[Paper Review] Low-Mass Proton-Antiproton Enhancement: Belle and BES Results, Premises of LEAR and Expectations from CLAS

B. O. Kerbikov, A. Stavinsky+1 more|ArXiv.org|Oct 23, 2003

Atomic and Molecular Physics3 citations

TL;DR

The paper proposes that the near-threshold proton-antiproton enhancement observed in Belle and BES experiments arises from the $^1S_0$ $N\bar{N}$ interaction, explained via an effective range analysis of LEAR data. It predicts a corresponding enhancement in photoproduction $\gamma p \to pp\bar{p}$ measurable by CLAS, with the effect driven by a strong $p\bar{p}$ $S$-wave scattering length and Coulomb-enhanced $D$-factor near threshold.

ABSTRACT

We present a simple explanation for the recently observed near-threshold proton-antiproton enhancement. It is described by a set of low-energy parameters deduced from the analysis of NantiN experiments at LEAR. We predict a related effect in photoproduction reaction under study by CLAS collaboration.

Motivation & Objective

• To explain the observed near-threshold $p\bar{p}$ enhancement in $B$ and $J/\psi$ decays using low-energy $N\bar{N}$ parameters from LEAR experiments.
• To resolve the discrepancy between $J/\psi \to \gamma p\bar{p}$ (with enhancement) and $J/\psi \to \pi^0 p\bar{p}$ (without enhancement) through $S$-wave dominance in $I=0$ channel.
• To extend the effective range formalism to predict a related signal in photoproduction, specifically $\gamma p \to pp\bar{p}$, for testing at CLAS.
• To account for key physical effects in $p\bar{p}$ interaction: Coulomb attraction, annihilation, isospin mixing, and $n\bar{n}$ channel threshold.

Proposed method

• Uses effective range analysis of $N\bar{N}$ scattering data from LEAR to extract low-energy parameters, particularly $S$-wave scattering lengths $a_0$ and $a_1$.
• Applies the Migdal-Watson formalism to factor out final-state interaction (FSI) effects via the enhancement factor $D(q) = |f(-q)|^{-2}$, where $f(-q)$ is the Jost function.
• Incorporates Coulomb effects via the Sakharov factor $c^2(q)$, which accounts for $p\bar{p}$ atomic-like binding at low $q$.
• Models the $p\bar{p}$ system with complex, isospin-mixed $S$-wave amplitudes including Schwinger correction $\Delta \approx -0.08$ fm$^{-1}$ and $n\bar{n}$ threshold effects.
• Derives the double-differential cross section using the Chew-Low formula and isolates the $m_{23}$-dependent invariant mass distribution via angular integration.
• Evaluates the enhancement factor $D(q)$ as a function of $Q = m_{23} - 2m$, showing threshold cusp and jump due to Coulomb and $n\bar{n}$ channel effects.

Experimental results

Research questions

• RQ1 Why is there a strong near-threshold $p\bar{p}$ enhancement in $J/\psi \to \gamma p\bar{p}$ but not in $J/\psi \to \pi^0 p\bar{p}$?
• RQ2 Can the low-energy $N\bar{N}$ parameters extracted from LEAR data explain the $p\bar{p}$ enhancement observed in Belle and BES experiments?
• RQ3 What is the expected signature of $p\bar{p}$ final-state interaction in photoproduction, and can it be detected at CLAS?
• RQ4 How do Coulomb attraction, annihilation, and isospin mixing affect the $p\bar{p}$ $S$-wave scattering amplitude near threshold?
• RQ5 To what extent can the $D(q)$ enhancement factor account for the observed structure without invoking new dynamics like gluonic states or fragmentation?

Key findings

• The $S$-wave $I=0$ $p\bar{p}$ scattering length $a_0 \approx (-1.2 + i0.9)$ fm (from [13]) shows strong attraction, explaining the near-threshold enhancement.
• The $I=1$ channel has a much smaller scattering length ($a_1 \approx (-0.1 + i0.4)$ fm), consistent with the absence of enhancement in $\pi^0 p\bar{p}$ final states.
• The enhancement factor $D(q)$ exhibits a sharp rise near threshold due to the interplay of phase space and the $S$-wave $I=0$ amplitude, peaking at $Q \approx 0$.
• The Coulomb factor $c^2(q)$ causes a tiny discontinuity in $D(q)$ at $q=0$, and a cusp at $q \approx 49$ MeV/c due to the $n\bar{n}$ threshold opening.
• The predicted $\gamma p \to pp\bar{p}$ cross section shows a significant enhancement near $m_{23} \approx 2m$, with a peak structure due to $D(q)$, making it measurable at CLAS.
• The model explains the Belle and BES data without invoking new physics, relying instead on established $N\bar{N}$ parameters from LEAR, with $D(q)$ as the dominant factor near threshold.