595)] may be affected by a new source of potentially large systematic errors if there are two Lambda _c(2595) poles.

Heavy baryon-antibaryon molecules in effective field theory

We discuss the effective field theory description of bound states composed of a heavy baryon and antibaryon. This framework is a variation of the ones already developed for heavy meson-antimeson states to describe the $X(3872)$ or the $Z_c$ and $Z_b$ resonances. We consider the case of heavy baryons for which the light quark pair is in S-wave and we explore how heavy quark spin symmetry constrains the heavy baryon-antibaryon potential. The one pion exchange potential mediates the low energy dynamics of this system. We determine the relative importance of pion exchanges, in particular the tensor force. We find that in general pion exchanges are probably non-perturbative for the $\Sigma_Q \bar{\Sigma}_Q$, $\Sigma_Q^* \bar{\Sigma}_Q$ and $\Sigma_Q^* \bar{\Sigma}_Q^*$ systems, while for the $\Xi_Q' \bar{\Xi}_Q'$, $\Xi_Q^* \bar{\Xi}_Q'$ and $\Xi_Q^* \bar{\Xi}_Q^*$ cases they are perturbative If we assume that the contact-range couplings of the effective field theory are saturated by the exchange of vector mesons, we can estimate for which quantum numbers it is more probable to find a heavy baryonium state. The most probable candidates to form bound states are the isoscalar $\Lambda_Q \bar{\Lambda}_Q$, $\Sigma_Q \bar{\Sigma}_Q$, $\Sigma_Q^* \bar{\Sigma}_Q$ and $\Sigma_Q^* \bar{\Sigma}_Q^*$ and the isovector $\Lambda_Q \bar{\Sigma}_Q$ and $\Lambda_Q \bar{\Sigma}_Q^*$ systems, both in the hidden-charm and hidden-bottom sectors. Their doubly-charmed and -bottom counterparts ($\Lambda_Q {\Lambda}_Q$, $\Lambda_Q {\Sigma}_Q^{(*)}$, $\Sigma_Q^{(*)} {\Sigma}_Q^{(*)}$) are also good candidates for binding.

Possible triple-charm molecular pentaquarks from ΞccD1/ΞccD2* interactions

In this work, we explore a systematic investigation on $S$-wave interactions between a doubly charmed baryon $\Xi_{cc}(3621)$ and a charmed meson in a $T$ doublet $(D_1,\,D_2^*)$. We first analyze the possibility for forming $\Xi_{cc}D_1/\Xi_{cc}D_2^*$ bound states with the heavy quark spin symmetry. Then, we further perform a dynamical study on the $\Xi_{cc}D_1/\Xi_{cc}D_2^*$ interactions within a one-boson-exchange model by considering both the $S$-$D$ wave mixing and coupled channel effect. Finally, our numerical results conform the proposals from the heavy quark spin symmetry analysis: the $\Xi_{cc}D_1$ systems with $I(J^P)=$ $0(1/2^+,\,3/2^+)$ and the $\Xi_{cc}D_2^*$ systems with $I(J^P)=$ $0(3/2^+,\,5/2^+)$ can possibly be loose triple-charm molecular pentaquarks. Meanwhile, we also extend our model to the $\Xi_{cc}\bar{D}_1$ and $\Xi_{cc}\bar D_2^*$ systems, and our results indicate the isoscalars of $\Xi_{cc}\bar{D}_1$ and $\Xi_{cc}\bar{D}_2^*$ can be possible molecular candidates.

Heavy-quark spin-symmetry partners of Zb(10610) and Zb(10650) molecules

Heavy-quark spin-symmetry (HQSS) partners of the isovector bottomonium like states Zb(10610) and Zb(10650) are predicted within the molecular picture. Treating both Zb’s as shallow bound states, we solve the system of coupled-channel integral equations for the contact plus one-pion exchange (OPE) potentials to predict the location of the partner states with the quantum numbers J++ (J = 0,1,2). In particular, we predict the existence of a narrow tensor 2++ state residing a few MeV below the B∗ B¯∗ threshold. It is emphasised that the tensor part of the OPE potential in combination with HQSS breaking due to the nonvanishing B∗ -B mass splitting has a significant impact on the location of this partner state.

Exotic molecular states in the decays of vector bottomonia

The most recent experimental data for the decays of the vector bottomonium γ(10860) proceeding through the formation of the states Zb(10610) and Zb(10650) are analysed simultaneously using solutions of the Lippmann-Schwinger equations which respect constraints from unitarity and analyticity. The interaction potential in the open-bottom channels $ {B^{(*)}}{\bar B^*} $ contains short-range interactions as well as the one-pion exchange; both types of the interaction are taken into account fully nonperturbatively. This way, all parameters of the interaction are fixed directly from the data and the pole positions for the Zb’s are determined as a prediction. In particular, both Zb states are found to be described by resonance poles located on the unphysical Riemann sheets in the vicinity of the corresponding thresholds. The heavy quark spin symmetry (HQSS) is employed to predict, in a parameter-free way, the pole positions and the line shapes in the elastic and inelastic channels for the Zbs’ spin partner states WbJ with the quantum numbers J++ (J = 0, 1, 2). Such spin partners can be produced in radiative decays of the vector bottomonium Υ(10860) and are expected to be detected in the Belle-II experiment.

Charmed dibaryon resonances in the potential quark model

Charmed dibaryon states with the spin-parity [Formula: see text], and [Formula: see text] are predicted for the two-body [Formula: see text] ([Formula: see text], [Formula: see text], or [Formula: see text]) systems. We employ the complex scaling method for the coupled channel Hamiltonian with the [Formula: see text]-CTNN potentials, which were proposed in our previous study. We find four sharp resonance states near the [Formula: see text] and [Formula: see text] thresholds. From the analysis of the binding energies of partial channel systems, we conclude that these resonance states are Feshbach resonances. We compare the results with the [Formula: see text] resonance states in the heavy quark limit, where the [Formula: see text] and [Formula: see text] thresholds are degenerate, and find that they form two pairs of the heavy-quark doublets in agreement with the heavy quark spin symmetry.

Remarks on the heavy-quark flavour symmetry for doubly heavy hadronic molecules

The possibility for a common effective field theory for hadronic molecules with different heavy-quark flavours is examined critically. It is argued that such a theory does not allow one to draw definite conclusions for doubly heavy molecules. In particular, it does not allow one to relate binding energies for the molecules in the c-quark and b-quark sectors with controlled uncertainties. Therefore, while this kind of reasoning does not preclude from employing heavy-quark spin symmetry for charmonium- and bottomonium-like states separately within a well established effective field theory framework, relations between different heavy-quark sectors can only be obtained using phenomenological approaches with uncontrolled uncertainties.

Heavy-quark symmetry partners of the Pc(4450) pentaquark

The spectrum of heavy-hadron molecules is constrained by heavy-quark symmetry in its different manifestations. Heavy-quark spin symmetry for instance connects the properties of the ground and excited states of heavy hadrons, while heavy-antiquark-diquark symmetry connects the properties of heavy antimesons ($\bar{D}$, $\bar{D}^*$) and doubly heavy baryons ($\Xi_{cc}$, $\Xi_{cc}^*$). A prediction of these symmetries is that if the $P_c(4450)$ is indeed a $\bar{D}^* \Sigma_c$ bound state, then there should be a series of $\bar{D}^* \Sigma_c^*$, $\Xi_{cc} \Sigma_c$, $\Xi_{cc}^* \Sigma_c$, $\Xi_{cc} \Sigma_c^*$ and $\Xi_{cc}^* \Sigma_c^*$ partners. The concrete application of heavy-quark spin symmetry indicates that, if the $P_c(4450)$ is a $\frac{3}{2}^{-}$ $\bar{D}^* \Sigma_c$ molecule, the existence of a $\frac{5}{2}^{-}$ $\bar{D}^* \Sigma_c^*$ partner with similar binding energy --- which we call $P_c(4515)$, given its expected mass --- is likely. Conversely, the application of heavy-antiquark-diquark symmetry indicates that the $0^+$ $\Xi_{cc} \Sigma_c$, $1^+$ $\Xi_{cc} \Sigma_c^*$, $2^+$ $\Xi_{cc}^* \Sigma_c$ and $3^+$ $\Xi_{cc}^* \Sigma_c^*$ molecules are likely to bind too, with binding energies in the $20-30\,{\rm MeV}$ range.

Model-independent determination of Bc+→ηcℓ+ν form factors

We derive model-independent bounds on the form factors for the decay $B_c^+ \to \eta_c\, \ell^+\, \nu$ including full mass effects, i.e. $\ell = e,\, \mu, \text{ and } \tau$. The bounds are obtained by using the BGL parameterization for the form factors, and fitting to the preliminary lattice data of the HPQCD Collaboration. Our main result after bounding the form factors is the Standard Model (SM) prediction for the ratio of branching fractions $R(\eta_c) = \mathcal{B}(B_c^+ \to \eta_c\, \tau^+\, \nu_{\tau}) / \mathcal{B}(B_c^+ \to \eta_c\, \mu^+\, \nu_{\mu})$. We find $R(\eta_c)|_{\text{SM}} = 0.31^{+0.04}_{-0.02}$, and argue that a measurement of $R(\eta_c)$ is within the reach of LHCb during the high luminosity run of the LHC. In addition, using the heavy-quark spin symmetry of the $B_c$ meson we relate our results for $B_c^+ \to \eta_c\, \ell^+\, \nu$ to those for $B_c^+ \to J/\psi\, \ell^+\, \nu$ yielding the estimate $R(J/\psi)|_{\text{SM}} = 0.26 \pm 0.02$ in good agreement with other determinations.

X(3872) and its heavy quark spin symmetry partners in QCD sum rules

X(3872) presents many surprises after its discovery more than ten years ago. Understanding its properties is crucial to understand the spectrum of possible exotic mesons. In this work, X(3872) meson and its heavy quark spin symmetry (HQSS) partners (including the mesons in the bottom sector) are studied within the QCD Sum Rules approach using a current motivated by the molecular picture of X(3872). We predict four heavy partners to X(3872) and bottomonium with the masses and J^{PC} quantum numbers. Obtained results are in good agreement with the previous studies and available experimental data within errors.

Quark spin structures of bottom-charmed threshold molecular states

The implementation of the heavy quark spin symmetry in possible molecular states at the mixed bottom-charm threshold is somewhat different from that at the open charm or bottom thresholds. In particular it depends on two parameters describing separately the symmetry for the bottom and for charmed quarks. The corresponding spin structures of the $S$-wave molecular states of the meson pairs $B^{(*)} D^{(*)}$ are discussed as well as their consequences for properties of possible near-threshold resonances, analogs of the known charmonium-like and bottomonium-like $X$ and $Z$ states.

Resonance states in the YcN potential model

We calculate two-body $J^{\pi}=0^{+}, 1^{+}$, and $J^{\pi}=2^{+}$ resonance states of $Y_{c}$ ($= \Lambda_{c}$, $\Sigma_{c}$, or $\Sigma_{c}^{*}$) and $N$ using the complex scaling method. We employ the $Y_{c}N$-CTNN potentials, which were proposed in our previous study, and obtain four resonances near $\Sigma_{c}N$ and $\Sigma_{c}^{*}N$ thresholds. From the analysis by the binding energies of partial channel systems, we conclude that these resonance states are Feshbach resonances. We compare the results with the $Y_{c}N$ resonance states in the heavy quark limit, where the $\Sigma_{c}N$ and $\Sigma_{c}^{*}N$ thresholds are degenerate, and find that they form two pairs of the heavy-quark doublets in agreement with the heavy quark spin symmetry.

Contribution of constituent quark model cbar{s} states to the dynamics of the D_{s0}^*(2317) and D_{s1}(2460) resonances

The masses of the D^*_{s0}(2317) and D_{s1}(2460) resonances lie below the DK and D^*K thresholds respectively, which contradicts the predictions of naive quark models and points out to non-negligible effects of the D^{(*)}K loops in the dynamics of the even-parity scalar (J^pi =0^+) and axial-vector (J^pi =1^+) cbar{s} systems. Recent lattice QCD studies, incorporating the effects of the D^{(*)}K channels, analyzed these spin-parity sectors and correctly described the D^*_{s0}(2317)-D_{s1}(2460) mass splitting. Motivated by such works, we study the structure of the D_{s0}^*(2317) and D_{s1}(2460) resonances in the framework of an effective field theory consistent with heavy quark spin symmetry, and that incorporates the interplay between D^{(*)}K meson–meson degrees of freedom and bare P-wave cbar{s} states predicted by constituent quark models. We extend the scheme to finite volumes and fit the strength of the coupling between both types of degrees of freedom to the available lattice levels, which we successfully describe. We finally estimate the size of the D^{(*)}K two-meson components in the D^*_{s0}(2317) and D_{s1}(2460) resonances, and we conclude that these states have a predominantly hadronic-molecular structure, and that it should not be tried to accommodate these mesons within cbar{s} constituent quark model patterns.