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 τ = 2. In contrast, quarkantiquark |qq scalar mesons have twist τ ≥ 3 since they have nonzero orbital angular momentum, and multi-quark states such as |qqqq tetraquarks yield twist τ ≥ 4. Thus, the production cross section for both |qq and |qqqq mesons will be suppressed by at least one power of momentum transfer relative to glueball production. For example, in single inclusive particle hadroproduction AB → CX, the cross section for glueball production at high transverse momentum pT and fixed xT = 2 p T √ s will dominate higher twist mesons by at least two powers of pT . 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 + → φf0 where the f0 can be tested to be a glueball versus another type of scalar meson.

Scalar resonance in graviton-graviton scattering at high-energies: the graviball

“…Recall that for pure non-abelian Yang-Mills there is theoretical evidence that its spectrum is filled by massive states (glueballs) emerging from the self-interactions of the gluons [16][17][18][19]. In full quantum chromodynamics (QCD) these states lead to a new form of matter and studies have identified resonances measured in experiment as having a dominant glueball nature [20][21][22][23].…”

Glueballs as the Ithaca of meson spectroscopy

“…(at fixed angle so that t ∝ s). This counting rule has recently been proposed [88,89] to aid with the identification of the scalar glueball among the f 0 states. For the glueballs with J P C = 0 ++ , the minimum Fock space component is | g • g with antialigned gluon spins and no orbital angular momentum.…”

“…Therefore n f + L = 2. This happens to be the slowest falloff among all the Fock space components that can contribute to the quark-gluon Fock expansion of a scalar meson: a few are shown in table 3 adapted from [88].…”

“…Left: Experimental ππ spectrum [90] from J/ψγππ. Right: example ππ spectrum resulting from e − e + → φfJ with E = 9 and 11 GeV, assuming that f0(1710) is the glueball and with absolute normalization taken from [88]. Whichever state dropped least in this plot upon having experimental data at hand would fit the role of the glueball.…”

“…Whichever state dropped least in this plot upon having experimental data at hand would fit the role of the glueball. Reprinted from [88] (Elsevier) under STM permissions guidelines.…”