[Paper Review] Two-component Duality and Strings

P. Freund|ArXiv.org|Aug 15, 2007

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TL;DR

This paper proposes that the two-component duality in early hadronic physics—dual to s-channel resonances and t-channel non-resonant background—corresponds to open strings (mesons, baryons) and closed strings (Pomeron), respectively. It shows that non-planar loop diagrams with flavor-singlet t-channel exchange, interpreted as closed-string propagation, naturally account for Pomeron exchange and explain the suppression of φπ over ρπ total cross-sections via quark mass differences, validating the FH-conjecture and linking duality to string structure.

ABSTRACT

A phenomenologically successful two-component hadronic duality picture led to Veneziano's amplitude, the fundamental first step to string theory. This picture is briefly recalled and its two components are identified as the open strings (mesons and baryons) and closed strings (Pomeron).

Motivation & Objective

• To reconcile the phenomenologically successful two-component duality in hadronic scattering with the emerging framework of string theory.
• To explain how the Pomeron, a t-channel exchange not dual to resonances, could arise from unitarity and duality principles.
• To identify the diagrammatic structure underlying the Pomeron as a non-planar loop diagram with flavor-singlet t-channel exchange.
• To demonstrate that the suppression of φπ over ρπ total cross-sections arises from differing quark masses in the closed-string picture.

Proposed method

• Analyzes the double-counting problem in summing s- and t-channel Bethe-Salpeter and fishnet diagrams for composite particles.
• Applies the Dolen-Horn-Schmid duality principle to show that s-channel resonances and t-channel Regge exchanges are dual, not additive.
• Introduces the FH-conjecture that the Pomeron is dual to non-resonant s-channel background, not to resonances.
• Identifies the non-planar loop diagram (Fig. 6 and 7) as the correct structure for Pomeron exchange, with identical quarks in t-channel pairs.
• Interprets the diagram as a closed string formed by merging two open strings, propagating, and splitting into two others, via the string picture (Fig. 8).
• Uses quark mass differences (non-strange vs. strange) to explain the suppression factor (mρ/mϕ)² ≈ 0.57 in φπ vs. ρπ cross-sections.

Experimental results

Research questions

• RQ1 How can the Pomeron, which is not dual to s-channel resonances, be consistently incorporated into a duality framework?
• RQ2 What diagrammatic structure in quantum field theory corresponds to the Pomeron as a t-channel flavor-singlet exchange dual to non-resonant s-channel background?
• RQ3 How does the string interpretation of the non-planar loop diagram explain the observed suppression of φπ over ρπ total cross-sections?
• RQ4 What is the connection between the critical dimension in string theory (26 for bosons, 10 for superstrings) and the analyticity of scattering amplitudes?
• RQ5 How does the transition from hadronic duality to string theory emerge from the structure of loop diagrams and unitarity?

Key findings

• The non-planar loop diagram (Fig. 7) with identical quarks in t-channel pairs selects the flavor singlet and avoids s-channel resonances, satisfying the FH-conjecture.
• The diagram corresponds to a closed string formed by merging two open strings (2 and 3), propagating as a closed string, and splitting into two others (1 and 4), as shown in Fig. 8.
• The Pomeron couples differently to ρ and φ mesons due to differing quark masses at the ends of the open string, leading to a suppression factor of (mρ/mϕ)² ≈ 0.57 for φπ cross-sections.
• The prediction dσJ/ψp/dt / dσρp/dt ≈ mρ⁴/mJ/ψ⁴ ≈ 0.0038 for J/ψp scattering was experimentally confirmed.
• Lovelace’s analysis of loop amplitudes revealed that analyticity is preserved only in 26 spacetime dimensions for bosonic strings, leading to critical string theory.
• The transition from hadronic duality to string theory was catalyzed by identifying the Pomeron as a closed string, with the non-planar diagram as the key structure.