Y-Unified GUTS: MSSM at large tan β Archana Anandakrishnan The Ohio State University October 3, 2013 Based on arXiv:1212.0542 (Phys. Rev. D 87, 055005 (2013)) & arXiv:1303.5125 & arXiv:1307.7723 (Accepted in PRD) & work in progress with Stuart Raby, B. Charles Bryant, Linda Carpenter (OSU), Kuver Sinha (Syracuse), Akın Wingerter(LPSC) Theory Seminar, Los Alamos National Lab 1
Outline Introduction to SO(10) SUSY GUTS Constraints from Yukawa Unification The Analysis Spectrum and Phenomenology Effective“Mirage” Mediation. Summary 2
Supersymmetric GUTS Dimopoulos, Raby, Wilczek (1981) (Fig. from Martin’s Primer) Argument in favor of SUSY, independent of the solution to hierarchy problem. Requires some superpartners of around the TeV scale. Unification of couplings at ∼ 10 16 GeV. 3
SO(10) GUTS and Yukawa Unification SO ( 10 ) → SU ( 3 ) C × SU ( 2 ) L × U ( 1 ) Y × U ( 1 )( B − L ) (3 , 2)1 / 3 , 1 / 3 + (¯ 3 , 1) − 4 / 3 , − 1 / 3 + (1 , 1) − 2 , 1 + (¯ 16 → 3 , 1)2 / 3 , − 1 / 3 + (1 , 2) − 1 , − 1 + (1 , 1)0 , 1 ¯ Q ¯ u ¯ e d L ν ¯ SO(10) GUTS are very economical: 16 dimensional representation. Only renormalizable Yukawa coupling is of the form, W ⊃ λ 16 10 16 allowing for unified Yukawa couplings at the GUT scale. Third family Yukawa Unification is consistent with current data. λ t = λ b = λ τ = λ ν τ = λ Effective higher dimensional operators could generate the first two family hierarchical Yukawa couplings. 4
Yunification and Boundary Conditions One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking 5
Blazek, Dermisek & Raby PRL 88, 11804; PRD 65, 115004 Baer & Ferrandis PRL 87, 211803 Auto, Baer, Balazs, Belayaev, Ferrandis,& Tata JHEP 0306:023 Tobe & Wells NPB 663,123 Dermisek, Raby, Roszkowski, & Ruiz de Austri JHEP 0304:037; JHEP 0509:029 Baer, Kraml, Sekmen, & Summy JHEP 0803:056; JHEP 0810:079 Badziak, Olechowski & Pokorski JHEP 2011:147 Gogoladze, & Shafi,Un JHEP 2012:028; PLB 704, 201 Ajaib, Gogoladze, Shafi, & Un JHEP 2013:139 AA & Raby arXiv:1303.5125 6
Recent papers on Yukawa unification (created using wordle) 7
A quick refresher GUT scale parameters of a ’minimal’ SO(10) SUSY GUT m 16 - Universal scalar mass m 10 - Universal Higgs mass M 1 / 2 - Universal gaugino mass A 0 - Trilinear coupling tan β - Ratio of the Higgs vev. g - Unified gauge coupling λ - Unified Yukawa coupling at the GUT scale 8
Higgs vev Ratio of the Higgs vev is defined as tan β = v u = � H u � v d � H d � Fermion masses are generated by coupling to the Higgs boson tt + λ b v d ¯ L ⊃ λ t v u ¯ bb + λ τ v d ¯ ττ The value of tan β is restricted by the requirement of Yukawa unification. tan β ≃ 50 9
Yunification and Boundary Conditions One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking tan β ≃ 50 10
Bottom quark mass In the large tan β regime, there are large corrections to the bottom quark mass. g 2 λ 2 µ M ˜ g tan β µ A t tan β 3 t δ m b / m b ≃ + m 2 m 2 12 π 2 32 π 2 ˜ ˜ t b Hall et. al; Carena et. al; Blazek et. al In order to fit data, δ m b / m b ≃ − (f ew )% µ M ˜ g > 0; ⇒ µ A t < 0 Trilinear Coupling A 0 < 0 11
Electroweak Symmetry Breaking The RGEs for the up and down-type Higgs mass squared can be written as: dm 2 2 � − 3 2 − 3 � 5 g 2 1 M 2 1 − 3 g 2 2 M 2 10 g 2 1 S + 3 λ 2 b X b + λ 2 Hd = τ X τ 16 π 2 dt dm 2 2 � − 3 2 + 3 � Hu 5 g 2 1 M 2 1 − 3 g 2 2 M 2 10 g 2 1 S + 3 λ 2 t X t + λ 2 = ν τ X ν τ 16 π 2 dt RGE evolution in standard MSSM scenarios SPS1a 600 m Ql ( µ 2 +m Hd 2 ) 1/2 400 M 3 GeV M 2 200 M 1 m Er 0 ( µ 2 +m Hu 2 ) 1/2 SOFTSUSY3.0.5 -200 2 4 6 8 10 12 14 16 log 10 ( µ /GeV) Fig from SOFTSUSY 12
Electroweak Symmetry Breaking The RGEs for the up and down-type Higgs mass squared can be written as: dm 2 2 � − 3 2 − 3 � Hd 5 g 2 1 M 2 1 − 3 g 2 2 M 2 10 g 2 1 S + 3 λ 2 b X b + λ 2 = τ X τ 16 π 2 dt dm 2 2 � − 3 2 + 3 � Hu 5 g 2 1 M 2 1 − 3 g 2 2 M 2 10 g 2 1 S + 3 λ 2 t X t + λ 2 = ν τ X ν τ 16 π 2 dt In Yunified models, since, λ t = λ b = λ τ = λ ν = λ , in order for REWSB, one needs m 2 Hu < m 2 Hd Non-universal Higgs masses! 13
Yunification and Boundary Conditions One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking tan β Corrections to bottom mass Non-universal Higgs mass 14
B s → X s γ BR ( B s → X s γ ) Exp = (3 . 43 ± 0 . 30) × 10 − 4 Exp BR ( B s → X s γ ) SM = (3 . 15 ± 0 . 23) × 10 − 4 SM NNLO In MSSM, ∝ µ A t χ + C ˜ m 2 tan β × sign ( C SM ) 7 7 ˜ Data constrains C eff = C SM + C SUSY ≃ ± C SM 7 7 7 7 C SUSY ≃ − 2 C SM , implying light scalars. 7 7 C SUSY ≃ 0, implying heavy scalars scalars. 7 Which possibility does data accommodate? 15
B → K ∗ µ + µ − Forward-Backward Asymmetry in B → K ∗ µ + µ − ! If C eff = + C SM , then A FB crosses zero at some momentum. 7 7 If C eff = − C SM , then there is no zero-crossing in the A FB . 7 7 Theory Binned theory LHCb 1 FB A 0.5 0 -0.5 LHCb Preliminary -1 0 5 10 15 20 2 2 4 q [GeV / c ] 2012 Result from LHCb Heavy Scalars 16
Breaking News! 17
B s → µ + µ − BR ( B s → µ + µ − ) Exp = (3 . 2 ± 1 . 5) × 10 − 9 2012 LHCb BR ( B s → µ + µ − ) SM = (3 . 37 ± 0 . 31) × 10 − 9 SM MSSM contributions are enhanced in the large tan β limit. BR ( B s → µ + µ − ) ∝ (tan β ) 6 M 4 A In MSSM models with large tan β , M A ≥ 1500 GeV Standard Model like Higgs 18
Yunification and Boundary Conditions One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking tan β Corrections to bottom mass Non-universal Higgs mass Flavor Physics 19
Discovery of the millenia CMS ; ATLAS M h = 125 . 3 ± 1 GeV 20
Light Higgs Mass Boundary conditions consistent with minimal Yukawa unification: √ m 16 > few TeV; m 10 ∼ 2 m 16 ; A 0 ∼ − 2 m 16 ; µ, M 1 / 2 << m 16 ; tan β ∼ 50 Bagger, Feng, et al Maximal mixing region - easy to get ∼ 125 GeV Higgs. Carena, Quiros, Wagner 21
Higgs and Bottom quark To fit bottom quark mass: g 2 λ 2 µ M ˜ g tan β µ A t tan β 3 t δ m b / m b ≃ + m 2 m 2 12 π 2 32 π 2 ˜ ˜ t b Fitting the Higgs mass: 7 χ 2 95% C.L. 6 5 90% C.L. 4 3 68% C.L. 2 2010 2092 1 1436 0 0 500 1000 1500 2000 2500 M (˜ g ) [GeV] m 16 = 20 TeV 22
Yunification and Boundary Conditions One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking tan β Corrections to bottom mass Non-universal Higgs mass Flavor Physics Higgs Mass 23
Neutrino sector Observables in the neutrino sector: sin 2 θ 12 = 0 . 27 − 0 . 34 sin 2 θ 23 = 0 . 34 − 0 . 67 sin 2 θ 13 = 0 . 016 − 0 . 030 (7 . 00 − 8 . 09) × 10 − 5 eV 2 ∆ m 2 = 21 (2 . 27 − 2 . 69) × 10 − 3 eV 2 ∆ m 2 = 31 (3 σ range) from Nu-fit Collaboration θ exp 9 ◦ (7 . 29 − 9 . 96) = 13 θ DR − model 6 ◦ � 13 DayaBay; Reno Flavor violating corrections to the K¨ ahler potential. Chen, Fallbacher et al 24
Yunification and Boundary Conditions One can use Yukawa Unification to constrain the GUT scale boundary conditions. Yukawa Unification & Soft SUSY breaking tan β Corrections to bottom mass Non-universal Higgs mass Flavour Physics Higgs Mass Neutrino masses and mixing angles 25
Dermisek-Raby Model Recent analysis by AA , S.Raby, and A. Wingerter 1212.0542 Sector Third Family Analysis # Full three family Analysis # gauge α G , M G , ǫ 3 3 α G , M G , ǫ 3 3 SUSY (GUT scale) m 16 , M 1 / 2 , A 0 , m Hu , m Hd 5 m 16 , M 1 / 2 , A 0 , m Hu , m Hd 5 ǫ , ǫ ′ , λ , ρ , σ , ˜ textures λ 1 ǫ , ξ 11 neutrino 0 M R 1 , M R 2 , M R 3 3 SUSY (EW scale) tan β , µ 2 tan β , µ 2 Total # 11 24 (Compared to 32 parameters in the CMSSM) ˜ χ a ( M χ χ a + 45 φ a φ a W ch . fermions = λ 16 3 10 16 3 + 16 a 10 χ a + ¯ 16 3 + 45 16 a + A 16 a ) ˆ ˆ M M Effective operators to generate the first two family and off-diagonal Yukawa couplings. 10 ~ 45 Φ a 10 M X _ 16 16 3 16 χ a 16 2 3 χ a 2 45 Φ a 10 A 10 M X M X _ _ χ a 16 16 b a χ a 16 χ a χ a 16 c b c 26
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