Exotic hybrid mesons in hard electroproduction

We estimate the sizeable cross section for deep exclusive electroproduction of an exotic $J^{PC}=1^{-+}$ hybrid meson in the Bjorken regime. The production amplitude scales like the one for usual meson electroproduction, i.e., as $1/Q^2$. This is due to the nonvanishing leading twist distribution amplitude for the hybrid meson, which may be normalized thanks to its relation to the energy-momentum tensor and to the QCD sum rules technique. The hard amplitude is considered up to next-to-leading order in ${\alpha }_S$ and we explore the consequences of fixing the renormalization scale ambiguity through the Brodsky-Lepage-Mackenzie (BLM) procedure. We study the particular case where the hybrid meson decays through a $\pi \eta$ meson pair. We discuss the $\pi \eta$ generalized distribution amplitude and then calculate the production amplitude for this process. We propose a forward-backward asymmetry in the production of $\pi$ and $\eta$ mesons as a signal for the hybrid meson production. We briefly comment on hybrid electroproduction at very high energy, in the diffractive limit where a QCD Odderon exchange mechanism should dominate. The conclusion of our study is that hard electroproduction is a promising way to study exotic hybrid mesons, in particular, at JLAB, HERA (HERMES), or CERN (Compass).

Figure 1

Typical diagram describing the electroproduction of a meson at lowest order. The gray blobs are nonperturbative matrix elements, namely, the meson distribution amplitude and the nucleon generalized parton distribution.

Figure 2

Differential cross section for $\rho$ and hybrid meson production with the default choice of the renormalization scale and different $x_B$ values.

Figure 3

Differential cross section for exotic hybrid meson electroproduction (dashed line) with ${\mu }_R^2=e^{-5.13}{Q}^2$ compared with the quark contribution to ${\rho }^0$ electroproduction (solid line) with ${\mu }_R^2=e^{-4.9}{Q}^2$, as a function of $Q^2$, for $x_B\approx 0.33$. The dashed-dotted line is the result of Vanderhaegen et al. [19] for $\rho$ electroproduction.

Figure 4

Typical diagram describing the electroproduction of $\pi \eta$ pair. The higher and lower blobs represent the GDA’s and GPD’s, respectively.

Figure 5

Typical process describing the electroproduction of a $\pi \eta$ pair.

Figure 6

The angular asymmetry as a function of $m_{\pi \eta }$.