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Register a new userAbsence of evidence for pentaquarks on the lattice
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We study the question of whether or not QCD predicts a pentaquark state. We use the improved, fixed point lattice QCD action which has very little sensitivity to the lattice spacing and also allows us to reach light quark masses. The analysis was performed on a single volume of size $(1.8 {rm fm})^3times 3.6 {rm fm}$ with lattice spacing of $a=0.102$ fm. We use the correlation matrix method to identify the ground and excited states in the isospin 0, negative parity channel. In the quenched approximation where dynamical quark effects are omitted, we do not find any evidence for a pentaquark resonance in QCD.
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Pentaquark states in lattice QCD probably lie close in energy to two particle scattering states. Correctly identifying the resonant state is a challenging, yet tractable, problem given the terascale computing facilities available today. We summarize the initial round of exploratory lattice calculations and discuss what should be accomplished in the next round.
On March 26th, 2019, at the Rencontres de Moriond QCD conference, the LHCb Collaboration reported the observation of three new pentaquarks, namely $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, which are consistent with the loosely bound molecular hidden-charm pentaquark states composed of an S-wave charmed baryon $Sigma_c$ and an S-wave anti-charmed meson ($bar{D}, bar{D}^*$). In this work, we present a direct calculation by the one-boson-exchange (OBE) model and demonstrate explicitly that the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ do correspond to the loosely bound $Sigma_cbar{D}$ with $(I=1/2,J^P=1/2^-)$, $Sigma_cbar{D}^*$ with $(I=1/2,J^P=1/2^-)$ and $Sigma_cbar{D}^*$ with $(I=1/2,J^P=3/2^-)$, respectively.
The strangeonium-like $sbar{s}g$ hybrids are investigated from lattice QCD in the quenched approximation. In the Coulomb gauge, spatially extended operators are constructed for $1^{--}$ and $(0,1,2)^{-+}$ states with the color octet $sbar{s}$ component being separated from the chromomagnetic field strength by spatial distances $r$, whose matrix elements between the vacuum and the corresponding states are interpreted as Bethe-Salpeter (BS) wave functions. In each of the $(1,2)^{-+}$ channels, the masses and the BS wave functions are reliably derived. The $1^{-+}$ ground state mass is around 2.1-2.2 GeV, and that of $2^{-+}$ is around 2.3-2.4 GeV, while the masses of the first excited states are roughly 1.4 GeV higher. This mass splitting is much larger than the expectation of the phenomenological flux-tube model or constituent gluon model for hybrids, which is usually a few hundred MeV. The BS wave functions with respect to $r$ show clear radial nodal structures of non-relativistic two-body system, which imply that $r$ is a meaningful dynamical variable for these hybrids and motivate a color halo picture of hybrids that the color octet $sbar{s}$ is surrounded by gluonic degrees of freedom. In the $1^{--}$ channel, the properties of the lowest two states comply with those of $phi(1020)$ and $phi(1680)$. We have not obtained convincing information relevant to $phi(2170)$ yet, however, we argue that whether $phi(2170)$ is a conventional $sbar{s}$ meson or a $sbar{s}g$ hybrid within the color halo scenario, the ratio of partial decay widths $Gamma(phi eta)$ and $Gamma (phi eta)$ observed by BESIII can be understood by the mechanism of hadronic transition of a strangeonium-like meson along with the $eta-eta$ mixing.
In this article, we review recent lattice calculations on the $x$-dependence of parton distributions, with the latter providing information on hadron structure. These calculations are based on matrix elements of boosted hadrons coupled to non-local operators and can be related to the standard, light-cone distribution functions via an appropriate factorization formalism. There is significant progress in several directions, including calculations of flavor singlet parton distribution functions (PDFs), first calculations of generalized parton distributions (GPDs), as well as the implementation of some of the approaches for the transverse-momentum-dependent PDFs (TMD PDFs). This new direction of lattice calculations is particularly interesting for phenomenological fits on experimental data sets, as the lattice results can help to improve the constraints on the distribution functions.
Several experimental groups have reported evidence for baryons with flavor exotic quantum numbers that cannot be explained as $qqq$ bound states but require a minimum of five quarks -- $qqqq bar q$. These pentaquark states include the $theta^{+}$, the $Xi^{--}$ and the $theta_{c}$. The reported widths of these new states are consistent with experimental resolution and may be as narrow as a few MeV/$c^2$ or less. Prior to 2003, experimental searches for flavor exotic baryons spanning several decades yielded negative results. There have also been a number of searches carried out since the reports of these new pentaquark states that do not confirm their existence. This review of both the positive and negative reports seeks to understand the current situation regarding the experimental evidence for pentaquarks.
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