Is $1^-+$ Meson a Hybrid?

Details Is $1^-+$ Meson a Hybrid? Is $1^-+$ Meson a Hybrid?

2012-02-10

arxiv.org/abs/1202.2205v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

17 pages, 16 figures

Scientific paper

We calculate the vacuum to meson matrix elements of the dimension-4 operator $\bar{\psi}\gamma_4\nblr_i \psi$ and dimension-5 operator $\bar{\psi}\eps\gamma_j\psi B_k$ of the $1^{-+}$ meson on the lattice and compare them to the corresponding matrix elements of the ordinary mesons to discern if it is a hybrid. For the charmoniums and strange quarkoniums, we find that the matrix elements of $1^{-+}$ are comparable in size as compared to other known $q\bar{q}$ mesons. They are particularly similar to those of the $2^{++}$ meson, since their dimension-4 operators are in the same Lorentz multiplet. We conclude that $1^{-+}$ is not a hybrid. As for the exotic quantum number is concerned, the non-relativistic reduction reveals that the leading terms in the dimension-4 and dimension-5 operators of $1^{-+}$ are identical up to a proportional constant and it involves a center-of-mass momentum operator of the quark-antiquark pair. This explains why $1^{-+}$ is an exotic in the constituent quark model where the center of mass of the $q\bar{q}$ is not a dynamical degree of freedom. There are no exotics quantum numbers in QCD and hadronic models which have constituents besides the quarks to allow the $q\bar{q}$ pair to recoil against them. To accommodate these quantum numbers for $q\bar{q}$ mesons in QCD and hadron models in the non-relativistic case, the parity and total angular momentum are modified to $P = (-)^{L + l +1}$ and $\vec{J} = \vec{L} + \vec{l} + \vec{S}$, where $L$ is the orbital angular momentum of the $q\bar{q}$ pair in the meson.

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