Electroweak Effective Theory - PDF Free Download

Electroweak Effective Theory Antonio Pich IFIC, Univ. Valencia - CSIC Schladming 2014, Styria, Austria, 1 8 March 2014

Coset Space Coordinates: G SU(2) L SU(2) R H SU(2) L+R H ξ(ϕ) g h ϕ ϕ G/H EWET A. Pich Schladming 2014 53

Coset Space Coordinates: G SU(2) L SU(2) R H SU(2) L+R H ξ(ϕ) ξ(ϕ) (ξ L (ϕ),ξ R (ϕ)) G g h ξ L (ϕ) ξ R (ϕ) G g L ξ L (ϕ)h (ϕ,g) G g R ξ R (ϕ)h (ϕ,g) ϕ ϕ G/H EWET A. Pich Schladming 2014 53

Coset Space Coordinates: G SU(2) L SU(2) R H SU(2) L+R H ξ(ϕ) ξ(ϕ) (ξ L (ϕ),ξ R (ϕ)) G g h ξ L (ϕ) ξ R (ϕ) G g L ξ L (ϕ)h (ϕ,g) G g R ξ R (ϕ)h (ϕ,g) ϕ ϕ G/H U(ϕ) ξ L (ϕ)ξ R (ϕ) G g L U(ϕ)g R EWET A. Pich Schladming 2014 53

Coset Space Coordinates: G SU(2) L SU(2) R H SU(2) L+R H ξ(ϕ) ξ(ϕ) (ξ L (ϕ),ξ R (ϕ)) G g h ξ L (ϕ) ξ R (ϕ) G g L ξ L (ϕ)h (ϕ,g) G g R ξ R (ϕ)h (ϕ,g) ϕ ϕ G/H U(ϕ) ξ L (ϕ)ξ R (ϕ) G g L U(ϕ)g R Canonical choice: ξ L (ϕ) = ξ R (ϕ) G u(ϕ) g L u(ϕ)h (ϕ,g) = h(ϕ,g)u(ϕ)g R { U(ϕ) = u(ϕ) 2 } = exp i 2 f Φ EWET A. Pich Schladming 2014 53

CCWZ Formalism: Callan Coleman Wess Zumino u(ϕ) G g L u(ϕ) h (ϕ,g) = h(ϕ,g) u(ϕ) g R SU(2) L+R triplets: X G h(ϕ,g) X h(ϕ,g) R 1 2 σ R, µ R = µ R +[Γ µ,r] u µ i ud µ U u = u µ, h µν = µ u ν + ν u µ Γ µ = 1 2 f µν ± = u Ŵ µν u ±u ˆB µν u { } u( µ i ˆB µ)u + u ( µ i Ŵ µ)u EWET A. Pich Schladming 2014 54

Resonance Effective Theory Towers of heavy states are usually present in strongly-coupled models of EWSB: Technicolour, Walking TC... The low-energy constants (LECs) of the Goldstone Lagrangian contain information on the heavier states. The lightest states not included in the Lagrangian dominate 1 Build L eff (ϕ i,r k ) with the lightest R k coupled to the ϕ i 2 Require a good UV behaviour Low # of derivatives 3 Match the two effective Lagrangians LECs EWET A. Pich Schladming 2014 55

LO Resonance EW Lagrangian Pich Rosell Sanz-Cillero L eff = L ϕ + R L R + R,R L RR + Triplets: V(1 ), A(1 ++ ) ; Singlet: S 1 (0 ++ ) L S1 +L A +L V = v 2 κ W S 1 u µ u µ + F A 2 2 A µνf µν L S1A = 2 λ SA 1 µ S 1 A µν u ν + F V 2 2 V µν f µν + + i G V 2 2 V µν [u µ u ν ] Antisymmetric V µν and A µν fields (better UV properties): L Kin = 1 λ R λµ νr νµ 1 2 2 M2 R RµνRµν + 1 2 µ S 1 µs 1 1 2 M2 S S 2 1 1 R=V,A EWET A. Pich Schladming 2014 56

Resonance Exchange G V V G V G V 2 2 M V V F V G V F V G V 2 q << 2 M V,A 2 M V V F 2 V 2 F V F V M V F A A F A F 2 A 2 M A a 1 = F2 V 4M 2 V + F2 A 4M 2 A, a 2 = a 3 = F VG V 4M 2 V, a 4 = a 5 = G2 V 4M 2 V EWET A. Pich Schladming 2014 57

Left (Ŵ µ ) and Right (ˆB µ ) Sources: U(ϕ) g L U(ϕ)g R Ŵ µ g L Ŵ µ g L +i g L µ g L, ˆBµ g R ˆBµ g R +i g R µ g R Left / Right (Vector / Axial) Currents EWET A. Pich Schladming 2014 58

Left (Ŵ µ ) and Right (ˆB µ ) Sources: U(ϕ) g L U(ϕ)g R Ŵ µ g L Ŵ µ g L +i g L µ g L, ˆBµ g R ˆBµ g R +i g R µ g R Left / Right (Vector / Axial) Currents Vector Form Factor: ϕ(p 1)ϕ(p 2) J µ V 0 = (p1 p2)µ F v ϕϕ(s) κ W F V V G V F v ϕϕ(s) = 1 + F V G V v 2 s M 2 V s EWET A. Pich Schladming 2014 58

Axial Form Factor: S 1(p 1)ϕ(p 2) J µ A 0 = (p1 p2)µ F a S 1 ϕ(s) κ W F A A λ 1 SA F a S 1 ϕ (s) = κ W (1 + F Aλ SA 1 κ W v 2 ) s MA 2 s EWET A. Pich Schladming 2014 59

Axial Form Factor: S 1(p 1)ϕ(p 2) J µ A 0 = (p1 p2)µ F a S 1 ϕ(s) κ W F A A λ 1 SA F a S 1 ϕ (s) = κ W (1 + F Aλ SA 1 κ W v 2 ) s MA 2 s Short-distance constraint: lim F a s S 1 ϕ (s) = 0 F A λ SA 1 = κ W v 2 EWET A. Pich Schladming 2014 59

Weinberg Sum Rules Chiral Symmetry: Π µν LR (q) d 4 x e iqx 0 T(J µ L (x)jν R (0) ) 0 = ( g µν q 2 +q µ q ν ) Π LR (q 2 ) = 0 EWET A. Pich Schladming 2014 60

Weinberg Sum Rules Chiral Symmetry: Π µν LR (q) d 4 x e iqx 0 T(J µ L (x)jν R (0) ) 0 = ( g µν q 2 +q µ q ν ) Π LR (q 2 ) = 0 OPE: Π µν LR (q) 0 only through order parameters of EWSB (operators invariant under H but not under G) Asymptotically-Free Theories: lim s s2 Π LR (s) = 0 (Bernard et al.) EWET A. Pich Schladming 2014 60

WSRs @ LO V, A Π LR (s) = v2 s + F 2 V M 2 V s F 2 A M 2 A s 1 st WSR: F 2 V F2 A = v2 2 nd WSR: F 2 V M2 V F2 A M2 A = 0 EWET A. Pich Schladming 2014 61

WSRs @ LO V, A Π LR (s) = v2 s + F 2 V M 2 V s F 2 A M 2 A s 1 st WSR: F 2 V F2 A = v2 2 nd WSR: F 2 V M2 V F2 A M2 A = 0 M 2 A FV 2 = v2 MA 2 M2 V, F 2 A = v2 M 2 V M 2 A M2 V, M A > M V EWET A. Pich Schladming 2014 61

WSRs @ LO V, A Π LR (s) = v2 s + F 2 V M 2 V s F 2 A M 2 A s 1 st WSR: F 2 V F2 A = v2 2 nd WSR: F 2 V M2 V F2 A M2 A = 0 M 2 A FV 2 = v2 MA 2 M2 V, F 2 A = v2 M 2 V M 2 A M2 V, M A > M V 1 st WSR likely valid also in gauge theories with non-trivial UV fixed points 2 nd WSR questionable (not valid) in walking (conformal) TC scenarios Appelquist Sannino, Orgogozo Rychkov EWET A. Pich Schladming 2014 61

Gauge Boson Self-Energies: S, T q 00000 11111 00000 11111 00000 11111 00000 11111 000 111 L = 1 2 W3 µ Πµν 33 (q2 )W 3 ν 1 2 Bµ Πµν 00 (q2 )B ν W 3 µ Πµν 30 (q2 )B ν W + µ Πµν WW (q2 )W ν ) Landau gauge (ξ = 0): Π µν ij (q 2 ) = ( g µν + qµ q ν q 2 Π ij (q 2 ) There is no mixing with the Goldstones T S 16π ( e3 g 2 e3 SM ) = 0.03±0.10 4π ( g 2 sin 2 e1 e SM ) 1 = 0.05±0.12 θ W e 3 = g g Π30(0) e 1 = Π33(0) Π WW(0) M 2 W Π 30(q 2 ) = g2 tanθ W 4 s [Π VV (s) Π AA (s)] = q 2 Π30(q 2 ) + g2 tanθ W 4 v 2 e SM 1,3 defined at M H = 126 GeV EWET A. Pich Schladming 2014 62

Dispersive Representation S = 16 g 2 tanθ W 0 ds s [ Im Π 30 (s) Im Π SM 30 (s) ] (Peskin-Takeuchi) Im Π SM 30 (s) = g2 tanθ W 192π 2 [ θ(s) ( 1 M2 H s ) 3 ( θ s MH) ] 2 (1 loop) EWET A. Pich Schladming 2014 63

Dispersive Representation S = 16 g 2 tanθ W 0 ds s [ Im Π 30 (s) Im Π SM 30 (s) ] (Peskin-Takeuchi) Im Π SM 30 (s) = g2 tanθ W 192π 2 [ θ(s) ( 1 M2 H s ) 3 ( θ s MH) ] 2 (1 loop) T = 4π g 2 cos 2 θ W 0 ds s 2 [ ρt (s) ρ SM T (s)] (Pich Rosell Sanz-Cillero) ρ T (s) = 1 π Im[Σ(0) (s) Σ (+) (s)] (Goldstone self-energies) ρ SM T (s) = 3g 2 s 64π 2 [ θ(s) + ( 1 M4 H s 2 )θ(s M 2H ) ] (1 loop) SM contribution defined at M H = 126 GeV EWET A. Pich Schladming 2014 63

Gauge Boson Self-Energies @ LO V, A S LO = 4π( F 2 V M 2 V ) F2 A MA 2, T LO = 0 Sensitive to vector and axial states M A > M V > 1.5 TeV MA TeV 4 SLO 2.5 3 2.0 1.5 2 1.0 1 0 MV TeV 0 1 2 3 4 0.5 0.0 0.5 MV TeV 0.5 1.0 1.5 2.0 2.5 3.0 3 σ bounds AP Rosell Sanz-Cillero ( ) 1 st +2 nd WSR: S LO = 4πv2 MV 2 1+ M2 V MA 2 1 st { ( WSR (M A > M V ): v 2 S LO = 4π M V 2 + FA 2 1 M V 2 1 )} M A 2 > 4πv2 M V 2 > 4πv2 M A 2 EWET A. Pich Schladming 2014 64

Gauge Boson Self-Energies @ NLO Sensitive to the light scalar S 1 (125) AP, Rosell, Sanz-Cillero V V V V S A A A A S S S 0.4 M V [1.5, 6.0] TeV 0 κ W 1 0.2 V V V V M V T 0.0 A A A A S S S S 0.2 Κ W 0.4 κ W g SWW g SM HWW = M2 V M 2 A [0.94, 1] 0.4 0.2 0.0 0.2 0.4 S M A M V > 4 TeV (95% CL) 1 st +2 nd WSRs EWET A. Pich Schladming 2014 65

Gauge Boson Self-Energies @ NLO Weaker assumptions: 1 st WSR only, M A > M V > 0.4 TeV 1.2 1.0 AP, Rosell, Sanz-Cillero ΚW 0.8 0.6 0.4 0.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 M V TeV 0.2 < M V M A < 1 0.02 < M V M A < 0.2 κ W g SWW /g SM very different from one HWW requires large (unnatural) mass splittings EWET A. Pich Schladming 2014 66

Linear Realization: SU(2) L U(1) Y Assumes that H(126) and ϕ combine into an SU(2) L doublet: Φ = ( Φ + Φ 0 ) = 1 2 (v +H) U( ϕ) ( 0 1 ) The SM Lagrangian is the low-energy effective theory with D = 4 L eff = L SM + D>4 i c (D) i O(D) D 4 i Λ 1 operator with D = 5: O (5) = L L Φ Φ T L c L 59 independent O (6) i 5 independent O (6) i (violates L by 2 units) preserving B and L (for 1 generation) Weinberg Buchmuller Wyler, Grzadkowski Iskrzynski Misiak Rosiek violating B and L (for 1 generation) Weinberg, Wilczek Zee, Abbott Wise, EWET A. Pich Schladming 2014 67

O G O G O W O W D = 6 Operators (other than 4-fermion ones) Grzadkowski Iskrzynski Misiak Rosiek X 3 Φ 6 and Φ 4 D 2 ψ 2 Φ 3 f ABC Gµ AνGBρ ν Gρ Cµ O Φ (Φ Φ) 3 O eφ (Φ Φ)( l pe rφ) f ABC G Aν µ Gν Bρ Gρ Cµ O Φ (Φ Φ) (Φ Φ) O uφ (Φ Φ)( q pu r Φ) ε IJK Wµ IνWJρ ν Wρ Kµ O ΦD ( Φ D µ Φ ) ( Φ D ) µφ O dφ (Φ Φ)( q pd rφ) εijk W Iν µ Wν Jρ Wρ Kµ X 2 Φ 2 ψ 2 XΦ ψ 2 Φ 2 D O ΦG Φ Φ G A µν GAµν O ew ( l pσ µν e r) τ I ΦW I µν O (1) Φl (Φ i D µφ)( l pγ µ l r) O Φ G Φ Φ G A µνg Aµν O eb ( l pσ µν e r) ΦB µν O (3) Φl (Φ i D I µ Φ)( l pτ I γ µ l r) O ΦW Φ Φ W I µν WIµν O ug ( q pσ µν T A u r) ΦG A µν O Φe (Φ i D µφ)(ē pγ µ e r) O Φ W Φ Φ W µνw I Iµν O uw ( q pσ µν u r) τ I ΦW µν I O (1) Φq (Φ i D µφ)( q pγ µ q r) O ΦB Φ Φ B µνb µν O ub ( q pσ µν u r) ΦB µν O (3) Φq (Φ i Dµ I Φ)( qpτi γ µ q r) O Φ B Φ Φ B µνb µν O dg ( q pσ µν T A d r) ΦG A µν O Φu (Φ i D µφ)(ū pγ µ u r) O ΦWB Φ τ I Φ W I µν Bµν O dw ( q pσ µν d r) τ I ΦW I µν O Φd (Φ i D µφ)( d pγ µ d r) O Φ WB Φ τ I Φ W I µν Bµν O db ( q pσ µν d r) ΦB µν O Φud i( Φ D µφ)(ū pγ µ d r) q = q L, l = l L, u = u R, d = d R, e = e R, p,r = generation indices EWET A. Pich Schladming 2014 68

D = 6 Four-Fermion Operators Grzadkowski Iskrzynski Misiak Rosiek ( LL)( LL) ( RR)( RR) ( LL)( RR) O ll ( l pγ µl r)( l sγ µ l t) O ee (ē pγ µe r)(ē sγ µ e t) O le ( l pγ µl r)(ē sγ µ e t) O (1) qq ( q pγ µq r)( q sγ µ q t) O uu (ū pγ µu r)(ū sγ µ u t) O lu ( l pγ µl r)(ū sγ µ u t) O (3) qq ( q pγ µτ I q r)( q sγ µ τ I q t) O dd ( d pγ µd r)( d sγ µ d t) O ld ( l pγ µl r)( d sγ µ d t) O (1) lq ( l pγ µl r)( q sγ µ q t) O eu (ē pγ µe r)(ū sγ µ u t) O qe ( q pγ µq r)(ē sγ µ e t) O (3) lq ( l pγ µτ I l r)( q sγ µ τ I q t) O ed (ē pγ µe r)( d sγ µ d t) O (1) qu ( q pγ µq r)(ū sγ µ u t) O (1) ud (ū pγ µu r)( d sγ µ d t) O (8) qu ( q pγ µt A q r)(ū sγ µ T A u t) O (8) ud (ū pγ µt A u r)( d sγ µ T A d t) O (1) qd ( q pγ µq r)( d sγ µ d t) O (8) qd ( q pγ µt A q r)( d sγ µ T A d t) ( LR)( RL) and ( LR)( LR) B-violating O ledq ( l p j er)( d sq j t ) O [ duq ε αβγ ε jk (d α p ) T ][ Cur β (q γj s ) T Clt k ] O (1) ( q j quqd p ur)ε jk ( q s k dt) [ Oqqu εαβγ ε jk (q αj p )T Cqr βk ][ (u γ s ) T ] Ce t O (8) quqd ( q p j TA u r)ε jk ( q s k [ TA d t) O qqq (1) ε αβγ ε jk ε mn (q αj p )T Cqr βk ][ (q γm s ) T Clt n ] O (1) lequ ( l p j er)ε jk ( q s k ut) O(3) qqq ε αβγ (τ I ε) jk (τ I [ ε) mn (q αj p )T Cqr βk ][ (q γm s ) T Clt n ] O (3) lequ ( l p j σµνer)ε jk ( q s k σµν u t) O duu ε [ ][ αβγ (dp α )T Cur β (u γ s ) T ] Ce t q = q L, l = l L, u = u R, d = d R, e = e R, p,r,s,t = generation indices EWET A. Pich Schladming 2014 69

Shifts of SM parameters: L (D=6) eff = i C i Λ 2 O i V(H) = λ ) 2 (Φ Φ v2 C ( ( 3 Φ Φ Φ) v 2 Λ 2 T = 1+ 3C Φ 8λ ) v 2 v Λ 2 EWET A. Pich Schladming 2014 70

Shifts of SM parameters: L (D=6) eff = i C i Λ 2 O i V(H) = λ ) 2 (Φ Φ v2 C ( ( 3 Φ Φ Φ) v 2 Λ 2 T = 1+ 3C Φ 8λ ) v 2 v Λ 2 ( Canonical Normalization: H ch kin H, ch kin = C Φ 1 ) v 2 4 C ΦD Λ 2 EWET A. Pich Schladming 2014 70

Shifts of SM parameters: L (D=6) eff = i C i Λ 2 O i V(H) = λ ) 2 (Φ Φ v2 C ( ( 3 Φ Φ Φ) v 2 Λ 2 T = 1+ 3C Φ 8λ ) v 2 v Λ 2 ( Canonical Normalization: H ch kin H, ch kin = C Φ 1 ) v 2 4 C ΦD Λ 2 M 2 H = 2λv 2 T ( 1 3C Φ 2λ ) v 2 Λ 2 +2ckin H Flavour: Y f M f L = Q r L[Y d ] rs Φd s R + [M f ] rs = v ( ) T [Y ψ ] rs v2 2 2Λ [C fφ] 2 rs [Y f ] rs = 1 v T [M f ] rs ( 1+cH kin ) v2 Λ 2 [C fφ] rs EWET A. Pich Schladming 2014 70

Shifts of SM parameters: L (D=6) eff = i C i Λ 2 O i V(H) = λ ) 2 (Φ Φ v2 C ( ( 3 Φ Φ Φ) v 2 Λ 2 T = 1+ 3C Φ 8λ ) v 2 v Λ 2 ( Canonical Normalization: H ch kin H, ch kin = C Φ 1 ) v 2 4 C ΦD Λ 2 Flavour: Y f M f L = Q r L[Y d ] rs Φd s R + 4G F 2 = 2 v 2 T M 2 H = 2λv 2 T ( 1 3C Φ 2λ ) v 2 Λ 2 +2ckin H [M f ] rs = v ( ) T [Y ψ ] rs v2 2 2Λ [C fφ] 2 rs [Y f ] rs = 1 v T [M f ] rs ( 1+cH kin + 1 ( 2 [ C (3) Λ ]ee +2[ C (3) ]µµ [ C 2 ll ]µe,eµ [ ] C ll Φl Φl ) v2 Λ 2 [C fφ] rs eµ,µe EWET A. Pich Schladming 2014 70 )

Gauge Fields: L (D=6) eff = i C i Λ 2 O i Alonso et al ḡ = g ( 1+C ΦB v 2 T Λ 2 ), ḡ = g ( 1+C ΦW v 2 T Λ 2 ), ḡ s = g s ( 1+C ΦG v 2 T Λ 2 ) tan θ W = ḡ ḡ + v2 T 2Λ 2 ) (1 ḡ 2 ḡ 2 C ΦWB MW 2 = v2 T 4 ḡ2, MZ 2 = v2 T (ḡ2 +ḡ 2) + v4 T {(ḡ2 4 8Λ 2 +ḡ 2) C ΦD +4ḡ ḡ } C ΦWB ē = ḡ sin θ W { 1 cot θ W v 2 T 2Λ 2 C ΦWB }, ḡ Z = ē sin θ W cos θ W { 1+ ḡ2 +ḡ 2 2ḡḡ v 2 T Λ 2 C ΦWB } ρ ḡ2 M 2 Z ḡ 2 Z M2 W = 1+ v2 T 2Λ 2 C ΦD EWET A. Pich Schladming 2014 71

Equivalent Bases of CP-even Operators (EW bosons only) BW HISZ GGPR Willenbrock Zhang O W = ǫ IJK W Iν µ WJρ ν WKµ ρ O WWW = Tr[ŴµνŴνρ Ŵ µ ρ ] O 3W = 1 3! g ǫ abcw aν µ Wb νρ Wcρµ O ΦW = Φ Φ W I µν WIµν O WW = Φ Ŵ µν Ŵ µν Φ O ΦB = Φ Φ B µνb µν O BB = Φ ˆBµν ˆBµν Φ O BB = g 2 H 2 B µνb µν O ΦWB = Φ σ I Φ W I µν Bµν O BW = Φ ˆBµν Ŵ µν Φ O W = (D µφ) Ŵ µν (D νφ) O HW = ig (D µ H) σ a (D ν H)W a µν O B = (D µφ) ˆBµν (D νφ) ( ) O HB = ig (D µ H) (D ν H)B µν O DW = Tr [D µ,ŵνρ][dµ,ŵνρ ] O 2W = 1 2 (Dµ W a µν )2 O DB = g 2 2 ( µb νρ)( µ B νρ ) O 2B = 1 2 ( µ B µν) 2 O W = ig 2 (H σ a D µ H)D ν W a µν O B = ig 2 (H D µ H) ν B µν O ΦD = (Φ D µ Φ) (Φ D µφ) O Φ,1 = (D µφ) ΦΦ (D µ Φ) O T = 1 2 (H D µ H) 2 O Φ = (Φ Φ) (Φ Φ) O Φ,2 = 1 2 µ(φ Φ) µ (Φ Φ) O H = 1 2 ( µ H 2 ) 2 O Φ = (Φ Φ) 3 O Φ,3 = 1 3 (Φ Φ) 3 O 6 = λ H 6 O Φ,4 = (D µφ) (D µ Φ)(Φ Φ) BW = Buchmuller Wyler, Grzadkowski et al. HISZ = Hagiwara et al. GGPR = Giudice et al. EWET A. Pich Schladming 2014 72

Anomalous Triple Gauge Couplings L WWV = i g WWV {g V 1 ( W + µν W µ V ν W + µ W µν V ν ) +κ V W + µ W ν V µν + λ V M 2 W } W µνw + νρ V ρ µ g WWγ = e = g cosθ W, g WWZ = g cosθ W, κ V = 1+ κ V, g V 1 = 1+ gv 1 Relevant operators: O W, O ΦWB, O (3) φl (BW) O WWW, O W, O B, O BW, O DW O 3W, O HW, O HB, O 2W, O W, O B (HISZ) (GGPR) D = 6 Relations: λ γ = λ Z, g Z 1 = κ Z +tan2 θ W κ γ EWET A. Pich Schladming 2014 73

Anomalous Triple Gauge Couplings HISZ basis: L eff = n f n Λ 2 O n Corbett Eboli González-Fraile González-García λ γ = λ Z = 3g2 M 2 W 2Λ 2 f WWW, κ γ = g2 v 2 8Λ 2 (f W +f B ) κ Z = g2 v 2 8Λ 2 ( f W tan 2 θ W f B ), g Z 1 = g 2 v 2 8cos 2 θ W Λ 2 f W (95% CL) Higgs data: (90% CL) 0.047 g Z 1 0.089, 0.19 κγ 0.099 0.019 κ Z 0.083 Combined: (90% CL) 0.005 g Z 1 0.040, 0.058 κγ 0.047 0.004 κ Z 0.040 LEP, D0, ATLAS assume λγ = λ Z = 0 EWET A. Pich Schladming 2014 74

Global Fit to L (D=6) eff Pomarol Riva GGPR basis: O H = 1 2 ( µ H 2 ) 2 O T = 1 2 (H D µh) 2 O 6 = λ H 6 O W = ig 2 (H σ a D µh)d νw aµν O B = ig 2 (H D µh) νb µν O BB = g 2 H 2 B µνb µν O GG = g 2 s H 2 G A µνg Aµν O HW = ig (D µ H) σ a (D ν H)W a µν O HB = ig (D µ H) (D ν H)B µν O 3W = 1 3! g ǫ abcwµ aνwb νρwc ρµ O yu = y u H 2 Q L HuR + h.c. O yd = y d H 2 Q L Hd R + h.c. O ye = y e H 2 L L He R + h.c. O u R = i (H D µh)(ū R γ µ u R ) O d R = i (H D µh)( d R γ µ d R ) O e R = i (H D µh)(ē R γ µ e R ) O q L = i (H D µh)( Q L γ µ Q L ) O (3)q L = i (H σ a D µh)( Q L σ a γ µ Q L ) O (3)ql LL = ( Q L σ a γ µq L )( L L σ a γ µ L L ) O (3)l LL = ( L L σ a γ µ L L )( L L σ a γ µl L ) EWET A. Pich Schladming 2014 75

LEP-I + SLC + KLOE (CKM univ) + pp l ν (LHC) Pomarol Riva c T (95% CL) c L q c R e c L 3 q c V c R u c LL 3 l c R d c LL 3 ql 0.010 0.005 0.000 0.005 0.05 0.025 0. 0.025 c L q3 c L 3 q3 All ; --- without KLOE ; include O t L + O(3)t L ; All other O i set to zero L = c T v 2 O T + c+ V M 2 W + cq L v 2 Oq L + c (3) q L O (3)q v 2 L (O W + O B ) + c(3)l LL O (3)l v 2 LL + ce R v 2 Oe R + cu R v 2 Ou R + cd R v 2 Od R + c (3) ql LL v 2 O (3)ql LL c ± V = 1 2 (c W ± c B ) EWET A. Pich Schladming 2014 76

Pomarol Riva LEP-II + H Zγ (LHC) H VV,f f (LHC) c V Κ HV (95% CL) Κ GG Κ HV Κ BB 0.10 0.05 0.00 0.05 0.002 0.001 0.000 0.001 0.002 All ; All other O i set to zero ; c H and c yf effects constrained to be below 50% of SM L TGC = κ+ HV m 2 W L Higgs = c H v 2 O H + (O HW + O HB ) + c V + κ HV 2m 2 W f=t,b,τ O + + κ 3W mw 2 O 3W c yf v 2 Oy + c6 f v 2 O6 + κ BB MW 2 O BB + κ GG MW 2 O GG + c V κ HV 2MW 2 O O ± (O W O B ) ± (O HW O HB ), O WW = 4O + O BB, κ ± HV = 1 2 (κ HW ± κ HB ) EWET A. Pich Schladming 2014 77

Renormalization Group Equations L (D=6) eff = i C i (µ) Λ 2 O i (µ) Loop Corrections µ dci dµ = j γ ij 16π 2 Cj Ci(µ) = Ci(Λ) j ( ) γ ij Λ Cj(Λ) log 16π2 µ Anomalous Dimensions: γ ij EWET A. Pich Schladming 2014 78

Anomalous Dimensions γ ij Complete 59 59 matrix computed in the BW basis: Jenkins et al. γ O ( 1,g 2,λ,y 2,g 4,g 2 λ,g 2 y 2,λ 2,λy 2,y 4,g 6,g 4 λ,g 6 λ ) g 3 X 3 H 6 H 4 D 2 g 2 X 2 H 2 yψ 2 H 3 gyψ 2 XH ψ 2 H 2 D ψ 4 g 3 X 3 g 2 0 0 1 0 0 0 0 H 6 g 6 λ λ,g 2,y 2 g 4,g 2 λ,λ 2 g 6,g 4 λ λy 2,y 4 0 λy 2,y 4 0 H 4 D 2 g 6 0 g 2,λ,y 2 g 4 y 2 g 2 y 2 g 2,y 2 0 g 2 X 2 H 2 g 4 0 1 g 2,λ,y 2 0 y 2 1 0 yψ 2 H 3 g 6 0 g 2,λ,y 2 g 4 g 2,λ,y 2 g 2 λ,g 4,g 2 y 2 g 2,λ,y 2 λ,y 2 gyψ 2 XH g 4 0 0 g 2 1 g 2,y 2 1 1 ψ 2 H 2 D g 6 0 g 2,y 2 g 4 y 2 g 2 y 2 g 2,λ,y 2 y 2 ψ 4 g 6 0 0 0 0 g 2 y 2 g 2,y 2 g 2,y 2 (X 2 H 2,X 2 H 2 ) submatrix computed in the HISZ basis Chen Dawson Zhang A submatrix computed in the GGPR basis J. Elias-Miro et al. EWET A. Pich Schladming 2014 79

Oblique Corrections (NLO) g 2 16π S M2 W Λ 2 [ ] {C [ ( )]} BW (µ)+ g2 M C 32π 2 WW +tan 2 2 θ W C BB 1 2 log H µ 2 g 2 sin 2 θ W 4π T v2 2Λ 2 C Φ,1 (HISZ basis) Mebane et al., Chen Dawson Zhang 0.10 0.05 c,1 2 TeV 2 0.00 Tree-level Bounds 0.05 0.10 0.4 0.2 0.0 0.2 0.4 c BW 2 TeV 2 EWET A. Pich Schladming 2014 80

OUTLOOK Effective Field Theory: powerful low-energy tool Mass Gap: E,m light Λ NP Assumption: relevant symmetries (breakings) & light fields Most general L eff (φ light ) allowed by symmetry Short-distance dynamics encoded in LECs LECs constrained phenomenologically Goal: get hints on the underlying fundamental dynamics New Physics EWET A. Pich Schladming 2014 81

Learning from QCD experience. EW problem more difficult Fundamental Underlying Theory unknown QCD? χpt Standard Model Additional dynamical input (fresh ideas!) needed EWET A. Pich Schladming 2014 82

A new boson discovered It behaves as the SM Higgs particle The SM appears to be the right theory at the EW scale New physics needed to explain many pending questions Flavour, CP, baryogenesis, cosmology... How far is the Scale of New-Physics Λ NP? Which symmetry keeps Å À away from Λ NP? Supersymmetry, scale/conformal symmetry... Eagerly awaiting more LHC data... EWET A. Pich Schladming 2014 83