Recent Results For And Odderon Picture

Fazal-e-Aleem and Sohail Afzal Tahir
Centre for High Energy Physics
University of the Punjab, Lahore-54590, Pakistan
faleem@hotmail.com

Abstract

Most recent results from the Fermilab on give an opportunity to study the
presence or otherwise of the Odderon at very high energies. In the light of these
results and future measurements at RHIC and LHC, an analytical study has been
made.


Most recently, result for the ratio of the real and imaginary parts of the scattering
amplitude has been reported by E-811 Collaboration [1]. The value = 0.135  0.044 poses very
interesting question. Does this value indicate the presence of the Odderon or is it consistent with
the predictions of the conventional models? We will try to address briefly this question in the
light of various models.
Lukaszuk and Nicolescu [2] first introduced the concept of Odderon in 1973 to account
for the difference of the total cross section, T and ratio of real to imaginary parts of scattering
-
amplitude, in pp and p p scattering. Kang and Nicolescu [3] in 1975 provided theoretical basis
for the Odderon. From the theoretical point of view this concept has been rediscovered in QCD.
Dynamical origin to this concept was provided by Lipatov [4] and collaborators [5], Kwiecinski
and Praszalowicz [6] and Islam [7]. In QCD, there are not only quark-Reggeons but also glue-
Reggeons. More generally, multi-Reggeized-gluon exchanges lead to contributions having the
Odderon quantum numbers. This is a very important theoretical fact, which provide physical basis
to the concept of Odderon. Much work has since been carried out on the origin and meanings of
the Odderon [8-11]. Theoretical status of the Odderon is now firm not only in the perturbative
QCD theory but also in the non-perturbative approach. In the perturbative treatment efforts are
mainly focused on the determination of the Odderon intercept [12,13]. However, a conclusive
experimental evidence of the Odderon is elusive.
The Odderon picture was first used by Gauron et al. [14] to account for the difference of
the total and differential cross section in the dip region at ISR. Bernard et al [15] later on showed
that UA4 results on could be described by the presence of Odderon. Their predictions are higher
than UA4/2 and E811 data. Jenkovszky et al [16] extended the idea to relate the small momentum
transfer hadron scattering and deep inelastic scattering. This relationship is useful for
understanding the origin of cross section from the point of view of hadronic structure and
interaction of its constituents. Rafique et al [17] used Odderon description to explain the then
available data for T and . Their predictions are in agreement for ratio but somewhat higher for
T. In another attempt, Odderon description was confronted by Fazal-e-Aleem et al [18,19] to fit
data for the differential cross section. Predictions of the model for T and are higher than the
current measurements. We thus find that the models incorporating Odderon predict high value


2


(~0.2) at FERMILAB, RHIC and LHC [20]. Recent results of 0.135  0.02 at UA4/2 and 0.135 
0.044 at E-811 Collaboration value do not seem to favour the presence of Odderon. In the simple
Regge picture of Landshoff and Donnachie [21], a constant value of = 0.12 is predicted which is
in agreement with the UA4/2 and E811 data. In the geometrical model [22] this value is predicted
to be
0.14 at SPS, FERMILAB and LHC, which is again consistent with E811 results. It is
interesting to note that at the time of publication of results of geometrical models, UA4
measurements of = 0 .24  0.04 suggested a new threshold and differed from the predicted
value of geometrical model. The new results of UA4/2 are consistent with geometrical models.
The
ratio
is of major interest in theory and experiment because of its close relationship
with the energy integrated inelasticity of the collision via the dispersion relation. This quantity
will in principle be accessible to measurements at RHIC and LHC energies. The kinematical
range to be covered corresponds to the Coulomb-nuclear interference region. The expected t
0

value at the RHIC and LHC are estimated to about 0.0005 and 0.0007 (GeV/c)2 respectively.
Measurement at smallest possible -t value will therefore minimize the extrapolation error and
provide us an ideal opportunity to have a very precise value for .
In the Eikonal models, the dip of the differential cross section is very sensitive to the
value. This clearly suggests that in case of higher measured value of at RHIC and LHC, the
structure in d/dt would disappear and turn into shoulder. It can be seen that current data for
differential cross section does not support a higher value of at RHIC and LHC within the
framework of geometrical picture.

Conclusions

1. The experimental evidence for the existence of Odderon is not yet convincing despite the
fact that QCD suggests presence of an Odderon. The ambiguity is for the reason that its
contribution is very small compared with the dominant C = + 1 exchange contribution.
Thus, reactions where C = + 1 is forbidden by selection rules, is the ideal place to test the
presence of Odderon. The only clear experimental evidence for the existence of an
Odderon comes from measurements of the differential cross section for high-energy
-
elastic pp and p p scattering in the dip region at around 2
t 3
.
1 GeV . The Odderon
contribution to this process is expected to be sensitive to the proton structure.
Measurements at RHIC and LHC will throw more light on this.

2. In order to further clarify the presence of Odderon, which now also has its dynamical
origin in QCD, it is important that the future measurements take the following fact in to
account. Unlike the conventional models, Odderon predicts that T, and d/dt in the
-
vicinity of dip region are not equal for pp and p p . It would be of interest, therefore, to
-
make a simultaneous measurement of these parameters at LHC for both pp and p p .
Also, as proposed by RHIC, a measurements of the total cross section in the region
between ISR and Collider which has remained unexplored, would be quite crucial for




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ruling out the presence or otherwise of Odderon. A small value of would provide
strong evidence in favor of the maximal Odderon.


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