Using QCD Counting rules to Identify the Production of Gluonium

Abstract

The empirical identification of bound states of gluons has remained a central goal of hadron spectroscopy. We suggest an experimentally challenging, but model--independent way to assess which zero charge, isospin-zero mesons have a large gluonium light-front wavefunction component in the quark and gluon Fock space of QCD. Our method exploits QCD counting rules which relate the power-law fall-off of production amplitudes at high momentum transfer to the meson's twist (dimension minus spin of its minimum interpolating operators). Scalar $0^+$ glueballs composed of two valence gluons with zero internal orbital angular momentum have twist $\tau=2$. In contrast, quark-antiquark $|q \bar q \rangle $ scalar mesons have twist $\tau \ge 3$ since they have nonzero orbital angular momentum, and multi-quark states such as $|q q \bar q \bar q \rangle$ tetraquarks yield twist $\tau \ge 4$. Thus, the production cross section for both $|q\bar{q}\rangle$ and $|qq\bar{q}\bar{q}\rangle$ mesons will be suppressed by at least one power of momentum transfer relative to glueball production. For example, in single inclusive particle hadroproduction $ A B \to C X$, the cross section for glueball production at high transverse momentum $p_T$ and fixed $x_T = 2 {p_T\over \sqrt s} $ will dominate higher twist mesons by at least two powers of $p_T$. Similarly, in exclusive production processes at large CM energy and fixed CM angle, the glueball rate dominates by a power of $s$: we illustrate the method with a simple reaction, $e^-e^+ \to \phi f_0$ where the $f_0$ can be tested to be a glueball versus another type of scalar meson.