Top Quark Physics at the LHC
(Theory)
Werner Bernreuther
RWTH Aachen
Physics Issues:
• Unique opportunity to investigate interactions of a bare quark
at energies ∼ a few 100 GeV
• Dynamics of top production and decay is not explored very precisely so far
Profile: mass, charge, spin, decay modes & width
Excellent probe of mechanism of electroweak gauge-symmetry breaking
New decay modes ? t → t̃ ..., FCNC decays t → c ?
or sizeable FCNC in top production: pp → tc̄ X ?
Good probe also for non-SM parity and/or non-SM CP violation
(induced, e.g., by non-standard Higgs bosons)
....
Strong and electroweak interaction effects of top quarks can be reliably predicted – asset!
Role of Top in the SM and beyond
• Top mass: important parameter for precision electroweak constraints
Recent CDF and D0 average: mt = 170.9 ± 1.8 GeV
EW fit in SM (LEP EWWG): mH < 182 GeV @ 95 % C.L.
80.5
LEP1 and SLD
LEP2 and Tevatron (prel.)
mW [GeV]
68% CL
80.4
80.3
mH [GeV]
114
300
150
∆α
1000
175
200
mt [GeV]
• Flavour physics: top mass and its couplings determine,
e.g., rare B decay modes:
B → Xsγ, Bs → µ+µ−, · · ·
• Higgs physics at LHC: Top quark probes (SM) Higgs sector through its
Yukawa coupling(s): gg → H, associated production tt̄H
Top plays an important role also in many SM extensions:
e.g. in MSSM: large top Yukawa coupling
→ rescues MSSM from LEP2 lower bound on mh
→ allows for radiative electroweak symmetry breaking
viable scenario in the MSSM
This mechanism is also essential for Little Higgs models
Top ↔ “dynamical” breaking of electroweak symmetry ?
i.e., condensation of tLt̄R or of tLχ̄R ?
OUTLINE
• Top decay
• tt̄ production
• Single top production
Top decay
In the SM: t quark decays almost 100 % into
t→b+W
+
Top decay width: Γt = 1.4 GeV → lifetime τt ' 4 × 10−25 sec
→ t and t̄ decay before they can form hadronic bound states (tq̄), (tqq 0)
top quark ∼ quasi-free, instable particle
→ top-quark spin effects are measurable – and calculable !
Decay vertex t → b + W +
tbW vertex ∝ b̄γ µ(fLPL + fR PR )tWµ− + b̄iσ µν mqν (gLPL + gR PR )tWµ− + h.c.
W
In the SM:
mb 6= 0 + QCD & EW corrections −→ P rob(hW = +1) ' 0.1%.
Do et al.
Exp. determination by helicity analysis; not yet measured precisely at Tevatron.
LHC perspectives: |fR | < 0.06, |gL| ' |gR | < 0.02
Hubaut et al. ; Aguilar-Saavreda et al.
Decays of (polarized) top quarks:
semileptonic decays: t −→ b `+ ν`,
b `+ ν` + gluons
non-leptonic decays: t −→ b q̄1 q2, b q̄1 q2 + gluons
respectively
t −→ jb j1 j2, jb j1 j2 j3
Differential distributions known at NLO in the SM couplings
Czarnecki, Jezabek, Kühn;
Fischer et al.;
Brandenburg, Si, Uwer; ...
In particular: Ensemble of top quarks self-analyses its spin polarization
dΓ
1
1
Decay distribution of (100 %) polarized t → f + ...
Γ d cos θ = 2 (1 + cf cos θf )
f
Best t-spin analyzers:
SL decays: charged lepton, c` = 0.999
NL decays: least energetic non-b jet, cj< = 0.47
Other top decay modes?
In SM: Br(t → W +s) < 10−3, Br(t → W +d) < 10−4
FCNC decays t → c g , t → c Z , t → c γ : Br < 10−11
FCNC modes can be somewhat larger in SM extensions
−5
< 10−6 in MSSM (Li et al.; Guasch et al., ....)
e.g., Br(t → cg ) <
10
,
Br(
t
→
cZ
)
∼
∼
Decay modes t → H + or t → t̃ ?
Tevatron constraints still leave some windows open
Production of top quarks at (future) accelerators
t̄t pairs
dominant reaction
Ntt̄/year
Tevatron: pp̄ 1.96 TeV
q q̄ → tt̄
∼ 104
LHC: pp 14 TeV
gg → tt̄
∼ 107 - 108
ILC: e+e− (500 GeV)
e+e− → tt̄
∼ 105
single top
dominant reaction
(Nt + Nt̄)/year
Tevatron:
u + b−→d + t
W
∼ a few ×103
LHC:
u + b−→d + t
W
∼ 106 - 107
tt̄ production at Tevatron and LHC:
main reactions
8
miss
< 2` + n ≥ 2 jets + PT
pp̄, pp → tt̄X →
` + n ≥ 4 jets + Pmiss
T
:
n ≥ 6 jets
within SM:
tt̄ production dominated by strong interactions: q q̄ → tt̄, gg → tt̄, · · ·
weak decays of t and t̄: t → b`ν` (semileptonic), t → bq q̄ 0 (non-leptonic)
BR(2`) : BR(` + jets) : BR(jets) ' 0.05 : 0.30 : 0.46 for ` = e, µ
Tevatron: σ(tt̄)exp = 7.3 ± 1.2 pb (from ` + jets channels)
LHC: σ(tt̄) ' 830 pb,
goal: δσ(tt̄)exp < 10%
Status of Theory (SM results):
• Spin-averaged cross sections
σ(pp, pp̄ → tt̄X), dσ/dpT , ... knownhto orderi α3s
+ resummed “threshold logarithms” α3s ln(1−z)
, z = Q2/ŝ
1−z
+
(Nason et al.; Beenakker et al.; Bonciani et al.; Kidonakis et al.; Cacciari et al.; ...)
• recent progress towards NNLO (O(α4s )) computations of σtt̄ (Mitov, Moch, Czakon)
• cross section for tt̄+ jet at NLO QCD (Dittmaier, Uwer, Weinzierl);
important background to Higgs searches: weak boson fusion W +W − → H , and tt̄H .
• Differential cross sections pp, pp̄ → tt̄X → final states,
including the t and t̄ spin d.o.f.
known to NLO QCD + O(α2s αW ) corrections (W.B., Brandenburg, Si,Uwer)
allows prediction of tt̄ spin correlations; large QCD-dominated effect.
• Mixed QCD-weak interaction corrections (O(α2s αW )):
(Beenakker et al.; W.B.,Fücker, Si;
Kühn, Scharf, Uwer)
irrelevant for σtt̄, but important for pT and Mtt̄ distributions for large pT , Mtt̄ ∼ TeV
(weak Sudakov logs)
Precision goals, e.g., for tt̄ cross section:
Tevatron: δσ(tt̄)th ∼ 10%
goal for LHC: δσ(tt̄)th ∼ 5%
(scale and PDF uncertainties)
Determination of the top quark mass
Fitting methods at Tevatron:
template method, matrix element method, ideogram method, ...
= 170.9 ± 1.8 GeV
Recent CDF & D0 average: mexp
t
Expts. use Born matrix elements in their fitting procedures
Experimental issues: (b) jet energy scale, b tagging, underlying events,...
mexp
has an error of 1 % – but which mass is measured?
t
• relation to mass parameter in Lagrangian?
• top mass used in Monte Carlos?
Problem hard to address - but becomes relevant now
Goals: δmexp
' 1.3 GeV (Tevatron), 1 GeV (LHC)
t
NLO QCD predictions for hadronic tt̄ production typically use on-shell mass mpole
,
t
pole
which seems natural choice. mt
has ambiguity of O(ΛQCD ), but
may eventually be replaced by some short-distance mass parameter;
i.e., this is not the problem.
mtop from peak of invariant mass distribution
Consider, e.g., reactions
pp, pp̄ → t̄tX → `−ν̄`jb̄ + jbj1j2 + soft hadrons
Top mass may be determined from
position of the peak of invariant mass distribution dσ/dMt,
Mt =
q
(pjb + pj1 + pj2 )2.
because of soft QCD effects (i.p. color recombination):
Obviously, peak position differs from mpole
t
• in perturbation theory:
non-factorizable QCD corr. to hard scattering 2→6 matrix elements.
computed to O(α3s ) (Beenakker et al.; W.B., Fücker, Meyer, Si)
small effect: shift of peak maximum with respect to mpole
only by <
t
∼ 100 MeV.
• non-perturbative soft QCD effects;
esp. color exchange between t, t̄ decay products and beam remnants.
Recent analysis by Skands, Wicke using a Monte Carlo model:
→ δmt ' 0.5 GeV (color recombination)
and δmt ' 1 GeV (parton shower)
Errors already partially included in present data analyses?
Recent interesting analysis by Fleming et al.,
but applicable only to e+e− production far above threshold:
e+e− → tt̄X
Define short distance jet mass mJ
as maximum of a perturbatively calculable jet function (∼ distorted Breit-Wigner)
mJ ↔ mpole
in perturbation theory
t
parameterize soft QCD effects (cross-talk between the 2 hemisphere jets in the above simple
kinematic situation); requires input from exp. jet analyses
t, t̄ polarization and tt̄ spin correlations
• polarization of t, t̄ in hadronic tt̄ production (very) small, ∼ 1%:
t polarization in production plane (parity-violating) due to weak interactions, e.g., < st · k̂t >
“normal” polarization (P-even, T-odd) due to QCD absorptive parts
• tt̄ spin correlations: large effect in the SM, dominated by QCD.
< (â · st)(b̂ · st̄) > = A/4
Strength depends on the choice of reference axes â, b̂. Choices:
â = k̂t, b̂ = k̂t̄
â = b̂ = p̂
(helicity basis; good for LHC)
(beam basis; good for Tevatron)
Top polarization, tt̄ spin correlations → at level of final states:
non-isotropic angular distributions and non-zero angular correlations with resp. to chosen reference
axes:
Suitable analysis channels:
tt̄ → `+`0− + · · ·
and lepton + jets channels:
tt̄ → `+j + · · ·
where j = jb̄ or j<.
(` = e, µ)
Predictions at level of t, t̄ decay products
Consider, e.g., dilepton channels
pp, pp̄ → tt̄ + X → `+`0− + X .
• double distribution:
1
d2 σ
σ d cos θ+ d cos θ−
θ+ = ∠(`+, â),
=
1
4 {1
+ B1 cos θ+ + B2 cos θ− − C cos θ+ cos θ−}
θ− = ∠(`0−, b̂) in resp. t, t̄ rest frames.
B1,2 ↔ polarization of t, t̄.
In SM: |B1|, |B2| < 1% (W.B.,Fücker, Si)
→ dσ/d cos θ± sensitive to non-SM P-violating interactions
C ↔ tt̄ spin correlations.
All-order formula (factorizable corrections):
C = A c+c−
• opening angle distribution also sensitive to tt̄ spin correlations:
1 dσ
σ d cos φ
φ = ∠(`+, `0−) in resp. t, t̄ rest frames.
=
1
2
(1 − D cos φ)
Predictions to NLO QCD
(PDF input: CTEQ6L and CTEQ6.1M)
Tevatron,
``
Chel
Cbeam
D
`+j
Chel
Cbeam
D
√
s = 1.96 TeV
LHC,
√
s = 14 TeV
LO
−0.471
0.928
0.297
NLO
−0.352
0.777
0.213
LO
0.319
−0.005
−0.217
NLO
0.326
−0.072
−0.237
−0.240
0.474
0.151
−0.168
0.370
0.101
0.163
0.158
−0.111
−0.115
W.B., A. Brandenburg, Z.G. Si, P.Uwer
• good choices: beam basis for Tevatron, helicity basis and opening angle distribution (D ) for LHC
• order αW α2s weak interaction corrections only a few percent (W.B., M. Fücker, Z.G. Si )
• effects enhanced by suitable cuts on Mtt̄
• LHC study of dilepton and lepton + jets events at the detector level:
F. Hubaut et al.: δD ' 4%, δChel ' 6%
−→ spin observables useful for probing the dynamics of tt̄ production & decay
sensitive to anomalous gtt̄ couplings (P. Haberl, O. Nachtmann, A. Wilch), to residual effects of heavy resonances,
....
Other observables sensitive to BSM physics:
pT distribution of top, and tt̄ invariant mass distribution Mtt̄ =
p
(pt + pt̄)2.
Precise SM predictions required,
mixed weak-QCD corrections of O(αW α2s ) become relevant (weak Sudakov logs) esp. for large
pT , Mtt̄ & 1 TeV.
Size of mixed contributions at LHC:
W.B., M. Fücker, Z.G. Si;
pp → tt̄ + X
J. Kühn, A. Scharf, P. Uwer
ratio (dσweak /dpT ) / (dσLO /dpT )
-0
ratio (dσweak /dMtt̄) / (dσLO /dMtt̄)
0
-0.05
-0.05
-0.1
-0.15
-0.2
-0.1
500
1000
p [GeV]
1500
2000
1000
T
solid: mH = 120 GeV,
dashed: mH = 200 GeV
2000
Mtt [GeV]
3000
4000
Main interest: Search for heavy resonances that strongly couple to tt̄
Extensions of SM, e.g. supersymmetric extensions, top-condensation, extra dim. models ...
→ heavy resonances ϕJ that strongly couple to top quarks
ϕJ : could be a Higgs boson, a bound state, a KK excitation ...
many investigations (more recent ones: Lillie et al., Djouadi et al.,.....)
Example: 2HDMs or MSSM → Higgs boson A with J P C = 0−+
A may be heavy, mA > 300 GeV
A→
/ W +W −, ZZ in lowest order, but A can strongly couple to top quarks
→ at LHC
gg −→ A −→ tt̄ −→ final state
gg −→ tt̄ −→ final state
interference of amplitudes leads to typical peak-dip resonance structure
LHC: pp → A + X → tt̄ + X → `+ Jets
Example: mA = 400 GeV, ΓA = 12 GeV, tan β = 4
dσ
tt̄ invariant mass distribution σ1 dM
(W.B., Flesch, Haberl)
tt̄
0.04
0.02
0
400
500
600
700
exp. resolution and understanding of non-resonant background crucial
Single top production:
• weak
inreplacements
production; in SM:
σtreplacements
∝ |Vtb|2
PSfraginteractions
replacements involved
PSfrag
PSfrag
• source of polarized
tops
g
g
in SM:
s channel
Wt+ channel
W +tW mode
W−
u
d
d
b
W−
d̄
b
b̄
Predictions:
u
W+
d¯
t
Harris et al., Campbell et al.,....(NLO QCD)
σT ev
t
σLHC
t̄
σLHC
[pb]
[pb]
[pb]
ub
d
t
t
b
g
d¯
b̄
b̄
W−
Kidonakis (NLO QCD + resummed “threshold” logs)
(NLO QCD)
0.54(4)
<0.1
0.14(3)
154
6.2
30
(NLO QCD)
150(6)
7.8(7)
44(5)
(resummed)
89
3.8
30
(NLO QCD)
1.0
0.44
1.15(7)
Recent evidence for single top production at Tevatron: D0 collab. (Dec. 2006)
• σt channel + σs channel + c.c. modes = 4.9 ± 1.4 pb
→ V − A coupling |Vtb fL | = 1.3 ± 0.2
(resummed)
Different final states for t-, s-channel and associated tW production
Large backgrounds from W bb̄, W + jets, tt̄, ...
At LHC:
S/B increases as compared to Tevatron
W
t-channel: u + b−→d + t:
largest rate, in final state: forward (d) jet,
t polarization largest along axis || spectator jet
(Mahlon, Parke).
W
s-channel: u + d¯−→t + b̄:
smallest rate, extra b jet in final state,
PDF uncertainites are smallest → |Vtb| from σs−channel . Goal: δVtb ∼ 5%
Production channels sensitive to different signals of new physics:
• t-channel → flavor-changing neutral currents
tc̄, tū production ∼ a few pb in unconstrained MSSM (Liu et al.)
larger tc̄ cross section in top-color type models (Cao et al.)
• tW mode → charged Higgs bosons
g + b → t + H − + c.c. mode
• s-channel → new charged boson resonances
W0
X+
u + d¯−→t + b̄
or
c + b̄−→t + b̄
where, e.g., X + = H + (charged Higgs), or Π+ (top-pion)
Conclusions
• Physics of top quarks remains to be fully explored,
both in tt̄ and in single top production & decay
• Unique opportunity to investigate the interactions of a bare quark
below attometer scale
• Excellent probe of mechanism of EWSB, of possible heavy resonances,
of possible FCNC interactions in the IW = +1/2 quark sector, ...
• SM predictions for top as a signal at LHC in reasonably good shape.
• Spin effects – useful tools in exploring the dynamics of top quarks
unique feature (as compared to b, c,..),
• Some challenges for theory:
Interpretation of mexp
(at <
t
∼1% level) in terms of Lagrangian mass
Precise predictions of distributions
σtt̄ to NNLO QCD