Top quark decay with dimension-six operators at NLO in QCD Cen - - PowerPoint PPT Presentation

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,

Leff = LSM + 1 Λ2 CiOi + 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(αs 1

Λ2 ).

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

LtbW = gW √ 2 ¯ t

• aLγµPL − bLR

2iσµν mt qνPR + (L ↔ R)

• bWµ

aL,R and bLR,RL coming from O(3)

ϕq = i 1

2 y2

t

• ϕ†←

→ D I

µϕ

• (¯

Qγµτ IQ) , Oϕϕ = iy2

t ( ˜

ϕ+Dµϕ)(¯ tγµb) OtW = ytgW (¯ Qσµντ It) ˜ ϕW I

µν ,

ObW = ytgW (¯ Qσµντ Ib)ϕW I

µν

t → bW helicity fraction with a CMDM operator. × OtG = gs(¯ QLσµνT AtR) ˜ ϕGA

µν,

QL = (tL, bL) , ϕ = higgs

Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

Flavor changing decay channel

FCNC decay channel

• J. Drobnak et al.

1007.2552

t → cV, with dimension-four and five operators. √

• J. J. Zhang et al.

1004.0898

Leff = v2 Λ2 aZ

L [gZ Zµ(¯

qLγµtL)] + v Λ2 bZ

LR [gZ Zµν(¯

qLσµνtR)] + v Λ2 bγ

LR [eFµν(¯

qLσµνtR)] + v Λ2 bg

LR

• gsGA

µν(¯

qLσµνTAtR)

• + (L ↔ R) + h.c.

Note in EFT we add ϕ to restore the full SM symmetry, i.e.

• gsGA

µν(¯

qLσµνTAtR)

• → gs(¯

qLσµνT AtR) ˜ ϕGA

µν ≡ O(13) uG

t → ch, through dimension-six operators. × LO: O(23)

uϕ

= −y3

t (ϕ†ϕ)(¯

qLtR) ˜ ϕ , O(32)

uϕ

= −y3

t (ϕ†ϕ)(¯

QLcR) ˜ ϕ (qL = (cL, sL), QL = (tL, bL)) NLO: O(23)

uG

= ytgs(¯ qLσµνT AtR) ˜ ϕGA

µν ,

O(32)

uG

= ytgs(¯ QLσµνT AcR) ˜ ϕGA

µν Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

Results

1

Top color dipole contribution to W helicity fractions in main decay channel.

2

FC decay t → c + h.

Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

t → b + W, zero helicity

Define W helicity fractions, Γ = Γ+ + Γ0 + Γ− , Fi = Γi/Γ NP effects from:

1

Anomalous couplings of Wtb: O(3)

ϕq = i 1

2 y2

t

• ϕ†←

→ D I

µϕ

• (¯

Qγµτ IQ) , Oϕϕ = iy2

t ( ˜

ϕ+Dµϕ)(¯ tγµb) OtW = ytgW (¯ Qσµντ It) ˜ ϕW I

µν ,

ObW = ytgW (¯ Qσµντ Ib)ϕW I

µν

Oϕϕ, ObW constrained from b → sγ O(3)

ϕq does not change helicities.

• B. Grzadkowski et al.

0802.1413

Focus on OtW

2

Top CMDM operator: OtG = ytgs(¯ QLσµνT AtR) ˜ ϕGA

µν Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

t → b + W, zero helicity

Result on zero helicity fraction F0 =0.689 − 0.040CtW 1TeV2 Λ2 + αs

• 0.005CtW

1TeV2 Λ2 + 0.007CtG 1TeV2 Λ2

• Cen Zhang

Top quark decay with dimension-six operators at NLO in QCD

t → b + W, zero helicity

Measurements from ttbar events

CMS PAS TOP-12-025 ATLAS-CONF-2013-033

F0 = 0.626 ± 0.034(stat.) ± 0.048(syst.) F− = 0.359 ± 0.021(stat.) ± 0.028(syst.) Constraints: LO CtW (TeV)2 Λ2 = 1.32 ± 0.86 NLO CtW (TeV)2 Λ2 = 1.168 + 0.015CtG(TeV)2 Λ2 ± 0.86

Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

t → b + W, zero helicity, scale dependence

The O(αs) mixing between OtG and OtW given by

CtG(µ) =CtG(mt )

• αs(µ)

αs(mt ) −

2 3β0

, β0 = 11 − 2 3 Nf CtW (µ) =CtW (mt )

• αs(µ)

αs(mt ) −

4 3β0 − 2CtG(mt )

  

• αs(µ)

αs(mt ) −

2 3β0 −

• αs(µ)

αs(mt ) −

4 3β0

   (Λ = 1 TeV, Ctw = 1) Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

t → c + h

The tch coupling comes from

O(23)

uϕ

= −y3

t (ϕ†ϕ)(¯

qLtR) ˜ ϕ , O(32)

uϕ

= −y3

t (ϕ†ϕ)(¯

QLuR) ˜ ϕ Typical value for BR(t → ch) in SM and NP models

• J. A. Saavedraa et al.

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: BR(t → ch)< 3 × 10−3

• F. Larios et al.

hep-ph/0412222

3σ discovery limits (100fb−1): BR(t → ch)≈ 5.8 × 10−5

• J. A. Saavedraa et al.

hep-ph/0409342

corresponds to Cuϕ

Λ2

≈

0.3 1TeV2 Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

t → c + h, diagrams

Operators:

1

O(23)

uϕ

= −y3

t (ϕ†ϕ)(¯

qLtR) ˜ ϕ O(32)

uϕ

= −y3

t (ϕ†ϕ)(¯

QLcR) ˜ ϕ

2

O(23)

uG

= ytgs(¯ qLσµνT AtR) ˜ ϕGA

µν

O(32)

uG

= ytgs(¯ QLσµνT AcR) ˜ ϕGA

µν

NLO diagrams

Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

t → c + h, result

Operators:

1

O(23)

uϕ

= −y3

t (ϕ†ϕ)(¯

qLtR) ˜ ϕ O(32)

uϕ

= −y3

t (ϕ†ϕ)(¯

QLcR) ˜ ϕ

2

O(23)

uG

= ytgs(¯ qLσµνT AtR) ˜ ϕGA

µν

O(32)

uG

= ytgs(¯ QLσµνT AcR) ˜ ϕGA

µν

Result BR(t → ch) =

• 0.545|Cuϕ|2 + αs
• 0.09|Cuϕ|2 − 0.25ReCuϕC∗

uG

• × 10−3
• 1TeV4

Λ4

• NLO correction can vary at 10% level if CuG ∼ Cuϕ

Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

t → c + h scale dependence

The O(αs) mixing between OuG and Ouϕ CuG(µ) =CuG(mt )

• αs(µ)

αs(mt ) −

2 3β0

, β0 = 11 − 2 3 Nf Cuϕ(µ) =Cuϕ(mt )

• αs(µ)

αs(mt ) 4

β0 +

12 7 CuG(mt )   

• αs(µ)

αs(mt ) 4

β0 −

• αs(µ)

αs(mt ) −

2 3β0

   (Λ = 1 TeV, Cuϕ = 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 in EFT at order O αs

Λ2

• .

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 mb = 0. F+ = 0.0017 at NNLO in QCD including mb = 0 effects.

• A. Czarnecki et al.

1005.2625

Sensitivity for LHC (L = 10fb−1):

• J. A. Saavedraa et al.

0705.3041

F+ ∼ ±0.002.

F+ =

• 1.67 − 0.043CtW 1TeV2

Λ2

+ (−0.52CtW + 0.13CtG) αs×1TeV2

Λ2

• × 10−3

Existing bounds OtW , from F0 measurement CtW ∼ (0.3, 2.0) OtG, from ttbar cross section CtG ∼ (−0.7, 2.2)

Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

αs contribution?

In EFT, the order of operator mixing can depend on convention. . . Consider mixing between O(23)

uG

= (¯ qLσµνT AtR) ˜ ϕGA

µν

and O(23)

uϕ

= −(ϕ†ϕ)(¯ qLtR) ˜ ϕ δZ ∼ gsy2

t

(but expect g2

s )

Redefine O(23)

uG

= ytgs(¯ qLσµνT AtR) ˜ ϕGA

µν

and O(23)

uϕ

= −y3

t (ϕ†ϕ)(¯

qLtR) ˜ ϕ ⇒ δZ ∼ αs In general, start with 2 fermions, add top Yukawa yt 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(αs) mixing, flavor diagonal

OtG = yt gs(¯ QσµνT At) ˜ ϕGA

µν

OtW = yt gW (¯ QσµντIt) ˜ ϕW I

µν

OtB = yt gY (¯ Qσµνt) ˜ ϕBµν Otϕ = −y3

t (ϕ†ϕ)(¯

Qt) ˜ ϕ OϕG = 1 2 y2

t (ϕ†ϕ)GA µνGµνA

Oϕ˜

G =

1 2 y2

t (ϕ†ϕ)˜

GA

µνGµνA

OG = 1 2 gsf ABCGAν

µ GBρ ν GCµ ρ

CP-even: ReCtG, ReCtW , ReCtB, ReCtϕ, CϕG, CG: γ = 2αs π          

1 6 9 8 1 3 1 3 5 9 1 3

−4 −1

1 2 Nf 6 − 11 4 Nf 6 + 7 4

          CP-odd: ImCtG, ImCtW , ImCtB, ImCtϕ, Cϕ˜

G:

γ = 2αs π       

1 6 1 3 1 3 5 9 1 3

−4 −1 − 1

4 Nf 6 − 11 4

       Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

O(αs) mixing, flavor diagonal

ObG = yt gs(¯ QσµνT Ab)ϕGA

µν

ObW = yt gW (¯ QσµντIb)ϕW I

µν

ObB = yt gY (¯ Qσµνb)ϕBµν Obϕ = −y3

t (ϕ†ϕ)(¯

Qb)ϕ CtG, CtW , CtB, Ctϕ: γ = 2αs π     

1 6 1 3 1 3

− 1

9 1 3

−1      and γ = 0 for O(3)

ϕQ = i

1 2 y2

t

• ϕ†←

→ D I

µϕ

• (¯

QγµτIQ) , O(1)

ϕQ = i

1 2 y2

t

• ϕ†←

→ D µϕ

• (¯

QγµQ) Oϕt = i 1 2 y2

t

• ϕ†←

→ D µϕ

• (¯

tγµt) , Oϕb = i 1 2 y2

t

• ϕ†←

→ D µϕ

• (¯

bγµb) , Oϕϕ = iy2

t ( ˜

ϕ+Dµϕ)(¯ tγµb) Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

O(αs) mixing, flavor changing

O(13)

uG

= yt gs(¯ qσµνT At) ˜ ϕGA

µν

O(13)

uW

= yt gW (¯ qσµντIt) ˜ ϕW I

µν

O(13)

uB

= yt gY (¯ qσµνt) ˜ ϕBµν O(13)

uϕ

= −y3

t (ϕ†ϕ)(¯

qt) ˜ ϕ γ = 2αs π     

1 6 1 3 1 3 5 9 1 3

−2 −1      O(13)

dG

= yt gs(¯ qσµνT Ab)ϕGA

µν

O(13)

dW

= yt gW (¯ qσµντIb)ϕW I

µν

O(13)

dB

= yt gY (¯ qσµνb)ϕBµν O(13)

dϕ = −y3 t (ϕ†ϕ)(¯

qb)ϕ γ = 2αs π     

1 6 1 3 1 3

− 1

9 1 3

−1      and γ = 0 for O(3,1+3)

ϕq

= i 1 2 y2

t

• ϕ†←

→ D I

µϕ

• (¯

qγµτIQ) O(1,1+3)

ϕq

= i 1 2 y2

t

• ϕ†←

→ D µϕ

• (¯

qγµQ) Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

O(αs) mixing, flavor changing

O(31)

uG

= yt gs(¯ QσµνT Au) ˜ ϕGA

µν

O(31)

uW

= yt gW (¯ QσµντIu) ˜ ϕW I

µν

O(31)

uB

= yt gY (¯ Qσµνu) ˜ ϕBµν O(31)

uϕ

= −y3

t (ϕ†ϕ)(¯

Qu) ˜ ϕ γ = 2αs π     

1 6 1 3 1 3 5 9 1 3

−2 −1      O(31)

dG

= yt gs(¯ QσµνT Ad)ϕGA

µν

O(31)

dW

= yt gW (¯ QσµντId)ϕW I

µν

O(31)

dB

= yt gY (¯ Qσµνd)ϕBµν O(31)

dϕ = −y3 t (ϕ†ϕ)(¯

Qd)ϕ γ = 2αs π     

1 6 1 3 1 3

− 1

9 1 3

−1      and γ = 0 for O(1+3)

ϕu

= i 1 2 y2

t

• ϕ†←

→ D µϕ

• (¯

tγµu) O(1+3)

ϕd

= i 1 2 y2

t

• ϕ†←

→ D µϕ

• (¯

bγµd) O(13)

ϕϕ = iy2 t ( ˜

ϕ+Dµϕ)(¯ tγµd) O(31)

ϕϕ = iy2 t (ϕ+Dµ ˜

ϕ)(¯ bγµu) Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

Analytical result, t → b + W

x = mW /mt Γ(+) = ReCtG Λ2 ααsm3

t

6πs2

W x2

• x log(x)
• (1 + x)3 log(1 + x) − (1 − x)3 log(1 − x)
• − 2x2(1 − x2) log(1 + x)

+x2 (x − 1)(x + 9)/2 + (2 + x2)π2/3 − (2 + 3x2) log x

• +x
• (x3 − 3x2 + 3x − 1)Li2(x) + (3x3 + 3x2 + 5x + 1)Li2(−x)
• Γ(0) =

ReCtG Λ2 ααsm3

t

6πs2

W x2

• x2(1 − x2)2 log

mt2 µ2 − (1 − x2)3 log(1 − x2) − 2x log x

• (1 + x)3 log(1 + x) − (1 − x)3 log(1 − x) −

x 2 (9x2 + 4)

• − (26x6 + 33x4 − 66x2 + 7)/12 − π2x2(3 + x2)/3 + 2x
• (1 − x)3Li2(x) − (1 + x)3Li2(−x)

Γ(−) = ReCtG Λ2 ααsm3

t

6πs2

W x2

• 2x2(1 − x2)2 log

mt2 µ2 + x log x

• (1 + x)3 log(1 + x) − (1 − x)3 log(1 − x)
• − (1 − x2)
• (1 − 4x2 + x4) log(1 + x) + (1 − x2)2 log(1 − x)
• − x2(2 + 3x2) log x

− x2 2 (11x4 − 31x2 + 8x + 12) + π2x2 3 − x

• (1 − 3x + 3x2 − x3)Li2(x) − (1 + x + 3x2 − x3)Li2(−x)

Cen Zhang Top quark decay with dimension-six operators at NLO in QCD

Analytical result, t → c + h

Γ(0) = |Cuϕ|2 Λ4 αm7

t

8m2

W s2 W

• 1 −

m2

H

m2

t

2 x = mH/mt Γ(1) Γ(0) = αs 36π(1 − x2)2 |CuG|2 |Cuϕ|2

• x8 − 8x6 − 342x4 + 620x2 − 271

+ 6x

• 4 − x2(26 − 5x2)
• π − 6 sin−1 x

2

• + 12(9x4 + 76x2 − 8) log x
• −

2αs 9π(1 − x2)2 Re(CuGC∗

uϕ)

|Cuϕ|2

• 6
• 6(1 − x2)2 log

mt µ + (5x4 + 2x2 + 4 log(1 − x2) − 2 log x) log x +  

• 4

x2 − 1(x4 − 6x2 + 8) + 2π   sin−1 x 2 + 6

• sin−1 x

2 2 + 12

• Li2(x2) − 2ReLi2

 

• x −

1 x   x 2 − i

• 1 −

x2 4    

• +
• 3π
• 4 − x2(x2 − 2)x − 3(x4 + 8x2 − 9)x2 − 5π2

− αs 9π 36 log mt µ + 4π2 − 51

• + 24Li2x2 + 24 log x log(1 − x2)

+ 24 x2 1 − x2 log x + 6

• 5 −

2 x2

• log(1 − x2)
• Cen Zhang

Top quark decay with dimension-six operators at NLO in QCD