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Holographic charm and bottom pentaquarks I: Mass spectra with spin effects

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 Added by Yizhuang Liu
 Publication date 2021
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and research's language is English




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We revisit the three non-strange pentaquarks $[frac 12frac 12^-]_{S=0,1}$ and $[frac 12frac 32^-]_{S=1}$ predicted using the holographic dual description, where chiral and heavy quark symmetry are manifest in the triple limit of a large number of colors, large quark mass and strong $^prime$t Hooft gauge coupling. In the heavy quark limit, the pentaquarks with internal heavy quark spin $S$ are all degenerate. The holographic pentaquarks are dual to an instanton bound to heavy mesons in bulk, without the shortcomings related to the nature of the interaction and the choice of the hard core inherent to the molecular constructions. We explicitly derive the spin-spin and spin-orbit couplings arising from next to leading order in the heavy quark mass, and lift totally the internal spin degeneray, in fair agreement with the newly reported charmed pentaquarks from LHCb. New charm and bottom pentaquark states are predicted.



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We analyze the decay modes of the three $[frac 12frac 12^-]_{S=0,1}$ and $[frac 12frac 32^-]_{S=1}$ non-strange pentaquarks with hidden charm and bottom, predicted by holographic QCD in the heavy quark limit. In leading order, the pentaquarks %are composed of heavy-light mesons in bulk bound to an instanton core. They are degenerate and stable by heavy quark symmetry. At next to leading order, the spin interactions lift the degeneracy and cause the pentaquarks to decay. We show that the open charm (bottom) decay modes dwarf the hidden charm (bottom) ones, with total widths that are consistent with those recently reported by LHCb for charm pentaquarks. Predictions for bottom pentaquarks are given.
We consider the photo-excitation of charm and bottom pentaquarks with the holographic assignments $[frac 12frac 12^-]_{S=0,1}$ and $[frac 12frac 32^-]_{S=1}$, in the photo-production of heavy vector mesons such as charmonia and bottomonia near threshold. We use a Witten diagram to combine the s-channel photo-excitation of holographic pentaquarks with a massive t-channel graviton or tensor glueball exchange, to extract the scattering amplitude for heavy meson photo-production in the threshold region. The pentaquark signal is too weak to be detected at current electron facilities.
Recently, the LHCb Collaboration reported three $P_c$ states in the ${J/psi}p$ channel. We systematically study the mass spectrum of the hidden charm pentaquark in the framework of an extended chromomagnetic model. For the $nnncbar{c}$ pentaquark with $I=1/2$, we find that (i) the lowest state is $P_{c}(4327.0,1/2,1/2^{-})$ [We use $P_{c}(m,I,J^{P})$ to denote the $nnncbar{c}$ pentaquark], which corresponds to the $P_{c}(4312)$. Its dominant decay mode is $Lambda_{c}bar{D}^{*}$. (ii) We find two states in the vicinity of $P_{c}(4380)$. The first one is $P_{c}(4367.4,1/2,3/2^{-})$ and decays dominantly to $N{J/psi}$ and $Lambda_{c}bar{D}^{*}$. The other one is $P_{c}(4372.4,1/2,1/2^{-})$. Its dominant decay mode is $Lambda_{c}bar{D}$, and its partial decay width of $Neta_{c}$ channel is comparable to that of $N{J/psi}$. (iii) In higher mass region, we find $P_{c}(4476.3,1/2,3/2^{-})$ and $P_{c}(4480.9,1/2,1/2^{-})$, which correspond to $P_{c}(4440)$ and $P_{c}(4457)$. In the open charm channels, both of them decay dominantly to the $Lambda_{c}bar{D}^{*}$. (iv) We predict two states above $4.5~text{GeV}$, namely $P_{c}(4524.5,1/2,3/2^{-})$ and $P_{c}(4546.0,1/2,5/2^{-})$. The masses of the $nnncbar{c}$ state with $I=3/2$ are all over $4.6~text{GeV}$. Moreover, we use the model to explore the $nnscbar{c}$, $ssncbar{c}$ and $ssscbar{c}$ pentaquark states.
The production of the hidden-charm pentaquarks $P_{c}$ via pion-induced reaction on a proton target is investigated within an effective Lagrangian approach. Three experimentally observed states, $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$, are considered in the calculation, and the Reggeized $t$-channel meson exchange is considered as main background for the reaction $pi ^{-}prightarrow J/psi n$. The numerical results show that the experimental data of the total cross section of the reaction $pi^{-}prightarrow J/psi n$ at $Wsimeq 5$ GeV can be well explained by contribution of the Reggeized $t$ channel with reasonable cutoff. If the branching ratios $Br[P_{c}rightarrow J/psi N]simeq 3%$ and $Br[P_{c}rightarrow pi N]simeq 0.05%$ are taken, the average value of the cross section from the $P_{c}(4312)$ contribution is about 1.2 nb/100 MeV, which is consistent with existing rude data at near-threshold energies. The results indicate that the branching ratios of the $P_{c}$ states to the $J/psi N$ and $pi N$ should be small. The shape of differential cross sections shows that the Reggeized $t$-channel provides a sharp increase at extreme forward angles, while the differential cross sections from the $P_{c}$ states contributions are relatively flat. High-precision experimental measurements on the reaction $pi ^{-}prightarrow J/psi n$ at near-threshold energies are suggested to confirm the LHCb hidden-charm pentaquarks as genuine states, and such experiments are also helpful to understand the origin of these resonance structures.
The primordial matter of quarks and gluons, which filled our universe just after few micro-seconds of its creation through Big Bang, is expected to be created in the laboratory by colliding nuclei at relativistic energies. The ongoing nuclear collision programs at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) are two experimental facilities, where matter in the state of Quark-Gluon Plasma (QGP) can be created and characterized. Heavy quarks, mainly charm and bottom quarks, are considered as novel probes to characterize QGP, and hence the QCD matter. Heavy quark diffusion coefficients play a significant role to understand the properties of QCD matter. Experimental measurements of nuclear suppression factor and elliptic flow are able to constrain the heavy quark diffusion coefficients, which is a key ingredient for the phenomenological study and disentangle different energy loss models. We give a general perspective of heavy quark diffusion coefficient in QGP and discuss its potential as a probe to disentangle different hadronization mechanisms, as well as to probe the initial electromagnetic field produced in non-central collisions. Experimental perspective on future measurements are discussed with special emphasis on heavy-flavors as next generation probes.
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