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CP-NONCONSERVATION+ by R.H. DALITZ Dept. of Theoretical Physics Oxford University, Oxford, Great Britain

1. INTRODUCTION

The standard model of the Electroweak Interactions, a gauge theory based on an SU(2)

x

U(1) symmetry spontaneously

broken, has been remarkably successful in accounting for a very wide range of data on these interactions. Consequently, in these lectures concerning CP-nonconservation in the weak interactions, we shall work entirely within the framework of this model, since this is the most economical approach until such time as this framework may be shown to be too restrictive for the interpretation of the observed facts. Unfortunately, the positive facts which we have concerning CP-nonconservation effects have been few in number for quite some time, although there appears hope of obtaining further facts from observations on the New Mesons, as well as from more precise experiments on the neutral K mesons, in the next few years, as we shall discuss below. The plan of the lectures is as follows. In Sec. 2, we discuss in a general way the various mechanisms by which CPnonconservation effects can arise within the SU(2)

x

U(l)

framework, given the quarks and leptons now known tu us. Sec. 3 +

Lectures presented at the XXI. Internationale Universitatswochen fUr Kernphysik,Schladming,Austria,Feb.25-March 6,1982.

394

then gives a phenomenological discussion of the CP-nono -0 conservation phenomena known for the K -K complex, leading on to a discussion in Sec. 4 of its interpretation, within the standard model, and of the aims of further experiments under way. In Sec. 5, we discuss the situation concerning 000

the New Mesons D , B and T

and the possibility for the ob-

servation of CP-nonconservation effects in their decay processes. In Sec. 6, we consider recent estimates for the magnitude of the electric dipole moment for the neutron, in relation to the experimental accuracy expected in the current round of experiments.

2. CP-NONCONSERVATION WITHIN THE SU (2) x U ( 1) STANDARD MODEL We shall not

review the SU(2) x U(1) gauge theories

of the electroweak interactions in detail here, but refer the reader to the parallel lectures given by Dr. G. Ecker at this School [1], and to the lectures given recently by Dr. J. Ellis elsewhere [2]. There are three places in these theories where the question of CP-nonconservation can arise.

2.1 The Quark Mixing Matrix Here we confine attention to the case where the theory is based on one Higgs doublet (~+,~o), and some number ng (generations) of quark doublets (Qu,Qd) where ~ and Qd denote the up and down states within each of these doublets. When the theory is spontaneously broken, the Higgs bosons (,

/12,~-) generate masses for the

w±

+

,(~

0-0 -~

)/

and ZO bosons, in a well-

known way [3], and are absorbed into the longitudinal componentF of these heavy weak bosons. Only one physical Higgs boson H survives, given by (2.1)

395

where v denotes the vacuum expectation value (2.2) The quarks gain masses through the quark-Higgs Yukawa couplings, ini