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Variations on the Gauge Sector of the Electroweak Model
Jean Pestieau1
Institut de physique théorique,
Université catholique de Louvain,
Belgium
11 August 2009
Starting from a 40 year old proposal, new relations between alpha, the fine structure constant, Z and W masses are proposed.
I. Forty years ago (1), it has been proposed the following determination of Z and W masses
(1)
(2)
with (2)
(3)
(4)
(The weak angle in Eqs (1) and (2) is the complementary angle of defined in Ref (1): ).
Then
(5)
(6)
to be compared with their experimental values (2)
(7)
(8)
Let us present variations on Eqs (1) and (2).
II. It is amusing to consider the following simple parametrizations:
A.
(9)
(10)
B.
(11)
(12)
with (3)
(13)
(14)
We used value of obtained from the empirical relation (4)
(15)
Note that
(16)
III. To make contact with a well known parametrization (2)
(17)
we write Eq. (11) as
(18)
Then
(19)
in the current context.
IV. It is interesting to note the following empirical formula (4):
where we have used
(23)
and Eqs (15-16).
V. About e and α
With α and e given in Eqs (13), we satisfy the following Equation (4)
(24)
when .
For example,
Comparing Eqs (15) and (24), we get
(25)
(In Ref. (4), the following approximation of Eq. (25) is used: .
It is worthwhile to note that
is satisfied when
jean.pestieau[*—at—*]uclouvain.be
File translated from the TEX file 40years.tex by TTM, version 3.85 on 15 Aug 2009, 01:23. Further edited with Bluefish 1.0.7.