Exploring Flavour Violation in an A 4 Inspired SUSY GUT J. Bernigaud - PowerPoint PPT Presentation

Exploring Flavour Violation in an A 4 Inspired SUSY GUT J. Bernigaud 1 , B. Herrmann 1 , S.F. King 2 and S.J. Rowley 2 1 LAPTh, Annecy 2 SHEP Group, University of Southampton 4 th December 2018 SHEP Internal Seminar, University of Southampton Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 1 / 17

Outline ◮ Introduction ◮ SUSY-breaking and Non-Minimal Flavour Violation ◮ SU (5) Unification and A 4 ◮ This work - NMFV Parameter Scan ◮ Results ◮ Conclusions and Outlook Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 2 / 17

Introduction Why SUSY? ◮ Still (mostly) cures the hierarchy problem ◮ Precise gauge coupling unification ◮ Rich phenomenology, some areas of which have received little attention Gauge couplings unify in MSSM [1] Why flavour violation? γ ◮ Many experimental results hint at departure from SM µ e ◮ Recent models can predict mixing - how much is allowed? [1] S. Martin, “A Supersymmetry primer” , Adv. Ser. Direct. High Energy Phys 18 (1998), hep-ph/9709356 Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 3 / 17

SUSY-Breaking in the MSSM Viable SUSY in nature must be broken General soft-breaking Lagrangian in the MSSM: � � = − 1 M 1 � B � B + M 2 � W � L MSSM W + M 3 � g � g + h . c . soft 2 Q † � U ∗ � D ∗ � E ∗ � Q � L � L † � U � D � E � − M 2 Q − M 2 L − M 2 U − M 2 D − M 2 E � � A U � U ∗ H u � Q + A D � D ∗ H d � Q + A E � E ∗ H d � − L + h . c . � � − m 2 H u H ∗ u H u − m 2 H d H ∗ µ H ∗ d H d − u H d + h . c . Parameters M Q , M L A U etc. are 3x3 matrices in ‘flavour space’ Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 4 / 17

Non-Minimal Flavour Violation Minimal Flavour Violation paradigm = ⇒ diagonal soft parameters.     m Q a U 0 0 0 0 11 11     m Q a U M Q = A U = 0 0 · 0 22 22 m Q a U 0 0 · · 33 33 Assumption in most analyses, no theory motivation Relax assumption = ⇒ Non-Minimal Flavour Violation (NMFV)     m Q ∆ Q ∆ Q a U ∆ aU ∆ aU 11 12 13 11 12 13     m Q ∆ Q ∆ aU a U ∆ aU M Q = A U = · 22 23 21 22 23 m Q ∆ aU ∆ aU a U · · 31 32 33 33 In a unified framework, flavour symmetries can generate NMFV Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 5 / 17

Dimensionless Parametrisation Reformulate NMFV by normalising to diagonal elements of soft matrices: (∆ q ij ) 2 (∆ u ij ) 2 (∆ d ij ) 2 ( δ Q ( δ U ( δ D LL ) ij = RR ) ij = RR ) ij = , , , ( M Q ) ii ( M Q ) jj ( M U ) ii ( M U ) jj ( M D ) ii ( M D ) jj ∆ au ∆ ad RL ) ij = v u RL ) ij = v d ij ij ( δ U ( δ D √ , √ , ( M Q ) ii ( M U ) jj ( M Q ) ii ( M D ) jj 2 2 (∆ ℓ ij ) 2 (∆ e ij ) 2 ∆ ae RL ) ij = v d ij ( δ L ( δ E ( δ E LL ) ij = , RR ) ij = , √ ( M L ) ii ( M L ) jj ( M E ) ii ( M E ) jj ( M L ) ii ( M E ) jj 2 Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 6 / 17

Outline ◮ Introduction ◮ SUSY-breaking and Non-Minimal Flavour Violation ◮ SU (5) Unification and A 4 ◮ This work - NMFV Parameter Scan ◮ Results ◮ Conclusions and Outlook Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 6 / 17

SU (5) Unification Collect SM fields into irreps. of SU(5):     d c u c − u c 0 u r d r r g b     d c u c 0 . u b d b     b r     d c F = 5 = , T = 10 = . . 0 u g d g     g     e − e c 0 . . . − ν e . . . . 0 L L Unification gives equalities between parameters at the GUT scale: δ E RR = δ Q LL ≡ δ T M Q = M U = M E ≡ M T δ D RR = δ L LL ≡ δ F M D = M L ≡ M F A D = ( A E ) T ≡ A FT RL ) T ≡ δ FT δ D RL = ( δ E δ U RL ≡ δ TT A U ≡ A TT Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 7 / 17

The A 4 × SU (5) Model Addition of discrete symmetry unifies three families of the 5 Representations: Unified breaking matrices:   F = 3 m F 0 0   M F = 0 m F 0 T = 1 = ⇒ 0 0 m F   m T 1 0 0   M T = 0 0 m T 2 0 0 m T 3 Break discrete symmetry = ⇒ NMFV patterns at the GUT scale - these incite flavour mixing at low scales Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 8 / 17

Outline ◮ Introduction ◮ SUSY-breaking and Non-Minimal Flavour Violation ◮ SU (5) Unification and A 4 ◮ This work - NMFV Parameter Scan ◮ Results ◮ Conclusions and Outlook Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 8 / 17

Explorative Study of NMFV ◮ MFV not theoretically well motivated ◮ Flavour violation could place additional constraints on models ◮ Relax assumptions, explore phenomenology Question What is the allowed flavour violation in such a scenario? ◮ Scan over NMFV parameters at the GUT scale simulataneously, run predictions to low scale, and determine degree of mixing permitted Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 9 / 17

MFV Benchmarks Parameter/Observable Scenario 1 Scenario 2 ◮ MFV points defined by m F 5000 5000 MFV Parameters at GUT scale 5000 5000 SUSY-breaking parameters m T 1 m T 2 200 233.2 m T 3 2995 2995 ◮ Perform NMFV scan a TT -940 -940 33 around these points a FT -1966 -1966 33 M 1 250.0 600.0 ◮ Scenario 1 inspired by M 2 415.2 415.2 previous work [2] 2551.6 2551.6 M 3 M H u 4242.6 4242.6 ◮ Scenario 2 motivated by M H d 4242.6 4242.6 tan β 30 30 experimental limits µ -2163.1 -2246.8 Table: GUT scale parameters that define MFV scenarios. [2] A. Belyaev, S.F. King and P. Schaefers, “Muon g-2 and dark matter suggest nonuniversal gaugino masses: SU ( 5 ) × A 4 case study at the LHC” , Phys. Rev. D 97 (2018), 1801.00514 Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 10 / 17

NMFV Parameter Scan Overarching Flat Random Scan Observable Constraint m h (125 . 2 ± 2 . 5) GeV MFV and NMFV Params BR ( µ → e γ ) < 4 . 2 × 10 − 13 SPhenoMSSM-4.0.3 [3] < 1 . 0 × 10 − 12 BR ( µ → 3 e ) < 3 . 3 × 10 − 8 BR ( τ → e γ ) < 4 . 4 × 10 − 8 BR ( τ → µγ ) Physical no < 2 . 7 × 10 − 8 Point BR ( τ → 3 e ) Spectrum, Excluded Neutral LSP? < 2 . 1 × 10 − 8 BR ( τ → 3 µ ) < 2 . 7 × 10 − 8 BR ( τ → e − µµ ) BR ( τ → e + µµ ) < 1 . 7 × 10 − 8 yes BR ( τ → µ − ee ) < 1 . 8 × 10 − 8 micrOMEGAs-4.3.5 [4] BR ( τ → µ + ee ) < 1 . 5 × 10 − 8 (3 . 32 ± 0 . 18) × 10 − 4 BR ( B → X s γ ) (2 . 7 ± 1 . 2) × 10 − 9 BR ( B s → µµ ) fail Constraint Prior Only < 4 . 4 × 10 − 8 BR ( B τ → µγ ) Checks (17 . 757 ± 0 . 312) ps − 1 ∆ M B s (3 . 1 ± 1 . 2) × 10 − 15 GeV ∆ M K pass 2 . 228 ± 0 . 29 ǫ K Prior and Posterior Distributions Ω DM h 2 0 . 1198 ± 0 . 0042 [3] W. Porod, “SPheno...” , Comput. Phys. Commun. 153 (2003), hep-ph/0301101 Table: Experimental constraints imposed on [4] G.Belanger et. al., “MicrOMEGAs...” , Comput. Phys. the A 4 × SU (5) parameter space in our study. Commun. 149 (2002), hp-ph/0112278 Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 11 / 17

Outline ◮ Introduction ◮ SUSY-breaking and Non-Minimal Flavour Violation ◮ SU (5) Unification and A 4 ◮ This work - NMFV Parameter Scan ◮ Results ◮ Conclusions and Outlook Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 11 / 17

Results: Summary Table Parameters Scenario 1 Scenario 2 Principle Constraints ( δ T ) 12 [-0.12, 0.12] † 1 h 2 , µ → e γ [-0.015, 0.015] Ω ˜ χ 0 ( δ T ) 13 [-0.06, 0.06] † [-0.3, 0.3] † 1 h 2 Ω ˜ χ 0 1 h 2 , µ → 3 e , µ → e γ , ( δ T ) 23 [0 , 0] ∗ [-0.1, 0.1 † ] Ω ˜ χ 0 ( δ F ) 12 [-0.008, 0.008] [-0.015, 0.015] † µ → 3 e , µ → e γ ( δ F ) 13 [-0.01, 0.01] † [-0.15, 0.15] † µ → 3 e , µ → e γ ( δ F ) 23 [-0.015, 0.015] † [-0.15, 0.15] † 1 h 2 , µ → e γ , µ → 3 e Ω ˜ χ 0 [-1, 1.5] † × 10 − 3 ( δ TT ) 12 [-3, 3.5] × 10 − 5 1 h 2 prior, Ω ˜ χ 0 [-6, 7] † × 10 − 5 [-4, 2.5] † × 10 − 3 ( δ TT ) 13 1 h 2 prior, Ω ˜ χ 0 [-0.5, 4] † × 10 − 5 ( δ TT ) 23 [-0.25, 0.2] † prior, Ω ˜ 1 h 2 χ 0 [-1.2, 1.2] † × 10 − 4 ( δ FT ) 12 [-0.0015, 0.0015] µ → 3 e , Ω ˜ 1 h 2 , µ → e γ χ 0 [-5, 5] × 10 − 4 1 h 2 , µ → 3 e , µ → e γ ( δ FT ) 13 [-0.002, 0.002] † Ω ˜ χ 0 [-1.2, 1.2] † × 10 − 4 ( δ FT ) 21 [0 , 0] ∗ 1 h 2 , prior Ω ˜ χ 0 [-6, 6] † × 10 − 4 ( δ FT ) 23 [-0.0022, 0.0022] † 1 h 2 , µ → e γ µ → 3 e , Ω ˜ χ 0 [-2, 2] † × 10 − 4 ( δ FT ) 31 [-0.0004, 0.0004] † 1 h 2 Ω ˜ χ 0 [-1.5, 1.5] × 10 − 4 1 h 2 ( δ FT ) 32 [0 , 0] ∗ Ω ˜ χ 0 Table: Estimated allowed GUT scale flavour-violation for both reference scenarios and impactful constraints. Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 12 / 17

2 1e 1e 2 Motivation for a Simultaneous Scan All constraints All constraints probability density probability density 1.0 0.5 0.0 0.5 1.0 1.0 0.5 0.0 0.5 1.0 ( δ F ) 12 / 10 − 2 ( δ F ) 12 / 10 − 2 Figure: Comparison of individual VS simultaneous scan in Scenario 1 for ( δ F ) 12 ; individual scan shown on the left, full scan on the right. Blue shows prior distribution, and red shows posterior after constraints are applied Sam Rowley Flavour Violation in the SU(5) MSSM 04/12/2018 13 / 17