CP Violation

Three possibilities for the origin of CP violation are discussed: (1) the Standard Model in which all CP violation is due to one parameter in the CKM matrix, (2) the superweak model in which all CP violation is due to new physics and (3) the Standard Model plus new physics. A major goal of B physics is to distinguish these possibilities. CP violation implies time reversal violation (TRV) but direct evidence for TRV is difficult to obtain.Comment: 13 pages, to be published in Lecture Notes of TASI-2000, edited by Jonathan L. Rosner, World Scientific, 200

CP violation and modular symmetries

We reconsider the origin of CP violation in fundamental theory. Existing string models of spontaneous CP violation make ambiguous predictions, due to the arbitrariness of CP transformation and the apparent non-invariance of the results under duality. We find an unambiguous modular CP invariance condition, applicable to predictive models of spontaneous CP violation, which circumvents these problems; it strongly constrains CP violation by heterotic string moduli. The dilaton is also evaluated as a source of CP violation, but is likely experimentally excluded. We consider the prospects for explaining CP violation in strongly-coupled strings and brane worlds.Comment: 6 pages, REVTeX 4b5+amssymb. 2 references added, substantially the same as published versio

A search for time-integrated CP violation in D0→h−h+D^{0} \rightarrow h^{-}h^{+} decays

The LHCb Collaboration has recently observed evidence of CP violation in neutral D meson decays. CP violation in the charm sector is generically expected to be very small in the Standard Model, but can be enhanced in many models of new physics. In this document we will present the results of a search for time-integrated \CP violation in $D^0 \rightarrow h^- h^+$ with $(h=K,\pi)$ decays, performed with around 0.6 fb$^{-1}$ of data collected by LHCb in 2011. The difference in CP asymmetry between $D^0 \rightarrow K^- K^+$ and $D^0 \rightarrow \pi^- \pi^+$, $\Delta A_{CP} = A_{CP}(K^- K^+) - A_{CP}(\pi^- \pi^+)$ is measured to be $\Delta A_{CP} = [-0.82 \pm 0.21 (stat.) \pm 0.11 (syst.)]$ . This differs from the hypothesis of CP conservation by 3.5 sigma.Comment: to appear in the proceedings of The 5th International Workshop on Charm Physics (Charm 2012

CP-odd invariants for multi-Higgs models and applications with discrete symmetry

CP-odd invariants are useful for studying the CP properties of Lagrangians in any basis. We explain how to build basis invariants for the scalar sector, and how to distinguish CP-odd invariants from CP-even invariants. Up to a certain order, we use these methods to systematically build all the CP-odd invariants. The CP-odd invariants signal either explicit or spontaneous violation of CP. Making use of the CP-odd invariants, we determine the CP properties of potentials with 3 and with 6 Higgs fields arranged as triplets of specific discrete symmetries in the $\Delta(3n^2)$ or $\Delta(6n^2)$ series (inlcuding $A_4$, $S_4$, $\Delta(27)$ and $\Delta(54)$ as well as the cases for $n>3$).Comment: 9 pages. Contribution to the proceedings of DISCRETE 2016, Warsa

CP Violation

Several pieces of direct and indirect evidence now suggest that the Kobayashi-Maskawa mechanism plays a distinguished role for CP violation at the electroweak scale. This talk provides a general overview of CP violation in its various contexts, emphasizing CP violation in flavour-violating interactions, such as due to the Kobayashi-Maskawa mechanism. I then review a few recent theoretical developments relevant to the interpretation of CP violation.Comment: 27 pages, LaTeX; plenary talk presented at the International Europhysics Conference on High Energy Physics, Budapest, July 2001; manuscript has some overlap with hep-lat/020101