First Extraction of the $φ$-$^{4}\mathrm{He}$ scattering length from near-threshold $φ$ photoproduction on helium-4

TL;DR

The work tackles how to quantify vector meson–nucleus interactions through near-threshold photoproduction and the extraction of scattering lengths. It employs the Vector Meson Dominance framework and LEPS data to connect differential cross sections at threshold to meson–nucleus scattering lengths, under an energy-independence assumption for dσ/dt. The key result is the first extraction of the φ–^4He scattering length, |α_{φ-^4He}| ≈ 3.33 × 10^-4 fm, which is markedly smaller than light targets like the nucleon or deuteron, signaling a weak φ-nucleus coupling. The study also highlights systematic trends where the scattering length is suppressed for heavier mesons and nuclei, suggests empirical scaling with threshold energy, and outlines future measurements to solidify these patterns and deepen understanding of in-medium hadron dynamics.

Abstract

We present a model-independent extraction of the phi-4He scattering length from near-threshold phi photoproduction on helium-4, based on LEPS Collaboration data for the coherent process gamma + 4He -> phi + 4He and the Vector Meson Dominance framework. Assuming an energy-independent differential cross section, we extract the absolute value of the phi-4He scattering length |alpha_{phi4He}| = (3.33 +- 0.06) x 10^{-4} fm from a fit at threshold t_thr. This value is orders of magnitude smaller than those for phi-N and phi-d scattering lengths, indicating an inverse dependence of |alpha_VA| on the target nucleus mass. Our results provide new insight into the phi-nucleus interaction, supporting the notion of weak phi-nucleus coupling. We further explore the dependence of |alpha_VA| on the vector meson mass, the target atom mass, and the threshold energy. An approximate exponential suppression of |alpha_VA| is observed with increasing vector meson mass or target atom mass, indicating that heavier vector mesons or heavier target nuclei exhibit weaker couplings in vector meson-nucleus interactions.

Figures (5)

• Figure 1: Differential cross sections of the coherent $\phi$ meson photoproduction ($\gamma$ + $^{4}$He $\rightarrow$$\phi$ + $^{4}$He) near the threshold as a function of the momentum transfer $-t$ off the helium-4 target LEPS:2017nqz. The six incident photon energies $E_{\gamma}$ (1.785, 1.935, 2.035, 2.135, 2.235 and 2.335 GeV) near the threshold of incoherent $\phi$ meson photoproduction are marked in the figure. The smaller error bars on the vertical axis indicate the statistical error, while the larger ones correspond to the sum of the statistical and systematic errors in quadrature.
• Figure 2: The scattering length of $\phi$-$^{4}$He interation obtained from the differential cross section of $\phi$ photoproduction off a helium-4 based on the VMD model, as shown by the magenta star marker. Comparison of the scattering lengths $|\alpha_{VA}|$ as a function of the inverse mass of vector mesons, including $\omega$, $\rho^{0}$, $\phi$, $J/\psi$, $\psi(2S)$ and $\Upsilon$. The red squares show the $|\alpha_{\omega n^{*}}|$, $|\alpha_{\omega p^{*}}|$, $|\alpha_{\omega p}|$ and $|\alpha_{\phi N}|$ scattering length at threshold $t_{thr}$ from our previous work Han:2022khg. The blue cricles show the Strakovsky's analysis of $\omega$Strakovsky:2014wja, $\phi$Strakovsky:2020uqs, $J/\psi$Pentchev:2020kao and $\Upsilon$Strakovsky:2021vyk. The green triangles shows the Wang's analysis $\rho^{0}$Wang:2022zwz and $\psi(2S)$Wang:2022xpw. The long blue dashed line is hypothetical for vector meson-nucleon scattering length. The black diamonds for $|\alpha_{\phi d}|$, $|\alpha_{\omega d}|$ and $|\alpha_{\rho^{0} d}|$ are taken from Wang's work Wang:2022tucWang:2023wlq; The black up triangles for $|\alpha_{\Upsilon d}|$ and $|\alpha_{J/\psi d}|$ are taken from Wang's prediction Wang:2023wlq; The long black dashed line is hypothetical for vector meson-deuteron scattering length.
• Figure 3: The scattering lengths of $\phi$-N, $\phi$-d and $\phi$-$^{4}$He interation as function as the the inverse of the target atom mass. Comparison of the scattering lengths $|\alpha_{VN}|$ as a function of the inverse mass of vector mesons, including $|\alpha_{\phi N}|$ scattering length at threshold $t_{thr}$ from our previous work Han:2022khg, $|\alpha_{\phi d}|$ from Wang's work Wang:2022tuc, and $\phi$-$^{4}$He from our this work. The long black dashed line is hypothetical for vector meson-nuleon and vector meson-nucleus scattering length, with the empirical formula being $|\alpha_{\phi N}| \sim 10^{-A}$, where $A$ is the atomic mass number treated as a free parameter.
• Figure 4: The scattering lengths of vector meson-nuleon, vector meson-deuteron and vector meson-$^{4}$He interation as function as the the inverse of the threshold energy $\sqrt{s_{thr}}$, where $s_{thr}$ = $(m_{V} + m_{N})^{2}$ with $m_{V}$ and $m_{N}$ being the masses of the vector meson and the target atom, respectively. The long blue dashed line is hypothetical for vector meson-nuleon and vector meson-nucleus scattering length, with the assumed formula being $|\alpha_{VA}|$$\sim$$p_{0} \times e^{\frac{p_1}{\sqrt{s_{thr}}}}$, where $p_0$ and $p_1$ are assumed free parameters.
• Figure 5: The scattering lengths of vector meson-nuleon, vector meson-deuteron and vector meson-$^{4}$He interation as function as the the inverse of the product of the the threshold energy $\sqrt{s_{thr}}$ and the square of the ratio of target atom mass $m_{T}$ to vector meson mass $m_{V}$. These long dashed lines are hypothetical for vector meson-nucleon and vector meson-nucleus scattering length, with the assumed formula being $|\alpha_{VA}|$$\sim$$p_0 \times e^{\frac{p_1}{\sqrt{s_{thr}}}\times (\frac{m_{T}}{m_{V}})^{2}}$, where $p_0$ and $p_1$ are assumed free parameters. Specifically, the blue dashed line represents the assumption for the vector meson-nucleon scattering length, the black dashed line represents the assumption for the vector meson-deuteron scattering length, the magenta dashed line represents the assumption for the vector meson-$^{4}$He scattering length.