Abstract
We elaborate on the dichotomy between the description of the semileptonic decays of heavy hadrons on the one hand and the semileptonic decays of light hadrons such as neutron beta decays on the other hand. For example, almost without exception the semileptonic decays of heavy baryons are described in cascade fashion as a sequence of two two-body decays B_1 rightarrow B_2 + W_mathrm{off-shell} and W_{mathrm{off-shell}} rightarrow ell + nu _ell whereas neutron beta decays are analyzed as true three-body decays n rightarrow p + e^- +{bar{nu }}_e. Within the cascade approach it is possible to define a set of seven angular observables for polarized neutron beta decays as well as the longitudinal, transverse and normal polarization of the decay electron. We determine the dependence of the observables on the usual vector and axial vector form factors. In order to be able to assess the importance of recoil corrections we expand the rate and the q^2 averages of the observables up to NLO and NNLO in the recoil parameter delta =(M_n-M_p)/(M_n+M_p)= 0.689cdot 10^{-3}. Remarkably, we find that the rate and three of the four parity conserving polarization observables that we analyze are protected from NLO recoil corrections when the second class current contributions are set to zero.
Highlights
The advantage of the cascade approach to polarized neutron decays is that one can define a larger number of unpolarized and neutron spin-related polarization observables than is possible in the three-body decay approach
We elaborate on the dichotomy between the description of the semileptonic decays of heavy hadrons on the one hand and the semileptonic decays of light hadrons such as neutron β decays on the other hand
Almost without exception the semileptonic decays of heavy baryons are described in cascade fashion as a sequence of two two-body decays B1 → B2 + Woff−shell and Woff−shell →
Summary
The advantage of the cascade approach to polarized neutron decays is that one can define a larger number of unpolarized and neutron spin-related polarization observables than is possible in the three-body decay approach. The set of sixteen double spin density matrix elements in Eq (1) contains twelve T -even and four T -odd structure functions. When counting the number of polarization observables one has to subtract the trace of the double density matrix since polarization observables correspond to normalized double spin density matrix elements This leaves one with eleven T -even and four T -odd observables. Where A ∼ H++ + H−−, B ∼ H++ − H−−, C ∼ ReH+− and D ∼ ImH+−, and Pn = |Pn| is the magnitude of the polarization of the neutron This leaves one with the three independent normalized observables given by B/A, C/A and D/A compared to the 15 observables in the helicity approach.
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