Determining the leading-order contact term in neutrinoless double β decay

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(p1)n(p2)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 1S0 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 1S0NN 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.

The unique Polyakov blocks

In this work we present a closed form expression for Polyakov blocks in Mellin space for arbitrary spin and scaling dimensions. We provide a prescription to fix the contact term ambiguity uniquely by reducing the problem to that of fixing the contact term ambiguity at the level of cyclic exchange amplitudes — defining cyclic Polyakov blocks — in terms of which any fully crossing symmetric correlator can be decomposed. We also give another, equivalent, prescription which does not rely on a decomposition into cyclic amplitudes. We extract the OPE data of double-twist operators in the direct channel expansion of the cyclic Polyakov blocks using and extending the analysis of [1, 2] to include contributions that are non-analytic in spin. The relation between cyclic Polyakov blocks and analytic Bootstrap functionals is underlined.

Vector meson-baryon octet interaction and resonances generated dynamically

The interaction potentials between vector mesons and baryon octet are calculated explicitly with a summation of t-, s-, and u- channel diagrams and a contact term originating from the tensor interaction. Altogether, 13 resonances are generated dynamically in different channels of strangeness zero by solving the relativistic Lippman-Schwinger equations in the S-wave approximation, and their masses, decay widths, isospins and spins are determined. Some resonances are well fitted with their counterparts listed in the newest review of Particle Data Group (PDG),1 while others might stimulate the experimental observation in these energy regions in the future.

THE ωρπ COUPLING IN THE VMD MODEL REVISITED

We determine the value of the ω-ρ-π mesons coupling (gωρπ), in the context of the vector meson dominance model, from radiative decays, the ω→3π decay width and the e+e-→3π cross-section. For the last two observables we consider the effect of either a heavier resonance (ρ′(1450)) or a contact term. A weighted average of the results from the set of observables yields gωρπ = 14.7±0.1 GeV -1 in absence of those contributions, and gωρπ = 11.9 ± 0.2 GeV -1 or gωρπ = 11.7 ± 0.1 GeV -1 when including the ρ′ or contact term, respectively. The inclusion of these additional terms makes the estimates from the different observables to lay in a more reduced range. Improved measurements of these observables and the ρ′(1450) meson parameters are needed to give a definite answer on the pertinence of the inclusion of this last one in the considered processes.