Mayda Velasco, Sven Heinemeyer, Andre de Gouvea, Steve Mrenna, Ayres Freitas,
Bob Oakes, Jeff Gronberg, Victoria Martin, Michal Szleper, Armin Apyan,
Michael Schmitt, Jack Gunion (by phone), Heather Logan (by phone),
David Asner (by phone, morning)
 
Linear Colliders -- What they can do for Cosmology (afternoon)
==============================================================

Mayda pointed out that potential supports of a LC program are
interested in knowing the direct connection between physics at a high
energy linear collider and cosmology.  The simple question is:  "What
can the LC contribute to cosmology?"  We already have some ideas,
namely,
  1- particle dark matter -- what is it?  what are its properties?
  2- neutrino properties -- are they exactly as in the SM?  They
       are important for understanding, e.g., galaxy formation.
       They are a key piece of the theory of leptogenesis.
  3- CP Violation -- This is intimately connected with the question
       of the baryon asymmetry.

The group discussed these issues and made a number of observations,
and there were even some plans for further work.

Particle Dark Matter
--------------------
We have in mind the LSP as the major constituent of dark matter. Jack
is working on a study of associated gaugino production at an
electron-photon collider.  The process would be
   e+gamma   -->   nu_e  + chargino_1-  + neutralino_2
with neutralino_2  -->  neutralino_1 + Z*.  The hope is to isolate
the elements of the neutralino mixing matrix.  This would require
high energy beams, on the order of 800 GeV or 1 TeV.  Jack had
looked into e+gamma -> nu_e + cha_1 + neut_1, but he finds that
the backgrounds from W production are too high.

Ayres commented on the production of neutralinos in an e+e- machine
via t-channel selectron exchange.  If the selectron mass is known
already, then the cross section depends on the other parameters of the
neutralino sector.  One might be able to ascertain whether the
lightest neutralino is mainly gaugino or Higgsino, and even whether mu
is complex.  Beam polarization would be very useful, perhaps crucial.

In this vein, Jack published some years ago a study on the production
of nearly mass generate charginos (ie, where the mass of the chargino
is only slightly larger than the mass of the lightest neutralino). In
this context of studying neutralino properties, it might be useful to
revisit that study, taking beam polarizations, etc., into account.
 

Lepton Number Violation
-----------------------
Mayda has proposed the process
    gamma gamma   -->  W+ W+  l-  l-    (or charge conjugate)
which would be mediated by a Majorana neutrino.  Andre has thought
about this, and concluded that the rate is hopelessly small, given
existing constraints from neutrinoless double-beta decay experiments.

He went on to explain that lepton number violation can be introduced
by higher-dimensional operators without inducing a high neutrino mass.
This means it would be worth looking for simpler processes such as
   gamma gamma   ->  tau mu   or    e mu    or   e tau,   etc.
Michael suggested that another possibility would be
   gamma gamma   ->  mu- mu- e+ e+    or something like that.

While evidence of lepton number violation would be very exciting,
it would be difficult to make contact with cosmology models directly.

Bob suggested that one emphasize models which conserve B-L, since they
are already well motivated.  One would have to respect the bounds
coming from the proton lifetime, however, these bounds are not
relevant for third-family processes.

Ayres pointed out that a Giga-Z machine would be a good place to look
at Z->tau+mu, etc., and that existing bounds on these processes could
be greatly improved. A projection would require a careful study of the
limiting backgrounds, which can be difficult to estimate at the level
of 10**-7.  For example, muon+bremsstrahlung can be mis-identified as
an electron or tau decay, and this limits the sensitivity of the
search. One should check the current bounds from LEP, as it is not
clear that they are finalized.

CP Violation
------------
We are interested in CP violation as it relates to baryogenesis.
There is a well known study by Carena, Wagner & friends in which
they discuss how radiative corrections to the Higgs couplings from
stop squarks induce CP violation in the Higgs sector.  This could
explain the baryon asymmetry of the universe provided the Higgs
mass is less than about 117 GeV, and the stop mass is less than
roughly 145 GeV.  There is an analysis of this scenario by OPAL
in which they report large holes in the Higgs exclusion, but it
was remarked by Steve that this comes from the fact that they did
not look for the case of h->AA which would lead to a multi-jet
final state.

The existence of a light stop represents an opportunity for the
Tevatron.

In consideration of a future LC, however, one would pose this
question: If electroweak baryogenesis is confirmed, how well can one
measure the complex parameters governing the stop sector?  Jack
remarked that he had a related study of looking for CP violation in
the top sector at a LC -- perhaps this could be applied to stops.  In
the context of a gamma-gamma collider, one might think about comparing
rates for stop-pair production as a function of the polarization
states of the photon beams.

A Giga-Z Machine
----------------
Mayda posed the question: What could be done if the positron beams
were unpolarized?  This question is motivated by a possible CLIC
scenario in which the luminosity would be 2.6 x 10**33 /cm2/sec.
This would be high enough for about a half a billion Z's.

Ayres answered that one could do the same asymmetry measurements as
were done by SLC, but with much smaller errors.  Steve pointed out
that the very small errors expected at, say, Tesla demanded the
`Blondel scheme' which requires a significant degree of positron
polarization.  This issue needs clarification.

Sven pointed out that one would still be able to measure alpha_s very
precisely, since this has no need of polarization.  He reminded us
that the main goals of a Giga-Z machine would be the measurement of
alpha_s and sin**2(theta_W).  So, if the measurements of the
asymmetries were still good, and if one obtained an excellent
measurement of alpha_s, all without positron polarization, then the
program would be a success.

Ayres sketched the main results of a recent paper on the study of
neutrino properties both from the indirect invisible width and from
the cross section for e+e- --> gamma+nu+nubar.  If the LC took data
above the Z pole, say in the range 140 - 180 GeV, then one can exploit
the interference between the Z and W-mediated processes to extract the
neutrino-Z coupling.

Another avenue would be a new experiment to measure the cross section
for elastic neutrino-electron scattering.  This is a relatively clean
way of obtaining the coupling of left-handed neutrinos, but is still
challenging due to the very small cross section.  It has been
considered previously in a number of contexts, such as the studies for
the neutrino factory and the proton driver upgrade, as well as the
so-called Minerva proposal.  The question today is: What can be done
at existing facilities, such as NUMI?

Returning to the Giga-Z machine, it was asked what could be learned
about CP violation in the B sector?  It is not clear that a Giga-Z
machine would add anything in the post-LHCb era.  Similarly, rare tau
decays will be better covered at the e+e- B factories.
 

Michael reminded of an idea to look at light binos through the process
e+e- -> mu+mu- bino bino (or any other leptonic final state). One can
imagine that this would be mediated by the exchange of a slepton.
Andre described the more general view.  Ayres has estimated the cross
section for the similar SM process, e+e- -> mu+mu- nu_tau nu_tau,
which is mediated by a virtual W, and found it to be extremely small,
below the limit of observability.
 

Neutrino Properties
-------------------
Andre pointed out that a study of slepton properties would be
very relevant to understanding neutrino properties.
 

At this point the meeting was adjourned.
 

Lorentz Invariance
------------------
Note: During the lunch time conversation, Steve pointed out that
Lorentz Invariance violation is an interesting topic related to
the origin of high energy cosmic rays.  This might be addressed
at a future LC, also.
 

----------------------------------------------------------------------
second half of minutes contributed by M.S.