Neutron beta-decay, Standard Model and cosmology

The precise value of the neutron lifetime is of fundamental importance to particle physics and cosmology. The neutron lifetime recently obtained, 878.5 +/- 0.7stat +/- 0.3sys s, is the most accurate one to date. The new result for the neutron lifetime differs from the world average value by 6.5 standard deviations. The impact of the new result on testing of Standard Model and on data analysis for the primordial nucleosynthesis model is scrutinized.


Introduction, present status of neutron β-decay studies
The problem of precise measurements of the neutron lifetime is important for elementary particle physics and cosmology. The decay of a free neutron into a proton, an electron, and an antineutrino is determined by the weak interaction comprising the transition of a d-quark into a u-quark.
In the Standard Model of elementary particles, the quark mixing is described by the Cabibbo-Kobayashi-Maskawa (CKM) matrix which must be unitary. The values of the individual matrix elements are determined by the weak decays of the respective quarks. In particular, the matrix element V ud can be determined from the data on nuclear β-decay and neutron β-decay. The extraction of V ud from the data on neutron β-decay is extremely tempting due to the theoretical simplicity of describing the neutron decay compared to the description of nuclear decay. Unfortunately, the experimental procedure is a very complicated one, since it requires precise measurements of the neutron lifetime τ n and the β-decay asymmetry A 0 .
The general formula for calculating |V ud | 2 is based on the neutron β-decay data τ n and A 0 [1] ( ) 2 ud 2 n (4908.7 1.9) , where f is the phase space factor, R δ ′ is a model-independent external radiative correction, R Δ is a model-dependent internal radiative correction, λ is the ratio of the axial-vector weak coupling constant to the vector coupling constant, F G is the Fermi weak coupling constant determined from the μ-decay, and ( ) ( ) The formula (1) takes into account accuracy of calculation of radiative correction [1]. Thus, the required relative accuracy of measuring the neutron lifetime τ n must be higher than 10 -3 and than 2·10 -3 for A 0 .
The accuracy of determination of neutron lifetime (τ n ) and asymmetry (A 0 ) of neutron β-decay have been increased during the last 30 years about 20 times. The next sections will be devoted to the analysis of the new result for neutron lifetime [4] and the most precise result of A 0 [2,3] for Standard Model and cosmology.

Standard Model with the most precision data of neutron β-decay
The main aim of precision measurements of neutron β-decay is to find deviations    inclined line demonstrates dependence of n V ud from λ, which corresponds to equation (1). The vertical line is λ-value from [2,3]. The crossing of these lines gives n V ud value determined from neutron β-decay. We can compare n V ud with 00 V ud and with ( ) For V-A test we have the following result: n V ud -00 V ud = (2.4±1.0)·10 -3 or 2.4σ.
As far as unitarity test is concerned the following equation can be written:

Neutron β-decay and cosmology
Precise measurements of the neutron lifetime are also critically important when of the helium-4 abundance comprises ±0.61% [6]. Similarly, a variation in the neutron lifetime by 1% changes η 10 by 17%, although the modern accuracy of estimation of this quantity amounts to ±3.3% [6].
Detailed analysis of the nucleosynthesis process in the early stages of the formation of the Universe was recently made by Mathews et al. [6]. They analyzed the effect of the new value of the neutron lifetime on the consistency of data on the initial abundances of D and 4 He isotopes and the data on baryon asymmetry η 10 . Fig. 4 displays the dependences of the initial abundance of 4 He (Y p ) on the baryon asymmetry 9 η 10 taken from Ref. [6]. Clearly, the use of the new value of the neutron lifetime improves the agreement between the data on the initial abundances of deuterium and helium, and those on baryon asymmetry. Although the accuracy of the cosmological data is much lower than that of measurements of the neutron lifetime, the shift of τ n from the world average value to the new value has a certain effect on the verification of the nucleosynthesis model in the early stages of the formation of the Universe.

Conclusion
The new measurement of neutron lifetime [4] improves It should be mentioned that at present time there are several projects for precision measurements of τ n and A 0 with relative accuracy 10 -3 [3,7] therefore we can hope to obtain rather soon important information about tests of Standard Model from neutron βdecay.