Photoproduction and detection of $ρ'\rightarrowπ^+π^-π^+π^-$ decays in ultra-peripheral collisions and at an electron-ion collider

TL;DR

The paper investigates photoproduction of the $ρ′$ meson decaying to $π^+π^-π^+π^-$ as a probe of nuclear structure across proton, ion, and electron–ion collision systems. It develops a two-component Reggeon–Pomeron model for $ ho′$ production on protons, then extends to nuclei via Glauber theory, and evaluates production in ultra-peripheral collisions and at an Electron–Ion Collider using eSTARlight/STARlight simulations. A key outcome is that ALICE data favor a branching ratio Br($ρ′→4π$) around 15% with a photon–meson coupling $f_V$ near the Klusek-Gawenda value; GVMD predictions yield tensions with the observed cross sections. The study finds high predicted rates for both UPCs and the EIC, indicating the $ρ′→4π$ channel can be observed with high efficiency and used to map low-$x$ nuclear structure and saturation, provided forward instrumentation can access the required kinematic regions. These results also offer a path to determine the absolute branching ratios and test two-resonance hypotheses, with extensions to other colliders (LHeC, EiCC) easily envisioned.

Abstract

Vector meson photoproduction is an important probe of nuclear structure. Light vector mesons are most sensitive to low$-x$ structure, as long as they are not too light for perturbative QCD calculations. The $ρ'$ is of interest as an intermediate mass state (between the $ρ$ and $J/ψ$) that is easier to detect than the $φ$. Using HERA data on proton targets, we make projections for lead/gold targets in UPCs at the Large Hadron Collider and RHIC, and for $ep$ and $eA$ collisions at a future Electron-Ion Collider (EIC). We compare the UPC projections with ALICE data, and constrain the branching ratio divided by the square of the photon-$ρ'$ coupling. The data prefer large couplings and small branching ratio, probably less than 25\%. The photon-meson coupling predicted by generalized vector meson dominance does not fit the data. The HERA $ep$ and ALICE UPC $e$Pb data exhibit very similar $4π$ mass spectra, indicating that, if the system is composed of two resonances, the products of their photon couplings with their four-pion branching ratios are similar. The predicted rates are high for both UPCs and the EIC. The $ρ'\rightarrowπ^+π^-π^+π^-$ decay can be observed at the EIC with high efficiency. In $ep$ collisions at the highest energy, the forward B0 detector is needed to observe this channel down to the lowest achievable Bjorken$-x$ values.

Figures (7)

• Figure 1: H1 SchmittH1prelim and fixed-target data Bingham:1972azDavier1973Schacht:1974fqAtiya:1979ipAston1981 on $\gamma p\rightarrow \rho'p\rightarrow\pi^+\pi^-\pi^+\pi^-$ along with our fit to the data. Model I is a fit to Eq. \ref{['eq:pomeronreggeon']} with all four parameters treated as free parameters. Model II is the reference fit used for the rest of the calculations in this paper. This fit has an additional term in the $\chi^2$, pulling $\epsilon$ toward the value from H1 SchmittH1prelim,as discussed in the text. Model III uses the set of parameters used in Ref. Klusek-Gawenda:2020gwa. Fit results are given in Tab. \ref{['tab:fitparam']}.
• Figure 2: Comparison of the invariant mass distribution of four pions from H1 collaboration (shown as gray squares) SchmittH1prelim and the ALICE collaboration ALICE:2024kjy in arbitrary units, normalized for easy shape comparison. Error bars are not shown for H1, but they are smaller than the error bars for ALICE.
• Figure 3: Differential cross-section $d\sigma/dy$ of $\rho' \rightarrow \pi^+ \pi^- \pi^+ \pi^-$ for Pb-Pb UPCs at $\sqrt{s_{NN}} = 5.36 \, \text{TeV}$ (top) and $e$Pb collisions at $18 \times 110 \, \text{GeV}$ (bottom). The curves show different branching ratios (B.R.) of $100\%$, $50\%$, $30\%$, and $10\%$. The orange marker indicates the ALICE data for the Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02 \, \text{TeV}$. For the UPCs(top plot), the left hand curves ($y<0$) use the coupling in Ref. Klusek-Gawenda:2020gwa, while the right hand curves ($y>0$) use the GVMD predictions. For ePb collisions (bottom plot), we use the coupling in Ref. Klusek-Gawenda:2020gwa.
• Figure 4: Two-dimensional scan of the differential cross section $d\sigma/dy$ (in mb) as a function of the branching ratio (B.R.) and the coupling $f_{V}^{2}/4\pi$. The color map shows the interpolated cross section values on a logarithmic scale. Overlaid lines indicate the central value of the ALICE measurement (red solid) together with the $\pm 1\sigma$ (black), $\pm 2\sigma$ (blue), and $\pm 3\sigma$ (orange) contours, where the $\sigma$ bands represent the ALICE measurement uncertainties (stat $\oplus$ syst). Horizontal solid black lines mark the reference couplings $f_{V}^{2}/4\pi = 65.6$ and $f_{V}^{2}/4\pi = 8.4$.
• Figure 5: Differential cross-section $d\sigma/dy$ for Pb-Pb UPCs at $\sqrt{s_{NN}} = 5.36 \, \text{TeV}$. The solid blue line represents the results with no cuts applied, while the dotted red, dashed green, and dashed-dotted yellow lines correspond to the cross sections in the ALICE ALICE:2024kjy, LHCb LHCb-PAPER-2024-042, CMS CMS-DP-2024-011 and expected ALICE 3 arXiv:2211.02491 acceptance, respectively.