Effective Operators In Top Quark Production and Decay Cen Zhang - PowerPoint PPT Presentation

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Effective Operators In Top Quark Production and Decay Cen Zhang Department of Physics University of Illinois at Urbana-Champaign Pheno 2010 May 11

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Outline Introduction 1 Effective Field Theory Higher Dimensional Operators Anomalous Top Quark Interactions 2 Operators That Contribute at Leading Order Deviation From the SM: Top Quark Decay Deviation From the SM: Single Top Production Deviation From the SM: Top Pair Production The Anomalous Coupling Approach 3

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Effective Field Theory Effective Field Theory When searching for new physics beyond the SM, one might see it directly ( Z ′ , etc.) see indirect effects (for example, the exchange of Z ′ between fermions appears as four-fermion interaction at low energy.) In the latter case, we desire a model-independent approach to parameterize new physics.

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Effective Field Theory Effective Field Theory An effective field theory approach is a two step process. First, one integrates out all new heavy states and obtains effective interactions involving only fields of the SM. These effective higher-dimensional operators are then used to compute the deviations from the SM and compare with the experimental data. O ( 5 ) O ( 6 ) � � i i L eff = L SM + c i + c i Λ 2 + · · · Λ Λ can be regarded as the scale of new physics.

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary The Operators Higher Dimensional Operators Dimension 5: O 5 = c ij � � � φ T ǫ L j � L iT ǫφ C + h . c . Λ (Weinberg 1979) Dimension 6: 63 independent operators after the EOMs are applied. (Buchmuller and Wyler 1986, Aguilar-Saavedra 2009) There is no odd-dimensional operator that conserves baryon and lepton number.

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary The Operators Operators That Contribute to Top Quark Interaction 1 At leading order Λ 2 , ignore bottom quark mass, we found operator process O φ q = i ( φ + τ i D µ φ )(¯ q γ µ τ i q ) + h . c . top decay, single top q σ µν τ i t )˜ φ W i O tW = (¯ µν + h . c . top decay, single top q σ µν λ A t )˜ q , gg → t ¯ φ G A O tG φ = (¯ single top, q ¯ µν + h . c . t µ G B ρ ν G C µ gg → t ¯ O G 3 = g s f ABC G A ν t ρ O φ G = 1 gg → t ¯ 2 ( φ + φ ) G A µν G A µν t q γ µ q ) . and 8 four-fermions contact interactions such as (¯ u γ µ u )(¯

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Operators That Contribute at Leading Order The Wtb coupling O φ q = i ( φ + τ i D µ φ )(¯ q γ µ τ i q ) + h . c . q σ µν τ i t )˜ φ W i O tW = (¯ µν + h . c .

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Operators That Contribute at Leading Order The G 3 , Chromomagnetic Moment, and Higgs-Gluon Interactions q σ µν λ A u )˜ O tG φ = (¯ φ G A µν

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Operators That Contribute at Leading Order The G 3 , Chromomagnetic Moment, and Higgs-Gluon Interactions O G 3 = g s f ABC G A µ ρ G C ρ ν G B ν µ O φ G = 1 2 ( φ + φ ) G A µν G A µν

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Results: Top Quark Decay Top Quark Decay The W helicity fractions are given by: √ m 2 2 C tW v 2 m t m W ( m 2 t − m 2 − 4 W ) t F 0 = m 2 t + 2 m 2 Λ 2 ( m 2 t + 2 m 2 W ) 2 W √ 2 m 2 2 C tW v 2 m t m W ( m 2 t − m 2 W ) + 4 W F L = m 2 t + 2 m 2 Λ 2 ( m 2 t + 2 m 2 W ) 2 W F R = 0

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Results: Top Quark Decay Polarized Decay Rate In the top quark rest frame: d cos θ i = 1 + α i cos θ i 1 d Γ Γ 2 Effects of new operators √ − m 2 t − 2 m 2 2 vm t m 2 W ( m 2 t − m 2 W ) + C tW 16 W α b = m 2 t + 2 m 2 g Λ 2 ( m 2 t + 2 m 2 W ) 2 W m 6 t − 12 m 4 t m 2 W + 3 m 2 t m 4 W ( 3 + 8 ln ( m t / m W )) + 2 m 6 W α ν = m 6 t − 3 m 2 t m 4 W + 2 m 6 W √ 2 vm t m 2 W ( m 6 t − 6 m 4 t m 2 W + 3 m 2 t m 4 W ( 1 + 4 ln ( m t / m W )) + 2 m 6 24 W ) − C tW g Λ 2 ( m 2 t + 2 m 2 W ) 2 ( m 2 t − m 2 W ) 2 α ¯ = 1 e

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Results: Single Top Production s,t-Channel Single Top Cao, Wudka and Yuan, 2007 Feynman Diagrams s-channel √ g 4 u ( u − m 2 C φ qv 2 g 4 u ( u − m 2 g 2 u ( u − m 2 t ) t ) g 3 su t ) 2 CtW mt v W ) 2 + 2 Cqq 1 b | 2 = 4 Σ | M u ¯ W ) 2 + − d → t ¯ 4 ( s − m 2 2 Λ 2 ( s − m 2 Λ 2 ( s − m 2 Λ 2 s − m 2 W ) 2 W t-channel √ g 4 s ( s − m 2 C φ q v 2 g 4 s ( s − m 2 g 3 st g 2 s ( s − m 2 1 t ) t ) 2 C tW m t v 2 C qq t ) Σ | M ub → dt | 2 = W ) 2 + − W ) 2 + 4 ( t − m 2 2 Λ 2 ( t − m 2 W ) 2 Λ 2 ( t − m 2 Λ 2 t − m 2 4 W √ g 4 u ( u − m 2 C φ q v 2 g 4 u ( u − m 2 g 3 ut g 2 u ( u − m 2 1 t ) t ) 2 C tW m t v 2 C qq t ) ut | 2 = Σ | M ¯ + − W ) 2 + db → ¯ 4 ( t − m 2 W ) 2 2 Λ 2 ( t − m 2 W ) 2 Λ 2 ( t − m 2 Λ 2 t − m 2 4 W

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Results: Single Top Production Angular Dependence (at √ s = 2 m t ) s-channel t-channel( ¯ db → ¯ t-channel( ub → dt ) ut )

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Results: Top Pair Production gg → t ¯ t Channel Feynman Diagrams

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Results: Top Pair Production gg → t ¯ t Channel Cho and Simmons, 1994 The squared amplitude: ( m 2 − t )( m 2 − u ) 256 | M | 2 = 3 g 4 − g 4 ( m 2 − t )( m 2 − u ) + g 4 m 2 ( s − 4 m 2 ) tu − m 2 ( 3 t + u ) − m 4 1 s s s ( m 2 − t ) 2 s 2 4 24 6 + g 4 tu − m 2 ( t + 3 u ) − m 4 − 3 g 4 tu − 2 m 2 t + m 4 − 3 g 4 tu − 2 m 2 u + m 4 s s s ( m 2 − u ) 2 s ( m 2 − t ) s ( m 2 − u ) 6 8 8 √ 4 s 2 − 9 tu − 9 m 2 s + 9 m 4 2 C tG φ g 3 + 9 C G 3 g 4 m 2 ( t − u ) 2 s vm s + ( m 2 − t )( m 2 − u ) ( m 2 − t )( m 2 − u ) 3 Λ 2 8 Λ 2 − C φ G g 2 s m 2 s 2 ( s − 4 m 2 ) 16 Λ 2 ( s − m 2 )( t − m 2 )( u − m 2 )

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Results: Top Pair Production u , d ¯ d → t ¯ u ¯ t Channel Result √ 2 C tG φ g 3 s ( M 1 + M 2 ) + 32 s vm 1 s s t | 2 g 2 + C 1 Λ 2 M 1 + C 2 36 | M u ¯ = Λ 2 M 2 u → t ¯ u u 9 Λ 2 √ 2 C tG φ g 3 1 s ( M 1 + M 2 ) + 32 s vm s s t | 2 g 2 + C 1 Λ 2 M 1 + C 2 36 | M d ¯ = Λ 2 M 2 d → t ¯ d d 9 Λ 2 where 1 O 1 q 1 γ µ λ A q 1 )(¯ q 3 γ µ λ A q 3 ) (¯ = 4 q 4 4 g 2 9 s 2 ( 3 m 4 − m 2 ( t + 3 u ) + u 2 ) s 1 M 1 = q 1 γ µ τ i λ A q 1 )(¯ q 3 γ µ τ i λ A q 3 ) O 2 (¯ = 4 q 4 4 g 2 9 s 2 ( 3 m 4 − m 2 ( 3 t + u ) + t 2 ) 1 s M 2 = O 3 u 1 γ µ λ A u 1 )(¯ u 3 γ µ λ A u 3 ) = (¯ 4 q 4 C 1 C 1 4 q + C 2 4 q + C 3 = 1 O 4 d 1 γ µ λ A d 1 )(¯ u 3 γ µ λ A u 3 ) u 4 q (¯ = 4 q 4 C 2 C 5 4 q + C 7 = u 4 q O 5 q 3 u 1 )(¯ u 1 q 3 ) (¯ = 4 q C 1 C 1 4 q − C 2 4 q + C 4 = d 4 q O 6 q 3 d 1 )(¯ d 1 q 3 ) (¯ = 4 q C 2 C 6 4 q + C 7 = d 4 q O 7 q 1 u 3 )(¯ u 3 q 1 ) = (¯ 4 q

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Anomalous Couplings Compared with Effective Operators Wtb vertex: b i σµν q ν g g ¯ b Γ µ tW − ¯ b γ µ ( V L P L + V R P R ) tW − ¯ ( g L P L + g R P R ) tW − µ = µ + √ √ µ MW 2 2 √ v 2 2 C tW v 2 V L = 1 + C ∗ g R = φ q Λ 2 Λ 2 O φ q = i ( φ † τ i D µ φ )(¯ q γ µ τ i q ) q σ µν τ i t ) ˜ φ W i O tW = (¯ µν 1 ( V R and g L do not enter at order Λ 2 .) gtt vertex: t λ a i σµν q ν t λ a ¯ t Γ µ a tG a µ = g s ¯ 2 γ µ tG a µ + g s ¯ ( d V + id A γ 5 ) tG a µ mt √ √ vmt vmt 2 2 d V = gs Re C tG φ d A = gs Im C tG φ Λ 2 Λ 2 q σ µν λ a t ) ˜ φ G a O tG φ = (¯ µν

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Summary The effective theory is a model-independent approach to parameterize new physics beyond the SM. The anomalous top quark interaction can be described using 13 dimensions-six operators. The anomalous couplings can be related to the coefficients of the effective operators.

Introduction Anomalous Top Quark Interactions The Anomalous Coupling Approach Summary Summary The effective theory is a model-independent approach to parameterize new physics beyond the SM. The anomalous top quark interaction can be described using 13 dimensions-six operators. The anomalous couplings can be related to the coefficients of the effective operators.