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Register a new userEffective Majorana mass matrix from tau and pseudoscalar meson lepton number violating decays
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An observation of any lepton number violating process will undoubtedly point towards the existence of new physics and indirectly to the clear Majorana nature of the exchanged fermion. In this work, we explore the potential of a minimal extension of the Standard Model via heavy sterile fermions with masses in the $[ 0.1 - 10]$ GeV range concerning an extensive array of neutrinoless meson and tau decay processes. We assume that the Majorana neutrinos are produced on-shell, and focus on three-body decays. We conduct an update on the bounds on the active-sterile mixing elements, $|U_{ell_alpha 4} U_{ell_beta 4}|$, taking into account the most recent experimental bounds (and constraints) and new theoretical inputs, as well as the effects of a finite detector, imposing that the heavy neutrino decay within the detector. This allows to establish up-to-date comprehensive constraints on the sterile fermion parameter space. Our results suggest that the branching fractions of several decays are close to current sensitivities (likely within reach of future facilities), some being already in conflict with current data (as is the case of $K^+ to ell_alpha^+ ell_beta^+ pi^-$, and $tau^- to mu^+ pi^- pi^-$). We use these processes to extract constraints on all entries of an enlarged definition of a $3times 3$ effective Majorana neutrino mass matrix $m_{ u}^{alpha beta}$.
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The Schechter-Valle theorem states that a positive observation of neutrinoless double-beta ($0 u beta beta$) decays implies a finite Majorana mass term for neutrinos when any unlikely fine-tuning or cancellation is absent. In this note, we reexamine the quantitative impact of the Schechter-Valle theorem, and find that current experimental lower limits on the half-lives of $0 u beta beta$-decaying nuclei have placed a restrictive upper bound on the Majorana neutrino mass $|delta m^{ee}_ u| < 7.43 times 10^{-29}~{rm eV}$ radiatively generated at the four-loop level. Furthermore, we generalize this quantitative analysis of $0 u beta beta$ decays to that of the lepton-number-violating (LNV) meson decays $M^- to {M^prime}^+ + ell^-_alpha + ell^-_beta$ (for $alpha$, $beta$ = $e$ or $mu$). Given the present upper limits on these rare LNV decays, we have derived the loop-induced Majorana neutrino masses $|delta m^{ee}_ u| < 9.7 times 10^{-18}~{rm eV}$, $|delta m^{emu}_ u| < 1.6 times 10^{-15}~{rm eV}$ and $|delta m^{mu mu}_ u| < 1.0 times 10^{-12}~{rm eV}$ from $K^- to pi^+ + e^- + e^-$, $K^- to pi^+ + e^- + mu^-$ and $K^- to pi^+ + mu^- + mu^-$, respectively. A partial list of radiative neutrino masses from the LNV decays of $D$, $D_s^{}$ and $B$ mesons is also given.
We study the discovery prospect of different three body lepton number violating~(LNV) meson decays $M_{1}^{-}toell_{1}^{-}ell_{2}^{-}M_{2}^{+}$ in the framework of right handed~(RH) neutrino extended Standard Model~(SM). We consider a number of ongoing experiments, such as, NA62 and LHCb at CERN, Belle II at SuperKEK, as well as at the proposed future experiments, SHiP, MATHUSLA and FCC-ee. The RH Majorana neutrino $N$ mediating these meson decays provides a resonant enhancement of the rates, if the mass of $N$ lies in the range $(100, text{MeV}-6, text{GeV})$. We consider the effect of parent mesons velocity, as well as, the effect of finite detector size. Using the expected upper limits on the number of events for the LNV decay modes, $M_{1}^{-} toell_1^{-}ell_2^{-}pi^{+}$~($M_{1}=B, B_c,D, D_{s},text{and},K$), we analyze the sensitivity reach of the mixing angles $|V_{e N}|^{2}$, $|V_{mu N}|^{2}$, $|V_{tau N}|^{2}$, $|V_{e N}V_{mu N}|$, $|V_{e N}V_{tau N}|$ and $|V_{mu N}V_{tau N}|$ as a function of heavy neutrino mass $M_{N}$. We show that, inclusion of parent meson velocity can account to a large difference for active-sterile mixing, specially for $D$, $D_s$ meson decay at SHiP and $K$ meson decay at NA62. Taking into account the velocity of the $D_s$ meson, the future beam dump experiment SHiP can probe $|V_{eN}|^2 sim 10^{-9}$. For RH neutrino mass in between 2 - 5 GeV, MATHUSLA can provide best sensitivity reach of active-sterile mixings.
We search for lepton-number- and baryon-number-violating decays $tau^{-}tooverline{p}e^{+}e^{-}$, $pe^{-}e^{-}$, $overline{p}e^{+}mu^{-}$, $overline{p}e^{-}mu^{+}$, $overline{p}mu^{+}mu^{-}$, and $pmu^{-}mu^{-}$ using 921 fb$^{-1}$ of data, equivalent to $(841pm12)times 10^6$ $tau^{+}tau^{-}$ events, recorded with the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider. In the absence of a signal, $90%$ confidence-level upper limits are set on the branching fractions of these decays in the range $(1.8$-$4.0)times 10^{-8}$. We set the worlds first limits on the first four channels and improve the existing limits by an order of magnitude for the last two channels.
We have calculated the decay $tau rightarrow u pi(K) gamma$. We present the photon energy spectrum, the meson-photon invariant mass spectrum and the integrated rate as a function of a photon energy cut or an invariant mass cut. Both the internal bremsstrahlung and the structure dependent radiation have been taken into account. To this aim we have parametrized the form factors $F_V$ and $F_A$, which determine the structure dependent radiation. Observables especially suited for the measurement of the structure dependent form factors are found and implications on the width of the $a_1$ discussed.
We study lepton flavor violating (LFV) tau and B decays in models with heavy neutrinos to constrain the mixing matrix parameters U_{tau N}. We find that the best current constraints when the heavy neutrinos are purely left-handed come from LFV radiative tau decay modes. To obtain competitive constraints in LFV B decay it is necessary to probe b -> X_{s} tau^{pm} e^{mp} at the 10^{-7} level. When the heavy neutrinos have both left and right-handed couplings, the mixing parameters can be constrained by studying LFV B decay modes and LFV tau decay into three charged leptons. We find that the branching ratios B(tau^{pm} -> l_1^{pm} l_2^{pm} l_3^{mp}), B(B_{s} -> tau^{pm} e^{mp}) and B(b -> X_{s} l_1^{pm} l_2^{mp}) need to be probed at the 10^{-8} level in order to constrain the mixing parameters beyond what is known from unitarity.
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