PRESENT STATUS OF EPSILON/EPSILON

Mohammad Saleem, Haris Rashid, Faisal Akram and Atif Shahbaz

Centre for High Energy Physics, Punjab University, Lahore. PAKISTAN.

ABSTRACT

We give the recent experimental results and theoretical analysis of CP violating
ratio epsilon/epsilon. The present status is discussed in the light of the standard
model.

The first observation of CP violation in the decay of neutral kaons was reported in 1964 [1]. This
occurred via the mixing of CP eigenstates and was called indirect CP violation. The observation of
direct CP violation which takes place in the decay process itself was very difficult to measure. This is
described by the parameter Re / where projects the direct CP violation while is associated with
the indirect CP violation. The first experimental result showing the existence of direct CP violation
was obtained in 1988 by Burkhardt et al.[2]. The experiment was performed by studying the decay of
kaons which come in two types: long-lived kaons, KL, and short-lived kaons, KS. The final results
published by NA31 and by E731 Collaborations are [3]

Re / = (23.0 " 6.5) x 10-4

Re / = (7.4 " 5.9) x 10-4,

respectively. The former result, although a very small number, is definitely different from zero and
therefore exhibits the direct CP violation while the latter result could be compatible with no direct
CP violation. It was therefore natural to design experiments which would give more precise results.
NA48 at CERN and KTeV at Fermilab were such experiments. The most recent values obtained in
these experiments are [4]:

Re / = (15.3 " 2.6) x 10-4

Re / = (20.7 " 2.8) x 10-4,

respectively. The result at NA48-CERN was computed with 3.3 million K 0 0 events collected
during the 1998 and 1999 running periods. The last two results were obtained by NA48 and KTeV
using the same experimental principle. That is in each experiment the double ratio of KL, and KS
going to neutral particles and to charged particles was measured. However, there are significant
differences in the experimental and analysis techniques of the two experiments. The new world
average value of Re / is (17.2 " 1.8) x 10-4 [5]. This confirms the existence of direct CP violation
in the neutral kaon system. It may be noted that the / programme of NA48 has been completed
with the successful 2001 data-taking [6]. The new data will improve the statistical accuracy and
perform a major check of its present result. Let us now see what is the theoretical status of /.
The first estimate of / was made more than a quarter of a century ago. It was only by


chance that although calculations were made on simple basis ignoring some important effects the
result was about 1/450, a value compatible with the present world average. Significant progress has
been made since then. Hambye et al [7] presented an analysis of the ratio /. They calculated the
hadronic matrix elements using the 1/NC expansion within the framework of the effective chiral
Lagrangian for pseudoscalar meson at leading plus next-to- leading order in the chiral expansion.
They obtained the results for three sets of Wilson coefficients. The result for the set LO, for C
between 600 and 900 MeV and for central values of the parameters is

14.8 x 10-4 # / # 19.4 x 10-4.
.
This technique was improved by Pallante, Scimemi and Pich [8] who in 2001 presented a detailed
analysis of / within the standard model, taking into account final state interactions. A matching
procedure between the effective short-distance Lagrangian and its corresponding low-energy
description in chiral perturbation theory was used to fix the relevant hadronic matrix elements at
leading order in the 1/NC expansion. They obtained

Re / = (17" 9) x 10-4.

The error is dominated by the uncertainty in the mass of the strange quark. A better estimate of this
mass would reduce the uncertainty up to about 30%. It may be emphasised that the mass of a strange
quark is crucial for the precise computation of /. Moreover, the calculations of hadronic matrix
elements have yet to reach a level of the NLO calculations of the Wilson coefficients. The
uncertainty in the final theoretical result arises due to the uncertainty in the calculations of these
quantities.
Wu [9] has made a prediction about / by investigating the low energy dynamics of QCD
with special attention to the matching between QCD and chiral perturbation theory, and also to some
useful algebraic chiral operator relations which survive even when the chiral loop corrections are
included. A value of
/ = (20 4 " 5 " 4) x 10-4
was obtained. This is also consistent with the world average.
Buras and Gerard [5] have shown that the recently obtained experimental value for / does
not require sizable 1/NC and isospin-breaking corrections. For long-distance hadron physics, isospin
symmetry and large NC limit are two powerful approximations. By making use of them, they have
shown that

Re / = (17.4 " 0.7) x 10-4.
Acknowledgment
Two of us (Haris Rashid and Atif Shahbaz) are grateful to the Pakistan Science Foundation for
financial assistance under Project No. P-PU/PHYS (117).

References
1. J. H. Christenson et al., Phys. Rev. Lett. 13, 138 (1964).
2. H. Burkhardt et al., Phys. Lett. B206, 169 (1988).
3. G. Barr et al., Phys. Lett. 317, 233 (1993); L. K. Gibbons et al., Phys. Rev. Lett. 70, 1203 (1993).
4. A. Lai et al., [NA48 Collaboration], CERN-EP-2001-067; R. Kessler,.


5. A. J. Buras and J. M. Gerard, .
6. G. Graziani, .
7. T. Hambye et al., ;  \& DO-TH 00/01.
8. E. Pallante et al., ; I. Scimemi et al., .
9. Y. L. Wu,  Plenary Talk at ICFP2001, Zhang-Jia-Jie.





