Flavour and CP Violation in Supersymmetric Models John Ellis Theory Division, LHCb, Jan. 27 th, 2009

Flavour and CP Violation - CKM model successful at present - A pillar of the Standard Model - What lies beyond it? 2008 Nobel Physics Prize: Kobayashi & Maskawa

Possible Discrepancies? B  vs sin 2  B s mixing phase  Bs  0?  K vs sin 2 

Where does the Matter come from? Dirac predicted the existence of antimatter: same mass opposite internal properties: electric charge, … Discovered in cosmic rays Studied using accelerators Matter and antimatter not quite equal and opposite: WHY? Need additional matter-antimatter difference to explain why the Universe contains mainly matter, not antimatter? LHCb and other experiments will look for answer

How to Create the Matter in the Universe? Need a difference between matter and antimatter observed in the laboratory Need interactions able to creat matter present in unified theories not yet seen by experiment Must break thermal equilibrium Possible in the decays of heavy particles Sakharov Will we be able to calculate using laboratory data?

Why Supersymmetry (Susy)? Intrinsic beauty Hierarchy/naturalness problem Unification of the gauge couplings Predict light Higgs < 150 GeV –As suggested by precision electroweak data Cold dark matter Essential ingredient in string theory (?)

SUSY Stabilizes the Higgs Mass 2 Consider generic fermion and boson loops: Each is quadratically divergent: ∫ Λ d 4 k/k 2 Leading divergence cancelled if 2 x 2 Supersymmetry!

Reasons to like Susy It enables the gauge couplings to unify It predicts m H < 150 GeV JE, Nanopoulos, Olive + Santoso: hep-ph/ As suggested by EW data

Astronomers say that most of the matter in the Universe is invisible Dark Matter ‘Supersymmetric’ particles ? We shall look for them with the LHC Dark Matter in the Universe

Particles + spartners 2 Higgs doublets, coupling μ, ratio of v.e.v.’s = tan β Unknown supersymmetry-breaking parameters: Scalar masses m 0, gaugino masses m 1/2, trilinear soft couplings A λ, bilinear coupling B μ Assume universality? constrained MSSM = CMSSM Single m 0, single m 1/2, single A λ, B μ : not string? Minimal Supersymmetric Extension of Standard Model (MSSM)

Mass Renormalizations Assuming universality at the GUT scale Gaugino masses: –M a = (α a / α GUT ) m 1/2, e.g., → M 2 / M 3 = α 2 / α 3 Squark and slepton masses: –Squark mass 2 : m m 1/2 2 –Left-handed slepton mass 2 : m m 1/2 2 –Right-handed slepton mass 2 : m m 1/2 2 Minimal flavour violation (MFV): –Flavour mixing of squarks and sleptons induced by CKM, neutrino mixing

Possible Nature of SUSY Dark Matter Particle No strong or electromagnetic interactions Otherwise would bind to matter Detectable as anomalous heavy nucleus Possible weakly-interacting scandidates Sneutrino (Excluded by LEP, direct searches) Lightest neutralino χ (partner of Z, H, γ) Gravitino (nightmare for astrophysical detection)

Current Constraints on the Simplest Minimal SUSY Model (CMSSM) Excluded because stau LSP Excluded by b  s gamma Favoured (?) by latest g - 2 assuming neutralino LSP WMAP constraint on relic density

How Soon Might the CMSSM be Detected? O.Buchmueller et al

Non-Universal Scalar Masses Different sfermions with same quantum #s? e.g., d, s squarks ? disfavoured by upper limits on flavour- changing neutral interactions Squarks with different #s, squarks and sleptons? disfavoured in various GUT models e.g., d R = e L, d L = u L = u R = e R in SU(5), all in SO(10) Non-universal susy-breaking masses for Higgses? Why not! 1 or 2 extra parameters in NUHM1,2

How Soon Might the NUHM1 be Detected? O.Buchmueller et al

B s  +  - in the CMSSM & NUHM1 Small difference from Standard Model in CMSSM Big increase possible in NUHM1

Minimal Flavour Violation (MFV) & Maximal CP Violation (MCP) All squark mixing due to CKM matrix Universal scalar masses at high scale for sparticles with same quantum numbers Parametrization: Maximally CP-violating MFV (MCPMFV) model has 19 parameters, of which 6 violate CP: Often assume universal ImM a, ImA f, but non- universality compatible with MFV: MCPMFV JE, Lee & Pilaftsis

Complexification of CMSSM With universality, just two new CP-violating parameters: –Arg(M a  ), Arg(A f  ) Loop-induced mixing ~ –(h,H,A) → (H 1,H 2,H 3 ) with indefinite CP Effects on masses, couplings J.E. + Lee + Pilaftsis

From LEP, from electric dipole moments Experimental Constraints red: n, blue: Tl Olive et al

Prospective LHC

Effects of CP Phases in MCPMFV Renormalization of phases Ino masses Heavy Higgs masses B s mixing JE + Lee + Pilaftsis: arXiv:

Effects of CP Phases in MCPMFV B s   b  s  Bu  Bu   Different regions allowed for different phases … … and hence A CP in b  s  JE + Lee + Pilaftsis, arXiv:

Thallium and Electron EDMs in the MCPMHV Possibility of non-trivial cancellations between the contributions of different phases JE, Lee & Pilaftsis, arXiv:

Neutron EDM in the MCPMHV Possibility of non-trivial cancellations between the contributions of different phases JE, Lee & Pilaftsis, arXiv:

Mercury EDM in the MCPMHV Possibility of non-trivial cancellations between the contributions of different phases JE, Lee & Pilaftsis, arXiv:

SUSY Electroweak Baryogenesis? Exploit phases in SUSY MCPMFV model Require light stop for first-order electroweak transition Higgs and stop masses tightly constrained by theory and experiment Carena, Nardini, Quiros and Wagner: arXiv:

Summary Observed CP violation described well by Kobayashi and Maskawa –Some hints of discrepancies? More CPV needed to explain matter in Universe Supersymmetry offers new CPV mechanisms –New CPV phases Opportunities in B decays, EDMs, …

Papers with J.S. Lee and A. Pilaftsis CERN LHC signatures of resonant CP violation in a minimal supersymmetric Higgs sector: hep-ph/ Resonant CP violation in MSSM Higgs production and decay at gamma gamma colliders: hep-ph/ Diffraction as a CP and lineshape analyzer for MSSM Higgs bosons at the LHC: hep-ph/ Resonant CP violation in Higgs radiation at e+ e- linear collider: hep- ph/ B-Meson Observables in the Maximally CP-Violating MSSM with Minimal Flavour Violation: arXiv: Electric Dipole Moments in the MSSM Reloaded: arXiv: CPsuperH2.0: an Improved Computational Tool for Higgs Phenomenology in the MSSM with Explicit CP Violation (with M. Carena and C. Wagner): arXiv: