Yukawa Unification, Flavour Symmetry & SUSY GUTs Qaisar Shafi - PowerPoint PPT Presentation

Yukawa Unification, Flavour Symmetry & SUSY GUTs Qaisar Shafi Bartol Research Institute Department Physics and Astronomy University of Delaware, USA Collaboration: Adeel Ajaib, K.S. Babu, Howard Baer, Ilia Gogoladze, Bin He, Tong Li, Azar Mustafayev, Fariha Nasir, Nobuchika Okada, Shabbar Raza and C. Salih Un. FLASY 2014, University of Sussex

Outline Supersymmetric GUTs & Yukawa Unification ( b − τ and t − b − τ ) Higgs & Sparticle Spectroscopy (including LSP neutralino DM) Flavor Symmetry and SUSY GUTs. Conclusions Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

Low Scale ( ∼ TeV) Supersymmetry (SUSY): Arguably the most compelling extension of the Standard Model; Resolves the gauge hierarchy problem (more or less); Provides cold dark matter candidate (LSP/Neutralino); Predicts new particles accessible at the LHC; these enable unification of the SM gauge couplings; 60 60 � 1 Α 1 � 1 MSSM SM Α 1 50 50 40 40 � 1 Α 2 Α i � 1 Α i � 1 � 1 Α 2 30 30 � 1 Α 3 20 20 � 1 Α 3 10 10 2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16 Log 10 � � � GeV � Log 10 � � � GeV � Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

Grand Unified Theories (GUTs) Unification of SM / MSSM gauge couplings; Unification of matter/quark-lepton multiplets; Electric charge quantization; Magnetic monopoles. Seesaw physics / neutrino oscillations; Quark-Lepton mass relations; New source for baryo-leptogenesis; Inflation / Observable gravity waves (Planck) Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

CMSSM: Limits on sparticle masses from ATLAS S.F.Brazzale, ICNFP13 Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

CMSSM: Limits on sparticle masses from ATLAS g � 1.7 TeV for m ˜ q ≃ m ˜ m ˜ g m ˜ g � 1.1-1.3 TeV for m ˜ q >> m ˜ g , Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

SUSY SO(10) Fermion families reside in 16 i ( i =1,2,3); � predicts ’right handed’ neutrino ⇒ non-zero neutrino masses through seesaw mechanism. Automatic Z 2 ’matter’ parity if SO (10) → MSSM using only tensor repsns. Also means stable cosmic strings (in addition to monopoles) Yukawa couplings include 16 i 16 j 10 , 16 i 16 j 126 , etc . 16 3 16 3 10 yields t − b − τ unification Y t = Y b = Y τ = Y ν (not so in non-SUSY SO(10)) In the ‘old days’ (B. Ananthanarayan, G. Lazarides and Q. Shafi, 1991) it was used to predict the top quark mass Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

Nowadays, one employs t − b − τ unification to make predictions, such as sparticle masses, which can be tested at the LHC (Baer et al.,Raby et al., ....); t − b − τ Yukawa unification can also be realized in SU (4) c × SU (2) L × SU (2) R , a maximal subgroup of SO(10); Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

b - τ Yukawa Unification in CMSSM Ilia Gogoladze, S. Raza and Q. Shafi, Phys.Lett. B706 (2012) 345-349 . SUSY SU (5): 5 3 × 10 3 × 5 H d ↑ ↑ ( L , b c ),( Q , τ c ) = ⇒ y b = y τ SUSY SO (10): 16 3 × 16 3 × 10 u , d Suppose 10 u ≡ H u while 10 d ≡ H d cos δ + . . . = ⇒ y b = y τ Quantify b - τ Yukawa unification(YU) by R b τ = max ( y b , y τ ) min ( y b , y τ ) Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

b - τ YU in CMSSM/mSUGRA m 0 , M 1 / 2 , A 0 , tan β, sign ( µ ) m 0 ≡ Universal soft SUSY breaking sfermion mass M 1 / 2 ≡ Universal SSB gaugino mass A 0 ≡ Universal SSB trilinear interaction tan β = v u v d µ ≡ SUSY bilinear Higgs parameter > 0 Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

Constraints 123 ≤ m h ( lightest Higgs mass ) ≤ 127 GeV , 0 . 8 × 10 − 9 < BR ( B s → µ + µ − ) < 6 . 2 × 10 − 9 , 0 . 15 < BR ( B u → τν τ ) MSSM < 2 . 03 (2 σ ) , BR ( B u → τν τ ) SM 2 . 99 × 10 − 4 ≤ BR ( b → s γ ) ≤ 3 . 87 × 10 − 4 (2 σ ) , 0 . 091 < Ω CDM h 2 < 0 . 1363 (5 σ ) , 3 . 4 × 10 − 10 ≤ ∆ a µ ≤ 55 . 6 × 10 − 10 (3 σ ) . Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

We performed random scans using ISAJET7.84 1 for the following parameter range 0 ≤ m 0 ≤ 20 TeV , 0 ≤ M 1 / 2 ≤ 5 TeV , − 3 ≤ A 0 / m 0 ≤ 3 , 2 ≤ tan β ≤ 60 , µ > 0 , m t = 173 . 3 GeV . 1F. E. Paige, S. D. Protopopescu, H. Baer and X. Tata, arXiv:0312045 [hep-ph] . Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

b - τ YU and finite threshold corrections 1 Dominant contributions to the bottom quark mass from the gluino and chargino loop g 2 y 2 µ m ˜ g tan β µ A t tan β δ y b ≈ + + . . . 3 t 12 π 2 m 2 32 π 2 m 2 1 2 where m 1 ≈ ( m ˜ b 1 + m ˜ b 2 ) / 2 and m 2 ≈ ( m ˜ t 2 + µ ) / 2 where λ b = y b and λ t = y t 1 L. J. Hall, R. Rattazzi and U. Sarid, Phys. Rev.D 50, 7048 (1994) Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

Importance of finite SUSY threshold corrections Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

χ 0 Gray points are consistent with REWSB and ˜ 1 LSP. Green points satisfy collider bounds and orange points are for 1 DM abundance Ω h 2 ≤ 1. χ 0 R ≤ 1 . 2. The brown points are subset of orange points that satisfy ˜ Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

Point 1 Point 2 m 16 17910 8975 M 1 263 329 tan β 43.2 33.1 A 0 / m 0 -2.35 -2.23 m t 173.3 173.3 µ 12053 6008 0 . 81 × 10 − 12 0 . 54 × 10 − 11 ∆( g − 2) µ m h 123 124.9 m H 5138 7049 m A 5105 7004 m H ± 5140 7050 m ˜ 174,374 170, 346 χ 0 1 , 2 m ˜ 12009, 12009 6032, 6032 χ 0 3 , 4 m ˜ 3768, 12026 349, 6047 χ ± 1 , 2 1078 1053 m ˜ g m ˜ 17865, 17915 8953, 8980 uL , R m ˜ 1462, 6738 205, 4705 t 1 , 2 m ˜ 17865, 17924 8953, 8985 dL , R m ˜ 6853, 9328 4813, 6660 b 1 , 2 m ˜ 17916 8977 ν 1 m ˜ 14786 7925 ν 3 m ˜ 17904, 17896 8967, 8969 eL , R m ˜ 10983, 14797 6819, 7956 τ 1 , 2 0 . 10 × 10 − 12 0 . 11 × 10 − 13 σ SI ( pb ) 0 . 21 × 10 − 11 0 . 40 × 10 − 10 σ SD ( pb ) Ω CDM h 2 156 0.104 R 1.00 1.15 The first point displays a solution for a perfect unification while the second point represents a solution for stop-NLSP. Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

b - τ Yukawa Unification in SU(5) Random scans were performed over the parameter space m 10 : 0 → 20 TeV m ¯ 5 : 0 → 20 TeV M 1 / 2 : 0 → 2 TeV A t : − 60 → 60 TeV A b = A τ : − 60 → 60 TeV m H u : 0 → 20 TeV m H d : 0 → 20 TeV tan β : 1 . 1 → 60 µ > 0 , m t = 173 . 3( GeV ) Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

Point 1 Point 2 Point 3 Point 4 m 10 2604 3849 18380 16800 m 5 3443 900.1 16450 18960 1049 1056 292.6 358.6 m 1 / 2 tan β 8.3 4.77 42.4 45 A t -5140 -7455 -44840 -39510 A b = A τ 41070 40830 -8170 23640 m Hd 3424 905 18500 17340 m Hu 1380 4700 14150 10410 sign ( µ ) + + + + m h 120.9 119.6 125.1 125.2 m A 929 797 18781 13544 µ 2934 2345 17562 17394 m ˜ 461, 882 467, 887 179, 362 179, 354 χ 0 1 , 2 2857, 2859 2291, 2295 16905, 16905 16406, 16406 m ˜ χ 0 3 , 4 m ˜ 881, 2857 887, 2311 368, 17075 357, 16429 χ ± 1 , 2 m ˜ 2385 2431 1089 1165 g m ˜ 3314, 3211 4336, 4405 18374, 18265 16788, 16608 uL , R 1211, 1798 1007, 2825 215, 10165 3289, 7153 m ˜ t 1 , 2 m ˜ 3315, 3984 4337, 2033 18374, 16488 16788, 19095 dL , R 1375, 2082 489, 2841 10198, 11734 7139, 12709 m ˜ b 1 , 2 m ˜ 3479, 2719 1321, 3731 16319, 18556 18850, 17052 eL , R m ˜ 876, 2939 803, 341 14263, 14864 11256, 16464 τ 1 , 2 Ω h 2 0.113 0.074 0.11 2269 ≫ 1 � σ v � ( v → 0) [ cm 3 / s ] 3.886 × 10 − 27 9.512 × 10 − 29 1.684 × 10 − 26 4.385 × 10 − 31 σ SI ( p ) × 10 12 [pb] 5.639 9.689 1.640 0.127 R 1.02 1.02 1.02 1.0 Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

b - τ YU in SU (5) or SO (10) with NUGM m 16 , m 10 , M i , A 0 , tan β, sign ( µ ) m 16 ≡ Universal soft SUSY breaking (SSB) sfermion mass m 10 ≡ Universal SSB MSSM Higgs mass. m 2 H u = m 2 H d at M GUT M 1 : M 2 : M 3 = 1 : 3 : − 2 at M GUT A 0 ≡ Universal SSB trilinear interaction tan β = v u v d µ ≡ SUSY bilinear Higgs parameter µ > 0 Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs

Point 1 Point 2 m 16 2405 3672 m 1 / 2 2000 1091 tan β 46.3 43.1 A 0 / m 16 2.81 2.26 1414 4309 m 10 sign ( µ ) + + m h 124.6 125 m A 1179 1023 µ 4298 2754 m ˜ 946, 4057 504, 2607 χ 0 1 , 2 4060, 5102 2623, 2806 m ˜ χ 0 3 , 4 m ˜ 4109, 5052 2632, 2779 χ ± 1 , 2 m ˜ 8108 4714 g 8123, 7238 5723, 5371 m ˜ uL , R 5505, 6854 2970, 3928 m ˜ t 1 , 2 m ˜ 8123, 7228 5723, 5369 dL , R m ˜ 5814, 6821 3575, 3921 b 1 , 2 m ˜ 4462, 2505 4210, 3690 eL , R m ˜ 949, 4147 2064, 3611 τ 1 , 2 Ω h 2 0.64 0.29 σ SI ( p ) × 10 12 [pb] 3.86 10.91 σ SDI ( p ) × 10 12 [pb] 326.3 2229.9 R 1.04 1.00 Benchmark points: The first point displays a solution for stau-neutralino coannihilation, while the second point depicts a solution with A-resonance. Qaisar Shafi Yukawa Unification, Flavour Symmetry & SUSY GUTs