CPviolation from the standard model to strings

Abstract

A review of CP violation from the Standard Model to strings is given which includes a broad landscape of particle physics models, encompassing the non-supersymmetric 4D extensions of the standard model, and models based on supersymmetry, on extra dimensions, on strings and on branes. The supersymmetric models discussed include complex mSUGRA and its extensions, while the models based on extra dimensions include 5D models including models based on warped geometry. CP violation beyond the standard model is central to achieving the desired amount of baryon asymmetry in the universe via baryogenesis and leptogenesis. They also affect a variety of particle physics phenomena: electric dipole moments, g − 2, relic density and detection rates for neutralino dark matter in supersymmetric theories, Yukawa unification in grand unified and string based models, and sparticle production cross sections, and their decays patterns and signatures at hadron colliders. Additionally CP violations can generate CP even-CP odd Higgs mixings, affect the neutral Higgs spectrum and lead to phenomena detectable at colliders. Prominent among these are the CP violation effects in decays of neutral and charged Higgs bosons. Neutrino masses introduce new sources of CP violation which may be explored in neutrino factories in the future. Such phases can also enter in proton stability in unified models of particle interactions. The current experimental status of CP violation is discussed and possibilities for the future outlined.

Maximal electric dipole moments of nuclei with enhanced Schiff moments

“…In figure 3 we show the cosines of the angles between the 6D MCPMFV vector representing the observable O d Ra and the EDM vectors, which are defined by Hg are larger, though decreasing as tan β grows. This can be understood by observing that the additional contributions to the Mercury EDM, beyond those from the couplingsḡ (0) , (1) πN N , increase with tan β.…”

“…We note that theḡ (1) πN N contribution the EDM of 225 Ra is about 200 times larger than to the Mercury EDM d I Hg [S], an enhancement due to the existence of a nearby parity-doublet states [25].…”

“…, as follows from assuming that the couplingsḡ (0) πN N andḡ (1) πN N are proportional to the matrix elements ofūu −dd andūu +dd in the nucleon state, respectively. It is known that the matrix element with the minus (−) sign is smaller than the one with the plus (+) sign by a a factor ∼ 5 to 10 [29].…”

“…in terms of the isoscalarḡ (0) πN N , isovectorḡ (1) πN N , and isotensorḡ (2) πN N T-violating pionnucleon couplings. The Schiff moment is linear in the CP-odd πN N couplingsḡ (i) πN N , and may be written as [19] …”

“…Electric dipole moments (EDMs) are among the most promising potential signatures for CP-violating physics beyond the Standard Model (SM), and one of the most promising options for extending the SM is provided by supersymmetry (SUSY) (for recent reviews, see [1,2]). The minimal SUSY extension of the SM (the MSSM) already contains many possible CP-violating phases, even in its minimally flavour-violating (MFV) version.…”