[Paper Review] Central hadron production in crossing of dedicated hadronic beams

Peter Minkowski|ArXiv.org|May 4, 2004

Particle physics theoretical and experimental studies20 references3 citations

TL;DR

This paper investigates central hadron production in high-energy hadronic collisions, focusing on the theoretical framework for detecting purely gluonic mesons (gluonic bound states) via double Pomeron exchange in experiments with rapidity gaps. It derives the spin-2 wave functions of adjoint string operators in QCD, showing that the right- and left-handed Weyl bilinear components vanish, implying that only the traceless symmetric part contributes to the physical spectrum, thus identifying a key signature for glueball states in exclusive production processes.

ABSTRACT

The original aim of this work, was to give a {\it brief} review of gluonic mesons, to be searched for in an experiment dedicated to central production of a relatively low mass hadronic system, whereby rapidity gaps are possible to impose, requiring initial hadron beams of sufficient energy and intensity. Sections 1 - 4 are devoted to this aim. The various theoretical ingrediants, covering several decades of thinking by many, including the author, are contained in 5 appendices, dedicated to specifically gluonic binaries within QCD and their underlying Yang-Mills base structure.

Motivation & Objective

• To develop a theoretical framework for detecting purely gluonic mesons (glueballs) in exclusive central hadron production experiments.
• To analyze the quantum numbers and spectral patterns of gluonic bound states within QCD, particularly focusing on their spin and parity structure.
• To derive the decomposition of adjoint string operators in terms of irreducible spin-2 representations, identifying the physical components that contribute to glueball states.
• To establish a connection between the Yang-Mills structure of QCD and observable signatures in high-energy hadronic collisions with rapidity gaps.
• To provide a foundation for experimental searches of glueballs using exclusive production processes at high-energy hadron colliders.

Proposed method

• Uses double Reggeon exchange and double-Pomeron exchange diagrams to model central production of hadronic states with rapidity gaps.
• Applies group-theoretic decomposition of the adjoint string bilinear operator into irreducible representations: $\varrho$, $P^{RR}$, $P^{LL}$, and $B^{\pm}$.
• Derives the spin projection operations on adjoint string operators using Lorentz group representations and Riemann normal gauge formalism.
• Identifies the physical glueball wave functions through the irreducible components of the energy-momentum and Weyl bilinear operators.
• Shows that the $P^{RR}$ and $P^{LL}$ components vanish, leaving only the symmetric traceless part $\varrho$ as the physical glueball state.
• Relates the resulting wave functions to the $II^{+}$ spectral series in the context of the Yang-Mills base structure.

Experimental results

Research questions

• RQ1 What are the quantum numbers (spin, parity, charge conjugation) of purely gluonic mesons in QCD?
• RQ2 How can the wave functions of glueballs be derived from the adjoint string operators in the Yang-Mills theory?
• RQ3 Which irreducible components of the adjoint string bilinear contribute to physical glueball states?
• RQ4 Can the double-Pomeron exchange mechanism with rapidity gaps serve as a clean signature for detecting glueballs?
• RQ5 What is the role of the symmetric traceless part $\varrho$ in the physical spectrum of glueballs?

Key findings

• The right- and left-handed Weyl bilinear components $P^{RR}$ and $P^{LL}$ vanish identically, implying they do not contribute to physical glueball states.
• The physical glueball wave functions are identified with the symmetric traceless part $\varrho$, which corresponds to the $II^{+}$ spectral series in the decomposition.
• The full adjoint string bilinear decomposes into $\varrho$, $B^{+}$, and $B^{-}$, with $\varrho$ being the only non-vanishing physical component.
• The wave function $\widetilde{t}(\{w^{RR}\}) = \widetilde{t}(\{w^{LL}\}) = 0$ confirms the absence of chiral Weyl states in the glueball spectrum.
• The derived structure matches the expected spin-2 glueball states in exclusive production, providing a theoretical basis for experimental detection via rapidity gaps.
• The formalism establishes a direct link between the Yang-Mills base structure and observable glueball states in high-energy hadronic collisions.