NONSTANDARD HIGGS-BOSON INTERACTIONS
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                            Rob Szalapski

        One method of testing the Standard Model (SM) is to parameterize 
deviations from its predictions in terms of nonstandard or anomalous 
coupling parameters.  One then attempts to measure these couplings with 
increasing precision, a null result supporting the SM and a nonzero result 
providing evidence for new physics.  Because there are so many open questions 
concerning the symmetry-breaking sector it is very natural to perform a search 
for nonstandard couplings of Higgs bosons.

        Not surprisingly, a large number of discussions have taken place 
concerning the measurement of nonstandard Higgs-boson couplings.  I intend to
discuss only one very attractive approach.  In this approach we assume that 
the SM is an approximation to some more complete theory, hence the energy-
dimension-four operators of the SM Lagrangian are the first terms in an 
expansion of the true Lagrangian; additional operators will appear at 
energy-dimension greater than four.  These operators will be constructed from
the fields which appear at low-energy.  Guided by the evidence that the 
SM is a gauge theory and the W and Z bosons are true gauge bosons we impose 
SU(2) X U(1) gauge invariance upon the effective Lagrangian.

        An (almost) exhaustive list of SU(2)XU(1)-gauge-invariant operators 
was published by Buchmuller and Wyler.  The number of possible operators 
through energy-dimension-six is simply too large to be manageable.  It is 
necessary to make additional assumptions about the underlying new physics 
if one is to proceed.  The case in which I am most interested is new physics 
that couples to the gauge bosons of the SM, but couplings to fermions are 
strongly suppressed.  This includes a large number of interesting scenarios,
such as new heavy and/or exotic fermions, new scalar particles, etc.  If one 
also assumes CP invariance then at most 12 additional operators need to be 
included through energy-dimension-six.  If the assumption of CP invariance is
dropped a manageable number of additional operators appear.

        Of these 12 operators mentioned above, a subset contributes to 
Higgs-boson couplings.  Some contribute only to self-couplings and are perhaps 
not so interesting at this point.  Several contribute to couplings to gauge 
bosons, and are quite interesting.  Of particular interest is the effect on 
rare decays of the Higgs; H ---> gamma gamma and H ---> Z gamma are tree-level 
processes in the energy-dimension-six Lagrangian, and rates may be significantly 
affected.  The HWW and HZZ couplings are also altered, but the deviations may 
be difficult to detect.  See, for example, K. Hagiwara, R. Szalapski and 
D. Zeppenfeld, Phys.Lett.B318:155-162,1993.  Additional studies have been 
appeared in a series of works by Gounaris and collaborators.

        The assumption that the couplings of the new physics to SM fermions is
suppressed is quite important.  Einhorn and collaborators have categorized 
effective operators according to how they might be generated by the new physics.
(See Arzt Phys.Lett.B342:189-195,1995 and related papers.)  Some operators 
may only be generated by new particles circulating in loops, and it is natural
that they possess relatively small coefficients.  Others might be obtained from 
a tree-level graph by setting q^2=0 in the propagator of a massive particle
leading to a relatively large coupling.  This is akin to the appearance of 
four-fermion operators in the Fermi Lagrangian which is valid at momenta that 
are small compared to the W mass.  The point I wish to make is the following.  
If the fermion couplings are not suppressed, then it is quite likely, by the 
above argument, that contact terms including fermions dominate.  This scenario 
has been discussed by, for example, W. Kilian, M. Kramer and P.M. Zerwas 
hep-ph/9603409 or Bohdan Grzadkowski and Jose Wudka, Phys.Lett.B364:49-54,1995.
        
        The many works on this subject primarily concern electron-positron 
colliders.  It would be quite valuable to have these works combined in a 
coherent framework.  Furthermore, I am not aware of much work concerning these 
couplings at muon or hadron colliders.  It would be good to compare and 
contrast the benefits of studying Higgs-boson physics at various types of 
colliders.  A nice feature of the gauge-invariant effective Lagrangian is 
that many couplings are related in a nontrivial way.  Hence one may take 
advantage of constraints from the low-energy and Z-pole data. Furthermore, if 
one is studying, for example, nonstandard Higgs physics at LEP II, then one 
may also anticipate constraints arising from processes with two-fermion final
states or W-boson pair production.