618
K. Kleinknecht and U. Uwer
9.8 Conclusion
Nearly 40 years after the discovery of CP violation, the nature of the phenomenon
has been clarified experimentally. In the K meson system, CP violation has been
discovered in the mixing (ε), in the decay (ε /ε, direct CP violation), and in the
interference between mixing and decay (m ε); in the B meson system, CP violation
in the interference between mixing and decay (sin 2β) as well as CP violation in the
decay have been observed. While finishing this article, the LHCb collaboration has
also reported the first observation of CP violation in the decay of neutral D mesons
to K + K − and π + π − (O(1.5 × 10 −3 )) [205]. All observations are consistent 8 with
the model of Kobayashi and Maskawa where the 3 × 3 mixing matrix of six quarks
has one non-trivial complex phase δ = (71.0 ± 0.3) ◦ . This leads to complex weak
coupling constants of quarks, and to T and CP violation.
In cosmology, CP violation together with a large departure from thermal
equilibrium via a first-order electroweak phase transition [206] and a baryon number
violation by instanton processes [207] could explain the observed baryon asymmetry. The source would be the asymmetric interactions of quarks and antiquarks with
the Higgs field [208]. The size of the observed CP violation in the quark sector,
expressed by the Jarlskog determinant, however is insufficient to explain the matter
asymmetry by several orders of magnitude [209]. Moreover, the low mass of the
Higgs boson disfavours baryogenesis during the electroweak phase transition [210].
A way out of this dilemma is the hypothesis that CP violation in the neutrino sector
could cause a lepton asymmetry. (B+L)-violating processes before the electroweak
phase transition could then convert the lepton asymmetry into a baryon asymmetry.
Leptogenesis would proceed through the production of heavy Majorana neutrinos in
the early Universe [211]. While the experimental proof of leptogenesis is difficult,
the observation of CP violation in the neutrino sector and the exploration of the
nature of the neutrino (Dirac or Majorana fermion) could establish strong hints.
In quark flavor physics the focus has changed after the successful establishment
of the Kobayashi-Maskawa paradigm. Today, the precise measurement of flavor
changing processes and CP asymmetries are used as tools to test the Standard
Model predictions. Tiny deviations between observations and theory predictions
could hint to additional quantum corrections modifying the size and the phase of
flavor changing amplitudes. The origin of these additional corrections could be
new heavy particles at mass scales much higher than the energies accessible by
today’s collider experiments. Experimental results on neutral meson mixing already
constrain the ratio between mass scale and the coupling strength of new particles to
values above 10 2 to 10 4 TeV, where the strongest bounds come from the neutral K
meson system [212]. The next generation of precision quark-flavor experiments will
8 For the D mesons the theoretical predictions still have large uncertainties. For K mesons recent
theoretical results on the value of the CP violating amplitude
//
both from dual QCD [213]
and from lattice QCD [214] deviate from the experimental value reported in Sect. 9.5, thus further
clarification is needed.
K. Kleinknecht and U. Uwer
9.8 Conclusion
Nearly 40 years after the discovery of CP violation, the nature of the phenomenon
has been clarified experimentally. In the K meson system, CP violation has been
discovered in the mixing (ε), in the decay (ε /ε, direct CP violation), and in the
interference between mixing and decay (m ε); in the B meson system, CP violation
in the interference between mixing and decay (sin 2β) as well as CP violation in the
decay have been observed. While finishing this article, the LHCb collaboration has
also reported the first observation of CP violation in the decay of neutral D mesons
to K + K − and π + π − (O(1.5 × 10 −3 )) [205]. All observations are consistent 8 with
the model of Kobayashi and Maskawa where the 3 × 3 mixing matrix of six quarks
has one non-trivial complex phase δ = (71.0 ± 0.3) ◦ . This leads to complex weak
coupling constants of quarks, and to T and CP violation.
In cosmology, CP violation together with a large departure from thermal
equilibrium via a first-order electroweak phase transition [206] and a baryon number
violation by instanton processes [207] could explain the observed baryon asymmetry. The source would be the asymmetric interactions of quarks and antiquarks with
the Higgs field [208]. The size of the observed CP violation in the quark sector,
expressed by the Jarlskog determinant, however is insufficient to explain the matter
asymmetry by several orders of magnitude [209]. Moreover, the low mass of the
Higgs boson disfavours baryogenesis during the electroweak phase transition [210].
A way out of this dilemma is the hypothesis that CP violation in the neutrino sector
could cause a lepton asymmetry. (B+L)-violating processes before the electroweak
phase transition could then convert the lepton asymmetry into a baryon asymmetry.
Leptogenesis would proceed through the production of heavy Majorana neutrinos in
the early Universe [211]. While the experimental proof of leptogenesis is difficult,
the observation of CP violation in the neutrino sector and the exploration of the
nature of the neutrino (Dirac or Majorana fermion) could establish strong hints.
In quark flavor physics the focus has changed after the successful establishment
of the Kobayashi-Maskawa paradigm. Today, the precise measurement of flavor
changing processes and CP asymmetries are used as tools to test the Standard
Model predictions. Tiny deviations between observations and theory predictions
could hint to additional quantum corrections modifying the size and the phase of
flavor changing amplitudes. The origin of these additional corrections could be
new heavy particles at mass scales much higher than the energies accessible by
today’s collider experiments. Experimental results on neutral meson mixing already
constrain the ratio between mass scale and the coupling strength of new particles to
values above 10 2 to 10 4 TeV, where the strongest bounds come from the neutral K
meson system [212]. The next generation of precision quark-flavor experiments will
8 For the D mesons the theoretical predictions still have large uncertainties. For K mesons recent
theoretical results on the value of the CP violating amplitude
//
both from dual QCD [213]
and from lattice QCD [214] deviate from the experimental value reported in Sect. 9.5, thus further
clarification is needed.