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Register a new userStudy on possible molecular states composed of $Lambda_cbar D$ ($Lambda_b B$) and $Sigma_cbar D$ ($Sigma_b B$) within the Bethe-Salpeter framework
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$P_c(4312)$ observed by the LHCb collaboration is confirmed as a pentaquark and its structure, production, and decay behaviors attract great attention from theorists and experimentalists. Since its mass is very close to sum of $Sigma_c$ and $bar D$ masses, it is naturally tempted to be considered as a molecular state composed of $Sigma_c$ and $bar D$. Moreover, $P_c(4312)$ is observed in the channel with $J/psi p$ final state, requiring that isospin conservation $P_c(4312)$ is an isospin-1/2 eigenstate. In literature, several groups used various models to estimate its spectrum. We systematically study the pentaquarks within the framework of the Bethe-Salpeter equation; thus $P_c(4312)$ is an excellent target because of the available data. We calculate the spectrum of $P_c(4312)$ in terms of the Bethe-Salpter equations and further study its decay modes. Some predictions on other possible pentaquark states that can be tested in future experiments are made.
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Recently a vector charmonium-like state $Y(4626)$ was observed in the portal of $D^+_sD_{s1}(2536)^-$. It intrigues an active discussion on the structure of the resonance because it has obvious significance for gaining a better understanding on its hadronic structure with suitable inner constituents. It indeed concerns the general theoretical framework about possible structures of exotic states. Since the mass of $Y(4626)$ is slightly above the production threshold of $D^+_sbar D_{s1}(2536)^-$ whereas below that of $D^*_sbar D_{s1}(2536)$ with the same quark contents as that of $D^+_sbar D_{s1}(2536)^-$, it is natural to conjecture $Y(4626)$ to be a molecular state of $D^{*}_sbar D_{s1}(2536)$, as suggested in literature. Confirming or negating this allegation would shed light on the goal we concern. We calculate the mass spectrum of a system composed of a vector meson and an axial vector i.e. $D^*_sbar D_{s1}(2536)$ within the framework of the Bethe-Salpeter equations. Our numerical results show that the dimensionless parameter $lambda$ in the form factor which is phenomenologically introduced to every vertex, is far beyond the reasonable range for inducing an even very small binding energy $Delta E$. It implies that the $D^*_sbar D_{s1}(2536)$ system cannot exist in the nature as a hadronic molecule in this model, so that we may not think the resonance $Y(4626)$ to be a bound state of $D^*_sbar D_{s1}(2536)$, but something else, for example a tetraquark and etc.
In this work, we preform a systematic investigation about hidden heavy and doubly heavy molecular states from the $D^{(*)}bar{D}^{(*)}/B^{(*)}bar{B}^{(*)}$ and $D^{(*)}D^{(*)}/bar{B}^{(*)}bar{B}^{(*)}$ interactions in the quasipotential Bethe-Salpeter equation (qBSE) approach. With the help of the Lagrangians with heavy quark and chiral symmetries, interaction potentials are constructed within the one-boson-exchange model in which we include the $pi$, $eta$, $rho$, $omega$ and $sigma$ exchanges, as well as $J/psi$ or $Upsilon$ exchange. Possible bound states from the interactions considered are searched for as the pole of scattering amplitude. The results suggest that experimentally observed states, $Z_c(3900)$, $Z_c(4020)$, $Z_b(10610)$, and $Z_b(10650)$, can be related to the $Dbar{D}^{*}$, $D^*bar{D}^{*}$, $Bbar{B}^{*}$, and $B^*bar{B}^{*}$ interactions with quantum numbers $I^G(J^P)=1^+(1^{+})$, respectively. The $Dbar{D}^{*}$ interaction is also attractive enough to produce a pole with $0^+(0^+)$ which is related to the $X(3872)$. Within the same theoretical frame, the existence of $Dbar{D}$ and $Bbar{B}$ molecular states with $0(0^+)$ are predicted. The possible $D^*bar{D}^*$ molecular states with $0(0^+, 1^+, 2^+)$ and $1(0^+)$ and their bottom partners are also suggested by the calculation. In the doubly heavy sector, no bound state is produced from the $DD/bar{B}bar{B}$ interaction while a bound state is found with $0(1^+)$ from $DD^*/bar{B}bar{B}^*$ interaction. The $D^*D^*/bar{B}^*bar{B}^*$ interaction produces three molecular states with $0(1^+)$, $0(2^+)$ and $1(2^+)$.
The $DD^{*}$ potentials are studied within the framework of heavy meson chiral effective field theory. We have obtained the effective potentials of the $DD^{*}$ system up to $O(epsilon^2)$ at one loop level. In addition to the one-pion exchange contribution, the contact and two-pion exchange interactions are also investigated in detail. Furthermore, we have searched for the possible molecular states by solving Schrodinger equation with the potentials. We notice that the contact and two-pion exchange potentials are non-negligible numerically and important for the existence of a bound state. In our results, no bound state is founded in the $I=0$ channel within a wide range of cutoff parameter, while there exists a bound state in the $I=1$ channel as cutoff is near $m_rho$ in our approach.
We evaluate the s-wave interaction of pseudoscalar and vector mesons with both charm and beauty to investigate the possible existence of molecular $BD$, $B^*D$, $BD^*$, $B^*D^*$, $Bbar D$, $B^*bar D$, $Bbar D^*$ or $B^* bar D^*$ meson states. The scattering amplitude is obtained implementing unitarity starting from a tree level potential accounting for the dominant vector meson exchange. The diagrams are evaluated using suitable extensions to the heavy flavor sector of the hidden gauge symmetry Lagrangians involving vector and pseudoscalar mesons{, respecting heavy quark spin symmetry}. We obtain bound states at energies above 7 GeV for $BD$ ($J^P=0^+$), $B^*D$ ($1^+$), $BD^*$ ($1^+$) and $B^*D^*$ ($0^+$, $1^+$, $2^+$), all in isospin 0. For $Bbar D$ ($0^+$), $B^*bar D$ ($1^+$), $Bbar D^*$ ($1^+$) and $B^*bar D^*$ ($0^+$, $1^+$, $2^+$) we also find similar bound states in $I=0$, but much less bound, which would correspond to exotic meson states with $bar b$ and $bar c$ quarks, and for the $I=1$ we find a repulsive interaction. We also evaluate the scattering lengths in all cases, which can be tested in current investigations of lattice QCD.
With the advent of the LHC, we will be able to probe New Physics (NP) up to energy scales almost one order of magnitude larger than it has been possible with present accelerator facilities. While direct detection of new particles will be the main avenue to establish the presence of NP at the LHC, indirect searches will provide precious complementary information, since most probably it will not be possible to measure the full spectrum of new particles and their couplings through direct production. In particular, precision measurements and computations in the realm of flavour physics are expected to play a key role in constraining the unknown parameters of the Lagrangian of any NP model emerging from direct searches at the LHC. The aim of Working Group 2 was twofold: on one hand, to provide a coherent, up-to-date picture of the status of flavour physics before the start of the LHC; on the other hand, to initiate activities on the path towards integrating information on NP from high-pT and flavour data.
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