<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nwhopkins@csd.uwm.edu wrote:\n> Jay R. Yablon wrote:\n> > I start with what at first seems an odd idea, that the weak\n> > interaction violates parity not only in the current / vector\n> > boson interactions, but in the mass term as well.\n> In the presence of the parity-violating interactions, any\n> non-zero scalar, bivector or pseudovector will spoil gauge\n> invariance -- which includes chiral mass terms.\n>\n> This is not a trivial result.\n\nIf you think a pseudo-scalar term is *nonetheless* necessary to derive\nthe results you\'re trying to get at, then this automatically means\nyou\'re dealing with a larger interaction model which includes\nU(1)xSU(2)xSU(3), but is parity-symmetric.\n\nNon-zero mass terms can be present in the theory, if there is a\nright-handed analogue SU(2)_R of SU(2). Indeed, the corresponding I3_R\nterm would just be:\nHypercharge - (Baryon-Lepton)/2\nor more precisely, inserting the coupling constants:\nI3R/gR = (Y/g\') - (B-L)/2\nwhere gR would be the coupling for SU(2)_R.\n\nSymmetry breaking would then be generating a charge of the form:\nQ/e = I3/g + Y/g\' = I3/g + I3R/gR + (B-L)/2.\nThe existence of the invariant\nL^2/gs^2 + 6 ((B-L)/2)^2 = 3/2\n(L the SU(3) charge), then suggests the identification\nL9 = sqrt(3/2) gs (B-L)\nof a 9th component for a U(3) interaction containing SU(3). With this,\nthe mixing relation would read:\nQ/e = I3/g + I3R/gR + sqrt(6) L9/gs\nwhich implies\n(1/e)^2 = (1/g)^2 + (1/gR)^2 + 6 (1/gs)^2\nand gives you, approximately,\ngR^2 ~~ 1/57.\nThe 2nd mass eigenstate would be Z, with the relation\nZ = e I3/g\' - e Y/g\nwhich implies a 3rd eigenstate, ALMOST EXACTLY, of the form:\nYR/g\' = B - L - Y/g\'\nor\n(Y + YR)/g\' = B - L\nwith a corresponding non-trivial relation between the SU(3) and U(1)_Y\n(and SU(2)_R) couplings of the form:\ngs^2 ~~ 12 g\'^2 ~~ 6 gR^2.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>
whopkins@csd.uwm.edu wrote:
> Jay R. Yablon wrote:
> > I start with what at first seems an odd idea, that the weak
> > interaction violates parity not only in the current / vector
> > boson interactions, but in the mass term as well.
> In the presence of the parity-violating interactions, any
> non-zero scalar, bivector or pseudovector will spoil gauge
> invariance -- which includes chiral mass terms.
>
> This is not a trivial result.
If you think a pseudo-scalar term is *nonetheless* necessary to derive
the results you're trying to get at, then this automatically means
you're dealing with a larger interaction model which includes
U(1)xSU(2)xSU(3), but is parity-symmetric.
Non-zero mass terms can be present in the theory, if there is a
right-handed analogue
of SU(2). Indeed, the corresponding
term would just be:
Hypercharge - (Baryon-Lepton)/2
or more precisely, inserting the coupling constants:
where gR would be the coupling for
.
Symmetry breaking would then be generating a charge of the form:
.
The existence of the invariant
(L the SU(3) charge), then suggests the identification
of a 9th component for a U(3) interaction containing SU(3). With this,
the mixing relation would read:
which implies
and gives you, approximately,
.
The 2nd mass eigenstate would be Z, with the relation
which implies a 3rd eigenstate, ALMOST EXACTLY, of the form:
or
with a corresponding non-trivial relation between the SU(3) and
(and
couplings of the form:
