Radiative corrections for neutron decay and search for new physics

The wait fored increased accuracy of neutron [beta]-decay experiments at the fresh Spallation Neutron Source could arise in more stringent tests of the Standard design For an unambiguous search for novel physics in neutron decay experiments and for a precise determination of fundamental constants, it is necessarily to understand and evaluate all corrections for neutron decay with higher accuracy than the awaited experimental precision. We discuss the possibility to estimate the accuracy of radiative corrections. fresh results based on the applications of effective field theory for neutron decay is presented

lock opener words: beta-decay; neutron; radiative corrections; standard model

1 Introduction and Discussion

Neutron [beta]-decay provides the greatest in quantity precise measurements of the relative axial-vector coupling constant [lambda]. The precise value of [lambda] is true important in many applications of the theory of weak interactions, especially in astrophysics, eg a star's neutrino production is proportional to [[lambda].sup.2]. More precise measurements of neutron [beta]-decay parameters are also real important in the search for novel physics. Since neutron decay rate is proportional to the Cabibbo-Kobayashi-Maskawa (CKM) matrix uncompounded body squared, |[V.sub.ud]|[.sup.2], we can obtain [Vsubud] (the u and d quark mixing matrix) independently of the nuclear type Currently, the most accurate value of the matrix uncompounded body [V.sub.ud] is obtained from the measurement of nuclear Fermi transitions in [0sup+] [right arrow] [0sup+] nuclear [beta]-decay. However, the process of the extraction of this matrix simple body involves calculations of radiative corrections for Fermi transition in nuclei. Despite the fact that these calculations have been done with high precision (see [1] and respects therein), it is impossible to sway the values of these nuclear corrections from independent experiments. It is awaited that the planned measurements of the neutron life time and angular coefficients will provide a value for the hadronic vector weak interactions constant with an accuracy comparable to or better than the value determined from the [0sup+] [right arrow] [0sup+] nuclear [beta]-decay experiments. The wait fored increase in the accuracy of experimental data in neutron decay will elevate the status of these experiments and rank them among the greatest in quantity important experiments in fundamental physics. With a more accurate value for [Vsubud] individual could possibly resolve the unitarity point in dispute of the CKM-matrix. The unitarity condition for the CKM matrix in the Standard Model

|[Vsubud]|[sup2] + |[V.sub.us]|[.sup.2] + |[Vsubub]|[sup2] = 1 (1)

gives a constraint upon the three matrix elements. sum of two units of matrix elements, [V.sub.us] = 02196 [+ or -] 00023 and [Vsubub] = 00036 [+ or -] 00007 [2] have been extracted from high activity physics experiments (see also [3 4]) The common value of [V.sub.ud] obtained from nuclear [0sup+] [right arrow] [0sup+] nuclear [beta]-decay 09740 [+ or -] 00005 [1] The [Vsubud] value obtained from neutron [beta]-decay is 09713 [+ or -] 00014 [5] When we use these values and uncertainties in Eq(1) there is at the horizontal of [10.sup.-3] room for novel physics (see for example [5 6 7 8 11 12] and regards therein). It has been argued that the deviation from unitarity could be related to uncertainties in determination of the parameter [V.sub.us] (see for example, [9 10]) However, the first simple body [V.sub.ud] gives the dominant contribution to the unitarity equation and, therefore, it is crucial to obtain a more precise value of [Vsubud] before we can draw conclusions about the validity of the Standard Model

To extract [Vsubud] from the wait fored high precision neutron decay data, individual has to evaluate all corrections for neutron decay with the appropriate accuracy. These corrections are important at the horizontal of a few percent, they are of the same order of magnitude as the wait fored deviations from the Standard type and they should be carefully re-examined. The main belong to is the accuracy and reliability of calculations of the radiative corrections, especially the individuals which are dominated by nucleon structure-dependent contributions.

It is well-known that in the tree approximation (neglecting recoil corrections and electron/proton polarization) the neutron decay rate [13] can be written in confines of the angular correlations coefficients a, A, B and D:

[d[T.sup.3]]/[d[E.sub.e]d[[OMEGA].sub.e]d[[OMEGA].sub.v]] = [PHI] ([Esube])[GsubFsup2]|[Vsubud]|[sup2] (1 + 3[[lambda].sup.2]) X (1 + b [[msube]/[Esube]] + a [[psube] * [p.sub.i]/[E.sub.e][E.sub.i]] + [sigma][A[[p.sub.e]/[E.sub.e]] + B[[p.sub.i]/[E.sub.i]] + D[[psube] X [p.sub.i]/[E.sub.e][E.sub.i]]]), (2)

Here, [sigma] is the neutron spin; [msube] is the electron mass, [Esube] [Esubv] [psube] and [psubv] are the energies and momenta of the electron and neutrino, respectively; and [GsubF] is Fermi constant of weak interaction (obtained from the [mu]-decay rate). The function [PHI] ([Esube]) includes normalization constants, phase-space factors, and standard Coulomb corrections. In the tree approximation the angular coefficients be pendent only on one parameter, [lambda]: