In this work, a comprehensive, two-photon-exchange (TPE)-consistent analysis of the unpolarized reduced cross section ${\sigma }_R(\varepsilon ,Q^2)$ for elastic electron-proton ($ep$) scattering is performed to search for possible contributions from a light neutral scalar mediator and to establish quantitative constraints in their absence. The framework incorporates the standard one-photon-exchange (OPE) term, the phenomenological TPE correction, and an additional scalar amplitude whose strength is governed by the dimensionless coupling ratio $\beta ={\alpha }_s/\alpha$, defined as the scalar proton-electron coupling ${\alpha }_s$ normalized to the electromagnetic fine-structure constant $\alpha$. The scalar strength $S\left(Q^2\right)$ is extracted from linear Rosenbluth fits to world ${\sigma }_R$ data at 134 $Q^2$ points spanning $0.0155\le Q^2\le 5.5{\mathrm{GeV}}^2$. The data exhibit no statistically significant deviation from the $\mathrm{OPE}+\mathrm{TPE}$ baseline, and the global profile likelihood saturates the physical boundary $\widehat{\beta }=0$ for all scanned mediator masses. One-sided 95% confidence-level upper limits ${\beta }_{95}\left(m_s\right)$ are obtained using a profile-likelihood construction over the mass range $0.04\le m_s\le 10\mathrm{GeV}$. Accordingly, the primary result of this work is the determination of quantitative exclusion limits on the scalar coupling, rather than evidence of a nonzero contribution. The resulting exclusion curve lies at the level of a few $\times {10}^{-3}$ to ${10}^{-2}$ depending on $m_s$, with systematic uncertainties increasing the limits by only 5–10% across most of the mass range. These limits improve upon, or are comparable to, previously reported electromagnetic-form-factor-based scalar constraints in the low- to intermediate-mass region and constitute the first dedicated, TPE-consistent ${\sigma }_R$-based search for light scalar exchange in elastic $ep$ scattering. No evidence for a scalar contribution is observed within the present experimental sensitivity.

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• Lepton induced nuclear reactions
• Particle interactions
• QCD in nuclear reactions
• Form factors