From: Igor Ivanov <i.ivanov@fz-juelich.de>
Subject: Re: Higgs found? Implies what?
Date: 18 Sep 2000 16:06:38 GMT
Newsgroups: sci.physics.research,sci.physics.particle
Summary: [missing]

John Baez wrote:
>  
> Thanks for your very informative post!  I enjoyed it a lot.  It's
> nice to hear exactly what we can and cannot conclude from at 115 GeV
> Higgs.

Thanks for the encouraging words. Not everyone can boast 
of such a comment from John Baez! :)

> It's just the above passage that I found difficult to follow.
> What's tan(beta)?  I don't think you explained that terminology.

tan(beta) is a key parameter of a 2HDM (and consequently, of MSSM).
When you introduce two Higgs doublets phi_1 and phi_2, and write
down the Higgs potential, then you find that the minimum occurs at some

        (  0  )           (  0  )
phi_1 = ( v_1 )   phi_2 = ( v_2 )
        
So, we get two vacuum expectation values v_1 and v_2.
(If we don't want an explicitly CP-violating theory, there should not
be any relative phase between v_1 and v_2.)

These two parameters are not independent, since they determine the
mass of the gauge bosons in an unambigous way, like:

m_W^2 = g^2*(v_1^2 + v_2^2)/2

The conclusion is that we are free to choose only their ratio v2/v1.
This is precisely the parameter called tan(beta):

tan(beta) = v2/v1

Such a presentation of this ratio is convenient, since the angle beta
turns out to be the mixing angle between the charged (the upper)
components
of the two doublets. For example, the physical charged Higgs boson H+ is

H+ = -sin(beta)*phi_1^{+} + cos(beta)*phi_2^{+}

and so on.


Now -- why tan(beta) is important for phenomenology.
It is important because it enters the expressions for coupling constants
of the Higgs bosons with matter. Since the mass of the lightest Higgs
boson
is significantly shifted by radiative corrections, this shift
will certainly feel the value of tan(beta). For example, at 
tan(beta) = 1.5, the upper bound on Mh is about 100-105 GeV (in MSSM),
while for large tan(beta) it can be pushed up to 125-130 GeV.

-- 
Igor Ivanov