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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