Top quark decay with dimension-six operators at NLO in QCD Cen Zhang CP3, Université catholique de Louvain in collaboration with F. Maltoni May 2013, Pheno Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
Motivation In the SM, t → b + W has been calculated at NNLO in QCD. A. Czarnecki et al. 1005 . 2625 In Effective Field Theory, � 1 � L eff = L SM + Λ 2 C i O i + h . c . The dimension-six operators Modify W helicity fractions in t → b + W . Give rise to flavor changing decay t → c + V and t → c + h . A model-independent calculation of 2-body top decay, at O ( α s 1 Λ 2 ) . Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
Motivation Look for NP in FCNC decay channels t → c + V and t → c + h , and W helicity fractions in t → b + W . Understand NLO QCD calculation in Effective Field Theory. (Possible technical issues such as operator running and mixing, higher rank loop integrals, etc.) Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
Main decay channel Main decay channel t → bW t → bW helicity fraction with a general Wtb coupling. √ J.Drobnak et al. 1010 . 2402 2 i σ µν � � L tbW = g W ¯ a L γ µ P L − b LR √ t q ν P R + ( L ↔ R ) bW µ m t 2 a L , R and b LR , RL coming from ϕ q = i 1 ϕ † ← → � � O ( 3 ) (¯ Q γ µ τ I Q ) , ϕ + D µ ϕ )(¯ t γ µ b ) 2 y 2 D I O ϕϕ = iy 2 µ ϕ t ( ˜ t O tW = y t g W (¯ Q σ µν τ I t ) ˜ ϕ W I O bW = y t g W (¯ Q σ µν τ I b ) ϕ W I µν , µν t → bW helicity fraction with a CMDM operator. × O tG = g s (¯ Q L σ µν T A t R ) ˜ ϕ G A µν , Q L = ( t L , b L ) , ϕ = higgs Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
Flavor changing decay channel J. Drobnak et al. FCNC decay channel 1007 . 2552 t → cV , with dimension-four and five operators. √ J. J. Zhang et al. 1004 . 0898 L eff = v 2 q L γ µ t L )] + v Λ 2 a Z Λ 2 b Z q L σ µν t R )] L [ g Z Z µ (¯ LR [ g Z Z µν (¯ + v q L σ µν t R )] + v � � Λ 2 b γ Λ 2 b g g s G A q L σ µν T A t R ) LR [ eF µν (¯ µν (¯ LR + ( L ↔ R ) + h . c . Note in EFT we add ϕ to restore the full SM symmetry, i.e. � � µν ≡ O ( 13 ) g s G A q L σ µν T A t R ) q L σ µν T A t R ) ˜ ϕ G A µν (¯ → g s (¯ uG t → ch , through dimension-six operators. × O ( 23 ) O ( 32 ) t ( ϕ † ϕ )(¯ = − y 3 t ( ϕ † ϕ )(¯ = − y 3 LO: q L t R ) ˜ ϕ , Q L c R ) ˜ ϕ u ϕ u ϕ ( q L = ( c L , s L ) , Q L = ( t L , b L )) O ( 23 ) O ( 32 ) = y t g s (¯ = y t g s (¯ q L σ µν T A t R ) ˜ ϕ G A Q L σ µν T A c R ) ˜ ϕ G A NLO: µν , µν uG uG Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
Results Top color dipole contribution to W helicity fractions in main 1 decay channel. FC decay t → c + h . 2 Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
t → b + W , zero helicity Define W helicity fractions, Γ = Γ + + Γ 0 + Γ − , F i = Γ i / Γ NP effects from: Anomalous couplings of Wtb : 1 ϕ q = i 1 ϕ † ← → O ( 3 ) � � 2 y 2 D I (¯ Q γ µ τ I Q ) , O ϕϕ = iy 2 ϕ + D µ ϕ )(¯ t γ µ b ) µ ϕ t ( ˜ t O tW = y t g W (¯ O bW = y t g W (¯ Q σ µν τ I t ) ˜ ϕ W I Q σ µν τ I b ) ϕ W I µν , µν O ϕϕ , O bW constrained from b → s γ O ( 3 ) B. Grzadkowski et al. ϕ q does not change helicities. 0802 . 1413 Focus on O tW Top CMDM operator: O tG = y t g s (¯ Q L σ µν T A t R ) ˜ ϕ G A 2 µν Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
t → b + W , zero helicity Result on zero helicity fraction 1 TeV 2 F 0 = 0 . 689 − 0 . 040 C tW Λ 2 � � 1 TeV 2 1 TeV 2 + α s 0 . 005 C tW + 0 . 007 C tG Λ 2 Λ 2 Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
t → b + W , zero helicity CMS PAS TOP-12-025 Measurements from ttbar events ATLAS-CONF-2013-033 F 0 = 0 . 626 ± 0 . 034 ( stat . ) ± 0 . 048 ( syst . ) F − = 0 . 359 ± 0 . 021 ( stat . ) ± 0 . 028 ( syst . ) Constraints: LO C tW ( TeV ) 2 = 1 . 32 ± 0 . 86 Λ 2 NLO C tW ( TeV ) 2 = 1 . 168 + 0 . 015 C tG ( TeV ) 2 ± 0 . 86 Λ 2 Λ 2 Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
t → b + W , zero helicity, scale dependence The O ( α s ) mixing between O tG and O tW given by 2 � − � α s ( µ ) 3 β 0 2 C tG ( µ ) = C tG ( m t ) , β 0 = 11 − N f α s ( m t ) 3 4 2 4 � − � − � − � � � α s ( µ ) 3 β 0 − 2 C tG ( m t ) α s ( µ ) 3 β 0 − α s ( µ ) 3 β 0 C tW ( µ ) = C tW ( m t ) α s ( m t ) α s ( m t ) α s ( m t ) ( Λ = 1 TeV, C tw = 1) Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
t → c + h The tch coupling comes from O ( 23 ) O ( 32 ) = − y 3 t ( ϕ † ϕ )(¯ = − y 3 t ( ϕ † ϕ )(¯ q L t R ) ˜ ϕ , Q L u R ) ˜ ϕ u ϕ u ϕ J. A. Saavedraa et al. Typical value for BR( t → ch ) in SM and NP models hep-ph/0409342 SM Quark singlet 2HDM 2HDM (flavor conserving) MSSM 3 × 10 − 15 4 × 10 − 5 1 . 5 × 10 − 3 10 − 5 10 − 5 Indirect bounds from Z → c ¯ c : F. Larios et al. BR( t → ch ) < 3 × 10 − 3 hep-ph/0412222 3 σ discovery limits ( 100fb − 1 ): J. A. Saavedraa et al. BR( t → ch ) ≈ 5 . 8 × 10 − 5 hep-ph/0409342 corresponds to C u ϕ 0 . 3 ≈ Λ 2 1TeV 2 Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
t → c + h , diagrams Operators: O ( 23 ) = − y 3 t ( ϕ † ϕ )(¯ 1 q L t R ) ˜ ϕ u ϕ O ( 32 ) t ( ϕ † ϕ )(¯ = − y 3 Q L c R ) ˜ ϕ u ϕ O ( 23 ) = y t g s (¯ q L σ µν T A t R ) ˜ ϕ G A 2 µν uG O ( 32 ) = y t g s (¯ Q L σ µν T A c R ) ˜ ϕ G A µν uG NLO diagrams Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
t → c + h , result Operators: O ( 23 ) = − y 3 t ( ϕ † ϕ )(¯ 1 q L t R ) ˜ ϕ u ϕ O ( 32 ) t ( ϕ † ϕ )(¯ = − y 3 Q L c R ) ˜ ϕ u ϕ O ( 23 ) q L σ µν T A t R ) ˜ ϕ G A = y t g s (¯ 2 µν uG O ( 32 ) = y t g s (¯ Q L σ µν T A c R ) ˜ ϕ G A µν uG Result � 0 . 545 | C u ϕ | 2 + α s � 0 . 09 | C u ϕ | 2 − 0 . 25 Re C u ϕ C ∗ �� BR ( t → ch ) = uG � � 1 TeV 4 × 10 − 3 Λ 4 NLO correction can vary at 10 % level if C uG ∼ C u ϕ Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
t → c + h scale dependence The O ( α s ) mixing between O uG and O u ϕ 2 � − � α s ( µ ) 3 β 0 2 C uG ( µ ) = C uG ( m t ) , β 0 = 11 − N f α s ( m t ) 3 � 4 � 4 2 � − � � � α s ( µ ) 12 α s ( µ ) α s ( µ ) 3 β 0 β 0 + β 0 − C u ϕ ( µ ) = C u ϕ ( m t ) C uG ( m t ) α s ( m t ) 7 α s ( m t ) α s ( m t ) ( Λ = 1 TeV, C u ϕ = 1) Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
Summary We calculate t → b + W , t → c + V and t → c + h � α s � in EFT at order O . Λ 2 Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
Backup slides Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
t → b + W , positive helicity F + = Γ + / Γ , fraction of positively polarized W . In SM, F + = 0 at tree-level if m b = 0. F + = 0 . 0017 at NNLO in QCD including m b � = 0 A. Czarnecki et al. effects. 1005 . 2625 J. A. Saavedraa et al. Sensitivity for LHC ( L = 10 fb − 1 ): 0705 . 3041 F + ∼ ± 0 . 002. � 1 . 67 − 0 . 043 C tW 1 TeV 2 + ( − 0 . 52 C tW + 0 . 13 C tG ) α s × 1 TeV 2 � × 10 − 3 F + = Λ 2 Λ 2 Existing bounds O tW , from F 0 measurement C tW ∼ ( 0 . 3 , 2 . 0 ) O tG , from ttbar cross section C tG ∼ ( − 0 . 7 , 2 . 2 ) Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
α s contribution? In EFT, the order of operator mixing can depend on convention. . . Consider mixing between O ( 23 ) O ( 23 ) q L σ µν T A t R ) ˜ ϕ G A = − ( ϕ † ϕ )(¯ = (¯ and q L t R ) ˜ ϕ µν u ϕ uG δ Z ∼ g s y 2 (but expect g 2 s ) t Redefine O ( 23 ) O ( 23 ) q L σ µν T A t R ) ˜ ϕ G A = − y 3 t ( ϕ † ϕ )(¯ = y t g s (¯ q L t R ) ˜ ϕ and u ϕ µν uG ⇒ δ Z ∼ α s In general, start with 2 fermions, add top Yukawa y t for each additional Higgs field, and gauge coupling for each additional gauge field. Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
O ( α s ) mixing, flavor diagonal CP-even: Re C tG , Re C tW , Re C tB , Re C t ϕ , C ϕ G , C G : 1 9 0 0 0 0 6 8 Q σ µν T A t ) ˜ ϕ G A 1 1 O tG = y t g s (¯ 0 0 0 0 3 3 µν 5 1 2 α s 0 0 0 0 9 3 O tW = y t g W (¯ Q σ µν τ I t ) ˜ ϕ W I γ = − 4 0 0 − 1 0 0 µν π Nf Q σ µν t ) ˜ 1 6 − 11 O tB = y t g Y (¯ 0 0 0 0 ϕ B µν 2 4 Nf 6 + 7 0 0 0 0 0 O t ϕ = − y 3 t ( ϕ † ϕ )(¯ Qt ) ˜ ϕ 4 1 y 2 t ( ϕ † ϕ ) G A µν G µν A O ϕ G = CP-odd: Im C tG , Im C tW , Im C tB , Im C t ϕ , C ϕ ˜ G : 2 1 y 2 t ( ϕ † ϕ )˜ G A µν G µν A O ϕ ˜ G = 1 0 0 0 0 2 6 1 1 0 0 0 1 2 α s 3 3 g s f ABC G A ν µ G B ρ ν G C µ O G = 5 1 γ = 0 0 0 ρ 2 9 3 π − 4 0 0 − 1 0 Nf − 1 6 − 11 0 0 0 4 4 Cen Zhang Top quark decay with dimension-six operators at NLO in QCD
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