Variational Monte Carlo Study of Pentaquark States

Abstract

Accurate numerical solution of the five-body Schrödinger equation is effected via variational Monte Carlo. The spectrum is assumed to exhibit a narrow resonance with strangeness S = +1. A fully antisymmetrized and pair-correlated five-quark wave function is obtained for the assumed nonrelativistic Hamiltonian which has spin, isospin, and color dependent pair interactions and manybody confining terms which are fixed by the non-exotic spectra. Gauge field dynamics are modeled via flux tube exchange factors. The energy determined for the ground states with J π = 1 2 − ( 1 2 + ) is 2.22 GeV (2.50 GeV). A lower energy negative parity state is consistent with recent lattice results. The short-range structure of the state is analyzed via its diquark content.A system of interacting, non-relativistic constituent quarks is the most simple, realistic model of hadronic systems. Solving the many-body Schrödinger equation to determine wave functions within this simple model is still a formidable task owing to the strong flavor, spin, and color dependence of the quark-quark interaction and traditionally requires some array of approximate methods to solve it. The controversial status of the recent evidence of a flavor exotic five-quark state warrants a careful treatment of this strongly interacting system. In this letter, the exercise of determining the wave function of five interacting constituent quarks in the flavor-exotic multiquark hadronic sector is solved using the variational Monte Carlo (VMC) technique. This technique is known to yield upper bounds on the ground state energy accurate to the level of a few percent in light nuclei with the number of nucleons A ≤ 6 [1].Recent experimental evidence [2,3,4,5,6,7,8,9,10,11,12,13] has revived interest in the multiquark flavorexotic sector of the hadronic spectrum. Various model calculations have been reported [14,15,16,17,18,19,20,21,22,23] which study the existence of a strangeness S = +1 resonance, dubbed θ + , about 100 MeV above threshold to nucleon-kaon decay with low mass of 1540(2) MeV and possibly extremely narrow width of 0.9(3) MeV [24]. Lattice results are available, including Refs. [25,26].The calculation of Ref. [19], working in the chiral quark soliton model, of an extremely small width, < 15 MeV stimulated experimental searches with some positive signals, although all of them had very low statistics with at most ∼ 100 counts above a comparable background [13]. Preliminary high statistics photoproduction data of the reaction γp → nK S from the CLAS collaboration [27] sets an upper limit on the yield of the θ + relative to the Λ * (1520) yield at 0.2%. No definitive structure in the nK-invariant mass spectrum is observed at 1540 MeV in this experiment. No experimental information is available on the spin or parity of the state in any experiment done to date.We study the θ + in the non-relativistic flux tube quark model with one-gluon exchange (OGE) and one-pion exchange (OPE) (between the light quarks). We take seriously the possibility that θ + is a narrow reson...

Stability of the pentaquark in a naive string model

“…Hence, we shall neglect this term and compute an upper bound with the flip-flop interaction alone. This is opposite to the choice made in [32], where only the connected-Steiner-tree term is adopted and the flip-flop one omitted.…”

Structure and decay width of the in a one-gluon exchange model

“…The calculated mass of the Θ + is higher than the observed mass (∼1540 MeV) by about 500-600 MeV. This appears to be common in all the calculations using the potential of OGE type [11,12,14] or the OGE plus one-pion exchange potential [13]. The zero-point energy term is uncertain, so it is hard to get an absolute mass unambiguously.…”

“…Though there are some attempts to predict the decay width of the Θ + in the constituent quark model [12,17,18], either the unbound nature of the Θ + is not taken into account or the assumption of its structure is too simple. Moreover, the correlated motion among the five quarks is usually truncated in the orbital, spin, isospin and color degrees of freedom or in some of them apart from a calculation [13]. For example, a treatment of hidden color components is not quite clear.…”

“…In these models the spin and parity of the Θ + was assumed to be J P = 1 2 + to account for its small decay width. Some dynamical calculations of the mass of the Θ + for different J P states have been performed in constituent quark models [11,12,13,14]. The quark model usually predicts a smaller mass for the negative parity Θ + than for the positive parity Θ + .…”

Variational Monte Carlo study of pentaquark states in a correlated quark model

“…The controversial status of the recent evidence of a flavor exotic five-quark state warrants a careful treatment of this strongly interacting system. We have determined the wave function of five interacting constituent quarks in the flavor-exotic multiquark hadronic sector is solved using the variational Monte Carlo (VMC) technique [1]. This technique is known to yield upper bounds on the ground state energy accurate to the level of a few percent in light nuclei with the number of nucleons A ≤ 6 [2].…”