Time-reversal violation in beta decay Page: 4 of 11
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
Time-Reversal Violation In Beta Decay
The fields e, u and d in Eqs. (4) - (7) are the mass eigenstates. The coupling constants are
in general complex, in which case the Hamiltonians violate T-invariance. The constant aLL in
Eq. (4) contains the SM contribution, and can therefore be written as , aLL = (aLL)sM + aLL,
where (aLL)sM = g2Vud/8Mw and a'LL represents contributions from new interactions.
The contribution of the Hamiltonian (3) to Dt and Rt in allowed beta decays is given by
[5]
Dt ~ aImaLR , (8)
R alb - -a(9
Rt ~ 9 gTImaLT - a gsImaLs , (9)
where the upper (lower) sign in the first term in Eq. (9) is for decays with e- (e+)in the final
state. In Eqs. (8) and (9) ik = aik/aLL (ik = LR, LT, LS); a and b are constants containing
the Fermi and Gamow-Teller matrix elements MF and MGT:
4Jj'jMFMGT[J/(J + 1)]1/2gvgA
9vIMFI2+ 94MGTI2
b - 4AJI JMGTI2g2 (11)
92V\MF 2 + 9A MGT 2
In Eq. (11) Ay is an angular momentum factor, defined in Ref. [5]. The quantities g gA (0)
(k = V, A, S, T) are defined by
(pI unadjn) = gv(g2)upgY un , (12)
(pjyvya5d~n) = gA(q2)uPY7xy5un , (13)
(plid~n) = gs(q2)u un , (14)
(pio-,dln) = gT(g2)peAun . (15)
CVC predicts gv = 1, and (neglecting the effects of the possible new interactions) the
experimental value of gA/9v is gA/gV = 1.2670 0.0030 [9]. The constants gs and gT were
calculated in Ref. [10] in connection with a study of neutral current interactions of a general
Lorentz structure. Employing a quark model with spherically symmetric wave functions, 9s
and 9T are given by gs = -2 + 09A ~ 0.6, 9T = s(2 + 3gA) ~ 1.46. The uncertainty in
these predictions has been estimated to be about 30% to 60% [10]. Including an uncertainty
of this size, one has
0.25Z9sZ 1 , (16)
0.6 < gT < 2.3 . (17)
For neutron decay MF = 1, MGT = V/', implying a ~ 0.87, b ~ 2.2, so that
(D) ~- 0.87ImdLR , (18)(Rt) ~ -0.539TImiLT - 0.44gsImaLs .9
3
(19)
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Herczeg, P. (Peter). Time-reversal violation in beta decay, article, January 1, 2003; United States. (https://digital.library.unt.edu/ark:/67531/metadc933676/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.