Flavor Violating Higgs Yukawa Couplings in Minimal Flavor Violation - PowerPoint PPT Presentation

Flavor Violating Higgs Yukawa Couplings in Minimal Flavor Violation Xing-Bo Yuan Central China Normal University based on arXiv: 1807.00921, in collaboration with Min He, Xiao-Gang He, XY, Jin-Jun Zhang CLHCP 2018, CCNU, Wuhan 20 Dec 2018

Higgs Discovery -1 -1 CMS s = 7 TeV, L = 5.1 fb s = 8 TeV, L = 5.3 fb 1 Local p-value σ 1 σ 2 -2 10 σ 3 -4 10 σ 4 -6 10 σ 5 -8 10 Combined obs. Combined obs. LHC Run I Exp. for SM H Exp. for SM H σ 6 → → γ γ γ γ H H → → -10 H H ZZ ZZ 10 ◮ mass: m h ≈ 125 GeV → → � H H WW WW → → τ τ τ τ H H → → σ H H bb bb 7 -12 10 ◮ spin 110 115 120 125 130 135 140 145 � m (GeV) H ◮ parity � ◮ Yukawa coupling 0 � Local p ATLAS 2011 - 2012 Obs. " -1 s = 7 TeV: Ldt = 4.6-4.8 fb ◮ gauge coupling Exp. � " -1 s = 8 TeV: Ldt = 5.8-5.9 fb ± 1 ! 1 0 ! ◮ self coupling ? -1 1 10 ! 2 ! -2 10 10 -3 3 ! LHC Run II/HL/CEPC/ILC 10 -4 4 ! -5 10 -6 10 5 ! 10 -7 -8 10 -9 10 6 ! -10 10 -11 10 110 115 120 125 130 135 140 145 150 m [GeV] H 2 / 17

Higgs After the Discovery Hierarchy Problem Vacuum Stability 180 10 7 10 10 Instability Instability Meta � stability Pole top mass M t in GeV t c 175 16 π 2 Λ 2 + . . . = 1,2,3 Σ 170 fine-tuning 10 12 Stability c 16 π 2 Λ 2 = 125 GeV 2 m 2 h, 0 + 165 115 120 125 130 135 Higgs mass M h in GeV � 2 + (2 m 2 Z Z µ Z µ ) h f i f i h µ W − µ + m 2 ∆ L H =+ µ 2 Φ † Φ − λ W W + v − m i ¯ Φ † Φ � v + h · X NP − 1 f i ( λ ij + iγ 5 ¯ ¯ √ λ ij ) f j h + . . . 2 S.Baek, XY, PLB, 2017 Many Parameters u c t ν 3 s d b ν 2 e µ τ ν 1 µ eV meV eV keV MeV GeV TeV 3 / 17

Higgs FCNC: exp µ e τ e + e − collider e B < 0 . 035% B < 0 . 61% ◭ direct search see also Xin Chen’s talk µ < 2 . 1 µ B < 0 . 25% µ = 1 . 09 +0 . 27 τ − 0 . 26 � indirect study u c t McWilliams, Li 1981 B < 0 . 12% u Shanker 1982 Barr, Zee 1990 c Kanemura, Ota, Tsumura 2006 B < 0 . 11% Davidson, Grenier 2010 Golowich et al 2011 µ tth = 1 . 3 +0 . 3 t − 0 . 3 Buras, Girrbach 2012 Blankenburg, Ellis, Isidori 2012 s d b Harnik, Kopp, Zupan 2013 Gorbahn, Haisch 2014 d Celis, Cirigliano, Passemar 2014 Chiang, He, Ye, XY 2017 s . . . . . . µ = 1 . 01 +0 . 20 b Flavor Problem = ⇒ MFV − 0 . 20 4 / 17

Higgs FCNC in EFT ◮ Effective Field Theory c i � Λ 2 O d =6 L full = L SM + + . . . i i ◮ Dim-4 operator in the SM ( ¯ ( ¯ Q L ˜ ( ¯ Q L HY d d R ) , HY u u R ) , Q L HY e e R ) , ◮ Dim-6 operator in the EFT (Warsaw) Grzadkowski, Iskrzynski, Misiak, Rosiek, 2010 O dH = ( H † H )( ¯ Q L HC dH d R ) , O uH = ( H † H )( ¯ Q L ˜ HC uH u R ) , O eH = ( H † H )( ¯ Q L HC eH e R ) , ◮ Yukawa interaction Harnik, Kopp, Zupan, 2013 Y f − v 2 v 2 Y = − 1 Y f f R v − 1 � � Y f = Y f − 1 L f f L ¯ ¯ ¯ ¯ ¯ √ √ f L Λ 2 C fH f R h + h . c . . Λ 2 C fH , 2 2 2 ◮ FCNCs arise in the mass eigenstate 5 / 17

Higgs FCNC in EFT with MFV Quark Sector some U (1) ′ s ◮ Flavor symmetry without Yukawa G QF = SU (3) Q L ⊗ SU (3) u R ⊗ SU (3) d R ◮ Flavor symmetry breaking −L Y = ¯ Q L HY d d R + ¯ Q L ˜ HY u u R + h . c . ◮ Flavor symmetry recovering: Yukawa coupling ⇒ spurion field Y u ∼ ( 3 , ¯ Y d ∼ ( 3 , 1 , ¯ 3 , 1 ) and 3 ) . ◮ EFT with Minimal Flavor Violation: dim-6 operators, constructed from SM and Yukawa spurion fields, are invariant under CP and G QF . D’Ambrosio, Giudice, G.Isidori, Strumia, 2009 O dH = ( H † H )( ¯ B = Y d Y † A = Y u Y † Q L HC dH d R ) , u , d ( 8 + 1 , 1 , 1 ) ( 8 + 1 , 1 , 1 ) C dH = f d ( A , B ) Y d ≡ ( ξ 0 1 + ξ 1 A + ξ 2 B + ξ 3 A 2 + ξ 4 B 2 + ξ 5 AB + ξ 6 BA + . . . . . . ) Y d 6 / 17

Higgs FCNC in EFT with MFV Quark Sector ◮ Higgs FCNC coupling C dH = f d ( A , B ) Y d ≡ ( ξ 0 1 + ξ 1 A + ξ 2 B + ξ 3 A 2 + ξ 4 B 2 + ξ 5 AB + ξ 6 BA + . . . . . . ) Y d ◮ Cayley-Hamilton identity for 3 × 3 invertible matrix X X 3 = Det X · 1 + 1 2[Tr X 2 − (Tr X ) 2 ] · X + Tr X · X 2 G. Colangelo, E. Nikolidakis, C. Smith, 2009 ◮ Higgs FCNC coupling after resummation L. Mercolli, C. Smith, 2009 f d ( A , B ) = κ 1 1 + κ 2 A + κ 5 B 2 + κ 6 AB + κ 8 ABA + κ 11 AB 2 + κ 13 A 2 B 2 + κ 15 B 2 AB + κ 16 AB 2 A 2 + κ 3 B + κ 4 A 2 + κ 7 BA + κ 10 BAB + κ 9 BA 2 + κ 14 B 2 A 2 + κ 12 ABA 2 + κ 17 B 2 A 2 B ◮ Approximation #1: neglect tiny imaginary parts of κ i ◮ Approximation #2: B ≈ 0 due to highly suppressed down-type Yukawa couplings 2 A 2 . f u ( A , B ) ≈ ǫ u 0 1 + ǫ u 1 A + ǫ u 2 A 2 f d ( A , B ) ≈ ǫ d 0 1 + ǫ d 1 A + ǫ d 7 / 17

Higgs FCNC in EFT with MFV Quark Sector ◮ Higgs Yukawa interaction in the interaction eigenstate Y d − v 2 Y = − 1 Y d d R v − 1 � � d L ¯ ¯ ¯ ¯ L d √ √ d L Λ 2 C dH d R h + h . c . 2 2 ◮ Interaction eigenstate = ⇒ mass eigenstate v 2 Y f = Y f − 1 ¯ ǫ d 0 1 + ǫ d 1 Y u Y † u + ǫ d 2 ( Y u Y † u ) 2 � � C dH = Y d Λ 2 C fH 2 u ) 2 � ¯ 1 ¯ Y u ¯ 2 ( ¯ Y u ¯ ǫ d 0 1 + ǫ d Y † u + ǫ d Y † Y d + O ( v 2 / Λ 2 ) . � = ǫ d i ≡ ( v 2 / Λ 2 ) ǫ d ◮ Higgs Yukawa interaction in the mass eigenstate ˆ i Y = − 1 L d ¯ ǫ d ǫ d ǫ d � 1 V † λ 2 2 V † λ 4 � √ d L (1 − ˆ 0 ) λ d − ˆ u V λ d − ˆ u V λ d d R h + h . c . 2 ≈ − 1 ¯ ǫ d ǫ d 1 V † λ 2 √ � � d L (1 − ˆ 0 ) λ d − ˆ u V λ d d R h + h . c . , 2 ǫ d 1 + λ 2 ǫ d ǫ d ◮ Approximation: (ˆ t ˆ 2 ) → ˆ 1 8 / 17

Higgs FCNC in EFT with MFV Lepton Sector ◮ Lepton MFV depends on the underlying mechanism for neutrino mass 2005 V. Cirigliano, B. Grinstein, G. Isidori, M. B. Wise 2006 V. Cirigliano, B. Grinstein 2009 M. B. Gavela, T. Hambye, D. Hernandez, and P. Hernandez 2011 R. Alonso, G. Isidori, L. Merlo, L. A. Munoz, and E. Nardi . . . . . . ◮ Type-I Seesaw O : complex orthogonal matrix, ˆ m ν = diag ( m 1 , m 2 , m 3 ) √ m ν = − v 2 Y ν = i 2 m ν U T , OM 1 / 2 2 Y ν M − 1 N Y T m 1 / 2 ν = U ˆ v U ˆ ν N ◮ Lepton MFV in Type-I Seesaw Casas, Ibarra, 2001 A ℓ = 2 M OO † ˆ m 1 / 2 m 1 / 2 U † v 2 U ˆ ν ν ◮ Higgs Yukawa interaction Y = − 1 L ℓ ¯ ǫ ℓ ǫ ℓ ǫ ℓ � 2 A 2 � √ ℓ L (1 − ˆ 0 ) λ ℓ − ˆ 1 A ℓ λ ℓ − ˆ ℓ λ ℓ ℓ R h , 2 In numerical analysis, M = 10 15 GeV , m 1(3) = 0 , and real matrix O 9 / 17

Higgs FCNC in EFT with MFV Y L = Y † ◮ Higgs Yukawa interaction R L Y = − 1 ¯ Y d ǫ d ǫ d 1 V † λ 2 √ f ( Y L P L + Y R P R ) fh R = (1 − ˆ 0 ) λ d − ˆ u V λ d 2 Y u ǫ u R = (1 − ˆ 0 ) λ u Y ℓ ǫ ℓ ǫ ℓ ǫ ℓ 2 A 2 R = (1 − ˆ 0 ) λ ℓ − ˆ 1 A ℓ λ ℓ − ˆ ℓ λ ℓ ◮ Higgs FCNC in up-sector is highly suppressed by λ 2 d � ǫ u 0 , ǫ d 0 , ǫ d 1 , ǫ ℓ 0 , ǫ ℓ 1 , ǫ ℓ � ◮ 6 free real parameter: hat suppressed 2 Constraints: B d , K 0 − ¯ K 0 mixing ◮ B s − ¯ B s , B d − ¯ ( ǫ d 1 ) ◮ h → ℓ i ℓ j ℓ i → ℓ j γ , ℓ i → ℓ j ℓ k ¯ ℓ l , µ → e conversion in nuclei ( ǫ u 0 , ǫ d 0 , ǫ ℓ 0 , ǫ ℓ 1 , ǫ ℓ 2 ) ( ǫ u 0 , ǫ d 0 , ǫ ℓ ◮ Higgs data@LHC Run I 0 ) ( ǫ d 1 , ǫ ℓ 1 , ǫ ℓ ◮ B s → ℓ i ℓ j 2 ) 10 / 17

Constraints from B s − ¯ B s mixing s b u, c, t s b W + W − h ¯ b s ¯ ◮ Observables: ∆ m d , ∆ m s , φ s , ∆ m K , ǫ K ¯ b ¯ s u, c, t ∆ m SM = 19 . 196 +1 . 377 ∆ m exp in unit of ps − 1 − 1 . 341 , = 17 . 757 ± 0 . 021 , s s ◮ Bound @95% CL | ǫ d 1 | < 0 . 59 ◮ Prediction @95% CL Γ( h → sd ) < 7 . 4 × 10 − 11 MeV Γ( h → sb ) < 2 . 0 × 10 − 3 MeV Γ( h → db ) < 9 . 4 × 10 − 5 MeV ◮ Discovery sensitivity@500GeV ILC with 4000 fb − 1 D.Barducci, A.J.Helmboldt, 2017 B ( h → bj ) � 0 . 5% with j a light quark 11 / 17

Constraints from Higgs data 0.6 0.6 0.4 0.4 0.2 0.2 d Ε 0 0.0 � Ε 0 0.0 � 0.2 � 0.2 � 0.4 � 0.4 � 0.6 � 0.6 � 0.6 � 0.4 � 0.2 0.0 0.2 0.4 0.6 � 0.6 � 0.4 � 0.2 0.0 0.2 0.4 0.6 u u Ε 0 Ε 0 ◮ 90% CL allowed regions of ( ǫ u 0 , ǫ d 0 , ǫ ℓ 0 ) ◮ LHC Run I data and Tevatron ◮ By Lilith package 12 / 17

Constraints from µ → eγ and µ → e in nuclei 0.10 S.I: ( ǫ ℓ 0 , ǫ ℓ 1 , ǫ ℓ S.II: ( ǫ u 0 , ǫ d 0 , ǫ ℓ 0 , ǫ ℓ 1 , ǫ ℓ 2 ) , 2 ) S.I combined h h S.II combined τ → µγ S.I Μ� e in Al � Mu2e 0.05 µ µ S.II Μ� e in Al � Mu2e τ τ ( ǫ u 0 , ǫ ℓ 0 , ǫ ℓ 1 , ǫ ℓ 2 ) τ µ + τ µ Y ∗ ττ P L + Y ττ P R Y ∗ τµ P L + Y µτ P R Y ∗ τµ P L + Y µτ P R Y ∗ µµ P L + Y µµ P R γ γ Ε 2 � 0.00 µ µ τ µ τ µ h γ , Z h γ, Z � 0.05 t t W W Normal Ordering D.Chang, W.S.Hou, � 0.10 Y.Okada, 1993 γ γ � 0.10 � 0.05 0.00 0.05 0.10 � Ε 1 µ τ µ h 1.0 Z h γ, Z S.I combined µ µ µ S.II combined τ µ W W S.I Μ� e in Al � Mu2e 0.5 S.II Μ� e in Al � Mu2e γ γ Ε 2 � 0.0 µ → e in nuclei h h µ µ ( ǫ u 0 , ǫ d 0 , ǫ ℓ 0 , ǫ ℓ 1 , ǫ ℓ µ Y ∗ µe P L + Y eµ P R e µ e µ e e e 2 ) Y ∗ µµ P L + Y µµ P R Y ∗ µe P L + Y eµ P R Y ∗ µe P L + Y eµ P R Y ∗ ee P L + Y ee P R h + γ + γ � 0.5 R.Harnik,J.Kopp, N N N N N N J.Zupan, 2012 Inverted Ordering ◮ dominated by µ → eγ at present � 1.0 � 1.0 � 0.5 0.0 0.5 1.0 µ → e in Al in future � Ε 1 13 / 17