1202.2205 (Yi-Bo Yang et al.)

Is $1^-+$ Meson a Hybrid?    [PDF]

Yi-Bo Yang, Yin Chen, Gang Li, Keh-Fei Liu

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.

View original: http://arxiv.org/abs/1202.2205