Impact of new particles on the ratio of Electromagnetic form factors

We consider the electromagnetic form factors ratio in the Rosenbluth and polarization methods. We explore the impact of adding new particles as the mediators in the electron-proton scattering on these ratios. Consequently, we find some bound on the scalar coupling as $α_{sc}\sim 10^{-5}$ for $m_{sc}\sim 5 MeV-2 GeV$ and $α_{sc}\sim 10^{-4}-10^{-3}$ for $m_{sc}\sim 2-10 GeV$. Meanwhile, the vector coupling is bounded as $α_v\sim 10^{-5}$ for $m_v\sim 5 MeV-1.1 GeV$ and $α_v\sim 10^{-4}-10^{-3}$ for $m_v\sim 1.2-10 GeV$. These constraints are in complete agreement with those which is found from other independent experiments.

💡 Research Summary

The paper addresses the long‑standing discrepancy between the proton electromagnetic form‑factor ratio R = G_E/G_M extracted using the Rosenbluth (cross‑section) method and the polarization‑transfer method in elastic electron‑proton scattering. While the Rosenbluth technique yields a ratio that falls slowly with increasing momentum transfer Q², polarization data show a much steeper decline, a problem often referred to as the “proton form‑factor puzzle.” Traditional explanations invoke hard two‑photon exchange (TPE), but TPE calculations are model‑dependent and recent measurements (OLYMPUS, VEPP‑3, CLASS) up to Q² ≈ 2 GeV² do not fully support the predicted size of the effect.

The authors propose that the exchange of a new light boson—either a scalar (φ) or a vector (V) particle—could modify the scattering amplitude and thus the extracted form‑factor ratio. They write down simple interaction Lagrangians:

• Scalar: L_sc = ½(∂φ)² − ½ m_sc² φ² + g_f^sc φ \barψ_f ψ_f
• Vector: L_v = −¼ V_μν V^{μν} + ½ m_v² V_μ V^{μ} + g_f^v \barψ_f γ^μ ψ_f V_μ

Here g_e and g_p denote the couplings to the electron and proton, respectively, and α_sc = g_e^sc g_p^sc/(4π), α_v = g_e^v g_p^v/(4π). In the limit of vanishing electron mass the interference term between photon and new‑boson exchange disappears, so the total cross‑section is simply the sum of the pure‑photon piece and a new contribution proportional to (g_e g_p)²/(q² − m²)².

For the scalar case the additional term contributes only to the electric form factor G_E, leaving the magnetic form factor unchanged. Consequently the Rosenbluth reduced cross‑section acquires an extra piece proportional to ζ²(1+τ)(1 − ε)/2, where ζ = α_sc F′(q²)/