Constraints on Higgs FCNC Couplings from Precision Measurement of B - PowerPoint PPT Presentation

Constraints on Higgs FCNC Couplings from Precision Measurement of B s → µ + µ − Decay Xing-Bo Yuan NCTS arXiv: 1703.06289, Cheng-Wei Chiang, Xiao-Gang He, Fang Ye, XY Joint Working Group: Electroweak/Flavor and Precision, WIN2017 23 JUNE 2017

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 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 / 19

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 v − m i ¯ ∆ L H =+ µ 2 Φ † Φ − λ Φ † Φ W W + � v + h · X NP − 1 f i ( λ ij + iγ 5 ¯ ¯ √ λ ij ) f j h + . . . 2 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 / 19

Higgs FCNC: exp µ e τ e + e − collider e B < 0 . 035% B < 0 . 61% ◭ direct search µ < 2 . 8 µ B < 0 . 25% µ = 1 . 1 ± 0 . 2 τ � indirect study u c t McWilliams, Li 1981 B < 0 . 55% u Shanker 1982 Barr, Zee 1990 c Kanemura, Ota, Tsumura 2006 B < 0 . 40% Davidson, Grenier 2010 Golowich et al 2011 µ tth = 2 . 3 +0 . 7 t − 0 . 6 Buras, Girrbach 2012 Blankenburg, Ellis, Isidori 2012 s d b Harnik, Kopp, Zupan 2013 Gorbahn, Haisch 2014 d Celis, Cirigliano, Passemar 2014 . . . . . . s µ = 0 . 70 +0 . 29 b − 0 . 27 4 / 19

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 Grzadkowski et al., 2010, Harnik, Kopp, Zupan, 2013 O uH = ( H † H )( ¯ Q L HC dH d R ) , O dH = ( H † H )( ¯ Q L ˜ HC uH u R ) , O eH = ( H † H )( ¯ Q L HC eH e R ) , ◮ Yukawa interaction f R − v 2 � � � � 1 + h f L Y f v 1 + 3 h f L C fH v ¯ ¯ ∆ L = − f R + h.c. √ √ 2Λ 2 v v 2 2 ◮ Yukawa interaction in mass eigenstate Y ij = Y ∗ ji , ¯ Y ij = ¯ Y ∗ ji ∆ L = − 1 f i ( Y ij + i ¯ ¯ √ Y ij γ 5 ) f j h, 2 5 / 19

Constraints and Predictions Constraints: µ µ µ µ µ µ µ µ Z Z ν µ ◮ B s → µ + µ − W W W W t t h t s t b s W s s b b b s b u, c, t s b ◮ B s − ¯ B s W − W + ¯ h ¯ s b ¯ s ¯ b u, c, t τ − τ − h h ◮ h → ττ τ + τ + µ − h ◮ h → µτ τ + Predictions: B ( B s → µτ ) , B ( B s → ττ ) , ... 6 / 19

B s → µ + µ − decay: SM and exp theoretical progress: ◮ B ( B s → µ + µ − ) SM = � � × 10 − 9 3 . 44 ± 0 . 19 De Bruyn et al 2012 ◮ B ( B s → µ + µ − ) avg = � � × 10 − 9 3 . 0 ± 0 . 5 Bobeth et al 2013 B ( B s → µ + µ − ) LHCb17 = � 3 . 0 ± 0 . 6 +0 . 3 � × 10 − 9 − 0 . 2 B ( B s → µ + µ − ) CMS13 = 3 . 0 +1 . 0 × 10 − 9 � � recent study: − 0 . 9 Altmannshofer et al 2017 Fleischer et al 2017 f B s B ( B s → µ + µ − ) × 10 +9 input: ( | V us | , | V ub | , | V cb | , γ ) N f = 2 + 1 + 1 3.54 3.31 3.00 B ∝ | V ∗ tb V ts | 2 f 2 B s N f = 2 + 1 3.68 3.44 3.11 FLAG [2016] HPQCD [2013] unit V cb , V ub N f = 2 + 1 N f = 2 + 1 + 1 avg. incl. excl. f B s 228 . 4 (3 . 7) 224 (5) MeV f B d 192 . 0 (4 . 3) 186 (4) MeV | V ∗ | V ∗ | V ub | | V cb | tb V ts | tb V td | unit 10 − 3 sl. incl. 4 . 45 ± 0 . 18 ± 0 . 31 42 . 42 ± 0 . 44 ± 0 . 74 41 . 6 ± 0 . 8 9 . 1 ± 0 . 5 10 − 3 sl. avg. 3 . 98 ± 0 . 08 ± 0 . 22 41 . 00 ± 0 . 33 ± 0 . 74 40 . 2 ± 0 . 8 8 . 8 ± 0 . 4 10 − 3 sl. excl. 3 . 72 ± 0 . 09 ± 0 . 22 38 . 99 ± 0 . 49 ± 1 . 17 38 . 2 ± 1 . 2 8 . 3 ± 0 . 4 7 / 19

B s → µ + µ − decay: theory µ µ µ µ µ µ µ µ Z Z ν µ W W W W t t h ◮ Effective Hamiltonian t b s t W b s b s b s H eff = − G F α e V tb V ∗ � � √ C A O A + C S O S + C P O P + h.c. ts πs 2 2 W ◮ Effective operator O S = m b m ℓ O P = m b m ℓ � �� µγ µ γ 5 µ � � �� � � �� � O A = qγ µ P L b ¯ ¯ , qP R b ¯ µµ ¯ , qP R b ¯ µγ 5 µ ¯ , m 2 m 2 W W S = m b m ℓ P = m b m ℓ O ′ � �� � O ′ � �� � qP L b ¯ µµ ¯ , ¯ qP L b µγ 5 µ ¯ . m 2 m 2 W W ◮ Branching ratio loop suppression; helicity suppression � B ( B q → ℓ + ℓ − ) = τ B q G 4 F m 4 1 − 4 m 2 | P | 2 + | S | 2 � W | V tb V ∗ tq | 2 f 2 B q M B q m 2 ℓ � , ℓ m 2 8 π 5 B q m 2 � m b � B q ( C P − C ′ P ≡ C A + P ) , 2 m 2 m b + m q W � m 2 1 − 4 m 2 � m b � B q ℓ ( C S − C ′ S ≡ S ) . m 2 2 m 2 m b + m q B q W ◮ Corrections from B s − ¯ B s mixing De Bruyn et al., 2012; Fleischer 2012 A ∆Γ = | P | 2 cos 2 ϕ P − | S | 2 cos 2 ϕ S � 1 + A ∆Γ y s � B ( B s → ℓ + ℓ − ) = B ( B s → ℓ + ℓ − ) , | P | 2 + | S | 2 1 − y 2 s B s → µ + µ − can provide excellent probe for the Higgs FCNC. 8 / 19

B s → µ + µ − decay: Higgs FCNC effects µ µ µ µ µ µ µ µ Z Z ν µ W W W W t t h ◮ Effective Hamiltonian t b s t W b s b s b s H eff = − G F α e V tb V ∗ � � √ C A O A + C S O S + C P O P + h.c. ts πs 2 2 W ◮ Effective operator O S = m b m ℓ O P = m b m ℓ � �� µγ µ γ 5 µ � � �� � � �� � O A = qγ µ P L b ¯ ¯ , qP R b ¯ µµ ¯ , ¯ qP R b µγ 5 µ ¯ , m 2 m 2 W W S = m b m ℓ P = m b m ℓ O ′ � �� � O ′ � �� � qP L b ¯ ¯ µµ , ¯ qP L b µγ 5 µ ¯ . m 2 m 2 W W ◮ Branching ratio loop suppression; helicity suppression � B ( B q → ℓ + ℓ − ) = τ B q G 4 F m 4 1 − 4 m 2 | P | 2 + | S | 2 � W | V tb V ∗ tq | 2 f 2 B q M B q m 2 ℓ � , ℓ m 2 8 π 5 B q m 2 � m b � B q ( C P − C ′ P ≡ C A + P ) , 2 m 2 m b + m q W � m 2 1 − 4 m 2 � m b � B q ℓ ( C S − C ′ S ≡ S ) . m 2 2 m 2 m b + m q B q W B depends on ( ¯ Y sb Y µµ , ¯ Y sb ¯ ◮ Contributions from the Higgs FCNC Y µµ ) π 2 1 1 C NP = κ ( Y sb + i ¯ C NP = iκ ( Y sb + i ¯ Y sb ) ¯ Y sb ) Y µµ , Y µµ , κ = . S P 2 G 2 V tb V ∗ m b m µ m 2 F ts h C ′ NP = κ ( Y sb − i ¯ C ′ NP = iκ ( Y sb − i ¯ Y sb ) ¯ Y sb ) Y µµ , Y µµ , S P 9 / 19

Bounds from B s → µ + µ − ◮ 95% CL bound Complex Y � 2 + � 2 < 1 . 26 3 � 5 . 6 × 10 5 ¯ � 1 − 6 . 0 × 10 5 ¯ Y sb ¯ � � � � 0 . 66 < Y sb Y µµ Y µµ Y sb Y ΜΜ � 10 � 6 � 2 ◮ dark region: 95% CL allowed Real Y 1 ◮ black: exp central value ◮ dashed: B exp / B theo = 1 . 1 0 ◮ dot-dashed: B exp / B theo = 0 . 9 � 2 � 1 0 1 2 Y sb Y ΜΜ � 10 � 6 � ◮ dotted: B exp / B theo = 0 . 7 8 B s �ΜΜ , Y sb � 1.3 � 10 � 4 SM B s �ΜΜ , Y sb � 3.4 � 10 � 4 6 h �ΜΜ ◮ light gray: 95% CL allowed with ¯ Y sb = 1 . 4 × 10 − 4 4 SM Y ΜΜ � Y ΜΜ ◮ dark gray: 95% CL allowed with ¯ Y sb = 3 . 4 × 10 − 4 ◮ blue: µ µµ < 2 . 8 at 95% CL ATLAS Run I + II 2 ◮ | ¯ Y sb | = 3 . 4 × 10 − 4 : maximal value allowed by B s − ¯ B s 0 � 2 � 4 � 2 0 2 4 SM Y ΜΜ � Y ΜΜ 10 / 19

B s − ¯ B s mixing s b u, c, t s b W − W + ◮ Effective Hamiltonian h ¯ ¯ s b ¯ s ¯ b u, c, t H ∆ B =2 = G 2 tb V ts ) 2 � 16 π 2 m 2 F W ( V ∗ C i O i + h.c.. i ◮ Effective operator RGE: Buras et al. 2001 = (¯ b α γ µ P L s α )(¯ = (¯ b α γ µ P L s α )(¯ O VLL b β γ µ P L s β ) , O LR b β γ µ P R s β ) , 1 1 O VRR = (¯ b α γ µ P R s α )(¯ b β γ µ P R s β ) , O LR = (¯ b α P L s α )(¯ b β P R s β ) , 1 2 = (¯ b α P L s α )(¯ = (¯ b α σ µν P L s α )(¯ O SLL b β P L s β ) , O SLL b β σ µν P L s β ) , 1 2 = (¯ b α P R s α )(¯ = (¯ b α σ µν P R s α )(¯ O SRR b β P R s β ) , O SRR b β σ µν P R s β ) . 1 2 ◮ Wilson coefficients from the Higgs FCNC = − 1 C SLL , NP 2 κ ( Y bs − i ¯ Y bs ) 2 , 1 κ = 8 π 2 = − 1 1 1 C SRR , NP 2 κ ( Y bs + i ¯ Y bs ) 2 , tb V ts ) 2 , 1 G 2 m 2 h m 2 ( V ∗ F W bs + ¯ C LR , NP = − κ ( Y 2 Y 2 bs ) , 2 11 / 19

B s − ¯ B s mixing ◮ Mass difference B s |H ∆ B =2 | B s �| = G 2 ∆ m s = 2 |� ¯ tb V ts | 2 � � � C i � ¯ � , 8 π 2 m 2 F W | V ∗ � B s |O i | B s � ◮ SM prediction ∆ m SM = (18 . 64 +2 . 40 − 2 . 27 )ps − 1 s ◮ Exp data ∆ m exp = (17 . 757 ± 0 . 021)ps − 1 s ◮ 95% CL bound complex Y sb + 2 . 1 ¯ � < 1 . 29 � 0 . 7 Y 2 Y 2 × 10 6 � � � 0 . 76 < � 1 − sb 12 / 19