A<sc>bstract</sc> In this paper we explorepp→W±(ℓ±ν)γto$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ 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$$ \mathcal{O}\left(1/{\Lambda}^2\right) $$ 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, ~$$ \mathcal{O}\left({E}^4/{\Lambda}^4\right) $$ , as dimension six squared. While energy-enhanced SMEFT contributions are a main focus, our calculation includes the complete set of$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ SMEFT effects consistent with U(3)5flavor symmetry. Additionally, we include the decay of theW±→ ℓ±ν, making the calculation actually$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ . As such, we are able to study the impact of non-resonant SMEFT operators, such as$$ \left({L}^{\dagger }{\overline{\sigma}}^{\mu }{\tau}^IL\right)\left({Q}^{\dagger }{\overline{\sigma}}^{\nu }{\tau}^IQ\right) $$ Bμν, which contribute to$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ directly and not to$$ \overline{q}{q}^{\prime}\to {W}^{\pm}\gamma $$ . We show several distributions to illustrate the shape differences of the different contributions.
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Determining the leading-order contact term in neutrinoless double β decay
A bstract We present a method to determine the leading-order (LO) contact term contributing to the nn → ppe − e − amplitude through the exchange of light Majorana neutrinos. Our approach is based on the representation of the amplitude as the momentum integral of a known kernel (proportional to the neutrino propagator) times the generalized forward Compton scattering amplitude n ( p 1 ) n ( p 2 ) W + ( k ) → $$ p\left({p}_1^{\prime}\right)p\left({p}_2^{\prime}\right){W}^{-}(k) $$ p p 1 ′ p p 2 ′ W − k , in analogy to the Cottingham formula for the electromagnetic contribution to hadron masses. We construct model-independent representations of the integrand in the low- and high-momentum regions, through chiral EFT and the operator product expansion, respectively. We then construct a model for the full amplitude by interpolating between these two regions, using appropriate nucleon factors for the weak currents and information on nucleon-nucleon ( NN ) scattering in the 1 S 0 channel away from threshold. By matching the amplitude obtained in this way to the LO chiral EFT amplitude we obtain the relevant LO contact term and discuss various sources of uncertainty. We validate the approach by computing the analog I = 2 NN contact term and by reproducing, within uncertainties, the charge-independence-breaking contribution to the 1 S 0 NN scattering lengths. While our analysis is performed in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme, we express our final result in terms of the scheme-independent renormalized amplitude $$ {\mathcal{A}}_{\nu}\left(\left|\mathbf{p}\right|,\left|\mathbf{p}^{\prime}\right|\right) $$ A ν p p ′ at a set of kinematic points near threshold. We illustrate for two cutoff schemes how, using our synthetic data for $$ {\mathcal{A}}_{\nu } $$ A ν , one can determine the contact-term contribution in any regularization scheme, in particular the ones employed in nuclear-structure calculations for isotopes of experimental interest.
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- PAR ID:
- 10251130
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2021
- Issue:
- 5
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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