Speaker
Description
We still do not know if the neutrino is a Majorana or a Dirac particle, i.e. if the neutrino is its own antiparticle or not. Also the absolute mass scale of the neutrino is unknown, only the relative scale is known from the neutrino-oscillation experiments. These unknown features of the neutrino can be
tackled by experiments trying to detect the neutrinoless double beta ($0\nu\beta\beta$) decay. The rate of $0\nu\beta\beta$ decay can be schematically written as (here we speak about the double beta-minus decay)
\begin{equation}
%\label{eq:0vbb}
0\nu\beta\beta-\mathrm{rate} \sim \left\vert M^{(0\nu)}{\rm GTGT}\right\vert^2 =
g{{\rm A},0\nu}^4 \left\vert \sum_{J^{\pi}}
(0^+f||\mathcal{O}^{(0\nu)}{\rm GTGT}(J^{\pi})||0^+_i)\right\vert^2 \,,
\end{equation}
where $M^{(0\nu)}_{\rm GTGT}$ is the double Gamow-Teller nuclear matrix element, $\mathcal{O}^{(0\nu)}_{\rm GTGT}$ denotes the transition operator mediating the $0\nu\beta\beta$ transition through the various multipole states $J^{\pi}$,
$0^+_i$ denotes the initial ground state, and the final ground state is denoted by $0^+_f$ (for simplicity, we
neglect the smaller double Fermi and tensor contributions). In the middle one has the intermediate states of multipolarity $J^{\pi}$, leading to the left-leg and right-leg transitions to the $J^{\pi}$ states. Here
$g^{\rm eff}_{{\rm A},0\nu}$ denotes the effective (quenched) value of the weak axial-vector coupling for $0\nu\beta\beta$ decay and it plays an extremely important role in determining the $0\nu\beta\beta$-decay rate since the rate is proportional to its 4$th$ power. The amount of quenching has become an important issue in the
neutrino-physics community due to its impact on the sensitivities of the present and future large-scale $0\nu\beta\beta$-decay experiments [1,2].
The ordinary muon capture (OMC) is a process where a muon $\mu^-$ is captured from the atomic $s$ orbital by the nucleus, quite like in the case of the nuclear electron capture (EC). Since the mass of the muon is some 200 times that of the electron, in the OMC the involved momentum exchange is much larger than in the EC, of the order of $100$ MeV/$c$. Also final states of high excitation energy and high multipolarity $J^{\pi}$ are excited. This makes the OMC a perfect probe of the right leg of $0\nu\beta\beta$ decay in the above equation. In [3] the OMC was proposed to serve as a probe of the nuclear wave functions of the intermediate states of the $0\nu\beta\beta$ decay. Also the effective value of $g_{\rm A}$ (and the induced weak currents) can be probed at the correct momentum-exchange range. Since the proposal made in [3], OMC studies have been performed for both light and heavy nuclei, relevant for the $\beta\beta$ decays [4]. In my talk I will highlight the present status of both the experimental and theoretical studies of the OMC.
*** REFERENCES ***
[1] J. Suhonen, Impact of the quenching of $g_{\rm A}$ on the sensitivity of
$0\nu\beta\beta$ experiments, Phys. Rev. C 96 (2017) 055501.
[2] J. Suhonen, Value of the axial-vector coupling strength in $\beta$ and
$\beta\beta$ decays: A review, Front. Phys. 5 (2017) 55.
[3] M. Kortelainen and J. Suhonen, Ordinary muon capture as a probe of virtual transitions of $\beta\beta$ decay, Europhys. Lett. 58 (2002) 666.
[4] H. Ejiri, J. Suhonen and K. Zuber, Neutrino-nuclear responses for astro-neutrinos, single beta decays and double beta decays, Phys. Rep. 797 (2019) 1.
