Acoplamientos anmalos del quark top: la preparacin terica para los - - PowerPoint PPT Presentation

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Acoplamientos anómalos del quark top: la preparación teórica para los datos

• J. A. Aguilar-Saavedra

Departamento de Física Teórica y del Cosmos Universidad de Granada

Universidad Complutense de Madrid, 16 abril de 2010

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Based on

JAAS, J. Carvalho, N. Castro, A. Onofre, F. Veloso, “Probing anomalous Wtb couplings in top pair decays”, EPJC ’07 JAAS, J. Carvalho, N. Castro, A. Onofre, F. Veloso, “ATLAS sensitivity to Wtb anomalous couplings in top quark decays”, EPJC ’08 JAAS, “Single top quark production at LHC with anomalous Wtb couplings”, NPB ’08 JAAS, “A minimal set of top anomalous couplings”, NPB ’09 JAAS, “A minimal set of top-Higgs anomalous couplings”, NPB ’09 JAAS, “Zt, γt and t production at hadron colliders via strong flavour-changing neutral couplings”, hep-ph ’09 JAAS, J. Bernabéu, coming soon

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Reminder The top quark program

The LHC top physics program aims to study the top quark with precision and possibly discover new physics

➀ The top quark as a window to new physics

couplings, rare decays

☞

t¯ t resonances

➁ The top quark to clean other windows to new physics

mass

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Top anomalous couplings: the preparation for data

• r the road from Lagrangians to measurements

➀ Set up the Lagrangians ➙

Which couplings are we really going to measure?

➁ Identify the observables and their dependence on couplings ➙

How are we going to extract couplings from experiment?

➂ Create tools for LHC analyses ➙

Topfit and Protos

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Lagrangians for anomalous couplings Framework: gauge-invariant effective operators

L = L4 + L6 + . . . where L4 = LSM

➙

SM Lagrangian L6 =

• x

αx Λ2 Ox

➙

Ox gauge-invariant building blocks Parameterise effects of new physics at scale Λ > v

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Gauge-invariant effective operators

Many effective operators can be written in general New physics contributions: some combination of them Not all of them independent

➙

related by equations of motion for free fields Important: the relations obtained from these equations are also valid for off-shell interactions

[Georgi NPB ’91 . . . ]

Huge effort to classify dim-6 effective operators removing redundant ones

[Buchmuller, Wyler NPB ’86]

☞

Most of work done . . . but still some redundant!

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Pictures for non-fans

A geometrical analogy To parameterise the plane, two linearly independent vectors are sufficient Three are too many, drop one!

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Pictures for non-fans

A geometrical analogy To parameterise the plane, two linearly independent vectors are sufficient One can use an orthonormal basis . . .

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Pictures for non-fans

A geometrical analogy To parameterise the plane, two linearly independent vectors are sufficient One can use a non-orthonomal one . . .

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Pictures for non-fans

A geometrical analogy To parameterise the plane, two linearly independent vectors are sufficient Results basis-independent . . . . . . but amount of work not! Orthonormal basis easier for calculations Important: look for a minimal basis to parameterise new physics

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Operators involving top trilinear interactions

O(3,ij)

φq

= i(φ†τ IDµφ)(¯ qLiγµτ IqLj) Oij

Du = (¯

qLi DµuRj) Dµ ˜ φ O(1,ij)

φq

= i(φ†Dµφ)(¯ qLiγµqLj) Oij

¯ Du = (Dµ¯

qLi uRj) Dµ ˜ φ Oij

φφ = i(˜

φ†Dµφ)(¯ uRiγµdRj) Oij

Dd = (¯

qLi DµdRj) Dµ φ Oij

φu = i(φ†Dµφ)(¯

uRiγµuRj) Oij

¯ Dd = (Dµ¯

qLi dRj) Dµ φ Oij

uW = (¯

qLiσµντ IuRj)˜ φ WI

µν

Oij

qW = ¯

qLiγµτ IDνqLjWI

µν

Oij

dW = (¯

qLiσµντ IdRj)φ WI

µν

Oij

qB = ¯

qLiγµDνqLjBµν Oij

uBφ = (¯

qLiσµνuRj)˜ φ Bµν Oij

uB = ¯

uRiγµDνuRjBµν Oij

uGφ = (¯

qLiλaσµνuRj)˜ φ Ga

µν

Oij

qG = ¯

qLiλaγµDνqLjGa

µν

Oij

uφ = (φ†φ)(¯

qLiuRj ˜ φ) Oij

uG = ¯

uRiλaγµDνuRjGa

µν

[Buchmuller, Wyler NPB ’86]

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Operators involving top trilinear interactions

O(3,ij)

φq

= i(φ†τ IDµφ)(¯ qLiγµτ IqLj) Oij

Du = (¯

qLi DµuRj) Dµ ˜ φ O(1,ij)

φq

= i(φ†Dµφ)(¯ qLiγµqLj) Oij

¯ Du = (Dµ¯

qLi uRj) Dµ ˜ φ Oij

φφ = i(˜

φ†Dµφ)(¯ uRiγµdRj) Oij

Dd = (¯

qLi DµdRj) Dµ φ Oij

φu = i(φ†Dµφ)(¯

uRiγµuRj) Oij

¯ Dd = (Dµ¯

qLi dRj) Dµ φ Oij

uW = (¯

qLiσµντ IuRj)˜ φ WI

µν

Oij

qW = ¯

qLiγµτ IDνqLjWI

µν

Oij

dW = (¯

qLiσµντ IdRj)φ WI

µν

Oij

qB = ¯

qLiγµDνqLjBµν Oij

uBφ = (¯

qLiσµνuRj)˜ φ Bµν Oij

uB = ¯

uRiγµDνuRjBµν Oij

uGφ = (¯

qLiλaσµνuRj)˜ φ Ga

µν

Oij

qG = ¯

qLiλaγµDνqLjGa

µν

Oij

uφ = (φ†φ)(¯

qLiuRj ˜ φ) Oij

uG = ¯

uRiλaγµDνuRjGa

µν

redundants dropped [Rattazzi, PhD Thesis] [Grzadkowski et al NPB ’04]

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Operators involving top trilinear interactions

O(3,ij)

φq

= i(φ†τ IDµφ)(¯ qLiγµτ IqLj) Oij

Du = (¯

qLi DµuRj) Dµ ˜ φ O(1,ij)

φq

= i(φ†Dµφ)(¯ qLiγµqLj) Oij

¯ Du = (Dµ¯

qLi uRj) Dµ ˜ φ Oij

φφ = i(˜

φ†Dµφ)(¯ uRiγµdRj) Oij

Dd = (¯

qLi DµdRj) Dµ φ Oij

φu = i(φ†Dµφ)(¯

uRiγµuRj) Oij

¯ Dd = (Dµ¯

qLi dRj) Dµ φ Oij

uW = (¯

qLiσµντ IuRj)˜ φ WI

µν

Oij

qW = ¯

qLiγµτ IDνqLjWI

µν

Oij

dW = (¯

qLiσµντ IdRj)φ WI

µν

Oij

qB = ¯

qLiγµDνqLjBµν Oij

uBφ = (¯

qLiσµνuRj)˜ φ Bµν Oij

uB = ¯

uRiγµDνuRjBµν Oij

uGφ = (¯

qLiλaσµνuRj)˜ φ Ga

µν

Oij

qG = ¯

qLiλaγµDνqLjGa

µν

Oij

uφ = (φ†φ)(¯

qLiuRj ˜ φ) Oij

uG = ¯

uRiλaγµDνuRjGa

µν

redundants dropped [JAAS NPB ’09]

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Operators involving top trilinear interactions

O(3,i+j)

φq

= 1/2 [O(3,ij)

φq

+ (O(3,ji)

φq

)†] i ≤ j Oij

Du = (¯

qLi DµuRj) Dµ ˜ φ O(1,i+j)

φq

= 1/2 [O(1,ij)

φq

+ (O(1,ji)

φq

)†] i ≤ j Oij

¯ Du = (Dµ¯

qLi uRj) Dµ ˜ φ Oij

φφ = i(˜

φ†Dµφ)(¯ uRiγµdRj) Oij

Dd = (¯

qLi DµdRj) Dµ φ Oi+j

φu = 1/2 [Oij φu + (Oji φu)†]

i ≤ j Oij

¯ Dd = (Dµ¯

qLi dRj) Dµ φ Oij

uW = (¯

qLiσµντ IuRj)˜ φ WI

µν

Oij

qW = ¯

qLiγµτ IDνqLjWI

µν

Oij

dW = (¯

qLiσµντ IdRj)φ WI

µν

Oij

qB = ¯

qLiγµDνqLjBµν Oij

uBφ = (¯

qLiσµνuRj)˜ φ Bµν Oij

uB = ¯

uRiγµDνuRjBµν Oij

uGφ = (¯

qLiλaσµνuRj)˜ φ Ga

µν

Oij

qG = ¯

qLiλaγµDνqLjGa

µν

Oij

uφ = (φ†φ)(¯

qLiuRj ˜ φ) Oij

uG = ¯

uRiλaγµDνuRjGa

µν

redundant combinations Oij

φq − (O ji φq)†

[JAAS NPB ’09] and Oij

φu − (O ji φu)† dropped

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Frequently asked questions Q: You are using the equations of motion. What you do is process-dependent, valid only for on-shell particles. A: No. Using the gauge-invariant EOM amounts to a field redefinition which leaves the path integral invariant up to higher-order terms. Q: You are changing the basis of Buchmüller & Wyler by some

• ther, to simplify top interactions.

A: No. I’m just dropping operators from that basis without introducing new ones. Q: Then, are there several redundant operators in the B & W basis? A: Indeed. Let’s see.

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Technical details for fans

Oij

qW,

Oij

qB,

Oij

uB,

Oij

qG,

Oij

uG

Oij

x = 1

2

• Oij

x + (O ji x )†

+ 1 2

• Oij

x − (O ji x )†

• int. by parts & gauge field EOM

Oij

qW + (O ji qW)†

= g 4 h O(3,ij)

φq

+ (O(3,ji)

φq

)†i + g 4 O(3,kkij)

lq

+ g 3 O(1,1,ikkj)

qq

+g 2 O(8,1,ikkj)

qq

− g 2 O(1,1,ijkk)

qq

Oij

qB + (O ji qB)†

= g 4 h O(1,ij)

φq

+ (O(1,ji)

φq

)†i − g′ 4 O(1,kkij)

lq

+ g′ Oikkj

qe + g′

6 O(1,1,ijkk)

qq

−2g′ 9 O(1,ikkj)

qu

− g′ 3 O(8,ikkj)

qu

+ g′ 9 O(1,ikkj)

qd

− g′ 6 O(8,ikkj)

qd

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Technical details for fans

Oij

qW,

Oij

qB,

Oij

uB,

Oij

qG,

Oij

uG

Oij

x = 1

2

• Oij

x + (O ji x )†

+ 1 2

• Oij

x − (O ji x )†

• int. by parts & gauge field EOM

Oij

uB + (O ji uB)†

= g 4 h Oij

φu + (Oji φu)†i

+ g′ 2 Okjik

lu − g′

2 Okkij

eu − g′

18 O(1,kjik)

qu

− g′ 12 O(8,kjik)

qu

+ 2g′ 3 O(1,ijkk)

uu

− g′ 6 O(1,ijkk)

ud

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Technical details for fans

Oij

qW,

Oij

qB,

Oij

uB,

Oij

qG,

Oij

uG

Oij

x = 1

2

• Oij

x + (O ji x )†

+ 1 2

• Oij

x − (O ji x )†

• int. by parts & gauge field EOM

Oij

qG + (O ji qG)†

= gs 2 O(8,1,ijkk)

qq

− 8gs 9 O(1,ikkj)

qu

+ gs 6 O(8,ikkj)

qu

− 8gs 9 O(1,ikkj)

qd

+gs 6 O(8,ikkj)

qd

Oij

uG + (O ji uG)†

= −8gs 9 O(1,kjik)

qu

+ gs 6 O(8,kjik)

qu

+ gs O(1,ikkj)

uu

− gs 3 O(1,ijkk)

uu

+gs 4 O(8,ijkk)

ud

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Technical details for fans

Oij

qW,

Oij

qB,

Oij

uB,

Oij

qG,

Oij

uG

Oij

x = 1

2

• Oij

x + (O ji x )†

+ 1 2

• Oij

x − (O ji x )†

dual fields & quark EOM & Bianchi

Oij

qW − (O ji qW)†

= −1 4 h Yu

jk Oik uW + Yd jk Oik dW − Yu† ki (Ojk uW)† − Yd† ki (Ojk dW)†i

Oij

qB − (O ji qB)†

= −1 4 h Yu

jk Oik uBφ + Yd jk Oik dBφ − Yu† ki (Ojk uBφ)† − Yd† ki (Ojk dBφ)†i

Oij

uB − (O ji uB)†

= 1 4 h Yu

ki Okj uBφ − Yu† jk (Oki uBφ)†i

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Technical details for fans

Oij

qW,

Oij

qB,

Oij

uB,

Oij

qG,

Oij

uG

Oij

x = 1

2

• Oij

x + (O ji x )†

+ 1 2

• Oij

x − (O ji x )†

dual fields & quark EOM & Bianchi

Oij

qG − (O ji qG)†

= −1 4 h Yu

jk Oik uGφ + Yd jk Oik dGφ − Yu† ki (Ojk uGφ)† − Yd† ki (Ojk dGφ)†i

Oij

uG − (O ji uG)†

= 1 4 h Yu

ki Okj uGφ − Yu† jk (Oki uGφ)†i

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Technical details for fans

Oij

Du,

Oij

¯ Du,

Oij

Dd,

Oij

¯ Dd

Oij

Dx,¯ Dx = 1

2

• Oij

Dx + Oij ¯ Dx

• ± 1

2

• Oij

Dx − Oij ¯ Dx

• int. by parts & scalar EOM

Oij

Du + Oij ¯ Du

= −m2¯ qLiuRj ˜ φ + λOij

uφ + Ye klOijkl lq + Yu† kl O(1,ijkl) qu

+ Yd

klO(1,ijkl) qq

Oij

Dd + Oij ¯ Dd

= −m2¯ qLidRjφ + λOij

dφ + Ye† kl (Olkji qde)† + Yu klO(1,klij) qq

+ Yd†

kl O(1,ijkl) qd

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Technical details for fans

Oij

Du,

Oij

¯ Du,

Oij

Dd,

Oij

¯ Dd

Oij

Dx,¯ Dx = 1

2

• Oij

Dx + Oij ¯ Dx

• ± 1

2

• Oij

Dx − Oij ¯ Dx

• int. by parts & algebra

Oij

Du − Oij ¯ Du

= −g 4Oij

uW + g′

4 Oij

uBφ − 1

2Yu†

jk

h (O(3,ki)

φq

)† − (O(1,ki)

φq

)†i +Yu†

ki (Ojk φu)† − Yd† ki (Ojk φφ)†

Oij

Dd − Oij ¯ Dd

= −g 4Oij

dW − g′

4 OdBφ − 1 2Yd†

jk

h O(3,ik)

φq

+ O(1,ik)

φq

i −Yu†

ki Okj φφ − Yd† ki Okj φd

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Technical details for fans

O(3,ij)

φq

, O(1,ij)

φq

, Oij

φu

• int. by parts & quark EOM

O(3,ij)

φq

− (O(3,ji)

φq

)† = Yu

jk Oik uφ − Yd jkOik dφ − Yu† ki (Ojk uφ)† + Yd† ki (Ojk dφ)†

O(1,ij)

φq

− (O(1,ji)

φq

)† = −Yu

jk Oik uφ − Yd jkOik dφ + Yu† ki (Ojk uφ)† + Yd† ki (Ojk dφ)†

O(ij)

φu − (O(ji) φu )†

= Yu

ki Okj uφ − Yu† jk (Oki uφ)†

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Technical details for fans

O(3,ij)

φq

, O(1,ij)

φq

, Oij

φu

Not all i, j flavour combinations independent!

➙

Instead of Oij

x

i, j = 1, 2, 3 use Oi+j

x

= 1 2

• Oij

x + (O ji x )†

i ≤ j = 1, 2, 3 and drop Oi−j

x

= 1 2

• Oij

x − (O ji x )†

i ≤ j = 1, 2, 3

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Technical details for fans

O(3,ij)

φq

, O(1,ij)

φq

, Oij

φu

Independent operators: O(3,i+j)

φq

= i 2

• φ†(τ IDµ − ←

− D µτ I)φ

• (¯

qLiγµτ IqLj) O(1,i+j)

φq

= i 2 (φ†← → Dµφ)(¯ qLiγµqLj) Oi+j

φu

= i 2 (φ†← → Dµφ)(¯ uRiγµuRj)

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Reminder

This is not a change of basis: operators in blue included in BW list

O(1,1,ijkl)

qq

= 1/2 (¯ qLiγµqLj)(¯ qLkγµqLl) O(8,1,ijkl)

qq

= 1/2 (¯ qLiγµλaqLj)(¯ qLkγµλaqLl) O(1,ijkl)

lq

= (¯ lLiγµlLj)(¯ qLkγµqLl) O(3,ijkl)

lq

= (¯ lLiγµτ IlLj)(¯ qLkγµτ IqLl) O(1,ijkl)

uu

= 1/2 (¯ uRiγµuRj)(¯ uRkγµuRl) Oijkl

eu = (¯

eRiγµeRj)(¯ uRkγµuRl) O(1,ijkl)

ud

= (¯ uRiγµuRj)(¯ dRkγµdRl) O(8,ijkl)

ud

= (¯ uRiγµλauRj)(¯ dRkγµλadRl) Oijkl

lu = (¯

lLiuRj)(¯ uRklLl) Oijkl

qe = (¯

qLieRj)(¯ eRkqLl) O(1,ijkl)

qu

= (¯ qLiuRj)(¯ uRkqLl) O(8,ijkl)

qu

= (¯ qLiλauRj)(¯ uRkλaqLl) O(1,ijkl)

qd

= (¯ qLidRj)(¯ dRkqLl) O(8,ijkl)

qd

= (¯ qLiλadRj)(¯ dRkλaqLl) Oijkl

qde = (¯

lLieRj)(¯ dRkqLl) O(1,ijkl)

qq

= (¯ qLiuRj) ˆ (¯ qLkǫ)TdRl ˜ Oijkl

lq = (¯

qLiuRj) ˆ (¯ lLkǫ)TeRl ˜

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Reminder

This is not a change of basis: operators in blue included in BW list

Oij

dBφ = (¯

qLiσµνdRj)φBµν Oij

dGφ = (¯

qLiλaσµνdRj)φGa

µν

Oij

φd = i(φ†Dµφ)(¯

dRiγµdRj) Oij

dφ = (φ†φ)¯

qLidRjφ

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Can redundant operators just be dropped?

Certainly

☞

One can write any dim 6 operator in terms of the reduced “basis” Many redundant operators already discarded in

[Buchmuller, Wyler NPB ’86]

Using a redundant operator or an equivalent expression are two ways

• f writing (parameterising) the same quantity, up to dim 8 terms

The contributions to amplitudes are the same at this order (dim 6)

☞

Explicitly checked in several examples

[JAAS NPB ’08 ’09]

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Which is the “right” set for the top quark?

Dropping Oij

qW, Oij qG, Oij Du, Oij Dd, . . .

top trilinear interactions are simplified several interesting process involve less diagrams Dropping for example 4f operators many calculations (e.g. top decay) unchanged: 4f are not involved still lots of 4f operators remain, little improvement

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Four-fermion operators contributing to single top (t, s-channel) (i, j, k, l are flavour indices)

O(1,1,ijkl)

qq

= 1/2 (¯ qLiγµqLj)(¯ qLkγµqLl) O(8,1,ijkl)

qq

= 1/2 (¯ qLiγµλaqLj)(¯ qLkγµλaqLl) O(1,ijkl)

ud

= (¯ uRiγµuRj)(¯ dRkγµdRl) O(8,ijkl)

ud

= (¯ uRiγµλauRj)(¯ dRkγµλadRl) O(1,ijkl)

qu

= (¯ qLiuRj)(¯ uRkqLl) O(8,ijkl)

qu

= (¯ qLiλauRj)(¯ uRkλaqLl) O(1,ijkl)

qd

= (¯ qLidRj)(¯ dRkqLl) O(8,ijkl)

qd

= (¯ qLiλadRj)(¯ dRkλaqLl) O(1,ijkl)

qq

= (¯ qLiuRj)([¯ qLkǫ]TdRl) O(8,ijkl)

qq

= (¯ qLiλauRj)([¯ qLkǫ]TλadRl)

10 for ub → dt 10 for cb → st

• ➙

total = 20 operators

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

If you think I’m missing four-fermion operators note that, for example

O(1,3,ijkl)

qq

≡ 1 2 (¯ qLiγµτ IqLj)(¯ qLkγµτ IqLl) = 2 3O(1,1,ilkj)

qq

+ O(8,1,ilkj)

qq

− O(1,1,ijkl)

qq

O(8,3,ijkl)

qq

≡ 1 2 (¯ qLiγµλaτ IqLj)(¯ qLkγµλaτ IqLl) = 32 9 O(1,1,ilkj)

qq

− O(8,1,ijkl)

qq

− 2 3O(8,1,ilkj)

qq

using λa, τ I completeness relations and Fierz rearrangements

☞

several four-fermion operators in BW list are redundant

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings

I choose to drop      Oij

qW,

Oij

qB,

Oij

uB,

Oij

qG,

Oij

uG

Oij

Du,

Oij

¯ Du,

Oij

Dd,

Oij

¯ Dd

O(3,i−j)

φq

, O(1,i−j)

φq

, Oi−j

φu

and will show how top interactions (and some selected observables) are simplified

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings Wtb vertex - before

LWtb = − g √ 2 ¯ b γµ (VLPL + VRPR) t W−

µ

− g √ 2 ¯ b iσµνqν MW (gLPL + gRPR) t W−

µ

− g √ 2 ¯ b qµ MW (f1LPL + f1RPR) + kµ MW (f2LPL + f2RPR)

• t W−

µ

− g √ 2 q2 M2

W

¯ b γµξW

L PL t W− µ

− g √ 2 1 M2

W

¯ b(q kµ − k · q γµ)hW

L PL t W− µ + h.c.

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings Wtb vertex - without redundant operators

More

LWtb = − g √ 2 ¯ b γµ (VLPL + VRPR) t W−

µ

− g √ 2 ¯ b iσµνqν MW (gLPL + gRPR) t W−

µ + h.c.

− g √ 2 ¯ b qµ MW (f1LPL + f1RPR) + kµ MW (f2LPL + f2RPR)

• t W−

µ

− g √ 2 q2 M2

W

¯ b γµξW

L PL t W− µ

− g √ 2 1 M2

W

¯ b(q kµ − k · q γµ)hW

L PL t W− µ + h.c.

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings Ztt vertex - before

LZtt = − g 2cW ¯ t γµ XL

ttPL + XR ttPR − 2s2 WQt

• t Zµ

− g 2cW ¯ t iσµνqν MZ

• dZ

V + idZ Aγ5

• t Zµ

− g 2cW ¯ t qµ MZ (f Z

1LPL + f Z 1RPR) + kµ

MZ (f Z

2LPL + f Z 2RPR)

• t Zµ

− g 2cW q2 M2

Z

¯ t γµ(ξZ

LPL + ξZ RPR) t Zµ

− g 2cW 1 M2

Z

¯ t(q kµ − k · q γµ)(hZ

LPL + hZ RPR) t Zµ

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings Ztt vertex - without redundant operators

More

LZtt = − g 2cW ¯ t γµ XL

ttPL + XR ttPR − 2s2 WQt

• t Zµ

− g 2cW ¯ t iσµνqν MZ

• dZ

V + idZ Aγ5

• t Zµ

− g 2cW ¯ t qµ MZ (f Z

1LPL + f Z 1RPR) + kµ

MZ (f Z

2LPL + f Z 2RPR)

• t Zµ

− g 2cW q2 M2

Z

¯ t γµ(ξZ

LPL + ξZ RPR) t Zµ

− g 2cW 1 M2

Z

¯ t(q kµ − k · q γµ)(hZ

LPL + hZ RPR) t Zµ

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings γtt vertex - before

Lγtt = −eQt¯ tγµt Aµ − e¯ t iσµνqν mt (dγ

V + idγ Aγ5) t Aµ

− e q2 m2

t

¯ t γµ(ξγ

L PL + ξγ RPR) t Aµ

− e 1 m2

t

¯ t(q kµ − k · q γµ)(hγ

LPL + hγ RPR) t Aµ

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings γtt vertex - without redundant operators

More

Lγtt = −eQt¯ tγµt Aµ − e¯ t iσµνqν mt (dγ

V + idγ Aγ5) t Aµ

− e q2 m2

t

¯ t γµ(ξγ

L PL + ξγ RPR) t Aµ

− e 1 m2

t

¯ t(q kµ − k · q γµ)(hγ

LPL + hγ RPR) t Aµ

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings gtt vertex - before

Lgtt = −gs¯ tλa 2 γµt Ga

µ − gs¯

tλa iσµνqν mt (dg

V + idg Aγ5) t Ga µ

− gs q2 m2

t

¯ t λaγµ(ξg

LPL + ξg RPR) t Ga µ

− gs 1 m2

t

¯ t λa(q kµ − k · q γµ)(hg

LPL + hg RPR) t Ga µ

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings gtt vertex - without redundant operators

More

Lgtt = −gs¯ tλa 2 γµt Ga

µ − gs¯

tλa iσµνqν mt (dg

V + idg Aγ5) t Ga µ

− gs q2 m2

t

¯ t λaγµ(ξg

LPL + ξg RPR) t Ga µ

− gs 1 m2

t

¯ t λa(q kµ − k · q γµ)(hg

LPL + hg RPR) t Ga µ

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings Htt vertex - before

LHtt = − 1 √ 2 ¯ t

• YV

t + iYA t γ5

• t H

− 1 √ 2 qµ mt ¯ t γµ ωL

ttPL + ωR ttPR

• t H
• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings Htt vertex - without redundant operators

More

LHtt = − 1 √ 2 ¯ t

• YV

t + iYA t γ5

• t H

− 1 √ 2 qµ mt ¯ t γµ ωL

ttPL + ωR ttPR

• t H
• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings Ztc vertex - before

LZtc = − g 2cW ¯ c γµ XL

ctPL + XR ctPR

• t Zµ

− g 2cW ¯ c iσµνqν MZ

• κL

ctPL + κR ctPR

• t Zµ

− g 2cW ¯ c qµ MZ (f ct

1LPL + f ct 1RPR) + kµ

MZ (f ct

2LPL + f ct 2RPR)

• t Zµ

− g 2cW q2 M2

Z

¯ c γµ(βZ

LPL + βZ RPR) t Zµ

− g 2cW 1 M2

Z

¯ c(q kµ − k · q γµ)(θZ

LPL + θZ RPR) t Zµ + h.c.

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings Ztc vertex - without redundant operators

More

LZtc = − g 2cW ¯ c γµ XL

ctPL + XR ctPR

• t Zµ

− g 2cW ¯ c iσµνqν MZ

• κL

ctPL + κR ctPR

• t Zµ + h.c.

− g 2cW ¯ c qµ MZ (f ct

1LPL + f ct 1RPR) + kµ

MZ (f ct

2LPL + f ct 2RPR)

• t Zµ

− g 2cW q2 M2

Z

¯ c γµ(βZ

LPL + βZ RPR) t Zµ

− g 2cW 1 M2

Z

¯ c(q kµ − k · q γµ)(θZ

LPL + θZ RPR) t Zµ + h.c.

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings γtc vertex - before

Lγtc = −e¯ c iσµνqν mt

• λL

ctPL + λR ctPR

• t Aµ

− e q2 m2

t

¯ c γµ(βγ

L PL + βγ RPR) t Aµ

− e 1 m2

t

¯ c(q kµ − k · q γµ)(θγ

L PL + θγ RPR) t Aµ + h.c.

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings γtc vertex - without redundant operators

More

Lγtc = −e¯ c iσµνqν mt

• λL

ctPL + λR ctPR

• t Aµ + h.c.

− e q2 m2

t

¯ c γµ(βγ

L PL + βγ RPR) t Aµ

− e 1 m2

t

¯ c(q kµ − k · q γµ)(θγ

L PL + θγ RPR) t Aµ + h.c.

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings gtc vertex - before

Lgtc = −gs ¯ c λa iσµνqν mt

• ζL

ctPL + ζR ctPR

• t Ga

µ

− gs q2 m2

t

¯ c λaγµ(βg

LPL + βg RPR) t Ga µ

− e 1 m2

t

¯ c λa(q kµ − k · q γµ)(θg

LPL + θg RPR) t Ga µ + h.c.

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings gtc vertex - without redundant operators

More

Lgtc = −gs ¯ c λa iσµνqν mt

• ζL

ctPL + ζR ctPR

• t Ga

µ + h.c.

− gs q2 m2

t

¯ c λaγµ(βg

LPL + βg RPR) t Ga µ

− e 1 m2

t

¯ c λa(q kµ − k · q γµ)(θg

LPL + θg RPR) t Ga µ + h.c.

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings Htc vertex - before

LHtc = − 1 √ 2 ¯ c

• ηL

ctPL + ηR ctPR

• t H

− 1 √ 2 qµ mt ¯ c γµ ωL

ctPL + ωR ctPR

• t H + h.c.
• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

A minimal set of top anomalous couplings Htc vertex - without redundant operators

More

LHtc = − 1 √ 2 ¯ c

• ηL

ctPL + ηR ctPR

• t H + h.c.

− 1 √ 2 qµ mt ¯ c γµ ωL

ctPL + ωR ctPR

• t H + h.c.
• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

In summary: ➀ Gauge interactions: only γµ and σµνqν terms ➁ Higgs: only scalar and pseudo-scalar terms ☞

This is general for any fermion and process, not only the top quark! This simplifies

• phenomenological analyses

Monte Carlo building

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Q & A:

Q: Why is this new? I’ve been using only γµ and σµνqν all my life! A: Yes, but possibly you were using top on-shell. This is valid for top off-shell, light quarks off-shell and bosons off-shell

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Top interactions tested at LHC involve general off-shell vertices Single top tW: Wtb with t / b off-shell t¯ tZ: Ztt with one t off-shell t¯ tγ: γtt with one t off-shell Zt production: Ztc with t / c off-shell γt production: γtc with t / c off-shell . . .

☞

The effort to obtain a minimal set of operators pays off: description completely general but much simpler

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Q & A:

Q: And what’s wrong with having a few extra parameters? A: If you rename a single parameter ‘a’ as ‘b + c’, you will not measure b nor c individually with your observables, which all depend on b + c

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Top-charm-Higgs vertex with redundant operators

LHtc = − 1 √ 2 ¯ c

• ηL

ctPL + ηR ctPR

• t H − 1

√ 2 qµ mt ¯ c γµ ωL

ctPL + ωR ctPR

• t H

H c t

Γ = A

• |ηL

ct + ωR ct|2 + |ηR ct + ωL ct|2

c g H t c

+

c g H t t

σ = B

• |ηL

ct + ωR ct|2 + |ηR ct + ωL ct|2

Suspicious coincidence . . . ω vertex is q-dependent!

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Minimal top-charm-Higgs vertex

LHtc = − 1 √ 2 ¯ c

• ηL

ctPL + ηR ctPR

• t H − 1

√ 2 qµ mt ¯ c γµ ωL

ctPL + ωR ctPR

• t H

H c t

Γ = A

• |ηL

ct|2 + |ηR ct|2

c g H t c

+

c g H t t

σ = B

• |ηL

ct|2 + |ηR ct|2

4 parameters → 2 parameters

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Some FCN Processes mediated by gtq (q = u, c) t → qg

g q t

gq → t

q g t

gq → Zt

q g Z t q

+

q g Z t t

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Lagrangians for gtu interactions

Dropping Oij

qG, Oij uG

Lgtu = −gs¯ c λa iσµνqν mt

• ζL

utPL + ζR utPR

• t Ga

µ + h.c.

with ζL

ut =

√ 2 gs C31∗

uGφ

vmt Λ2 , ζR

ut =

√ 2 gs C13

uGφ

vmt Λ2 [JAAS NPB’09]

Dropping 4f operators L′

gtu = iαtu

Λ2 O31

uG + iαut

Λ2 O13

uG + βtu

Λ2 O31

uGφ + βut

Λ2 O13

uGφ + h.c.

[Ferreira, Santos PRD ’06 − 09]

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Some observables for gtu anomalous couplings

Γ(t → ug) = 4 3αsmt

• |ζL

ut|2 + |ζR ut|2

ζL

ut =

√ 2vmt gsΛ2 » β∗

tu +

imt 2 √ 2v (α∗

tu + αut)

– ζR

ut =

√ 2vmt gsΛ2 » βut + imu 2 √ 2v (αut + α∗

tu)

–

Γ(t → ug) = m3

t

12πΛ4

• m2

t |αtu + α∗ ut|2 + 16ˆ

v2 |βtu|2 + |βut|2 +8ˆ vmt Im βtu(α∗

tu + αut)}

=

[Ferreira, Santos PRD ’06]

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Some observables for gtu anomalous couplings

σ(gu → t) = 2.162 × 106 |ζL

ut|2 + |ζR ut|2

pb

ζL

ut =

√ 2vmt gsΛ2 » β∗

tu +

imt 2 √ 2v (α∗

tu + αut)

– ζR

ut =

√ 2vmt gsΛ2 » βut + imu 2 √ 2v (αut + α∗

tu)

–

σ(gu → t) = 1 Λ4

• 342|αtu + α∗

ut|2 + 5413

• |βtu|2 + |βut|2

+2722 Im βtu(α∗

tu + αut)} pb

≃

[Ferreira, Santos PRD ’06]

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Some observables for gtu anomalous couplings

σ(gu → Zt) = 2.321 × 104|ζL

ut|2 + 2.378 × 104|ζR ut|2 pb

ζL

ut =

√ 2vmt gsΛ2 » β∗

tu +

imt 2 √ 2v (α∗

tu + αut)

– ζR

ut =

√ 2vmt gsΛ2 » βut + imu 2 √ 2v (αut + α∗

tu)

–

σ(gu → Zt) = 1 Λ4

• 3.88|αtu + α∗

ut|2 + 61.3|βtu|2 + 62.8|βut|2

+30.8 Im βtu(α∗

tu + αut)} pb

≃

[Ferreira, Santos PRD ’06]

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Extracting the Lagrangian from experiment

★ Identification of relevant observables ★ Comparison of sensitivities to anomalous couplings given their experimental uncertainties (syst and stat)

☞

example: Wtb vertex

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Observables for Wtb anomalous couplings

Present CDF & D0 analyses Use W helicity fractions in t → Wb FR, FL, F0 sensitive to anomalous couplings

[Kane, Ladinsky, Yuan PRD ’92]

Dependence on couplings: simple analytical expressions up to corrections of order mb/mt ∼ 0.03

[Chen, Larios, Yuan PLB ’05]

Combination of F and single top σ barring cancellations among anomalous couplings

[Chen, Larios, Yuan PLB ’05]

• But. . . at LHC we can and must do better!

☞

combined effort of theorists and experimentalists

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

New observables for Wtb anomalous couplings

LHC precision determined by systematic uncertainties

☞

investigate new observables New observables ρR,L = FR,L F0 , A± asym.

[JAAS et al. EPJC ’08]

smaller systematics enhanced sensitivity Expected limits for ATLAS, 10 fb−1 / VL = 1, VR = 0

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

W rest frame observables

ℓ distribution in W rest frame

1 Γ dΓ d cos θ∗

ℓ

= 3 8(1 − cos θ∗

ℓ )2 FL + 3

4 sin2 θ∗

ℓ F0

+ 3 8(1 + cos θ∗

ℓ )2 FR

(Fi = Γi/Γ)

[Kane, Ladinsky, Yuan PRD ’92]

t W ℓ ν b θ∗

l

FL, FR, F0 partial widths to W with helicity −1, +1, 0 in top rest frame, FL + FR + F0 = 1 by definition they depend on Wtb couplings VL, VR, gL, gR distribution independent of top spin

➙

good for t¯ t production

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

W helicity fractions and related observables

• 1
• 0.75
• 0.5
• 0.25

0.25 0.5 0.75 1 cos θl

*

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 / Γ dΓ / d cos θl

* Analytical MC simulation

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

W helicity fractions and related observables

• 1
• 0.75
• 0.5
• 0.25

0.25 0.5 0.75 1 cos θl

*

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 / Γ dΓ / d cos θl

* Analytical MC simulation

fit

➙

F0, FL , FR (with F0 + FL + FR = 1)

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

W helicity fractions and related observables

• 1
• 0.75
• 0.5
• 0.25

0.25 0.5 0.75 1 cos θl

*

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 / Γ dΓ / d cos θl

* Analytical MC simulation

fit

➙

F0, FL , FR (with F0 + FL + FR = 1) fit

➙

ρR ≡ FR

F0 , ρL ≡ FL F0

(independent parameters) ρR

☞

best limit on VR, gL

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

W helicity fractions and related observables

• 1
• 0.75
• 0.5
• 0.25

0.25 0.5 0.75 1 cos θl

*

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 / Γ dΓ / d cos θl

* Analytical MC simulation

A+ A−

fit

➙

F0, FL , FR (with F0 + FL + FR = 1) fit

➙

ρR ≡ FR

F0 , ρL ≡ FL F0

(independent parameters) ρR

☞

best limit on VR, gL count events

➙

A±

• asym. around ∓(22/3 − 1)

A+

☞

best limit on gR

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Use accurate theoretical expressions for observables

LHC excellent precision

☞

are mb/mt effects relevant? F’s with anomalous couplings linear terms ∝ mb/mt gLVL quadratic terms ∝ g2

L

☞

• f the same order!

Expected limits for ATLAS, 10 fb−1 / VL = 1, VR = 0

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Use accurate theoretical expressions for observables

Top partial widths to polarised W

ΓR,L = g2| q | 32π (h |VL|2 + |VR|2i “ 1 − x2

W + x2 b

” + m2

t

M2

W

h |gL|2 + |gR|2i “ 1 − x2

W − 2x2 b − x2 Wx2 b + x4 b

” −4xb Re VLV∗

R − 4xb Re gLg∗ R − 2

mt MW Re ˆ VLg∗

R + VRg∗ L

˜ “ 1 − x2

W − x2 b

” +2 mt MW xb Re ˆ VLg∗

L + VRg∗ R

˜ “ 1 + x2

W − x2 b

”ff ± g2 64π m3

t

M2

W

n −x2

W

h |VL|2 − |VR|2i + h |gL|2 − |gR|2i “ 1 − x2

b

” +2xW Re ˆ VLg∗

R − VRg∗ L

˜ + 2xWxb Re ˆ VLg∗

L − VRg∗ R

˜¯ “ 1 − 2x2

W − 2x2 b + x4 W − 2x2 Wx2 b + x4 b

” Γ0 = g2| q | 32π ( m2

t

M2

W

h |VL|2 + |VR|2i “ 1 − x2

W − 2x2 b − x2 Wx2 b + x4 b

” + h |gL|2 + |gR|2i “ 1 − x2

W + x2 b

” −4xb Re VLV∗

R − 4xb Re gLg∗ R − 2

mt MW Re ˆ VLg∗

R + VRg∗ L

˜ “ 1 − x2

W − x2 b

” +2 mt MW xb Re ˆ VLg∗

L + VRg∗ R

˜ “ 1 + x2

W − x2 b

”ff

xb = mb/mt , xW = mW/mt

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Allowing for cancellations

Model-independent analysis

☞

fit the four Wtb couplings using many observables σ, F insufficient to constrain VR, gL simultaneously

☞

find new observables spin asymmetry ratio rbl = Ab Al easily improves combined limits

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Top rest frame observables

Polarised top decay in top rest frame

1 Γ dΓ d cos θX = 1 + αX cos θX 2 [Jezabek, Kuhn PLB ’94]

t

• s
• pℓ
• pb
• pν

θb θℓ θν

αℓ+, αν, αb called ‘spin analysing power’ of ℓ+, ν, b they depend on Wtb couplings VL, VR, gL, gR SM values

αℓ+ = 1 αν = −0.32 αb = −0.41 tree level αℓ+ = 0.998 αν = −0.33 αb = −0.39

• ne loop

[Bernreuther et al. NPB ’04]

top spin not directly measurable

➙

look for spin asymmetries

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Top spin asymmetries

tj production: spin asymmetries

X = top decay product

➙

• pX = momentum in t rest frame
• pj = jet momentum in t rest frame

Q = cos( pX, pj)

➙

AX ≡ N(Q > 0) − N(Q < 0) N(Q > 0) + N(Q < 0) = 1 2 P αX [P = 0.95 (t) P = −0.93 (¯ t)]

[Mahlon, Parke PLB ’00]

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Ratios of top spin asymmetries

Ratios of asymmetries depend only on α t¯ t production

➙

Abj Aℓj = ˜ Abj ˜ Aℓj = αb αℓ ≡ rbℓ tj/t¯ bj production

➙

Ab Aℓ = αb αℓ = rbℓ Guessed precision in plot . . . hope it’s realistic rbl = −0.406 ± 0.032

SM central value, relative error 8%

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Summary: observables to fit Wtb vertex ➀ Single top cross sections

σ = σSM

• V2

L + κVR V2 R + κVLVR VLVR + κgL g2 L + κgR g2 R + . . .

• ➁ W helicity observables in t → Wb → ℓνb

helicity fractions FR, FL, F0 and ratios ρR,L angular asymmetries A± . . .

➂ Spin asymmetry ratios in single and pair production

single top: Ab, Aℓ . . . top pair: All, Aℓj . . . ratios independent of production mechanism rbl = Ab Aℓ = Abj Aℓj , rνl, . . .

➃ More to come . . .

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

TopFit: the global fit to the Wtb vertex

After the reduction in the number of meaningful parameters, we can

• btain model-independent measurements and limits

(or with very few assumptions)

General Wtb vertex

LWtb = − g √ 2 ¯ b γµ (VLPL + VRPR) t W−

µ

− g √ 2 ¯ b iσµνqν MW (gLPL + gRPR) t W−

µ + h.c.

q = pt − pb = pW

no-lose bet: ★ either we find Wtb anomalous couplings ★

• r we clean the room to probe NP in production
• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

TopFit: the global fit to the Wtb vertex An example: the input

Exact expressions for W helicity ratios and spin analysing powers in top decay t → Wb → f f ′b Their expected ATLAS precision with 10 fb−1 Expressions for single top xsec with anomalous couplings including theoretical uncertainty Expected ATLAS precision for tW xsec with 10 fb−1 Guesstimated ATLAS precision for Aℓ, Ab and other new asymmetries with 10 fb−1

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Coming soon . . .

Estimated limits for LHC (8-dimensional region) (VL, Re VR) (Re gL, Re gR)

Many cancellations possible in single observables

➙

life is not easy All of them allowed in the fit

➙

reduced by combination Model-independent measurement of Wtb vertex and single top P

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Coming soon . . .

Estimated limits for LHC (8-dimensional region) (Re VR, Im VR) (Re gL, Im gL) (Re gR, Im gR)

Many cancellations possible in single observables

➙

life is not easy All of them allowed in the fit

➙

reduced by combination Model-independent measurement of Wtb vertex and single top P

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Protos: Monte Carlo with anomalous couplings

Generator Protos (PROgram for TOp Simulations) for

➀ Single top and t¯

t production with anomalous Wtb couplings

➁ Top FCNC production and decay

Includes the minimal sets of top anomalous couplings arising from dim 6 effective operators

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Protos: simplification using minimal set

Vertices simpler, and amplitudes also involve less diagrams Example: tW− production with Wtb anomalous couplings

s-channel

b g W t b

t-channel

b g W t t

new diagram

b g W t

gWtb required by gauge symmetry if redundant operators included

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Protos: simplification using minimal set

Vertices simpler, and amplitudes also involve less diagrams Example: tW− production with Wtb anomalous couplings

s-channel

b g W t b

t-channel

b g W t t

new diagram not needed

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Equivalent parameterisations of the same new physics

One can either Use for example Oij

Du − Oij ¯ Du, which involves Wtb couplings

and an associated gWtb vertex

➙

The extra diagram with the quartic vertex must appear Replace Oij

Du − Oij ¯ Du by an equivalent expression (up to dim 8)

which involves γµ, σµνqν already present from other operators and does not have any gWtb vertex

➙

The contribution to the amplitudes is the same but the parameterisation is much simpler

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Gauge invariance at work: an example

Contributions to gb → tW

b g W t b b g W t t b g W t

=

b g W t b b g W t t

kµ kµ gµν γµ, σµνqν γµ, σµνqν

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Protos: Monte Carlo with anomalous couplings General features

★ Matrix elements calculated with HELAS ★ Top and W off-shell (Breit-Wigner resonances) ★ Spin information kept in decay chain ★ Integration done with VEGAS ★ Many numerical outputs (checks) provided: W helicity fractions, angular asymmetries, t¯ t spin correlations . . . ★ Implemented in ATLAS framework

(full simulation samples available)

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Protos for Wtb anomalous couplings

The generator includes: single top in all channels, with double counting removal top pair production

. . . but why is this necessary?

Event samples with Wtb anomalous couplings necessary for several LHC analyses W helicity measurements with templates Limits on anomalous Wtb couplings from single top

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Generating templates for W helicities

• 1
• 0.75
• 0.5
• 0.25

0.25 0.5 0.75 1 cos θl

*

0.02 0.04 0.06 0.08 0.10 σ (normalised)

Set L Set 0 Set R

Parameters mt = 175 GeV

WL: VL ≃ −0.4917 VR = 0 gL ≃ 0 gR ≃ −1.069 W0: VL ≃ 1.513 VR = 0 gL ≃ −0.0191 gR ≃ 0.6956 WR: VL = 0 VR ≃ 0.4917 gL ≃ 1.069 gR ≃ 0

distributions for pure WL, WR, W0

➙

detector simulation

➙

fit FL, FR, F0 with real data

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Generating templates for W helicities

Top and W boson invariant mass keep Breit-Wigner shape in all cases

150 155 160 165 170 175 180 185 190 195 200 sqrt [pt

2] (GeV)

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 σ (normalised)

Set L Set 0 Set R

60 65 70 75 80 85 90 95 100 sqrt [pW

2 ] (GeV)

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 σ (normalised)

Set L Set 0 Set R

This can only be done consistently with Wtb anomalous couplings

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Testing efficiency variations with anomalous couplings

When limits on Wtb anomalous couplings are extracted from total cross sections the efficiency variations must be taken into account σµν couplings affect kinematics

➙

affect efficiency This can be done by extracting limits assuming SM efficiency and testing the variations within the limits obtained

[JAAS NPB ’08]

☞

Samples required with anomalous couplings

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Testing efficiency dependence on anomalous couplings

Fast simulation + typical cuts

Parameters

SM: VL = 1 rest zero + typical limits from global fit [JAAS NPB ’08] Set A: VL = 1 VR = 0.3 gL = 0.15 Set B: VL = 1 gR = 0.024

Final state 1 (tj) SM Set A Set B tj 2.02 ± 0.02 2.08 ± 0.02 2.07 ± 0.02 t¯ bj 1.44 ± 0.02 1.40 ± 0.02 1.46 ± 0.02 t¯ b 0.76 ± 0.01 0.73 ± 0.01 0.74 ± 0.01 tW− 0.173 ± 0.008 0.161 ± 0.007 0.173 ± 0.008 tW−¯ b 0.146 ± 0.004 0.150 ± 0.004 0.151 ± 0.004 Final state 2 (t¯ b) SM Set A Set B tj 0.102 ± 0.005 0.103 ± 0.005 0.104 ± 0.005 t¯ bj 0.328 ± 0.009 0.315 ± 0.009 0.328 ± 0.009 t¯ b 2.70 ± 0.03 2.75 ± 0.03 2.70 ± 0.03 tW− 0.073 ± 0.005 0.082 ± 0.005 0.065 ± 0.005 tW−¯ b 0.071 ± 0.003 0.071 ± 0.003 0.071 ± 0.003 Final state 3 (tjj) SM Set A Set B tj 0.146 ± 0.006 0.158 ± 0.006 0.132 ± 0.006 t¯ bj 0.294 ± 0.008 0.313 ± 0.009 0.292 ± 0.008 t¯ b 0.33 ± 0.10 0.38 ± 0.10 0.32 ± 0.10 tW− 2.38 ± 0.03 2.47 ± 0.03 2.39 ± 0.03 tW−¯ b 2.37 ± 0.02 2.38 ± 0.02 2.36 ± 0.02

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Single top and t¯ t generators are LO but ...

★ t¯ bj kinematics similar to NLO

[Campbell et al. JHEP ’09]

★ For t¯ b too

[Sullivan PRD ’04]

★ QCD corrections to decay

➙

effective gR coupling

effect 1/3 smaller than ATLAS sensitivity [JAAS et al. EPJC ’08]

★ Hard extra jets do not affect top decay kinematics

(but may affect reconstruction)

★ t¯ t + 1j does not change spin correlations

(checked with Alpgen)

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Lagrangians for anomalous couplings A minimal set of top anomalous couplings Observables for Wtb anomalous couplings Tools for LHC analyses

Protos for top FCNC processes

The generator includes: single top: pp → Zt/γt/t/Ht top pair production with t → Zq/γq/gq/Hq more to come . . . Simulated event samples for these processes absolutely necessary to compare with real data and extract limits on top FCN interactions

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Conclusion (I)

★ Fermion trilinear interactions arising from dim 6 gauge-invariant effective operators are simpler than expected

γµ, σµνqν terms for gauge bosons scalar and pseudo-scalar for the Higgs

★ This is the minimal structure: if more operators are found redundant it will not be simplified further ★ Dropping one operator or another is a matter of taste, but our choice seems simpler for top phenomenology

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Conclusion (II)

The (other) preparation for data

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Conclusion (II)

The (other) preparation for data

➀

Establish the Lagrangian, minimal but general

✔

(that is, to know which the anomalous couplings are)

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Conclusion (II)

The (other) preparation for data

➀

Establish the Lagrangian, minimal but general

✔

(that is, to know which the anomalous couplings are)

➁

Identify the observables, look for improvements

✔

Use accurate theoretical expressions for them

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Conclusion (II)

The (other) preparation for data

➀

Establish the Lagrangian, minimal but general

✔

(that is, to know which the anomalous couplings are)

➁

Identify the observables, look for improvements

✔

Use accurate theoretical expressions for them

➂

A program to fit the data

✔

TopFit http://www-ftae.ugr.es/topfit/

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Conclusion (II)

The (other) preparation for data

➀

Establish the Lagrangian, minimal but general

✔

(that is, to know which the anomalous couplings are)

➁

Identify the observables, look for improvements

✔

Use accurate theoretical expressions for them

➂

A program to fit the data

✔

TopFit http://www-ftae.ugr.es/topfit/

➃

Generators involving top anomalous couplings

✔

Protos http://www-ftae.ugr.es/protos/

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Conclusion (II)

The (other) preparation for data

➀

Establish the Lagrangian, minimal but general

✔

(that is, to know which the anomalous couplings are)

➁

Identify the observables, look for improvements

✔

Use accurate theoretical expressions for them

➂

A program to fit the data

✔

TopFit http://www-ftae.ugr.es/topfit/

➃

Generators involving top anomalous couplings

✔

Protos http://www-ftae.ugr.es/protos/

➄

Ready and waiting for the data at 7 TeV!

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Contributions to Wtb vertex δVL = C(3,3+3)∗

φq

v2 Λ2 δgL = √ 2C33∗

dW

v2 Λ2 δVR = 1 2C33

φφ

v2 Λ2 δgR = √ 2C33

uW

v2 Λ2

Back

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Contributions to Ztt vertex δXL

tt =

• C(3,3+3)

φq

− C(1,3+3)

φq

v2 Λ2 δXR

tt = − C3+3 φu

v2 Λ2 δdZ

V =

√ 2 Re

• cWC33

uW − sWC33 uBφ

v2 Λ2 δdZ

A =

√ 2 Im

• cWC33

uW − sWC33 uBφ

v2 Λ2

Back

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Contributions to γtt vertex δdγ

V =

√ 2 e Re

• cWC33

uBφ + sWC33 uW

vmt Λ2 δdγ

A =

√ 2 e Im

• cWC33

uBφ + sWC33 uW

vmt Λ2

Back

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Contributions to gtt vertex δdg

V =

√ 2 gs Re C33

uGφ

vmt Λ2 δdg

A =

√ 2 gs Im C33

uGφ

vmt Λ2

Back

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Contributions to Htt vertex δYV

t = −3

2 Re C33

uφ

v2 Λ2 δYA

t = −3

2 Im C33

uφ

v2 Λ2

Back

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Contributions to Ztc vertex δXL

ct = 1

2

• C(3,2+3)

φq

− C(1,2+3)

φq

v2 Λ2 δXR

ct = −1

2

• C2+3

φu

v2 Λ2 δκL

ct =

√ 2

• cWC32∗

uW − sWC32∗ uBφ

v2 Λ2 δκR

ct =

√ 2

• cWC23

uW − sWC23 uBφ

v2 Λ2

Back

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Contributions to γtc vertex δλL

ct =

√ 2 e

• sWC32∗

uW + cWC32∗ uBφ

vmt Λ2 δλR

ct =

√ 2 e

• sWC23

uW + cWC23 uBφ

vmt Λ2

Back

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Contributions to gtc vertex δζL

ct =

√ 2 gs C32∗

uGφ

vmt Λ2 δζR

ct =

√ 2 gs C23

uGφ

vmt Λ2

Back

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Contributions to Htc vertex δηL

ct = −3

2 C32∗

uφ

v2 Λ2 δηR

ct = −3

2 C23

uφ

v2 Λ2

Back

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...

Operator contributions to top vertices Comparison between Tevatron and LHC

Comparison between Tevatron and LHC

Comparing CDF 1.9 fb−1

[PLB ’09]

LHC 10 TeV 100 pb−1

(estimated)

Assuming VL = 1, VR = 0

• J. A. Aguilar-Saavedra

Acoplamientos anómalos del quark top ...