Relativistic Hamiltonian Model for Higgs Resonance Page: 140
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Relativistic Hamiltonian Model for Higgs Resonance *
Charles B. Chiu, E. C. G. Sudarshan, and G. Bhamathia
Center for Particle and Department of Physics, University of Texas, Austin, Texas 78712, USA
a Department of Physics, University of Texas, Austin, Texas 78712, USA
North Texas Research Institute, University of North Texas, Denton, Texas 76203, USA
Z. Naturforsch. 52a, 140-142 (1997)
We construct a relativistic Hamiltonian model for Higgs resonance. Resonance trajectories are
studied as a function of the parameters of the model. The possibility of a narrow width Higgs
resonance in 1 TeV region cannot be ruled out from general considerations. Our model may serve
as a phenomenological guide in the search for Higgs resonance.
This is a brief report on our recent work . The
Higgs mechanism plays the crucial role in the unified
electroweak theory. Through spontaneous symmetry
breaking, the weak gauge bosons, W and Z, acquire
mass, while the photon remains massless. This ex-
plains why in the low energy region, weak interaction
is much weaker than electromagnetic interaction. The
Higgs mechanism also implies the existence of the
Higgs particle. So far this particle has not been found.
In the minimal standard model, the mass, or more
precisely the bare mass, of the Higgs particle is a free
parameter. It is related to A0, the coupling in the
quartic interaction, through the relation mo = 2, v2,
where v is the vacuum expectation of the original
Higgs field, which is about 1/4 TeV. We consider the
scenario where the bare mass of the Higgs particle is
very large, and in turn the coupling is strong. Here
presumably the gauge interaction of the Higgs particle
and its interaction with fermions are relatively unim-
Our main interest is the physics, say at the energy
scale of 1 TeV. This energy scale is significantly above
the masses of Wand Z. Here the interaction of Higgs
particle with the gauge bosons is predominantly with
the longitudinal components of the gauge bosons,
which will be designated by the lower case symbols
W, z. These longitudinal components form an iso-
* Presented by Charles Chiu at a Workshop in honor of
E. C. G. Sudarshan's contributions to Theoretical
Physics, held at the University of Texas in Austin, Septem-
ber 15-17, 1991; "... My best wishes to George Sudar-
shan for many more years of inspirations to our scientific
Reprint requests to Prof. Dr. Charles B. Chiu.
topic triplet of scalars. The interaction among this
triplet is similar to the interaction among the isotriplet
of pions. We recall, in the it + it - and 7t0 r7 channels
there is the I = S = 0, - resonance. Similarly one may
expect the presence of Higgs resonance in the w + w-
and zz channels.
Various approaches have been used to study the
occurrence of Higgs resonance in the w+ w~ and zz
channels. A partial list here includes : the N/D
method, the 1/N expansion in the O(2 N) model, and
various "unitarization schemes". For the latter, one
finds that the Higgs resonance is present in the Pad6
approximation, and is absent in the K-matrix ap-
proach. We construct a Hamiltonian model for the
I = S = 0 eigenchannel, which is a linear combination
of the w + w - and zz channels. Our model is based on
a relativistic hamiltonian theory . Instead of the
usual Hamiltonian, which specifies the energy of the
system, we work with the "relativistic hamiltonian",
which specifies the square of the center of mass energy.
It is a Lorentz scalar. The matrix element of the free
Hamiltonian is given by H (s, s') = s 6 (s - s'). In-
spired by the separable potential model , we assume
that the matrix element of the interaction term is fac-
torizable, i.e. H 1 (s, s') = - g (s) g (s'). Here a negative
sign is appropriate for the present case, which corre-
sponds to an attractive potential.
The solution of the eigenvalue equation of the full
hamiltonian H 4 = (H + H1) = . is given by
/3(s) t - s +irE
# = 1 + Kg2, 2 2(s')ds'
s - s' + i
0932-0784 / 97 / 0100-0140 $ 06.00 C - Verlag der Zeitschrift fur Naturforschung, D-72072 Tubingen
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Chiu, Charles B.; Sudarshan, E.C.G. & Bhamathi, G. Relativistic Hamiltonian Model for Higgs Resonance, article, February 1, 1997; Berlin, Germany. (digital.library.unt.edu/ark:/67531/metadc990973/m1/1/: accessed January 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting University of North Texas.