Constraining New Physics with Combined Low and High Energy - PowerPoint PPT Presentation

Introduction U ( 3 ) 5 Invariant Operators Comments On Non- U ( 3 ) 5 Invariant Operators Constraining New Physics with Combined Low and High Energy Observables A combined effective operator analysis of precision data James Jenkins Theoretical Division, T-2 Los Alamos National Laboratory 2009 Phenomenology Symposium, Madison, WI James Jenkins Low & High Energy Constraints

Introduction U ( 3 ) 5 Invariant Operators Comments On Non- U ( 3 ) 5 Invariant Operators Outline Introduction 1 Operator Set Observables U ( 3 ) 5 Invariant Operators 2 Global Analysis Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators 3 James Jenkins Low & High Energy Constraints

Introduction Operator Set U ( 3 ) 5 Invariant Operators Observables Comments On Non- U ( 3 ) 5 Invariant Operators Operator Set U ( 3 ) 5 Invariant Operators O WB = ( h † σ a h ) W a µν B µν , O h = | h † D µ h | 2 1 O s ( ℓγ µ ℓ )( ℓγ µ ℓ ) , O s ℓ q = ( ℓγ µ ℓ )( q γ µ q ) , O t ℓ q = ( ℓγ µ σ a ℓ )( q γ µ σ a q ) , ℓℓ = 2 O ℓ e = ( ℓγ µ ℓ )( e γ µ e ) , O qe = ( q γ µ q )( e γ µ e ) , O ℓ u = ( ℓγ µ ℓ )( u γ µ u ) , O ℓ d = ( ℓγ µ ℓ )( d γ µ d ) , 1 ( e γ µ e )( e γ µ e ) , O eu =( e γ µ e )( u γ µ u ) , O ed =( e γ µ e )( d γ µ d ) . O ee = 2 O s h ℓ = i ( h † D µ h )( ℓγ µ ℓ ) + h . c ., O t h ℓ = i ( h † D µ σ a h )( ℓγ µ σ a ℓ ) + h . c ., O s hq = i ( h † D µ h )( q γ µ q ) + h . c ., O t hq = i ( h † D µ σ a h )( q γ µ σ a q ) + h . c ., O hu = i ( h † D µ h )( u γ µ u ) + h . c ., O hd = i ( h † D µ h )( d γ µ d ) + h . c ., O he = i ( h † D µ h )( e γ µ e ) + h . c . O W = ǫ abc W a ν µ W b λ W c µ ν λ These interfere with dominant Standard Model processes James Jenkins Low & High Energy Constraints

Introduction Operator Set U ( 3 ) 5 Invariant Operators Observables Comments On Non- U ( 3 ) 5 Invariant Operators Operator Anatomy Each operator is associated with a dimensionless coupling constant a i v 2 O i a i = v 2 × T flavor a , b ... Λ 2 i Operators will shift parameters ( α, M Z , G F ... ) and contribute to physical processes directly. Goal is to calculate corrections to observables (linear in a i ) and bound operators: Globally Using individual operators We Use v = 174 GeV James Jenkins Low & High Energy Constraints

Introduction Operator Set U ( 3 ) 5 Invariant Operators Observables Comments On Non- U ( 3 ) 5 Invariant Operators Precision Observables Included Measurements Weak charge in Cs and Tl (Atomic Parity Violation) Neutrino Deep Inelastic Scattering (DIS) data (NuTeV) Z-Pole Observables LEP2 fermion pair production W pair production differential cross-sections W mass measurements From this, we create a χ 2 function quadratic in a i parameters. This contains 237 (generally correlated) terms! Our global analysis is extended from a Mathematica Notebook by Han & Skiba, 2005 James Jenkins Low & High Energy Constraints

Introduction Operator Set U ( 3 ) 5 Invariant Operators Observables Comments On Non- U ( 3 ) 5 Invariant Operators Added low energy observable: ∆ CKM Consider the unitarity of the CKM matrix. We write: | V ud | 2 + | V us | 2 + | V ub | 2 ≡ 1 + ∆ CKM , where the deviation from unitarity receives contributions as � � ∆ CKM = 2 ( a hq 3 − a hl 3 ) − ( a lq 3 − a ll 3 ) . This is experimentally constrained to be ∆ CKM = ( − 2 ± 6 ) × 10 − 4 (Dominant Superallowed Modes) ∆ CKM constrains operators ℓℓ = 1 O s 2 ( ℓγ µ ℓ )( ℓγ µ ℓ ) , O t ℓ q = ( ℓγ µ σ a ℓ )( q γ µ σ a q ) , O t h ℓ = i ( h † D µ σ a h )( ℓγ µ σ a ℓ ) + hc ., O t hq = i ( h † D µ σ a h )( q γ µ σ a q ) + hc . James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators Simple Error Propagation Maximum deviation of a quantity composed of n observables: n ∂ ∆ CKM ∂ ∆ CKM ( δ ∆ CKM )) 2 = � M ij δ a i δ a j . ∂ a i ∂ a j i , j Plugging in numbers from precision data yields δ ∆ CKM = 2 . 94 × 10 − 3 . This is 4 . 8 times larger than the experimentally extracted ∆ CKM uncertainty of 6 × 10 − 4 ! James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators Allowed Contours Alternate value: ∆ CKM = − 0 . 0025 ± 0 . 0006 James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators Pseudo-Pull Plot Contributions from various measurement types James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators Observable Correlations Assuming the dominance of a single operator O i , we substitute a i for ∆ CKM using a i = ± 1 2 ∆ CKM This leads to direct correlations between any two observables! In particular, the χ 2 functions become simple quadratics: χ 2 O s O t O t O t Measurement ℓℓ ℓ q h ℓ SM hq 1 . 2 e 3 ∆ + 2 . 8 e 6 ∆ 2 1 . 2 e 3 ∆ + 2 . 8 e 6 ∆ 2 1 . 2 e 3 ∆ + 2 . 86 ∆ 2 1 . 2 e 3 ∆ + 2 . 8 e 6 ∆ 2 ∆ CKM 0.11 − 2 . 4 e 2 ∆ + 2 . 7 e 3 ∆ 2 − 4 . 7 e 2 ∆ + 1 . 1 e 5 ∆ 2 MW 0.65 − 2 . 2 e 1 ∆ + 6 . 8 e 4 ∆ 2 6 . 9 e 1 ∆ + 3 . 3 e 5 ∆ 2 1 . 5 e 2 ∆ + 2 . 2 e 5 ∆ 2 Zline 0.96 3 . 6 e 2 ∆ + 6 . 8 e 3 ∆ 2 4 . 7 e 2 ∆ + 8 . 1 e 3 ∆ 2 8 . 0 e 0 ∆ + 8 . 2 e 1 ∆ 2 bc 0.90 − 3 . 3 e 2 ∆ + 8 . 2 e 4 ∆ 2 − 4 . 3 e 2 ∆ + 1 . 4 e 5 ∆ 2 pol 0.98 2 . 1 e 2 ∆ + 1 . 8 e 4 ∆ 2 2 . 6 e 2 ∆ + 3 . 1 e 4 ∆ 2 QFB 0.57 9 . 1 e 1 ∆ + 1 . 9 e 3 ∆ 2 6 . 1 e 1 ∆ + 9 . 6 e 2 ∆ 2 1 . 9 e 2 ∆ + 8 . 2 e 3 ∆ 2 6 . 1 e 1 ∆ + 9 . 6 e 2 ∆ 2 DIS 1.27 1 . 3 e 0 ∆ + 1 . 8 e 0 ∆ 2 2 . 6 e 1 ∆ + 3 . 1 e 2 ∆ 2 − 7 . 9 e 1 ∆ + 2 . 9 e 3 ∆ 2 2 . 6 e 1 ∆ + 3 . 1 e 2 ∆ 2 QW 0.54 − 3 . 5 e 1 ∆ + 1 . 3 e 3 ∆ 2 1 . 2 e 2 ∆ + 1 . 6 e 4 ∆ 2 − 4 . 3 e 1 ∆ + 2 . 0 e 3 ∆ 2 − 2 . 2 e 1 ∆ + 5 . 4 e 2 ∆ 2 hadLEP 0.66 µ LEP 2 . 2 e 1 ∆ + 1 . 3 e 3 ∆ 2 1 . 1 e 0 ∆ + 5 . 4 e 0 ∆ 2 0.85 − 4 . 1 e − 1 ∆ + 8 . 2 e 2 ∆ 2 9 . 1 e − 3 ∆ + 3 . 3 e 0 ∆ 2 τ LEP 0.85 − 7 . 4 e − 1 ∆ + 2 . 4 e 1 ∆ 2 9 . 1 e − 1 ∆ + 1 . 9 e − 1 ∆ 2 eOPAL 0.77 7 . 2 e 0 ∆ + 1 . 3 e 2 ∆ 2 9 . 1 e − 1 ∆ + 6 . 8 e 0 ∆ 2 − 1 . 6 e 0 ∆ + 6 . 3 e 0 ∆ 2 WL3 1.09 7 . 4 e 0 ∆ + 1 . 8 e 4 ∆ 2 1 . 3 e 1 ∆ + 1 . 2 e 4 ∆ 2 7 . 8 e 0 ∆ + 3 . 0 e 4 ∆ 2 1 . 7 e 1 ∆ + 1 . 9 e 4 ∆ 2 tot 0.86 James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators Individual Operator Constraints James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators Individual Operator Constraints James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators Z-Line Correlations (Light Fermions) James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators Z-Pole Polarized Lepton Asymmetries James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators Z-Pole Heavy Fermion Observables James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators Other Correlations James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators DIS Correlation (without NuTeV) James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators The NuTeV Anomaly The Standard Model Lagrangian may be written as: √ � �� � L ¯ R ¯ g ν νγ µ P L ν + g ν g f f γ µ P L f + g f f γ µ P R f L = − 4 2 G F L ¯ R ¯ νγ µ P R ν . NuTeV constrains the coupling combinations L ) 2 + ( 2 g ν g 2 ( 2 g ν L g u L g d L ) 2 = L R ) 2 + ( 2 g ν g 2 ( 2 g ν L g u L g d R ) 2 = R They find g 2 L = 0 . 30005 ± 0 . 00137 ( EW Fit : 0 . 3042 ) g 2 R = 0 . 03076 ± 0 . 00011 ( EW Fit : 0 . 0301 ) Usually interpreted as a 3 σ deviation in sin 2 θ w James Jenkins Low & High Energy Constraints

Introduction Global Analysis U ( 3 ) 5 Invariant Operators Individual Operator Analysis Comments On Non- U ( 3 ) 5 Invariant Operators NuTeV Correlations James Jenkins Low & High Energy Constraints