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- W1798317623 abstract "We calculate the vacuum to meson matrix elements of the dimension-4 operator $overline{ensuremath{psi}}{ensuremath{gamma}}_{4}{stackrel{ensuremath{leftrightarrow}}{D}}_{i}ensuremath{psi}$ and dimension-5 operator $overline{ensuremath{psi}}{ensuremath{epsilon}}_{ijk}{ensuremath{gamma}}_{j}ensuremath{psi}{B}_{k}$ of the ${1}^{ensuremath{-}+}$ 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 ${1}^{ensuremath{-}+}$ are comparable in size as compared to other known $qoverline{q}$ mesons. They are particularly similar to those of the ${2}^{++}$ meson, since their dimension-4 operators are in the same Lorentz multiplet. Based on these observations, we find no evidence to support the notion that the lowest ${1}^{ensuremath{-}+}$ mesons in the $coverline{c}$ and $soverline{s}$ regions are hybrids. As far as the exotic quantum number is concerned, the nonrelativistic reduction reveals that the leading terms in the dimension-4 and dimension-5 operators of ${1}^{ensuremath{-}+}$ are identical up to a proportional constant and it involves a center-of-mass momentum operator of the quark-antiquark pair. This explains why ${1}^{ensuremath{-}+}$ is an exotic quantum number in the constituent quark model where the center of mass of the $qoverline{q}$ is not a dynamical degree of freedom. Since QCD has gluon fields in the context of the flux tube which is appropriate for heavy quarkoniums to allow the valence $qoverline{q}$ to recoil against them, it can accommodate such states as ${1}^{ensuremath{-}+}$. By the same token, hadronic models with additional constituents besides the quarks can also accommodate the $qoverline{q}$ center-of-mass motion. To account for the quantum numbers of these $qoverline{q}$ mesons in QCD and hadron models in the nonrelativistic case, the parity and total angular momentum should be modified to $P=(ensuremath{-}{)}^{L+l+1}$ and $stackrel{ensuremath{rightarrow}}{J}=stackrel{ensuremath{rightarrow}}{L}+stackrel{ensuremath{rightarrow}}{l}+stackrel{ensuremath{rightarrow}}{S}$, where $L$ is the orbital angular momentum of the $qoverline{q}$ pair in the meson." @default.
- W1798317623 created "2016-06-24" @default.
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- W1798317623 date "2012-11-15" @default.
- W1798317623 modified "2023-09-26" @default.
- W1798317623 title "Is the1−+meson a hybrid?" @default.
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- W1798317623 doi "https://doi.org/10.1103/physrevd.86.094511" @default.
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