Les Houches 2009

Angular distributions in top decay

A probe of new physics and top-polarization

at

Physics at TeV Colliders23 June, 2009

Ecole de Physique, Les Houches

by

Ritesh K SinghLehrstuhl für Theoretische Physik II, Universität Würzburg, Germany

Ritesh SINGH – p. 1/13

Les Houches 2009

top-quark : A looking glass

The mass of the top-quark is very large (mt ∼ 175 GeV)

its decay width (Γt ∼ 1.5 GeV) is much larger than the typical scaleof hadronization, i.e. it decays before getting hadronized. The spininformation of top-quark is translated to the decay distribution.

Ritesh SINGH – p. 2/13

Les Houches 2009

top-quark : A looking glass

The mass of the top-quark is very large (mt ∼ 175 GeV)

its decay width (Γt ∼ 1.5 GeV) is much larger than the typical scaleof hadronization, i.e. it decays before getting hadronized. The spininformation of top-quark is translated to the decay distribution.

the decay lepton angular distribution is insensitive to theanomalous tbW couplings, and hence a pure probe of new physicsin top-production process; observed for top-pair production at

e+e− (Rindani, Grzadkowski) as well as γγ collider (Ohkuma,Godbole).

Ritesh SINGH – p. 2/13

Les Houches 2009

top-quark : A looking glass

The mass of the top-quark is very large (mt ∼ 175 GeV)

its decay width (Γt ∼ 1.5 GeV) is much larger than the typical scaleof hadronization, i.e. it decays before getting hadronized. The spininformation of top-quark is translated to the decay distribution.

the decay lepton angular distribution is insensitive to theanomalous tbW couplings, and hence a pure probe of new physicsin top-production process; observed for top-pair production at

e+e− (Rindani, Grzadkowski) as well as γγ collider (Ohkuma,Godbole).

the angular distribution of b-quark is very sensitive to theanomalous tbW couplings and can be used to probe it.

Ritesh SINGH – p. 2/13

Les Houches 2009

top-quark : A looking glass

The mass of the top-quark is very large (mt ∼ 175 GeV)

its decay width (Γt ∼ 1.5 GeV) is much larger than the typical scaleof hadronization, i.e. it decays before getting hadronized. The spininformation of top-quark is translated to the decay distribution.

the decay lepton angular distribution is insensitive to theanomalous tbW couplings, and hence a pure probe of new physicsin top-production process; observed for top-pair production at

e+e− (Rindani, Grzadkowski) as well as γγ collider (Ohkuma,Godbole).

the angular distribution of b-quark is very sensitive to theanomalous tbW couplings and can be used to probe it.

leptons from top decay provide a clean and un-contaminated

probe of top-production mechanism.

Ritesh SINGH – p. 2/13

Les Houches 2009

top-quark : A looking glass

The mass of the top-quark is very large (mt ∼ 175 GeV)

its decay width (Γt ∼ 1.5 GeV) is much larger than the typical scaleof hadronization, i.e. it decays before getting hadronized. The spininformation of top-quark is translated to the decay distribution.

the decay lepton angular distribution is insensitive to theanomalous tbW couplings, and hence a pure probe of new physicsin top-production process; observed for top-pair production at

e+e− (Rindani, Grzadkowski) as well as γγ collider (Ohkuma,Godbole).

the angular distribution of b-quark is very sensitive to theanomalous tbW couplings and can be used to probe it.

leptons from top decay provide a clean and un-contaminated

probe of top-production mechanism.

We have a clean looking glass for new physics.

Ritesh SINGH – p. 2/13

Les Houches 2009

Anomalous t-decay

Anomalous tbW vertex :

Γµ =g√2

[

γµ(f1LPL + f1RPR) − iσµν

mW

(pt − pb)ν (f2LPL + f2RPR)

]

Ritesh SINGH – p. 3/13

Les Houches 2009

Anomalous t-decay

Anomalous tbW vertex :

Γµ =g√2

[

γµ(f1LPL + f1RPR) − iσµν

mW

(pt − pb)ν (f2LPL + f2RPR)

]

In the SM, f1L = 1, f1R = 0, f2L = 0, f2R = 0.

Contribution from f1R, f2L are proportional to mb.

Ritesh SINGH – p. 3/13

Les Houches 2009

Anomalous t-decay

Anomalous tbW vertex :

Γµ =g√2

[

γµ(f1LPL + f1RPR) − iσµν

mW

(pt − pb)ν (f2LPL + f2RPR)

]

In the SM, f1L = 1, f1R = 0, f2L = 0, f2R = 0.

Contribution from f1R, f2L are proportional to mb.

1

Γt

dΓt

d cos θf

=1

2

(

1 + αf Pt cos θf

)

αl = 1 −O(f2i )

αb = −[

m2t − 2m2

W

m2t + 2m2

W

]

+ ℜ(f2R)

[

8mtmW (m2t − m2

W )

(m2t + 2m2

W )2

]

+ O(

mb

mW

, f2i

)

Ritesh SINGH – p. 3/13

Les Houches 2009

Anomalous t-decay

Anomalous tbW vertex :

Γµ =g√2

[

γµ(f1LPL + f1RPR) − iσµν

mW

(pt − pb)ν (f2LPL + f2RPR)

]

In the SM, f1L = 1, f1R = 0, f2L = 0, f2R = 0.

Contribution from f1R, f2L are proportional to mb.

1

Γt

dΓt

d cos θf

=1

2

(

1 + αf Pt cos θf

)

αl = 1 −O(f2i )

αb = −[

m2t − 2m2

W

m2t + 2m2

W

]

+ ℜ(f2R)

[

8mtmW (m2t − m2

W )

(m2t + 2m2

W )2

]

+ O(

mb

mW

, f2i

)

The full quadratic contribution is being calculated by:Eduard Boos, Viacheslav Bunichev, Maxim Kiryushin

Ritesh SINGH – p. 3/13

Les Houches 2009

Lepton distribution

JHEP 0612, 021 (2006), [hep-ph/0605100]

AB t P1 ... Pn−1

b W+

l+ ν

Lepton distribution is independent of anomalous tbW coupling if

t-quark is on-shell; narrow-width approximation for t-quark,

Ritesh SINGH – p. 4/13

Les Houches 2009

Lepton distribution

JHEP 0612, 021 (2006), [hep-ph/0605100]

AB t P1 ... Pn−1

b W+

l+ ν

Lepton distribution is independent of anomalous tbW coupling if

t-quark is on-shell; narrow-width approximation for t-quark,

anomalous couplings f1R, f2R and f2L are small,

Ritesh SINGH – p. 4/13

Les Houches 2009

Lepton distribution

JHEP 0612, 021 (2006), [hep-ph/0605100]

AB t P1 ... Pn−1

b W+

l+ ν

Lepton distribution is independent of anomalous tbW coupling if

t-quark is on-shell; narrow-width approximation for t-quark,

anomalous couplings f1R, f2R and f2L are small,

narrow-width approximation for W -boson,

Ritesh SINGH – p. 4/13

Les Houches 2009

Lepton distribution

JHEP 0612, 021 (2006), [hep-ph/0605100]

AB t P1 ... Pn−1

b W+

l+ ν

Lepton distribution is independent of anomalous tbW coupling if

t-quark is on-shell; narrow-width approximation for t-quark,

anomalous couplings f1R, f2R and f2L are small,

narrow-width approximation for W -boson,

b-quark is mass-less,

Ritesh SINGH – p. 4/13

Les Houches 2009

Lepton distribution

JHEP 0612, 021 (2006), [hep-ph/0605100]

AB t P1 ... Pn−1

b W+

l+ ν

Lepton distribution is independent of anomalous tbW coupling if

t-quark is on-shell; narrow-width approximation for t-quark,

anomalous couplings f1R, f2R and f2L are small,

narrow-width approximation for W -boson,

b-quark is mass-less,

t → bW (ℓνℓ) is the only decay channel for t-quark.

Ritesh SINGH – p. 4/13

Les Houches 2009

Polarization of t-quark: top-down

Polarized cross-sections :

Z

d3pt

2Et(2π)3

n−1Y

i=1

d3pi

2Ei(2π)3

!

(2π)4

2Iρ(λ, λ′) δ4

kA + kB − pt −

n−1X

i=1

pi

!!

= σ(λ, λ′).

Ritesh SINGH – p. 5/13

Les Houches 2009

Polarization of t-quark: top-down

Polarized cross-sections :

Z

d3pt

2Et(2π)3

n−1Y

i=1

d3pi

2Ei(2π)3

!

(2π)4

2Iρ(λ, λ′) δ4

kA + kB − pt −

n−1X

i=1

pi

!!

= σ(λ, λ′).

Total cross-section :

σtot = σ(+, +) + σ(−,−)

Ritesh SINGH – p. 5/13

Les Houches 2009

Polarization of t-quark: top-down

Polarized cross-sections :

Z

d3pt

2Et(2π)3

n−1Y

i=1

d3pi

2Ei(2π)3

!

(2π)4

2Iρ(λ, λ′) δ4

kA + kB − pt −

n−1X

i=1

pi

!!

= σ(λ, λ′).

Total cross-section :

σtot = σ(+, +) + σ(−,−)

Polarization density matrix :

Pt =1

2

(

1 + η3 η1 − iη2

η1 + iη2 1 − η3

)

,

η3 = (σ(+, +) − σ(−,−)) /σtot

η1 = (σ(+,−) + σ(−, +)) /σtot

i η2 = (σ(+,−) − σ(−, +)) /σtot

Ritesh SINGH – p. 5/13

Les Houches 2009

Polarization of t-quark: bottom-up

Polarization of t-quark through decay asymmetries:

αb = −0.4

αl = +1.0

αf

η3

2=

σ(pf .s3 < 0) − σ(pf .s3 > 0)

σ(pf .s3 < 0) + σ(pf .s3 > 0)

αf

η2

2=

σ(pf .s2 < 0) − σ(pf .s2 > 0)

σ(pf .s2 < 0) + σ(pf .s2 > 0)

αf

η1

2=

σ(pf .s1 < 0) − σ(pf .s1 > 0)

σ(pf .s1 < 0) + σ(pf .s1 > 0)si.sj = −δij pt.si = 0

For pµt = Et(1, βt sin θt, 0, βt cos θt), we have

sµ1 = (0,− cos θt, 0, sin θt), sµ

2 = (0, 0, 1, 0), sµ3 = Et(βt, sin θt, 0, cos θt)/mt.

Ptlong is implemented in SHERPA.

Ritesh SINGH – p. 6/13

Les Houches 2009

Polarization of t-quark: Reconstruction

η2 : transverse polarization normal to the production plane.

Simplest quantity to measure;requires reconstruction of t-production plane;

Ritesh SINGH – p. 7/13

Les Houches 2009

Polarization of t-quark: Reconstruction

η2 : transverse polarization normal to the production plane.

Simplest quantity to measure;requires reconstruction of t-production plane;

η1 : transverse polarization in the production plane.

requires reconstruction of t-production plane and cos θt;

Ritesh SINGH – p. 7/13

Les Houches 2009

Polarization of t-quark: Reconstruction

η2 : transverse polarization normal to the production plane.

Simplest quantity to measure;requires reconstruction of t-production plane;

η1 : transverse polarization in the production plane.

requires reconstruction of t-production plane and cos θt;

η3 : average helicity.

requires reconstruction of t-production plane, cos θt and Et;

Ritesh SINGH – p. 7/13

Les Houches 2009

Polarization of t-quark: Reconstruction

η2 : transverse polarization normal to the production plane.

Simplest quantity to measure;requires reconstruction of t-production plane;

η1 : transverse polarization in the production plane.

requires reconstruction of t-production plane and cos θt;

η3 : average helicity.

requires reconstruction of t-production plane, cos θt and Et;

Energy and angular distribution of leptons in lab frame can be used asa measure of the t-polarization.

Ritesh SINGH – p. 7/13

Les Houches 2009

Polarization estimation: Φℓ

Lab frame azimuthal distribution of leptons: (JHEP 0612, 021 (2006))

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0 1 2 3 4 5 6

(1/σ

) dσ

/dφ l

[ra

d-1]

φl [rad]

η3 = +0.83η3 = -0.83η3 = +0.73η3 = -0.48

Ritesh SINGH – p. 8/13

Les Houches 2009

Polarization estimation: Φℓ

Lab frame azimuthal distribution of leptons: (JHEP 0612, 021 (2006))

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0 1 2 3 4 5 6

(1/σ

) dσ

/dφ l

[ra

d-1]

φl [rad]

η3 = +0.83η3 = -0.83η3 = +0.73η3 = -0.48

Aℓ =σ(cos φl > 0) − σ(cos φl < 0)

σ(cos φl > 0) + σ(cos φl < 0)

Used for:

• Z′ at LHC (Les Houches 05)

• g(1) in RS model at LHC

(Nucl. Phys. B797, 1, (2008))

Ritesh SINGH – p. 8/13

Les Houches 2009

Polarization estimation: Φℓ

Lab frame azimuthal distribution of leptons: (JHEP 0612, 021 (2006))

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

Al(m

tt)

mtt [ x 103 GeV]

[ p p → t t ]

E1

SMSM + RS

Aℓ =σ(cos φl > 0) − σ(cos φl < 0)

σ(cos φl > 0) + σ(cos φl < 0)

Used for:

• Z′ at LHC (Les Houches 05)

• g(1) in RS model at LHC

(Nucl. Phys. B797, 1, (2008))

Ritesh SINGH – p. 8/13

Les Houches 2009

Polarization estimation: Φℓ

0

0.5

1

1.5

2

2.5

3

3.5

4

0 π/2 π 3π/2 2π

2π/σ

dσ/

dφ

φ (rad)

Pa = ( 0.734,-0.6)η3 < 10-3, η1 = +0.085

b/a = π η1/4 = +0.067

lνb

lMa+b cos(φ)

∆ =

∣

∣

∣

∣

dσ

dφl

− dσ

dφb

∣

∣

∣

∣

Depends upon:

• Top polarization

• pTt

distribution

Ritesh SINGH – p. 9/13

Les Houches 2009

Polarization estimation: Φℓ

0

0.5

1

1.5

2

2.5

3

3.5

4

0 π/2 π 3π/2 2π

2π/σ

dσ/

dφ

φ (rad)

Pp = ( 0.8,-0.6)η3 = +0.559, η1 = -0.504

b/a = π η1/4 = -0.396

lνb

lMa+b cos(φ)

∆ =

∣

∣

∣

∣

dσ

dφl

− dσ

dφb

∣

∣

∣

∣

Depends upon:

• Top polarization

• pTt

distribution

Ritesh SINGH – p. 9/13

Les Houches 2009

Polarization estimation: Φℓ

0

0.5

1

1.5

2

2.5

3

3.5

4

0 π/2 π 3π/2 2π

2π/σ

dσ/

dφ

φ (rad)

Pm = (-0.8, 0.6)η3 = -0.471, η1 = +0.591

b/a = π η1/4 = +0.464

lνb

lMa+b cos(φ)

∆ =

∣

∣

∣

∣

dσ

dφl

− dσ

dφb

∣

∣

∣

∣

Depends upon:

• Top polarization

• pTt

distribution

Next we look at LHC examples.

Ritesh SINGH – p. 9/13

Les Houches 2009

LHC: pp → tj → bl+νl j

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 π/4 π/2 3π/4 π

(1/σ

) dσ

/dΦ

Φ

Leptonb-quark

∆ =

∣

∣

∣

∣

dσ

dφl

− dσ

dφb

∣

∣

∣

∣

Depends upon:

• Top polarization

• pTt

distribution

σ = 14.6 pbη3 = −0.196

Model: SM

"Partial" analysis with anomalous tbW coupling at D0

Phys. Rev. Lett. 102, 092002 (2009)

Cuts: No cuts

Ritesh SINGH – p. 10/13

Les Houches 2009

LHC: pp → tj → bl+νl j

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 100 200 300 400 500 600 700 800

(1/

σ) d

σ/dp

tT

ptT

∆ =

∣

∣

∣

∣

dσ

dφl

− dσ

dφb

∣

∣

∣

∣

Depends upon:

• Top polarization

• pTt

distribution

σ = 14.6 pbη3 = −0.196

Model: SM

"Partial" analysis with anomalous tbW coupling at D0

Phys. Rev. Lett. 102, 092002 (2009)

Cuts: No cuts

Ritesh SINGH – p. 10/13

Les Houches 2009

LHC: pp → tt̄ → bl+νl b̄l−ν̄l

0

1

2

3

4

5

6

7

8

9

0 π/4 π/2 3π/4 π

(1/σ

) dσ

/dφ

φ

Leptonb-quark

∆ =

∣

∣

∣

∣

dσ

dφl

− dσ

dφb

∣

∣

∣

∣

Depends upon:

• Top polarization

• pTt

distribution

σ = 41.5 fbη3 = +0.819

Model: SM+g(1)

Mg = 3000 GeV, Γg = 500 GeV

CtL = 1.118, Ct

R = 5.201Cuts: mtt̄ := [2500, 3500] GeV

Ritesh SINGH – p. 11/13

Les Houches 2009

LHC: pp → tt̄ → bl+νl b̄l−ν̄l

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0 200 400 600 800 1000 1200 1400 1600 1800

(1/

σ) d

σ/dp

tT

ptT

∆ =

∣

∣

∣

∣

dσ

dφl

− dσ

dφb

∣

∣

∣

∣

Depends upon:

• Top polarization

• pTt

distribution

σ = 41.5 fbη3 = +0.819

Model: SM+g(1)

Mg = 3000 GeV, Γg = 500 GeV

CtL = 1.118, Ct

R = 5.201Cuts: mtt̄ := [2500, 3500] GeV

Ritesh SINGH – p. 11/13

Les Houches 2009

LHC: pp → t̃1˜̄t → bl+νlχ̃

01 b̄l−ν̄lχ̃

01

0

0.5

1

1.5

2

2.5

3

3.5

0 π/4 π/2 3π/4 π

(1/σ

) dσ

/dΦ

Φ

Leptonb-quark

∆ =

∣

∣

∣

∣

dσ

dφl

− dσ

dφb

∣

∣

∣

∣

Depends upon:

• Top polarization

• pTt

distribution

σ = 9.53 × 10−2 fbη3 = +0.92

Model: MSSMMt̃1

= 760 GeV, Mχ1= 184 GeV

Br(t̃1 → tχ̃01) = 0.407

Cuts: No cuts.

Ritesh SINGH – p. 12/13

Les Houches 2009

LHC: pp → t̃1˜̄t → bl+νlχ̃

01 b̄l−ν̄lχ̃

01

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 200 400 600 800 1000 1200 1400 1600 1800

(1/

σ) d

σ/dp

tT

ptT

∆ =

∣

∣

∣

∣

dσ

dφl

− dσ

dφb

∣

∣

∣

∣

Depends upon:

• Top polarization

• pTt

distribution

σ = 9.53 × 10−2 fbη3 = +0.92

Model: MSSMMt̃1

= 760 GeV, Mχ1= 184 GeV

Br(t̃1 → tχ̃01) = 0.407

Cuts: No cuts.

Ritesh SINGH – p. 12/13

Les Houches 2009

Polarization estimation: Eℓ

Lab frame energy distribution of leptons:

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 20 40 60 80 100 120 140 160 180 200 220

(1/σ

) dσ

/dE

llab [

GeV

-1]

Ellab [GeV]

QED : η3 = +0.83QED : η3 = -0.83

NSM : η3 = +0.73NSM : η3 = -0.48

Ritesh SINGH – p. 13/13

Les Houches 2009

Polarization estimation: Eℓ

Lepton energy fraction in lab frame u = El/(El + Eb)

Shelton Phys. Rev. D 79, 014032 (2009)(Plots from Rohini’s talk @TOP09)

0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

(1/Γ

) dΓ

/du

u

P = 1

P = 0

P = -1

f2R= -0.3f2R= 0.0f2R= 0.3

Ritesh SINGH – p. 13/13

Les Houches 2009

Polarization estimation: Eℓ

Lepton energy fraction in lab frame u = El/(El + Eb)

Shelton Phys. Rev. D 79, 014032 (2009)(Plots from Rohini’s talk @TOP09)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

(1/Γ

) dΓ

/du

u

P = 0.2

P = 0

P = -0.2

f2R= -0.3f2R= 0.0f2R= 0.3

Ritesh SINGH – p. 13/13