Développement et optimisation d'un système de polarisation de ...

tel-00726870, version 1 - 31 Aug 2012
26 1.1. The Electric Dipole moment
Indeed, the P and T operators applied on E and S give:
E P
−→ − E S P
−→ S
E T
−→ E S T
−→ −S Both T and P are violated. Assuming the CPT theorem, the EDM violates CP since T is
broken.
Figure 1.1: Scheme showing the CP and T violation of a particle with an electric dipole moment.
The search for a non zero EDM is motivated by new CP violation sources beyond the
Standard Model. The two potentially CP violation sources within the SM are described below:
one concerning the strong sector, the other one the electroweak sector [11].
In quantum chromodynamics, the interaction Lagrangian can be broken up in two parts: one
concerning the interaction of quarks and gluons and a part relative to the non trivial vacuum
structure of the theory [12] This second part can be written:
Lθ = − θ
T r ˜FµνF
16π2 µν
with Fµν the gluon field strength tensor, and ˜ Fµν its dual counterpart, defined by
˜Fµν = 1
2 ɛµναβF αβ . The Lagrangian is also parameterized by the θ angle, which is a QCD
phase called vacuum angle, and defined over [0, 2π]. From this angle the parameter ¯ θ can be
determined [13]. This parameter is naturally supposed to be close to unity. EDM of neutron
is directly proportional to ¯ θ: we have dn ∼ ¯ θ × 2 × 10 −16 e cm [14]. The current limit on dn is
∼ 10 −26 e cm [3], constrains ¯ θ to ¯ θ ∼ 10 −10 ! This unexpected situation is known as "the strong
CP problem" [15]. To solve this problem, Peccei and Quinn [16] bring into play a new particle:
the axion, but this particle has not been observed yet.
Another CP violation source can be observed within the SM, in the electroweak sector. This
source concerns the complex phase δ of the Cabibbo-Kobayashi-Maskawa matrix which describes
the quarks mixing flavors.
The complex phase of the CKM matrix is related to the quarks EDM. Shabalin [17] has shown
that there is no contribution to a quark EDM up to three loops. It can be demonstrated using the
unitarity of the CKM matrix. The calculated quark EDM are: dd ∼ du ∼ 10 −34 e cm. Another
approach consists in using only a two quarks interaction (the third one being spectator) [18].
(1.2)