Super-allowed Fermi beta-decay

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Abstract

A final analysis of Jπ=0+0+ super-allowed Fermi transitions yields |Vud|2=0.9500±0.0007; |Vud|2+|Vus|2+|Vub|2=0.9999±0.0011 with the operational vector coupling constant GV*/(c)3=(1.15052±0.00021)×10-5GeV-2.

Section snippets

Background

Several papers, of which the most recent is Ref. [1], have examined the extraction of the Vud element of the Cabibbo–Kobayashi–Maskawa (CKM) matrix from super-allowed Fermi beta-decay within Jπ=0+; T=1 isomultiplets. Such decay is, in principle, extremely simple: in a zero-order, charge-independent world it would, by comparison with muon-decay, give immediate access to |Vud|. Chief interest in Vud resides in the association of that element of the CKM matrix with the Vus and Vub elements in

The phase-space factor

The phase-space factor f, a critical element in quantitative analysis, may be evaluated either by full monolithic solution of the Dirac equation for the departing positron moving under the electromagnetic influence of a residual nucleus of given form, as pursued in Ref. [3] and related papers, or by explicit exposure of, and separate evaluation of the effects of, the several elements that define the physical structure and influence of the residual nucleus as has been pursued in the series of

Input data

The present work is chiefly procedural; for purposes of comparison it uses the same input data as Ref. [1]; more recent data have negligible effect upon present conclusions as to Vud and unitarity.

The correction terms

We now display, in Table 2, the effects of the several correction terms, as set out in Eq. (3), that arise in the analysis of these super-allowed Fermi transitions. Although our final evaluation of the Fermi constant will employ only transitions through 46V we list the corrections through 54Co to illuminate continuing trends.

Sensitivity to the nuclear charge distribution

The f-values depend upon the nuclear charge radius and also upon the form of the charge distribution, both radial and angular. Here we do not discuss in detail the effect on the phase-space factor of possible departures from (intrinsic) spherical symmetry of the participating nuclei, i.e. the angular effect to which reference has just been made: a detailed study [5] suggested that such influence upon f for cases of present interest would be less than 0.01% although approaching that figure in

The extrapolation to Zf=0.5; (ft)02* and (ft)03*

Table 2 has displayed the effects, individually upon the several bodies of our concern, of various omissions from the full X-factor of Eq. (3). Our chief overall interest, however, is in the effect of such omissions upon our inferred extrapolations to Zf=0.5, viz. (ft)02* and (ft)03* as defined and used in Refs. [1], [2]. Here (ft)2*=ft(1+ΔR)(1-δC), ΔR being the overall radiative correction as defined in Eq. (204) of Ref. [4] and δC the nuclear mismatch as discussed in Ref. [4]; (ft)3*=ft(1+ΔR)(

CKM unitarity

To test CKM unitarity in respect of the first row of the matrix we need, in addition to |Vud|2, both |Vus|2 and |Vub|2. The last is very small [7]:|Vub|2=(1.3±0.5)×10-5and may safely be ignored for the unitarity test. |Vus|, however, is important but is the object of some present uncertainty:fromRef.[7]:|Vus|2=0.0484±0.0011,fromRef.[8]:|Vus|2=0.0506±0.0012,fromRef.[9]:|Vus|2=0.0507±0.0010.Eq. (15) is the global recommendation of the current Review of Particle Physics; Eq. (16) derives from

The operational GV*

The analysis of Section 7 may, alternatively, be used to derive (see Section 6 of Ref. [2]):GV*/(c)3=(1.15052±0.00021)×10-5GeV-2.

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