zack sullivan - smu

CTEQ Summer School 2007

THE TRUTH ABOUT tt PRODUCTION

q

q

t

tg

g

t

t

g

g

t

t

g

g

t

t

Zack SullivanSouthern Methodist University

Zack Sullivan, Southern Methodist University – p.1/34

“This is the top quark.”


Contents

What we want to know

1. mt: Top-quark mass— and EW physics

2. σtt: Top-quark cross section— threshold region— new physics

3. yt: Top-quark Yukawa— ttH and tH−

4. ~st: Top decay and spin— longitudinal W -bosons


Of course the top had been found before. . .

Phys. Lett. B 182, 388 (1986)


The real evidence. . . (1995)


Why study the top-quark mass?Answer: Electroweak (EW) precision physics

EW radiative corrections depend on the top-quark mass (mt).Using the value measured at the Fermilab Tevatron, EW precision fitsconstrain the Higgs boson mass MH .Both the top quark and Higgs contribute at 1-loop to the W/Z propagtors.

Assuming α, GF , and MZ as inputs, M2W at 1-loop is:

M2W =

πα√2GF sin2 θW

1

1 − ∆r(mt, mH)

where ∆r(mt, mH) ≈ ctm2t = cH ln(M2

H/M2Z) + · · ·

Inverting the formula provides a logarithmic contraint on MH .Higgs searchers put it differently: the top quark provides a largecorrection to the Higgs self-energy.

H H

t

t

+ H H

t


Constraints on Higgs mass from W and t

MH is logarithmically sensitive to variations of MW and mt.

80.2

80.3

80.4

80.5

80.6

130 150 170 190 210

mH [GeV]114 300 1000

mt [GeV]

mW

[G

eV]

Preliminary

68% CL

∆α

LEP1, SLD DataLEP2, pp

− Data End of Run I

mt = 174.3 ± 5.1 GeV (3%)(Better than EW precision)

Early Summer 2005mt = 178.0 ± 4.3 GeV (fishy)

Late Summer 2005mt = 172.7 ± 2.9 GeV

Top-Quark Mass [GeV]

mt [GeV]140 160 180 200

χ2/DoF: 9.2 / 10

CDF 170.1 ± 2.2

D∅ 172.0 ± 2.4

Average 170.9 ± 1.8

LEP1/SLD 172.6 + 13.2172.6 − 10.2

LEP1/SLD/mW/ΓW 178.9 + 11.7178.9 − 8.6

80.3

80.4

80.5

150 175 200

mH [GeV]114 300 1000

mt [GeV]

mW

[G

eV]

68% CL

∆α

LEP1 and SLDLEP2 and Tevatron (prel.)

Winter 2007mt = 170.9 ± 1.8 GeV(Same as the firsttt event. . .)Tevatron EWWG


Famous “blue-band” plotsMuch ado about nothing

0

1

2

3

4

5

6

10030 500

mH [GeV]

∆χ2

Excluded

∆αhad =∆α(5)

0.02758±0.000350.02749±0.00012incl. low Q2 data

Theory uncertainty

Early summer 2005,Higgs searchers euphoric:“Higgs on the verge of discovery”

MH = 117+67−45 GeV

MH < 251 GeV(95%)

0

1

2

3

4

5

6

10030 300

mH [GeV]

∆χ2

Excluded Preliminary

∆αhad =∆α(5)

0.02758±0.000350.02749±0.00012incl. low Q2 data

Theory uncertaintymLimit = 144 GeV

Winter 2007,Higgs searchers euphoric:“Higgs on the verge of exclusion”

MH = 78+33−24 GeV

MH < 144 − 187 GeV(95%)1. These plots are only valid in the SM.2. Shift was less than 1σ. Zack Sullivan, Southern Methodist University – p.8/34

How well do we need to know mt?There is a better way to look at this in the SM.

80.25 80.30 80.35 80.40 80.45

MW [GeV]

0.2312

0.2315

0.2318

0.2320

0.2322

0.2325

sin2 θ ef

flept

todays uncertainty

∆α

mt

mH

δ(∆α) = +− 0.00016

SM (mH = 120, 200 GeV)

mt = 172.3 ... 176.3 GeV

∆mH = 0.2 GeV

68% CL:

LEP2/Tevatron

LHC

Beneke et al., hep-ph/0003033

• Assume MH is known.

• MW will be measured to ∼ 20 MeV⇒ Need mt to ∼ 3 GeV.

(We already know it to 1.8 GeV.)

• A linear collider can measure MW

to ∼ 6 MeV.Giga-Z can measure sin2 θW ∼ 10−5

⇒ Need mt to ∼ 1 GeV.

The bottom line: We have already saturated the information we canextract about a SM Higgs from top-quark measurements given anynear-term collider (i.e., LHC).My personal opinion: These indirect constraints are fun, but cannot betaken too seriously. Direct measurements will be made soon that will showus what Nature does.


How well do we want to know mt?Most excitement about Higgs production has nothing to do with the SM.

Models of new physics predict differentsensitivity to the top-quark mass.SUSY Higgs masses are VERY sensitive tothe top-quark mass

∆M2H ≈ 3GF m4

t√2π2 sin2 β

ln

(

m2t

m2t

)

• Experimental error from LHC may reach∼ 200 MeV (using rare decays)

• δMH ∼ δmt, so we will wantδmt ∼ 100 MeV.Warning: 4-loop corrections arecomparable in size.This needs major effort

If a smaller error in mt is achieved, we gainindirect access to MA, At, m1/2, etc.

150 200 250 300 350 400 450 500MA [GeV]

115

120

125

130

135

mh [G

eV]

∆mhexp mt = 175 GeV, tanβ = 5

theory prediction for mhδmt

exp = 2.0 GeVδmt

exp = 1.0 GeVδmt

exp = 0.1 GeV

200 400 600 800 1000 1200 1400m1/2 [GeV]

0

100

200

300

400

m0 [G

eV]

mh = 118 GeV

δmt = 2.0 GeV

δmt = 0.1 GeV

tanβ = 10, A0 = 0, µ > 0, mt = 175 GeV


MW vs. mt for MSSM Higgs

160 165 170 175 180 185mt [GeV]

80.20

80.30

80.40

80.50

80.60

80.70

MW

[GeV

]

SM

MSSM

MH = 114 GeV

MH = 400 GeV

light SUSY

heavy SUSY

SMMSSM

both models

Heinemeyer, Hollik, Stockinger, Weber, Weiglein ’07

experimental errors 68% CL:

LEP2/Tev (MW = 80.398 ± 0.025 GeV, mt = 170.9 ± 1.8 GeV)

Tev/LHC (δMW = 15 MeV, δmt = 1.0 GeV)

ILC/GigaZ (δMW = 7 MeV, δmt = 0.1 GeV)

“SUSY Higgs is favored”

160 165 170 175 180 185mt [GeV]

80.20

80.30

80.40

80.50

80.60

80.70

MW

[GeV

]

SM

MSSM

MH = 114 GeV

MH = 400 GeV

light SUSY

heavy SUSY

SMMSSM

both models

Heinemeyer, Hollik, Stockinger, Weber, Weiglein ’07

experimental errors: LEP2/Tevatron (today)

68% CL

95% CL

99.7% CL

No one tends to show this plot.

It is clear that whatever physics explains electroweak symmetrybreaking, there is at least an effective interaction whose mass scale is low.


How do we get to accurate top-quark mass?

Tevatron• Run IIa (2fb−1) predicted reach of ±3 GeV

Already at ±1.8 GeV (comb.) with 1 fb−1.• Expected a systematic brick wall at ±2 GeV.

So far, things are scaling like luminosity.• One major improvement:

Kinematic fits to MWb were usedA better choice assigns each event aprobability that is a function of mt.

)-1Integrated Luminosity (pb10

210

310

4

2(t

otal

) G

eV/c

t M∆

1

10

CDF Top Mass Uncertainty(l+l and l+j channels combined)

CDF Results

Run IIa goal (TDR 1996)

(syst)∆, Fix L(stat) / ∆Scale (assumes no improvements)

L(total) / ∆Scale (improvements required)

-11 fb -12 fb -14 fb -18 fb

M/M < 1%

∆

LHC• Several channels can reach < 1 GeV (stat.)• To reach systematics < 1 GeV use:

MJ/Ψ`ν w/ template for mt. (∼ 300 fb−1)

(e )µ+ +

/ψ( µµ)Jµ+

t tb

j

j

W W

ν

_ +

b_

_

.

Linear collider

• Strive for δmt ∼ 100 − 200 MeV.Requires a scan of tt threshold (understanding threshold is key)

To reach any of these accuracies requires better understanding oftt production & kinematics, and backgrounds. Zack Sullivan, Southern Methodist University – p.12/34

Residual errors in the top-quark massThe dominant errors at the Tevatron are now entirely due to modelling.

Systematic uncertainties (GeV/c2)

JES residual 0.42

Initial state radiation 0.72

Final state radiation 0.76

Generator 0.19

Background composition and modeling 0.21

Parton distribution functions 0.12

b-JES 0.60

b-tagging 0.31

Monte Carlo statistics 0.04

Lepton pT 0.22

Multiple Interactions 0.05

Total 1.36

One reducible uncertainty comes from modelling of the b jet, and itsenergy scale. This will improve with additional data.A recent study of QCD color-reconnection in showering may indicatelarger than expected showering ambiguities ∼ 1.5 GeV. Significantcomparisons with data are required before this will be resolved.Skands, Wicke, hep-ph/0703081 Zack Sullivan, Southern Methodist University – p.13/34

Top-quark pair (tt) production

qq → tt

Leading contribution atTevatron

Tev (RunII) 85%LHC 10%

q

q

t

t

gg → tt

Leading contribution at LHC

Tev (RunII) 15%LHC 90%

g

g

t

t

g

g

t

t

g

g

t

t

At the Tevatron, tt is produced close the the kinematic threshold s ≈ 4m2t ,

so x ∼ 0.2. At LHC x ∼ 0.02.A few dozen reconstructed tt pairs in Run I of the Tevatron was enoughfor discovery.At Run II there are already hundreds.At LHC there will be about 1 pair/second produced!


NLO calculations• The production rate of tt is a sensitive probe of strong interactions.

• tt production is already becoming a precision measurement.⇒ Very precise theory is required to understand the dynamics andmatch the experimental precision that will be available.

pp, pp → tt: O(αs) virtual corrections

The O(αs) virtual corrections to the cross-section arise from the

interference between the tree level amplitude A0(qq, gg → tt) and the

one-loop virtual amplitude Avirt1 (qq, gg → tt):

dσvirtij = d(PS2)

∑

2Re(Avirt1 A∗

0)

where Avirt1 (qq, gg → tt) receives contributions from self-energy, vertex and

box type loop-corrections:

q

q

t

t

q

q

t

t q

q t

t

g

g

t

t

g

g

t

t

g

g

t

t

most of which contains UV and IR divergences that need to be extracted

analytically.

pp, pp → tt: O(αs) real corrections

The O(αs) real corrections to the cross-section arise from the square of the

real gluon/quark emission amplitude Areal1 (qq, gg, qg → tt + (g/q/q)):

dσrealij = d(PS2+(g/q/q))

∑

|Areal1 |2

where Areal1 receives contributions from diagrams like:

q

q

t

t

g(k)q

q

t

t

g(k)

g

g

t

t

g(k)g

g

t

t

g(k)

q,q(k)

g

q,q(k)

t

t

IR singularities are extracted by looking for the region of the tt + (g/q/q)

phase space where sik → 0, where:

sik = 2pi ·k = 2Eik0(1 − βi cos θik)

• k0 → 0 : soft singularities (both massless and massive particles);

• cos θik → 0: collinear singularities (massless particles only, βi = 0).

Complete NLO calculations exist for total and differential cross sections.Nason, Dawson, Ellis, NPB 303, 607 (88), NPB 327, 49 (89);Beenakker, Kuijf, van Neerven, Smith, PRD 40, 54 (89);plus Meng, Schuler, NPB 351, 507 (91)

But this is not enough at the Tevatron. . .


Large threshold corrections in tt

The top-quark decays before the bound state forms. However,pseudo-bound states of tt near threshold (s = 4m2

t ) cause largelogarithmic enhancements to the cross section.Schematically, the tt NLO cross section is

σNLOij (m2

t , µ) =α2

s(µ)

m2t

{

c0ij + 4παs(µ)

[

c1ij(ρ) + c1

ij(ρ) ln

(µ2

m2t

)]}

; ρ =4m2

t

s

Near threshold, the LO cross section vanishes:

c0qq(ρ) ≈ TRCF

2Ncπβ

β→0−→ 0; c0gg(ρ) ≈ TR

N2c − 1

(CF − CA/2)πββ→0−→ 0

At NLO there are soft and collinear singularities:

c1qq(ρ)

β→0−→ 1

4π2c0qq(ρ)

[

(CF − CA/2)π2

2β+ 2CF ln2(8β2) − (8CF + CA) ln(8β2)

]

c1gg(ρ)

β→0−→ 1

4π2c0gg(ρ)

[N2

c + 2

Nc(N2c − 2)

π2

4β+ 2CA ln2(8β2) − (9N2

c − 20)CA

N2c − 2

ln(8β2)

]

c1qq(ρ)

β→0−→ 1

4π2c0qq(ρ)

[−2CF ln(4β2) + C2(µ

2/m2t )]

c1gg(ρ)

β→0−→ 1

4π2c0gg(ρ)

[−2CA ln(4β2) + C3(µ

2/m2t )]


Threshold resummationThreshold logarithms can be resummed via exponentiation, similar tothe case of Drell-Yan (DY) or e+e− →jets.Challenges are IS/FS interference, scale difference between mt and vt.

Historically, logs are resummed in moment space (Mellin-transform space)The cross section for the N -th moment under a Mellin-transform is:

σN (m2t ) =

∫ 1

0

dρ ρN−1σ(ρ, m2t )

The threshold region corresponds to the lim N → ∞, which leads tothreshold corrections of the form:

σLON

[

1 +

∞∑

n=1

αns

2n∑

m=1

cn,m lnm N

]

In Drell-Yan, this structure exponentiates to a radiative form factor ∆DY,N :

∆DY,N (αs) = exp

[ ∞∑

n=1

αns

n+1∑

m=1

Gn,m lnm N

]

= exp[

g(1)DY αs ln2 N︸︷︷︸

LL

+ g(2)DY αs ln N︸︷︷︸

NLL

+ g(3)DY α2

s lnN︸︷︷︸

NNLL

+ · · ·]


Realization of threshold resummation in tt

Generalizing Drell-Yan-like resummation to tt requires:— Dealing with soft-gluons from IS, FS, and IS/FS interference.— Dealing with gg color octet states.

The solution is to recast the cross section for moment N in the form:

σij =∑

I,J

M†ij,I,N [∆ij,N ]I,JMij,J,N

where the sum on I, J is over all color states, [∆ij,N ]I,J is the radiationform factor, and M are matrices in color space.The advantage is that it describes a formal expansion of the logarithmsthat can be improved to NNLL, NNNLL, NNNNLL, (and then you collapse)Formalism: Kidonakis, Sterman, PLB 387, 867 (96)

Implementation:Bonciani, Catani, Mangano, Nason, NPB 529, 424 (98)Kidonakis, Vogt, PRD 68, 114014 (03)Cacciari, Frixione, Mangano, Nason, JHEP 04, 68 (04)

Prior to this formalism there were 2 competing calculations thatperformed the integrations by truncating the moments. This wasmathematically inconsistent, but gave reasonable numerical results.May we never go back. . .Berger, Contapaganos, PRD 54, 2085 (96)Catani, Mangano, Nason, Trentadue, NPB 478, 273 (96)


Nomenclature and uncertaintiesBad nomenclature“NNLO-NNNLL”

This is horrible nomenclature.This is really NLO+the Sudakov-like re-summation we saw above, where theexponent is re-expanded to NNNLL.There is nothing NNLO about it. )2Top Quark Mass (GeV/c

160 162 164 166 168 170 172 174 176 178 180

) (pb

)t t

→ p(pσ

0

2

4

6

8

10

12

Cacciari et al. JHEP 0404:068 (2004) uncertainty±Cacciari et al.

Kidonakis,Vogt PIM PRD 68 114014 (2003)Kidonakis,Vogt 1PI

-1CDF II Preliminary 760 pb

Unusual uncertaintiesNLO scale uncertainty of ±10% −→ ±5% w/ NLL correctionIncluding PDF uncertainty, −→ ±15% at TevatronThere is an additional uncertainty due to expansion kinematics:

• 1 particle inclusive (1PI): s = (pq + pq)2

• Pair invariant mass (PIM): s = M 2tt = (pt + pt)

2

σ ±1PI/PIM±scale± PDFRun I 5.24± 0.31 ± 0.2 ±0.6 pbRun II 6.77± 0.42 ± 0.1 ±0.7 pb

LHC is not dominated bythreshold kinematics:σ = 825 ± 50 ± 100 ± 90 pb.Full NNLO is needed!


Tevatron data

) (pb)t t→ p(pσ0 2 4 6 8 10 12 14

0

9Cacciari et al. JHEP 0404:068 (2004)Kidonakis,Vogt PRD 68 114014 (2003)

2=175 GeV/ctAssume m*CDF Preliminary

Combined(old SLT,all-had)*

0.4±0.6±0.5±7.3)-1(L= 760 pb (lumi)± (syst) ±(stat)

All-hadronic: Vertex Tag*

0.5±1.52.0±1.0 ±8.3)-1(L=1020 pb

MET+Jets: Vertex Tag*

0.4±0.91.4±1.2 ±6.1)-1(L= 311 pb

Lepton+Jets: Soft Muon Tag 0.5±0.91.0±1.7 ±7.8)-1(L= 760 pb

Lepton+Jets: Vertex Tag*

0.5±0.8±0.5±8.2)-1(L=1120 pb

Lepton+Jets: Kinematic ANN*

0.3±0.9±0.6±6.0)-1(L= 760 pb

Dilepton*

0.4±0.7±1.1±6.2)-1(L=1200 pb

Lepton+Track*

0.5±0.5±1.3±9.0)-1(L=1070 pb

dilepton/l+jets (topological)

dilepton* (topological)

ltrack/emu* (combined)

tau+jets* (b-tagged)

alljets (b-tagged)

l+jets (b-tagged)

l+jets* (NN b-tagged)

l+jets* (topological)

230 pb–17.1

+1.2

-1.2

+1.4

-1.1pb

1050 pb–16.8

+1.2

-1.1

+0.9

-0.8pb

370 pb–18.6

+1.9

-1.7

+1.1

-1.1pb

350 pb–15.1

+4.3

-3.5

+0.7

-0.7pb

410 pb–14.5

+2.0

-1.9

+1.4

-1.1pb

420 pb–16.6

+0.9

-0.9

+0.0

-0.0pb

910 pb–18.3

+0.6

-0.5

+0.9

-1.0pb

910 pb–16.3

+0.9

-0.8

+0.7

-0.7pb

0 2 4 6 8 10 12

DØ Run II * = preliminary

σ (pp→ tt) [pb]

Winter 2007

Kidonakis and Vogt, PRD 68, 114014 (2003)

Cacciari et al., JHEP 0404, 068 (2004)mtop = 175 GeV

l+jets* (μ-tagged)

420 pb–17.3

+2.0

-1.8

+0.0

-0.0pb

(GeV)s1800 1850 1900 1950 2000

) (pb

)t t

→ p(pσ

0

2

4

6

8

10

12

2

=170 GeV/ctm

2

=175 GeV/ctm

2

=180 GeV/ctm

2=175 GeV/ctCacciari et al. JHEP 0404:068 (2004) m

CDF Run 2 Preliminary-1Combined 760 pb

CDF Run 1-1Combined 110 pb

Great agreement so far!Lighter top-quark mass preferred.Experiment will be betterthan theory soon.


tt threshold at a linear collider (LC)

There is a subtle question when you try tomake a precision measurement of QCD:What mass do you use?The pole mass is not defined beyond ΛQCD.In fact it is not well-defined at all, sincethere are no free quarks. 344 346 348 350 352

0.25

0.5

0.75

1

1.25

1.5

1.75

Yakovlev,Groote PRD63, 074012(01)

Solution: Use the 1S mass (pseudo bound state)There are large non-relativisitic corrections

σtt ∝ v∑(αs

v

)

×{

1∑

(αs ln v)

}

×{

LO(1) + NLO(αs, v) + NNLO(α2s, αsv, v2)

LL + NLL + NNLL

}

Normalization changes, but peak stable.δσtt is ±6% before ISR/beamstrahlungδmt ∼ 100 MeV is attainable Hoang, hep-ph/0310301


Looking for Z ′ resonancesNearly any model you write down that has an extended gauge structure[U(1), SU(2), etc.], KK modes of the Z or gluon, axigluons, top color, etc.will produce a new neutral current, generically called a Z ′.If you couple to quarks, you have the possibility of resonant productionand decay to top pairs at a hadron collider.

• All of limits are for models with enhanced coupling and narrow width.• There is no direct reach for a SM-like Z ′ right now.• MZ′ < 720 GeV leptophobic, KK limit not strictly applicable.


Top-quark Yukawa coupling yt

The top quark mass is generated as the coupling strength between thetop quark and Higgs LYukawa = −ytttH.

⇒yt ≈√

2mt

246 GeV= 0.98 ± 0.01

We want to measure yt directly to 1% to confirm its relationship with thetop-quark mass.

• Higgs exchange at threshold is too weak.

• Gluon-gluon fusion is indirect(and may be subject to interference effects)

g

gt

t

tH

• ttH associated production allows direct determination

We will see the reach is limited at LHC or a LC. Zack Sullivan, Southern Methodist University – p.23/34

ttH at LHC

Extracting yt from ttH requires anaccurate prediction for the measuredcross section.Fortunately, there are 2 fully differentialNLO calculations performed in differentways — they agreeBeenakker et al, NPB 653, 151 (03)Dawson et al, PRD 68, 034022 (03)

Unfortunately, uncertainties are large(∼20%):

µ : ±15%, PDF: ±6%, mt : ±7%

Combining H → bb and H → WW at LHC⇒ δyt ∼ ±10% at best

Let’s look at this more closely. . .

100 120 140 160 180 200Mh (GeV)

0

200

400

600

800

1000

1200

1400

σ LO,N

LO (f

b)

σLO , µ=µ0

σNLO , µ=µ0

σLO , µ=2µ0

σNLO , µ=2µ0

√s=14 TeV

µ0=mt+Mh/2

CTEQ5 PDF’s

Dawson et al, PRD 68, 034022 (03)

120 140 160 180 200 220 240

mh

0

5

10

15

20

25

30

35

40

45

50

y t/y

t

LHC, 300 fb-1 @ High Luminosity

2

3

2 +3

Maltoni, Rainwater, Willenbrock,PRD 66, 034022 (02)Zack Sullivan, Southern Methodist University – p.24/34

Production modes at LHC

Extraction of yt is part of a larger plan to extract several couplings at onceat the LHC.

Can the top Yukawa coupling be measured?

It comes from a more general strategy aimed at determining several

couplings at once. Consider all accessible channels at the LHC:

gg→ HWBFttHWH

l ττ l bbl ZZ l WWl γγ

MH (GeV)

∆σH/σ

H (%

)

0

5

10

15

20

25

30

35

40

110 120 130 140 150 160 170 180

• Below 130-140 GeV

gg → H , H → γγ,WW, ZZ

qq → qqH , H → γγ,WW, ZZ, ττ

qq, gg → ttH , H → bb, ττ

• Above 130-140 GeV

gg → H , H → WW, ZZ

qq → qqH , H → γγ,WW, ZZ

qq, gg → ttH , H → WW

( ttH : F.Maltoni, D.Rainwater, S.Willenbrock, A.Belyaev, L.R. )

• Below 130-140 GeVgg → H → γγ, WW, ZZqq → qqH →qq + (γγ, WW, ZZ, ττ)

qq/gg → ttH → tt + (bb, ττ)

• Above 130-140 GeVgg → H → WW, ZZqq → qqH → qq + (γγ, WW, ZZ)

qq/gg → ttH → ttWW

Maltoni, Rainwater, Willenbrock; Belyaev, Reina


Using ratios to get yt

Given a particular production and decay channel, we find in the narrowwidth approximation:

σi(H) × BR(H → jj)exp =σth

i (H)

Γthi

ΓjΓi

Γtot

Define the combination

Zij =ΓjΓi

Γtot

Each width is proportional to the (Yukawa)2.Current LHC estimates are:Ratios of couplings can be determined in a model-independent mannerat the 10–20% level. E.g.,

y2t

y2g

∝ Γt

Γg=

ZtτZWγ

ZWτZgγ

Assuming Γtot = Γb + Γτ + ΓW + ΓZ + Γg + Γγ , individual couplings can bedetermined to 10–30%.


ttH at a linear collider and yt

Calculating ttH at an e+e− collideris very challenging.

• There are many 10%corrections near threshold.

• There are now a fewNLO calculations:You, et al., PLB 571, 85 (03)Belanger, et al., PLB 571, 163 (03)Denner, et al., PLB 575, 290 (03)

• SUSY corrections tend to reduceσttH another 20–30%J.J. Liu, et al., PRD 72, 033010 (05)

This measurement is only tenablewith a high energy linear collider≥ 800 GeV and lots of luminosity.At best you get ±10% if MH < 180 GeV

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K. Desch, M. Schumacher, Model independent extraction of top Yukawa coupling from LHC+LC, CERN, 14/02/03

2

TopTop YukawaYukawa coupling at 800 coupling at 800 GeVGeV LC:LC:

A. Gay

rather tiny cross section:

Spira et al.

limited mass reach�Bottom line: There is no known way to get δyt below 10%,and certainly not to 1%. Maybe you can figure this out. . .


tH− at the Tevatron and LHCIn any 2HDM there is a charged Higgs.

• If the neutral Higgs(es) are SM-likethey may be unobservable.H± may be the only one we see.

• If mt > MH , then we can look fort → bH+ in tt production.Both t → bH+ and H+ → tb ratesare known at NLO

Carena et al., NPB 577, 88 (00)

Current limits are poor:BR(t → bH+) < 0.2–0.8 CDF, D0/

• Fully differential tH−/tH+ NLO ratesalso known Berger et al., hep-ph/0312286Needed to utilize correlations indecays

• In SUSY, corrections can be 50% if theµ-parameter or tan β are large.

g t

H−b

b

b

10-4

10-3

10-2

150 200 250 300

σtot (pp→tH−+X) [pb]

tanβ = 30

mH[GeV]

σincl,NLO

σincl,LO

σoff-shellσBW

σsum

mt=mH+mb±2Γt

Tevatron

10-1

1

200 300 400 500

σtot (pp→tH−+X) [pb]

tanβ = 30

mH[GeV]

σincl,NLO

σincl,LO

σoff-shell

σBW

σsum

mt=mH+mb±2Γt

150

LHC


Top quark decaysThe large width of the top quark (∼ 1.5 GeV) allows it to decay beforeit depolarizes (∼ λ2

QCD/mt = 1 MeV), or hadronizes (∼ λQCD = 300 MeV).A. Falk, M. Peskin, PRD 49, 3320 (1994)

q

W

t −i g√2Vtqγ

µ 12 (1 − γ5)

In single-top we looked at the polarization of the top-quark.In tt we use the event rate to look at the polarization of the W .The V − A interaction means the W only couples to the left-handedpiece of the top-quark. If mb = 0, the spin-1 W boson comes outleft-handed sz = −1 or longitudinal sz = 0, never right-handed sz = +1.W polarization is embedded in the angular distribution of its decayproducts in the W rest frame.

+Wb neg. direc-

tion of top

+l

lν

*θ1/2

1/21

+Wb neg. direc-

tion of top

+l

lν

*θ

1/2

1/21


Deriving the width to polarized W bosonsThe amplitude for (t(pt) → b(pb)W

+(pW )) follows from the Feynman rule:

A(t → bW+) = −ig

2√

2Vtbu(pb)γ

µ(1 − γ5)u(pt)ελ?µ (pW )

The width to a given W -boson polarization is:1

2mt

∫

dPS∑

|A(t → bW+)|2

Assume the top-quark in unpolarized (the gluon produces right/leftequally in tt, though we are ignoring spin correlation between tops).In the rest frame of the top quark we have:

pt = (mt, 0, 0, 0)

pW = (EW , 0, p sin θtW , p cos θt

W )

pb = (Eb, 0,−p sin θtW ,−p cos θt

W )

ε0 =1

MW(p, 0, EW sin θt

W , EW cos θtW )

ε± =1√2(0, 1,±i cos θt

W ,∓ sin θtW )

where EW =m2

t+m2

W

2mt

and p =m2

t−m2

W

2mt

.Zack Sullivan, Southern Methodist University – p.30/34

The fraction of longitudinal W bosonsThe amplitude squared is:

∑

|A(t → bW+)|2 =g2

8|Vtb|2Tr[( /pt + mt) /ε?

λ(1 − γ5)( /pb + mb) /ελ]

If we ignore the b mass for the moment we get: (r = MW /mt)

∑

|A−|2 =2GF m4

t√2

|Vtb|22r2(1 − r2)

∑

|A0|2 =2GF m4

t√2

|Vtb|2(1 − r2)

The fraction of longitudinal W -bosons is:

F0 ≡ Γ0

Γtot=

1

1 + 2r2=

m2t

m2t + 2M2

W

' 0.69

If you turn back on the b mass, F+ = 3 × 10−4.Current experimental results are:F0 = 0.59 ± 0.14 (CDF)F+ = −0.03 ± 0.07 or < 0.10 at 95% C.L. (CDF)F+ = 0.056 ± 0.10 or < 0.23 at 95% C.L. (D0/)

*θcos -1 -0.5 0 0.5 1

* θdc

osdN

0

0.2

0.4

0.6

0.8 left-handedlongitudinalright-handedsum (SM)


Conclusions1. The study of tt has become a game precision measurements.

• The top-quark now has the best measured mass (1%) of any quark.mt = 170.9 ± 1.8 GeV

• The measured top-quark cross section has uncertaintiescomparable in size to the theoretical calculations.σexp = 7.3 ± 0.8 pb, σth = 6.8 ± 0.8 pb at Run II (175 GeV)

We are theory and physics modeling constrained!

• We need a better handle on W+heavy-quark final states— dominates mass uncertainty.

• We need even higher order calculations valid near threshold— NNLO/NNNNLL

• To utilize this information we need higher-order (3-loop, soon 4-loop)calculations of EW processes.


Conclusions2. We have a prediction for the top-quark Yukawa yt = 0.98 ± 0.01.

• It will be very difficult to test this to better than 10%.The experimental backgrounds are tough.

3. The study of spin correlations and W polarization are a nicecomplement to single-top-quark studies.• In principle there is information about yt embedded in F0,

but it is difficult to extract.• These correlations will be more important when you look for

new physics at LHC that is hiding under the 1 top-pair/secondbackground.

4. I did not cover evidence that the top-quark really is charge 2/3,and not −4/3.

5. I did not cover new ttj calculation, or color-flow issues.

We are in an age of precision QCD!Your help will be needed in maximizing our understanding of the fantasticdata we now have from the Tevatron and will have from LHC.


I end where I began. . .


zack sullivan - smu

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