A case study of SMEFT $$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ effects in diboson processes: pp → W±(ℓ±ν)γ

Abstract

Abstract In this paper we explore pp → W±(ℓ±ν)γ to $$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ O 1 / Λ 4 in the SMEFT expansion. Calculations to this order are necessary to properly capture SMEFT contributions that grow with energy, as the interference between energy-enhanced SMEFT effects at $$ \mathcal{O}\left(1/{\Lambda}^2\right) $$ O 1 / Λ 2 and the Standard Model is suppressed. We find that there are several dimension eight operators that interfere with the Standard Model and lead to the same energy growth, ~ $$ \mathcal{O}\left({E}^4/{\Lambda}^4\right) $$ O E 4 / Λ 4 , as dimension six squared. While energy-enhanced SMEFT contributions are a main focus, our calculation includes the complete set of $$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ O 1 / Λ 4 SMEFT effects consistent with U(3)5 flavor symmetry. Additionally, we include the decay of the W±→ ℓ±ν, making the calculation actually $$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ q ¯ q ′ → ℓ ± νγ . As such, we are able to study the impact of non-resonant SMEFT operators, such as $$ \left({L}^{\dagger }{\overline{\sigma}}^{\mu }{\tau}^IL\right)\left({Q}^{\dagger }{\overline{\sigma}}^{\nu }{\tau}^IQ\right) $$ L † σ ¯ μ τ I L Q † σ ¯ ν τ I Q Bμν, which contribute to $$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ q ¯ q ′ → ℓ ± νγ directly and not to $$ \overline{q}{q}^{\prime}\to {W}^{\pm}\gamma $$ q ¯ q ′ → W ± γ . We show several distributions to illustrate the shape differences of the different contributions.