Flavor Physics and Dark Matter in SUSY GUT Models Yudi Santoso Based on works with Bhaskar Dutta & Yukihiro Mimura PRD80:095005,2009 PHENO 2010, Madison, 11 th May 2010 1
Supersymmetry Why SUSY? It provides solution to hierarchy problem, improves gauge coupling unification, provides dark matter particle. Unsolved problem: How do we understand flavor structure within SUSY? (How SUSY is broken?) 2
Flavor & SUSY Flavor puzzle of SUSY: (without restriction by hand) soft breaking terms allow large flavor changing processes. FCNC can be suppressed by flavor universal SUSY breaking: Universal squarks and sleptons masses m ˜ U , m ˜ D , m ˜ Q , m ˜ L , m ˜ E = Im 0 . Universal trilinear coupling coefficents A = Y A 0 ( Y = Yukawa). Nevertheless, nonuniversality still arises through RGE, ⇒ FCNC through radiative correction. Within SUSY GUT - How the quark sector is related to the lepton sector? 3
B s mixing B s − ¯ Large phase is measured: CDF: φ s ∈ [0 . 28 , 1 . 29] (PRL100 (2008) 161802) D0 : φ s = 0 . 57 +0 . 30 − 0 . 24 (stat) +0 . 02 − 0 . 07 (syst) (PRL101 (2008) 241801) Standard Model: φ s = 2 β s ≡ 2 arg ( − V ts V ∗ tb /V cs V ∗ cb ) ≃ 0 . 04 s s i W b b j i W W s s j b W b 4
B s mixing - SUSY B s − ¯ Chargino box diagrams. Double penguin diagrams through heavy Higgs. This is ∝ tan 4 β and ∝ 1 /m 4 A (Recall also that BR ( B s → µµ ) ∝ tan 6 β ) Define C B s e 2 iφ Bs = M SM 12 + M NP 12 M SM 12 then φ s = 2( β s − φ B s ) 5
Neutrino in the GUT-shell Observation: θ 12 (solar) - large, θ 23 (atmospheric) - large, θ 13 (reactor) - small, and small neutrino masses. Light neutrinos through seesaw: M light = f � ∆ L � − Y ν M − 1 R Y T ν � H 0 u � 2 ν Seesaw type II I ∆ L is an SU(2) L triplet, and f is a Majorana coupling 1 2 LL ∆ L . Large mixing through Majorana coupling (type II) or Dirac coupling (type I). 6
GUT boundary condition Squark and slepton mass matrices: 0 [ 1 − κ F U F diag( k 1 , k 2 , 1) U † M 2 F = m 2 F ] ˜ Minimal type SU(5) : κ Q = κ U c = κ E c = 0 κ L = κ D c , U L = U D c , Minimal type SO(10) : κ Q = κ U c = κ D c , U Q = U U c = U D c , κ L = κ E c (To obey proton decay constraint. Dutta, Mimura and Mohapatra, PRL 94 (2005) 091804, PRD 72 (2005) 075009) 7
Neutralino Dark Matter Direct detection cross section 4 p | ( A u f u /m u + A c f c /m c + A t f t /m t ) πm 4 σ ˜ ≃ χ 0 1 − p +( A d f d /m d + A s f s /m s + A b f b /m b ) | 2 where, f q ≡ � p | m q ¯ qq | p � /m p , and f u ≃ 0 . 027 ; f d ≃ 0 . 039 ; f s ≃ 0 . 36 ; f c = f b = f t ≃ 0 . 043 g 2 2 m d,s,b � � − sin α F h + cos α F H A d,s,b = m 2 m 2 4 M W cos β cos β H h g 2 2 m u,c,t � cos α F h + sin α F H � A u,c,t = m 2 m 2 4 M W sin β sin β h H 8
SU(5) m A − µ plane tan β = 40, A 0 = 0, m 1/2 = 500 GeV, m 0 = 500 GeV tan β = 40, A 0 = 0, m 1/2 = 500 GeV, m 0 = 1 TeV 1000 1000 1000 1000 800 800 800 800 µ [GeV] µ [GeV] 0 . 5 0.5 × 10 -8 pb 600 600 600 600 × 1 0 - 8 p b 2 × 10 -8 1 1 2 × 10 -8 0 -8 2 2 1 -8 400 400 400 400 5 × 0 1 3 5 × 3 200 200 400 400 600 600 800 800 1000 1000 200 200 400 400 600 600 800 800 1000 1000 m A [GeV] m A [GeV] | 2 φ B s | = 0 . 5 rad. 9
SO(10) m A − µ plane tan β = 40, A 0 = 0, m 1/2 = 500 GeV, m 0 = 500 GeV tan β = 40, A 0 = 0, m 1/2 = 800 GeV, m 0 = 500 GeV 1000 1000 1500 1500 3 × 10 -8 1 × 10 -8 2 × 10 -8 1 × 10 -8 0.05 800 800 0.5 × 10 -8 pb µ [GeV] µ [GeV] 0 1000 1000 . 1 600 600 1 0.5 × 10 -8 pb 2 400 400 1 3 × 10 -8 2 × 10 -8 5 2 500 500 5 200 200 200 200 400 400 600 600 800 800 1000 1000 200 200 400 400 600 600 800 800 1000 1000 m A [GeV] m A [GeV] | 2 φ B s | = 0 . 5 rad. 10
10 3 10 3 SO(10) Br(B s → µ + µ - ) × 10 -8 10 2 10 2 750 GeV V 10 10 e G 500 GeV 0 5 2 V e T 1 = µ 1 1 -1 -1 10 10 -4 -4 -3 -3 -2 -2 -1 -1 10 10 10 10 10 10 10 10 1 1 10 10 σ χ -p × 10 -6 pb tan β = 40 , A 0 = 0 , m 0 = 500 GeV, m 1 / 2 = 500 GeV 11
10 3 10 3 SU(5) Br(B s → µ + µ - ) × 10 -8 10 2 10 2 750 GeV 500 GeV V 10 10 e G 0 5 2 µ = 1 TeV 1 1 -1 -1 10 10 -4 -4 -3 -3 -2 -2 -1 -1 10 10 10 10 10 10 10 10 1 1 10 10 σ χ -p × 10 -6 pb tan β = 40 , A 0 = 0 , m 0 = 500 GeV, m 1 / 2 = 500 GeV 12
Conclusion We have looked at models of SUSY GUT in which B s − ¯ B s mixing phase can be large and with large neutrino mixing. Combined with other flavor changing constraints and dark matter constraints we found that the funnel region is still allowed by both SU(5) and SO(10), and favored by SU(5). Stronger constraints from upcoming experimental results can provide further hints on the SUSY GUT model. 13
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