Nonstandard Couplings Oblique Parameters A Global Fit Summary Constraints on Nonstandard Top Quark Couplings from Precision Electroweak Data Cen Zhang Department of Physics University of Illinois at Urbana-Champaign 10 May / Pheno 2011 arXiv:1104.3122, Nicolas Greiner, Scott Willenbrock, Cen Zhang Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings Oblique Parameters Effective Theory and Operators A Global Fit Constraint on OtW Summary Constraints on Nonstandard Top Quark Couplings Nonstandard top quark couplings can be constrained: Directly from colliders (cross sections, branching ratios, etc): Degrande, Gerard, Grojean, Maltoni, Servant, 11 Aguilar-Saavedra, Carvalho, Castro, Onofre, Veloso, 07 Cao, Wudka, Yuan, 07 From B physics ( B meson decay, B ¯ B mixing): Grzadkowski,Misiak, 08 Drobnak, Fajfer, Kamenik, 11 Indirectly from Precision Electroweak Data ( Z -pole, W -mass, DIS, LEP2, etc.) Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings Oblique Parameters Effective Theory and Operators A Global Fit Constraint on OtW Summary History of Top Quark Mass Quigg Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings Oblique Parameters Effective Theory and Operators A Global Fit Constraint on OtW Summary Effective Theory Approach Effective Field Theory � 1 � L eff = L SM + Λ 2 C i O i + h . c . The Operators: O ( 3 ) O ( 1 ) φ q = i ( φ † τ I D µ φ )(¯ q γ µ τ I q ) , φ q = i ( φ † D µ φ )(¯ q γ µ q ) , O φ b = i ( φ † D µ φ )(¯ O φ t = i ( φ † D µ φ )(¯ t γ µ t ) , b γ µ b ) , O φφ = i (˜ q σ µν τ I t )˜ φ † D µ φ )(¯ t γ µ b ) , φ W I O tW = (¯ µν , q σ µν τ I b ) φ W I q σ µν t )˜ O bW = (¯ O tB = (¯ µν , φ B µν , q σ µν b ) φ B µν . O bB = (¯ Couplings can be computed from C i : v 2 V R = C φφ v 2 V L = C ( 3 ) Λ 2 , 2 Λ 2 , · · · , (Aguilar-Saavedra, 08) φ q Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings Oblique Parameters Effective Theory and Operators A Global Fit Constraint on OtW Summary Effective Theory Approach Effective Field Theory � 1 � L eff = L SM + Λ 2 C i O i + h . c . The Operators: O ( 3 ) φ q = i ( φ † τ I D µ φ )(¯ q γ µ τ I q ) , O ( 1 ) φ q = i ( φ † D µ φ )(¯ q γ µ q ) , O φ b = i ( φ † D µ φ )(¯ O φ t = i ( φ † D µ φ )(¯ t γ µ t ) , b γ µ b ) , O φφ = i (˜ q σ µν τ I t )˜ φ † D µ φ )(¯ t γ µ b ) , φ W I O tW = (¯ µν , q σ µν τ I b ) φ W I q σ µν t )˜ O bW = (¯ O tB = (¯ φ B µν , µν , q σ µν b ) φ B µν . O bB = (¯ Couplings can be computed from C i : v 2 V R = C φφ v 2 V L = C ( 3 ) Λ 2 , 2 Λ 2 , · · · , (Aguilar-Saavedra, 08) φ q Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings Oblique Parameters Effective Theory and Operators A Global Fit Constraint on OtW Summary Constraint from Direct Measurement Constraint on O tW , from the decay of the top quark to W boson of a given helicity: C tW Λ 2 = 1 . 1 ± 2 . 1 TeV − 2 ( CDF ) , C tW Λ 2 = − 0 . 8 ± 1 . 2 TeV − 2 ( D0 ) . Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings S Oblique Parameters T A Global Fit U Summary Loop Corrections to W , Z , γ Π WW ( q 2 ) Π ZZ ,γγ,γ Z ( q 2 ) Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings S Oblique Parameters T A Global Fit U Summary The S Parameter In d dimension, √ � m 2 4 m 2 t − m 2 C tW 2 m W m t 5 1 m Z Z s 2 t α S = N c − γ + ln 4 π − ln µ 2 − 2 arctan + 2 . W 2 π 2 Λ 2 � 3 ǫ m Z 4 m 2 t − m 2 Z Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings S Oblique Parameters T A Global Fit U Summary The S Parameter In d dimension, √ � m 2 4 m 2 t − m 2 C tW 2 m W m t 5 1 m Z Z s 2 t α S = N c − γ + ln 4 π − ln µ 2 − 2 arctan + 2 . W 2 π 2 Λ 2 � 3 ǫ m Z 4 m 2 t − m 2 Z At tree level, need to include O WB = ( φ † τ I φ ) W I µν B µν , Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings S Oblique Parameters T A Global Fit U Summary The S Parameter In d dimension, √ � m 2 4 m 2 t − m 2 C tW 2 m W m t 5 1 m Z Z s 2 t α S = N c − γ + ln 4 π − ln µ 2 − 2 arctan + 2 . W 2 π 2 Λ 2 � 3 ǫ m Z 4 m 2 t − m 2 Z At tree level, need to include O WB = ( φ † τ I φ ) W I µν B µν , In the MS scheme, α S = 4 C WB ( µ ) v 2 s W c W Λ 2 √ � 4 m 2 t − m 2 − ln m 2 C tW 2 m W m t 5 m Z Z 3 s 2 t + N c µ 2 − 2 arctan + 2 W 2 π 2 Λ 2 � m Z 4 m 2 t − m 2 Z Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings S Oblique Parameters T A Global Fit U Summary The T Parameter T = 0 At tree level, need O ( 3 ) = ( φ † D µ φ )[( D µ φ ) † φ ] . φ v 2 T = − C ( 3 ) φ Λ 2 Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings S Oblique Parameters T A Global Fit U Summary The U Parameter U is finite, because there is no available counterterm at dimension-six. √ � � 2 4 m 2 t − m 2 m 2 m 2 m 2 � � � C tW 2 m W m t m Z s 2 Z t t W U = N c + − 1 ln 1 − − 2 arctan . W π 2 Λ 2 m 2 m 2 m 2 � m Z 4 m 2 t − m 2 W W t Z From PDG, U = 0 . 06 ± 0 . 10, for m t = 173 GeV and m h = 117 GeV , so C tW Λ 2 = − 0 . 7 ± 1 . 1 TeV − 2 . � C tW � 1 . 10 ± 2 . 06 TeV − 2 � ( from CDF ) , Λ 2 = − 0 . 79 ± 1 . 19 TeV − 2 ( from D0 ) . Note that we have negleted other dim-6 operators that contribute at tree level, except for O WB and O ( 3 ) φ . Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings S Oblique Parameters T A Global Fit U Summary The U Parameter U is finite, because there is no available counterterm at dimension-six. √ � � 2 4 m 2 t − m 2 m 2 m 2 m 2 � � � C tW 2 m W m t m Z s 2 Z t t W U = N c + − 1 ln 1 − − 2 arctan . W π 2 Λ 2 m 2 m 2 m 2 � m Z 4 m 2 t − m 2 W W t Z From PDG, U = 0 . 06 ± 0 . 10, for m t = 173 GeV and m h = 117 GeV , so C tW Λ 2 = − 0 . 7 ± 1 . 1 TeV − 2 . � C tW � 1 . 10 ± 2 . 06 TeV − 2 � ( from CDF ) , Λ 2 = − 0 . 79 ± 1 . 19 TeV − 2 ( from D0 ) . Note that we have negleted other dim-6 operators that contribute at tree level, except for O WB and O ( 3 ) φ . Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings S Oblique Parameters T A Global Fit U Summary The U Parameter U is finite, because there is no available counterterm at dimension-six. √ � � 2 4 m 2 t − m 2 m 2 m 2 m 2 � � � C tW 2 m W m t m Z s 2 Z t t W U = N c + − 1 ln 1 − − 2 arctan . W π 2 Λ 2 m 2 m 2 m 2 � m Z 4 m 2 t − m 2 W W t Z From PDG, U = 0 . 06 ± 0 . 10, for m t = 173 GeV and m h = 117 GeV , so C tW Λ 2 = − 0 . 7 ± 1 . 1 TeV − 2 . � C tW � 1 . 10 ± 2 . 06 TeV − 2 � ( from CDF ) , Λ 2 = − 0 . 79 ± 1 . 19 TeV − 2 ( from D0 ) . Note that we have negleted other dim-6 operators that contribute at tree level, except for O WB and O ( 3 ) φ . Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
Nonstandard Couplings Oblique Parameters Operators and Measurements A Global Fit Results Summary More operators and data... Operators O ( 3 ) O ( 1 ) φ q = i ( φ † τ I D µ φ )(¯ q γ µ τ I q ) , φ q = i ( φ † D µ φ )(¯ q γ µ q ) , O φ t = i ( φ † D µ φ )(¯ t γ µ t ) , O φ b = i ( φ † D µ φ )(¯ b γ µ b ) , q σ µν τ I t ) ˜ φ W I q σ µν τ I b ) φ W I O tW = (¯ O bW = (¯ µν , µν , q σ µν t ) ˜ q σ µν b ) φ B µν . O tB = (¯ φ B µν , O bB = (¯ Data Notation Measurement Z-pole Γ Z Total Z width σ had Hadronic cross section R f ( f = e , µ, τ, b , c ) Ratios of decay rates A 0 , f FB ( f = e , µ, τ, b , c , s ) Forward-backward asymmetries s 2 ¯ Hadronic charge asymmetry l A f ( f = e , µ, τ, b , c , s ) Polarized asymmetries Total cross sections for e + e − → f ¯ Fermion pair σ f ( f = q , µ, τ ) f Forward-backward asymmetries for e + e − → f ¯ A f production at LEP2 FB ( f = µ, τ ) f DIS Q W ( Cs ) Weak charge in Cs and Q W ( Tl ) Weak charge in Tl atomic parity violation Q W ( e ) Weak charge of the electron g 2 L , g 2 ν µ -nucleon scattering from NuTeV R g ν e V , g ν e ν - e scattering from CHARM II A W mass m W W mass from LEP and Tevatron Nicolas Greiner, Scott Willenbrock, Cen Zhang Constraints on Nonstandard Top Quark Couplings
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