Constituent counting rule for exclusive production of heavy quarkoniumlike exotic resonance and a light hadron

TL;DR

This paper derives a scaling rule for the production rates of heavy quarkoniumlike exotic states and light hadrons in exclusive processes, based on constituent quark counting in a specific energy regime.

Contribution

It introduces a constituent counting rule for exclusive production of heavy exotic hadrons, applicable in the nonrelativistic heavy quark regime at intermediate energies.

Findings

Rate scales as E^{1-n} where n is the number of constituent quark pairs.

Applicable in energy range E such that m_Q >> E >> Λ_QCD.

Provides a theoretical framework for analyzing exotic hadron production.

Abstract

The exclusive processes are considered, where a point-like source of heavy quark-antiquark pairs $Q \bar Q$, e.g. their electromagnetic current, produces a pair consisting of a heavy quarkoniumlike exotic meson (tetraquark) or baryon (pentaquark) and a light meson or an antibaryon. For a sufficiently large mass of the heavy quark $m_Q$ there is a range of the energy $E$ above the $Q \bar Q$ threshold, where $E \ll m_Q$ and still the energy is large compared to the strong interaction scale, $E \gg \Lambda_{QCD}$. It is shown that in this energy range, where the heavy quarks are nonrelelativistic, a specific `intermediate asymptotic' behavior sets in determined by the number $n$ of the pairs of constituent quarks, with the rate scaling as $E^{1-n}$.