Hybrid Meson Decay from Lattice

Ziwen Fu NCNR, NIST

In addition to the conventional hadrons containing valence quarks and valence antiquarks, quantum chromodynamics (QCD) suggests the existence of the hybrid hadrons containing valence gluons besides quarks and antiquarks, and some experiments may have found some. A decisive experimental confirmation of its existence, however, is still needed. At present, lattice simulations have offered the practicable ways of theoretically guiding us to search for the hybrid states(H). We study the spectroscopy and the decay rate of the heavy hybrid mesons made of a bottom quark, an antibottom quark, and a gluon to selected channels, and use lattice methods to extract the transition matrix elements in full QCD. Of particular interest are the spin-exotic hybrid mesons. For sufficiently heavy quarks (e.g., bottom quark), we can use the leading Born-Oppenheimer (LBO) approximation to calculate the static potential energy at all quark-antiquark separations. Then, by solving the Schrodinger equation with this potential, we reconstruct the motion of the heavy quarks. In a similar way we can determine decay rates. Moreover, we use the numerical lattice method to calculate the mass of the f_0 meson at a single lattice spacing and light quark mass, namely, m(f_0) = (768 +/- 136) MeV. Most of all we consider decay channels involving the emission of a scalar meson. We obtain the partial decay rate for the channel H ---> chi_b + pion + pion, namely, 3.62(98) MeV. All of our results are consistent with those of other researchers. Knowledge of the masses and the decay rates should help us considerably in experimental searches for the hybrid mesons.

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