ZEUS-Note-93-048
Limits on Squark Masses in an R-Parity Violating Supersymmetry Model
Doug Gingrich
Using an integrated luminosity of 26 nb 
, we set limits on the
d-, u- and t-squark masses in an R-parity violating supersymmetry
model.
At HERA, the production of squarks in some R-parity violating
supersymmetry models is analogous to the s-channel production of
leptoquarks [1, 2, 3, 4].
The leptoquark and squark production cross-sections are identical up to
an un-measured overall normalization given by the coupling constants of
the models.
In particular, the form of the cross-section for the S 
-leptoquark and
d-squark are identical for a vanishing coupling of the leptoquark to
a right-handed electron and quark.
Similarly the cross-section for the 
-leptoquark
and 
-squark (or 
-squark)
are identical.
What distinguishes these exotic particles is their decay modes. Unlike the leptoquark, the additional R-parity conserving supersymmetry decays are available to the squarks. Hence searches for leptoquarks at HERA also enable weak limits to be set on squark masses.
The R-parity conserving supersymmetry decay width,
, for a squark, 
, decaying
to a quark, q, and photino, 
, is related to the
R-parity violating supersymmetry decay width, 
, for a
squark decaying to a quark and lepton, 
, by the ratio [1]
where 
is the first generation
( 
) R-parity violating supersymmetry
coupling.
The R-parity violating supersymmetry decay width is identical to the
leptoquark decay width [4].
In the model of t-squark production and decay that we are
considering [3], the t-squark is a mixture of mass eigenstates
where one of the eigenstates is assumed to have a mass less than the
t-quark mass.
The t-squark is related to the mass eigenstates by a mixing angle,
which we take to be zero and thus obtain worse-case limits.
With these conditions the t-squark decay width is identical to the
-leptoquark decay width.
We point out that in the case of an equal squark and photino mass,
the R-parity conserving supersymmetry decay vanishes, and hence the
squark and leptoquark decays are indistinguishable.
Alternatively for a vanishing photino mass, the R-parity conserving
supersymmetry decay strength has its maximum value.
Equating the product of the cross-section and branching ratio for
leptoquarks to that of squarks, we obtain a relationship between the
squark couplings and leptoquark coupling to a left-handed electron,
: For the d-squark and S -leptoquark
for the u-squark and -leptoquark
and for the t-squark and -leptoquark
The results in reference 5 for the upper limit on the acceptance
corrected number of events for various leptoquark masses were used to
derive limits on the R-parity violating supersymmetry couplings for
various squark masses.
Figure 1 shows limits on the first generation R-parity violating
supersymmetry coupling, , as a function of the
d- and u-squark masses.
Figure 1a and 1d were obtained from a search for events consistent
with an electron-jet final state and figure 1b for events consistent
with a neutrino-jet final state.
Figure 1c shows the combined limits from a search for both final
states for the d-squark.
The limits for the t-squark coupling, 
, are
identical to the u-squark limit for zero photino mass.
In each figure the top curve is for the case of zero photino mass, the
middle middle curve for when the photino mass is 18 GeV, and the
bottom curve for a photino mass equal to the squark mass.
We observe, that currently ZEUS is not very sensitive to the photino
mass nor is able to significantly distinguish leptoquark and squark
limits in an R-parity violating supersymmetry model.
For values of the R-parity violating supersymmetry couplings equal to
the nominal electroweak coupling, the following lower limits on squark
masses are obtained at the 95% confidence level:
,
and
.