## Final Report Summary - ELECTROWEAK (ELECTROWEAK PROCESSES IN SYSTEMS BOUND BY THE STRONG INTERACTION)

Within the project FP7-MC-IOF-298364, ELECTROWEAK, the researcher Oscar Moreno and his collaborators have performed theoretical analyses of a variety of electromagnetic and weak processes that take place within physical systems bound by the strong interaction, particularly atomic nuclei and hadrons. The scattering of leptons (electrons, neutrinos) off nuclei has had a prominent role among these processes. The outgoing phase of this project has taken place from April 25, 2013 to April 24, 2015 at the Laboratory for Nuclear Science and Center for Theoretical Physics of the Massachusetts Institute of Technology (MIT), U.S.A., with Prof. Thomas William Donnelly as scientist in charge. The return phase has taken place from April 25, 2015 to April 24, 2016 at Universidad Complutense de Madrid (UCM), Spain, with Prof. Elvira Moya de Guerra as scientist in charge.

We have carried out a theoretical study of nuclear and nucleon structure effects in parity-violating elastic electron scattering off nuclei. The violation of parity originates from the interference between the electromagnetic and the weak interactions, which show different behavior under inversion of spatial coordinates; some parity-violating observables accurately probe details of the underlying fundamental interactions, including values of fundamental constants, as well as of the structure of the target. We chose for our studies nuclear targets and kinematic conditions of the electrons according to the suggestions of experimental groups that needed theoretical guidance to prepare proposals for facilities such as the MESA accelerator in Mainz (Germany), Jefferson Lab or Cornell accelerator (U.S.A.). Among the structure details we have considered are the content of strange quarks and antiquarks in protons and neutrons (in addition to the constituent up and down quarks), the isospin mixing (the distribution of protons relative to the one of the neutrons), the electromagnetic distortion of the incoming electron due to the target charge, meson-exchange currents, inelastic transitions to excited states of the target and higher-order corrections. An essential point in these studies was the estimation not only of the size of the nuclear or nucleon structure effects on the parity-violating observables, but also of the corresponding uncertainties by using a variety of nuclear models (a sort of ‘theoretical error bars’).

We have also developed theoretical models for neutrino scattering off nuclei. We used, on the one hand, a scaling approach to compute quasielastic contributions together with meson-exchange currents, the impact of the latter being evaluated and discussed using a convenient parametrization of a fully relativistic calculation. These results can be implemented in the Monte Carlo simulations of neutrino event generators that model neutrino-nucleus interactions, as the ones that take place in neutrino oscillation experiments at the detection stage. In another study, this time of inclusive cross-sections, the superscaling model used for the quasielastic region was extended to the pion production region, and the results were compared with inclusive data from the T2K and SciBooNE experiments.

We have also developed the theoretical formalism of semi-inclusive neutrino-nucleus interactions, which are those processes where a charged lepton (electron, muon) and an ejected nucleon (usually a proton) are detected after the neutrino-nucleus interaction. The formalism includes expressions for the generalized Rosenbluth factors (related to the neutrino kinematics), for the hadronic responses (related to the nuclear target structure and the dynamics of the process), the latter without specification of a nuclear model, as well as for the cross section. Subsequently we applied this formalism to the semi-inclusive deuteron disintegration by neutrinos and computed inclusive and semi-inclusive cross-sections for a large set of kinematic conditions using plane-wave impulse, plane-wave Born, and distorted-wave Born approximations. Among the applications of this work one finds the accurate determination of the incoming neutrino energy by measuring the charged lepton and the nucleon after the deuteron break-up, as well as studies of the axial form factor of the target. Finally, we have worked on yet another type of neutrino-nucleus interaction, coherent scattering, and have related in a simple manner the corresponding cross section with the parity-violating asymmetry and the cross section of elastic electron scattering. This method may allow us to find beyond-Standard-Model features in the neutrino weak neutral interaction and can also be applied to nuclear structure studies. We have extended the formalism from neutrinos to general weakly-interacting particles, that are dark matter candidates, considering a wide range of masses and velocities. And also related to dark matter candidate interactions with nuclei, we have studied the effect of the production of hypothetical sterile neutrinos in the keV mass scale in the spectra of nuclear beta decay and electron capture. Results for beta decay in Tritium and electron capture in Holmium and Lead isotopes have been obtained.

On single and double beta decay, our work has included theoretical and experimental studies of Gamow-Teller strength distributions in neutron-deficient isotopes in the region of Lead, the analysis of theoretical matrix elements of the two neutrino process and the calculation of two-neutrino and zero-neutrino double beta decay matrix elements in closure approximation.

Some of the results described above that have been obtained during the execution of the project can be found in the following references, where the researcher is a co-author:

- On parity violation: Phys. Rev. C 89 (2013) 015501(“Nuclear structure uncertainties in parity-violating electron scattering from carbon 12”). AIP Conf. Proc. 1563 (2013) 82 (“Nuclear physics aspects involved in studies of low-Q parity-violating electron scattering from nuclei”). Rom. J. Phys. 58 (2013) 1270 (“Nuclear structure aspects of atomic parity violation in Barium”). J. Phys. G: Nucl. Part. Phys. 42 (2015) 034006 (“Evaluation of theoretical uncertainties in parity-violating electron scattering from nucleons and nuclei”). Phys. Rev. C 92 (2015) 055504 ("Unified approach to electron and neutrino elastic scattering off nuclei with an application to the study of the axial structure").

- On neutrino-nucleus scattering: Phys. Rev. D 90 (2014) 013014 (“Semi-inclusive charged-current neutrino-nucleus reactions”). Phys. Rev. D 92 (2015) 053006 ("Coincidence charged-current neutrino-induced deuteron disintegration"). Rev. D 91 (2015) 073004 (“Meson-exchange currents and quasielastic predictions for charged-current neutrino - carbon 12 scattering in the superscaling approach”). J. Phys. G: Nucl. Part. Phys. 43 (2016) 045101 (“Charged-current inclusive neutrino cross sections in the superscaling model including quasielastic, pion production and meson-exchange contributions”). AIP Conf. Proc. 1577 (2016) 030005 (“Charged-current inclusive neutrino cross sections in the superscaling model”).

- On sterile neutrinos and WIMPs in ordinary nuclear processes: Nucl. Phys. B 866 (2013) 177 ("Role of sterile neutrino warm dark matter in rhenium and tritium beta decays"). Submitted to Phys. Rev. D, arXiv:1603.05932v1 ("Elastic vector and axial scattering of weakly interacting particles off nuclei"). Submitted to Advances in High Energy Physics ("Warm dark matter sterile neutrinos in electron capture and beta decay spectra").

- On single and double beta decay: AIP Conf. Proc. 1572 (2013) 3 ("Testing the Single-State Dominance Hypothesis"). Rom. J. Phys. 58 (2013) 9 ("Gamow-Teller strength distributions in the double-beta decay partners Te 128 - Te 130 and Xe 128 - Xe 130"). AIP Conf. Proc. 1681 (2015) 050007 ("Beta-decay properties of neutron-deficient Pt, Hg, and Pb isotopes"). J. Phys: Conf. Ser. 665 (2016) 012044 ("Nuclear astrophysics with radioactive ions at FAIR"). Phys. Rev. C 92 (2015) 044321 ("Shapes of Pb-192, Pb-190 ground states from beta-decay studies using the total-absorption technique"). J. Phys: Conf. Ser. 665 (2016) 012044 ("Nuclear astrophysics with radioactive ions at FAIR"). Submitted to Advances in High Energy Physics ("Nuclear structure calculations for two-neutrino double-beta decay").

Some results have also been presented by the researcher of the project in international workshops and conferences, such as the Pittsburgh Neutrino Generator Workshop (U.S.A., 2013); the Mainz Institute of Theoretical Physics Workshop on Low-Energy Precision Physics (Germany, 2013); the INT Workshop on Neutrino–Nucleus Interaction for Current and Next Generation Neutrino Oscillation Experiments (U.S.A, 2013); the Workshop From Parity-Violation to Hadron Structure PAVI 14 (U.S.A., 2014); the Jefferson Lab Workshop on Final State Nucleons for Neutrino-Nucleus Interaction (U.S.A., 2015); the Cornell Intense Electron Beams Workshop (U.S.A., 2015); the ‘VII Conference of the National Center for Particle, Astroparticle and Nuclear Physics’ (Spain, 2015); the ‘CEA Workshop on Two-body current contributions in neutrino-nucleus scattering’ (France, 2016).

We have carried out a theoretical study of nuclear and nucleon structure effects in parity-violating elastic electron scattering off nuclei. The violation of parity originates from the interference between the electromagnetic and the weak interactions, which show different behavior under inversion of spatial coordinates; some parity-violating observables accurately probe details of the underlying fundamental interactions, including values of fundamental constants, as well as of the structure of the target. We chose for our studies nuclear targets and kinematic conditions of the electrons according to the suggestions of experimental groups that needed theoretical guidance to prepare proposals for facilities such as the MESA accelerator in Mainz (Germany), Jefferson Lab or Cornell accelerator (U.S.A.). Among the structure details we have considered are the content of strange quarks and antiquarks in protons and neutrons (in addition to the constituent up and down quarks), the isospin mixing (the distribution of protons relative to the one of the neutrons), the electromagnetic distortion of the incoming electron due to the target charge, meson-exchange currents, inelastic transitions to excited states of the target and higher-order corrections. An essential point in these studies was the estimation not only of the size of the nuclear or nucleon structure effects on the parity-violating observables, but also of the corresponding uncertainties by using a variety of nuclear models (a sort of ‘theoretical error bars’).

We have also developed theoretical models for neutrino scattering off nuclei. We used, on the one hand, a scaling approach to compute quasielastic contributions together with meson-exchange currents, the impact of the latter being evaluated and discussed using a convenient parametrization of a fully relativistic calculation. These results can be implemented in the Monte Carlo simulations of neutrino event generators that model neutrino-nucleus interactions, as the ones that take place in neutrino oscillation experiments at the detection stage. In another study, this time of inclusive cross-sections, the superscaling model used for the quasielastic region was extended to the pion production region, and the results were compared with inclusive data from the T2K and SciBooNE experiments.

We have also developed the theoretical formalism of semi-inclusive neutrino-nucleus interactions, which are those processes where a charged lepton (electron, muon) and an ejected nucleon (usually a proton) are detected after the neutrino-nucleus interaction. The formalism includes expressions for the generalized Rosenbluth factors (related to the neutrino kinematics), for the hadronic responses (related to the nuclear target structure and the dynamics of the process), the latter without specification of a nuclear model, as well as for the cross section. Subsequently we applied this formalism to the semi-inclusive deuteron disintegration by neutrinos and computed inclusive and semi-inclusive cross-sections for a large set of kinematic conditions using plane-wave impulse, plane-wave Born, and distorted-wave Born approximations. Among the applications of this work one finds the accurate determination of the incoming neutrino energy by measuring the charged lepton and the nucleon after the deuteron break-up, as well as studies of the axial form factor of the target. Finally, we have worked on yet another type of neutrino-nucleus interaction, coherent scattering, and have related in a simple manner the corresponding cross section with the parity-violating asymmetry and the cross section of elastic electron scattering. This method may allow us to find beyond-Standard-Model features in the neutrino weak neutral interaction and can also be applied to nuclear structure studies. We have extended the formalism from neutrinos to general weakly-interacting particles, that are dark matter candidates, considering a wide range of masses and velocities. And also related to dark matter candidate interactions with nuclei, we have studied the effect of the production of hypothetical sterile neutrinos in the keV mass scale in the spectra of nuclear beta decay and electron capture. Results for beta decay in Tritium and electron capture in Holmium and Lead isotopes have been obtained.

On single and double beta decay, our work has included theoretical and experimental studies of Gamow-Teller strength distributions in neutron-deficient isotopes in the region of Lead, the analysis of theoretical matrix elements of the two neutrino process and the calculation of two-neutrino and zero-neutrino double beta decay matrix elements in closure approximation.

Some of the results described above that have been obtained during the execution of the project can be found in the following references, where the researcher is a co-author:

- On parity violation: Phys. Rev. C 89 (2013) 015501(“Nuclear structure uncertainties in parity-violating electron scattering from carbon 12”). AIP Conf. Proc. 1563 (2013) 82 (“Nuclear physics aspects involved in studies of low-Q parity-violating electron scattering from nuclei”). Rom. J. Phys. 58 (2013) 1270 (“Nuclear structure aspects of atomic parity violation in Barium”). J. Phys. G: Nucl. Part. Phys. 42 (2015) 034006 (“Evaluation of theoretical uncertainties in parity-violating electron scattering from nucleons and nuclei”). Phys. Rev. C 92 (2015) 055504 ("Unified approach to electron and neutrino elastic scattering off nuclei with an application to the study of the axial structure").

- On neutrino-nucleus scattering: Phys. Rev. D 90 (2014) 013014 (“Semi-inclusive charged-current neutrino-nucleus reactions”). Phys. Rev. D 92 (2015) 053006 ("Coincidence charged-current neutrino-induced deuteron disintegration"). Rev. D 91 (2015) 073004 (“Meson-exchange currents and quasielastic predictions for charged-current neutrino - carbon 12 scattering in the superscaling approach”). J. Phys. G: Nucl. Part. Phys. 43 (2016) 045101 (“Charged-current inclusive neutrino cross sections in the superscaling model including quasielastic, pion production and meson-exchange contributions”). AIP Conf. Proc. 1577 (2016) 030005 (“Charged-current inclusive neutrino cross sections in the superscaling model”).

- On sterile neutrinos and WIMPs in ordinary nuclear processes: Nucl. Phys. B 866 (2013) 177 ("Role of sterile neutrino warm dark matter in rhenium and tritium beta decays"). Submitted to Phys. Rev. D, arXiv:1603.05932v1 ("Elastic vector and axial scattering of weakly interacting particles off nuclei"). Submitted to Advances in High Energy Physics ("Warm dark matter sterile neutrinos in electron capture and beta decay spectra").

- On single and double beta decay: AIP Conf. Proc. 1572 (2013) 3 ("Testing the Single-State Dominance Hypothesis"). Rom. J. Phys. 58 (2013) 9 ("Gamow-Teller strength distributions in the double-beta decay partners Te 128 - Te 130 and Xe 128 - Xe 130"). AIP Conf. Proc. 1681 (2015) 050007 ("Beta-decay properties of neutron-deficient Pt, Hg, and Pb isotopes"). J. Phys: Conf. Ser. 665 (2016) 012044 ("Nuclear astrophysics with radioactive ions at FAIR"). Phys. Rev. C 92 (2015) 044321 ("Shapes of Pb-192, Pb-190 ground states from beta-decay studies using the total-absorption technique"). J. Phys: Conf. Ser. 665 (2016) 012044 ("Nuclear astrophysics with radioactive ions at FAIR"). Submitted to Advances in High Energy Physics ("Nuclear structure calculations for two-neutrino double-beta decay").

Some results have also been presented by the researcher of the project in international workshops and conferences, such as the Pittsburgh Neutrino Generator Workshop (U.S.A., 2013); the Mainz Institute of Theoretical Physics Workshop on Low-Energy Precision Physics (Germany, 2013); the INT Workshop on Neutrino–Nucleus Interaction for Current and Next Generation Neutrino Oscillation Experiments (U.S.A, 2013); the Workshop From Parity-Violation to Hadron Structure PAVI 14 (U.S.A., 2014); the Jefferson Lab Workshop on Final State Nucleons for Neutrino-Nucleus Interaction (U.S.A., 2015); the Cornell Intense Electron Beams Workshop (U.S.A., 2015); the ‘VII Conference of the National Center for Particle, Astroparticle and Nuclear Physics’ (Spain, 2015); the ‘CEA Workshop on Two-body current contributions in neutrino-nucleus scattering’ (France, 2016).