From: sichase@csa1.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.physics
Subject: Re: Right handed neutrino
Date: 6 Apr 92 20:12:07 GMT
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
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In article <1992Apr5.234748.21465@news.Hawaii.Edu>, vijay@wiliki.eng.hawaii.edu (Vijay Fafat) writes...
>Hi,
>  I had read long back in one of the Asimovs that only a left handed neutrino
>exists in Nature. Recently, I also read that if the neutrino has a non-zero
>mass, then a right-handed neutrino HAS to exist and would be very heavy. Now
>I have one question : Suppose the neutrino HAS a non-zero mass and Suppose I see a left-handed neutrino going.I decide to overtake it (this is possible in principle since the neutrino would be moving slower than light if it has a non-zero mass). As I over<1992Apr5.234748.21465@news.Hawaii.Edu>                      
>handed neutrino (Visualize its "screwing" motion w.r.t. the spin direction)
>However, I would measure its rest mass to be the same as before i.e. that of
>a left handed neutrino. So do I get a LIGHT right-handed neutrino? Where am I
>going wrong?
> 

Yes, you get a light right-handed neutrino.  As you pointed out, chirality is
not Lorentz invariant for massive particles.  I don't know about this "heavy
right-handed neutrino" business.  Perhaps someone else knows what is refered to
here.

>PS : Another thread on the net is following the number of generations of 
>neutrinoes. Can somebody point out why there should be such an asymmetry 
>between left- and right- neutrinoes?

No.  Nobody knows why weak interactions should be completely left-handed
(maximally parity-violating).  In fact, this problem has lead people to suggest
that there might be right-handed currents mediated by additional W's and Z's,
often called Wr and Zr, which for some unknown reason are much more massive 
than the "normal" weak bosons.  This would mean that the right-handed
interaction that they mediate would be much weaker than the left-handed one
that we observe.  

We can however work backwards to set some limits on the right-handed boson mass.
By virtue of the fact that we see no right-handed currents at today's level 
of precision, we can say that if they exist such particles weigh more than
about 400 GeV.  (Exact numbers depend on the experiment you quote).  This
translates into a low-energy effective coupling of less than about 5%
right-handed contribution.  

It surprised me when I learned that we have only very loose constraints on 
various possible contributions to the low-energy weak lagrangian.  For example,
the best experiments eliminate possible Tensor contributions (which would
modify the V-A theory) to about the 10% level.  Not so great, huh?  These
experiments are VERY difficult to do with high precision, which is a big reason
why the recent CERN results on Z physics have made such a big splash.  There
aren't too many ways to do high precision weak-interaction physics.  

Bottom line:  These right-handed (V+A) currents might well exist.  There is 
no reason to expect that they don't.  There is in fact some theoretical bias in
favor of their existence.  (It eliminates the problem of explaining their
absence!)  Of course, if they are found, it then poses a new problem - what is
responsible for the left-right symmetry breaking which gives the right-handed
bosons more mass than the left-handed ones.  There are a variety of "Left-Right
Symmetric" models on the market to deal with these issues.  But we have no
experimental data to address this problem - yet.

-Scott