Theoretical results for top quark processes · Aliev et al, CPC 182, 1034 (2011) total-pQCD Ahrens...

Theoretical results for top quark processes

Nikolaos Kidonakis(Kennesaw State University)

• tt total and differential cross sections

• Single top: t and s channels

• tW− and tH− production

• ttW and ttZ production

• FCNC processes

N. Kidonakis, Snowmass 2013, Brookhaven, April 2013 1

Top-pair production

q

q

t

t

• qq → ttdominant at Tevatron

g

g

t

t

g

g

t

t

g

g

t

t• gg → ttdominant at LHC

QCD corrections significant for top pair productionKnown fully at NLO (differential) and NNLO (numerical total only)Soft-gluon corrections are dominant near thresholdNNLL resummation of soft-gluon corrections

NNLO expansions (differential and total)


tt cross section at the LHC

165 170 175 180m

t (GeV)

100

120

140

160

180

200

220

σ (p

b)

NNLO approx+- scale and pdfCMSATLAS

pp -> tt at LHC S1/2

= 7 TeV

165 170 175 180m

t (GeV)

160

180

200

220

240

260

280

300

320

340

σ (p

b)

NNLO approx+- scale and pdfCMS

pp -> tt at LHC S1/2

= 8 TeV

Very good agreement at both 7 and 8 TeV LHC energies


Differences between various resummation/NNLO approx approaches

Total vs differential cross sectionmoment-space pQCD vs SCET

Name Observable Soft limitsingle-particle-inclusive (1PI) dσ/dpT dy s4 = s + t1 + u1 → 0

pair-invariant-mass (PIM) dσ/dMttdθ (1 − z) = 1 − M2tt/s → 0

production threshold σ β =√

1 − 4m2t /s → 0

The more general approach is double-differential→ pT and rapidity distributions

total-only approaches are limit/special case (absolute vs partonic threshold)

For differential calculations, further differences arise from how the relations + t1 + u1 = 0 is used in the plus-distribution coefficients, how subleadingterms are treated, damping factors, etc.

see N. Kidonakis and B.D. Pecjak, Eur. Phys. J C 72, 2084 (2012)

for details and review


150 200 250 300 350

σ (pb)

NLO

NNLO Czakon et al

Kidonakis

Aliev et al

Ahrens et al

Beneke et al

Cacciari et al

Top quark theoretical calculationsLHC 7 and 8 TeV m

t=173 GeV σ (pp->tt) +- scale MSTW2008 pdf

Comparison of various NNLO approx approachesall with the same choice of parameters

Kidonakis, PRD 82, 114030 (2010) differential-pQCDAliev et al, CPC 182, 1034 (2011) total-pQCDAhrens et al, PLB 703, 135 (2011) differential-SCETBeneke et al, NPB 855, 695 (2012) total-SCETCacciari et al, PLB 710, 612 (2012) total-pQCD

6 6.5 7 7.5 8 8.5 9

σ (pb)

NLO

NNLO

Kidonakis

Aliev et al

Ahrens et al

Beneke et al

Cacciari et al

Top quark theoretical calculationsTevatron 1.96 TeV m


750 800 850 900 950 1000 1050 1100 1150

σ (pb)

NLO

NNLO

Kidonakis

Aliev et al

Ahrens et al

Beneke et al

Top quark theoretical calculationsLHC 14 TeV m



Varying degree of success of the various approaches

The Kidonakis PRD 82 result is very close to the exact NNLO:both the central values and the scale uncertainty are nearly the sametrue for all collider energies and top quark masses

This was expected from comparison to NLO, and comparison of 1PIresults at NNLO in 2003

(PRD 68, N. Kidonakis & R. Vogt; see also discussion in PRD78 and PRD82)

less than 1% difference between NLO approximate and exact cross sectionsat both NLO and NNLO

In near future add approximate NNNLO

(see N. Kidonakis PRD 73,034001 (2006) for early NNNLO results)

This is the only calculation for partonic threshold at the double differentialcross section level using the standard moment-space resummation in pQCD

stability of the theoretical NNLO approx result over the past decade

the reliability of the NNLO approximate result and near-identical value toexact NNLO is very important for several reasons

• provides confidence of application to other processes (single-top, W, etc)• used as background for many analyses (Higgs, etc)

• means that we have near-exact NNLO pT and rapidity distributions


Soft-gluon approximation for distributions

The approximation works very well both for total cross sections and differential

distributions

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

T (GeV)

0.01

0.1

1

dσ/d

p T (

pb/G

eV)

NLO approxNLO exact

Top quark pT distribution at LHC S

1/2=8 TeV µ=m

t=173 GeV

excellent approximation:1% difference between NLO approximate and exact differential distributions

For best prediction add NNLO approx corrections to exact NLO cross section


Top quark pT distribution

0 50 100 150 200 250 300 350 400p

T (GeV)

0

20

40

60

80

dσ/d

p T (

fb/G

eV)

D0

NNLO approx mt/2<µ<2m

t

Top quark pT at Tevatron S

1/2=1.96 TeV m=170 GeV

200 250 300 350 4000.1

1

10

0 50 100 150 200 250 300 350 400p

T (GeV)

0

0.002

0.004

0.006

0.008

1/σ

dσ/

dpT (

GeV

-1)

NNLO approx +- scale+ CMS l+jets

Normalized top pT distribution at LHC S

1/2=7 TeV m

t=173 GeV

Excellent agreement of NNLO approx results with Tevatron and LHC data


Top quark pT distribution at the LHC

0 200 400 600 800 1000 1200 1400p

T (GeV)

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

dσ/d

p T (

pb/G

eV)

8 TeV µ=mt

8 TeV µ=mT

7 TeV µ=mt

7 TeV µ=mT

Top quark pT distribution at LHC NNLO approx m

t=173 GeV

0 50 100 150 200 250 300 350p

T (GeV)

0

0.5

1

1.5

2

dσ/d

p T (

pb/G

eV)

NLO 8 TeVNLO 7 TeVNNLOappr 8 TeVNNLOappr 7 TeV

Top quark pT distribution at LHC µ=m

t=173 GeV


Top quark rapidity distribution at LHC

-3 -2 -1 0 1 2 3Y

0

20

40

60

80

dσ/d

Y (

pb)

NNLOappr 8 TeVNLO 8 TeVNNLOappr 7 TeVNLO 7 TeV

Top quark rapidity distribution at LHC µ=mt=173 GeV

-3 -2 -1 0 1 2 3Y

0

0.1

0.2

0.3

0.4

1/σ

dσ/

dY

NNLO approx +- scaleCMS dileptons

Normalized top Y distribution at LHC S1/2

=7 TeV mt=173 GeV

excellent agreement with data


Single-top partonic processes at LO

b

q (q)

W

t

q′ (q′)• t channel: qb → q′t and qb → q′tdominant at Tevatron and LHC

q′

q

W

t

b• s channel: qq′ → btsmall at Tevatron and LHC

g

b

W

t

g

b

t

W

• associated tW production: bg → tW−

very small at Tevatron, significant at LHC

Related process: bg → tH−


Single top t-channel cross sections at LHC

165 170 175 180m

t (GeV)

0

20

40

60

80

100

σ (p

b)

8 TeV top7 TeV top8 TeV antitop7 TeV antitop

t-channel LHC NNLO approx (NNLL) µ =mt

1 2 3 4 5 6 7 8 9 10 11 12 13 14S

1/2 (TeV)

1

10

100

σ (p

b)

NNLO approx+ - scale and pdf D0CDFCMSATLAS

t-channel total cross section mt=172.5 GeV

LHC t t Total (pb)

7 TeV 43.0+1.6−0.2

± 0.8 22.9 ± 0.5+0.7−0.9

65.9+2.1−0.7

+1.5−1.7

8 TeV 56.4+2.1−0.3

± 1.1 30.7 ± 0.7+0.9−1.1

87.2+2.8−1.0

+2.0−2.2

14 TeV 154+4

−1± 3 94+2

−1

+2

−3248+6

−2

+5

−6

mt = 173 GeV

± scale ± pdf errors with MSTW2008 NNLO pdf 90% CL

ratio σ(t)/σ(t) = 1.88+0.11

−0.09at 7 TeV - compares well with ATLAS result 1.81+0.23

−0.22


t-channel top and antitop pT distributions at LHC

20 40 60 80 100 120 140p

T (GeV)

0

0.2

0.4

0.6

0.8

dσ/d

p T (

pb/G

eV)

8 TeV7 TeV

t-channel top quark pT distribution at LHC µ=m

t=173 GeV

NNLO approx (NNLL)

20 40 60 80 100 120 140p

T (GeV)

0

0.2

0.4

0.6

0.8

dσ/d

p T (

pb/G

eV)

8 TeV7 TeV

t-channel antitop quark pT distribution at LHC µ=m

t=173 GeV

NNLO approx (NNLL)

100 200 300 400 500 600 700 800 900 1000p

T (GeV)

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

dσ/d

p T (

pb/G

eV)

14 TeV 8 TeV 7 TeV

t-channel top quark pT distribution at LHC µ=m

t=173 GeV

NNLO approx (NNLL)

100 200 300 400 500 600 700 800 900 1000p

T (GeV)

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

dσ/d

p T (

pb/G

eV)

14 TeV 8 TeV 7 TeV

t-channel antitop quark pT distribution at LHC µ=m

t=173 GeV

NNLO approx (NNLL)


Single top s-channel cross sections at LHC

165 170 175 180m

t (GeV)

0

2

4

6

8

σ (p

b)

8 TeV top7 TeV top8 TeV antitop7 TeV antitop

s-channel LHC NNLO approx (NNLL) µ =mt

2 3 4 5 6 7 8 9 10 11 12 13 14S

1/2 (TeV)

1

10

σ (p

b)

NNLO approx +-scale&pdfATLAS 95% CL limit

s-channel total cross section mt=172.5 GeV

LHC t t Total (pb)

7 TeV 3.14 ± 0.06+0.12−0.10

1.42 ± 0.01+0.06−0.07

4.56 ± 0.07+0.18−0.17

8 TeV 3.79 ± 0.07 ± 0.13 1.76 ± 0.01 ± 0.08 5.55 ± 0.08 ± 0.21

14 TeV 7.87 ± 0.14+0.31

−0.283.99 ± 0.05+0.14

−0.2111.86 ± 0.19+0.45

−0.49

mt = 173 GeV

NNLO approx: enhancement over NLO (same pdf) is ∼ 10%


Associated tW− production at the LHC

2 3 4 5 6 7 8 9 10 11 12 13 14S

1/2 (TeV)

1

10

100

σ (p

b)

NNLO approx+- scale&pdfCMSATLAS

tW- + tW

+ cross section m

t=172.5 GeV

0 50 100 150 200p

T (GeV)

0

0.02

0.04

0.06

0.08

0.1

dσ/d

p T (

pb/G

eV)

8 TeV 7 TeV

tW-channel top quark pT distribution at LHC µ=m

t=173 GeV

NNLO approx (NNLL)

LHC tW− (pb)

7 TeV 7.8 ± 0.2+0.5−0.6

8 TeV 11.1 ± 0.3 ± 0.7

14 TeV 41.8 ± 1.0+1.5−2.4

mt = 173 GeV

NNLO approx corrections increase NLO cross section by ∼ 8%

Cross section for tW+ production is identical


Associated production of a top quark with a charged Higgs

200 400 600 800 1000m

H- (GeV)

0.001

0.01

0.1

1σ

(pb)

14 TeV 8 TeV 7 TeV

bg-> tH- at LHC NNLO approx (NNLL) tanβ=30 µ=m

H-

NNLO approx corrections increase NLO cross section by ∼ 15 to ∼ 20%


Associated production of a tt pair with bosons

Campbell and Ellis, JHEP 1207 (2012) 052


ttW production

d

u

t

W−

t

u

d

W+

t

t

6 6.5 7 7.5 8 8.5 9

S1/2

(TeV)

0

50

100

150

σ (f

b)

t t W+

t t W-

pp -> t t W+ and pp -> t t W

-

mt=173.5 GeV µ=m

t+m

W/2 σ (pp->ttW) +- scale CTEQ6.6M pdf

Garzelli, Kardos, Papadopoulos, Trocsanyi, JHEP 1211 (2012) 056


ttZ production

g

g

t

t

Z

g

g t

t

Z

q

q t

t

Z

q

q

t

t

Z

6 6.5 7 7.5 8 8.5 9

S1/2

(TeV)

100

150

200

250

σ (f

b)

t t Z

pp -> t t Z m

t=173.5 GeV µ=m

t+m

Z/2 σ (pp->ttZ) +- scale CTEQ6.6M pdf

Garzelli, Kardos, Papadopoulos, Trocsanyi, JHEP 1211 (2012) 056


FCNC processes

Single-top production via flavor-changing neutral currentsAnomalous couplings in Lagrangian, e.g.

∆Leff

=1

ΛκtqV e t σµν q F

µν

V+ h.c.

gu → tZg

u

ut

Z

g t

t

u Z

gu → tγg

u

ut

γ

g t

t

u γ

eu → ete e

γ

u t

e e

Z

u t

decrease of scale dependence, significant corrections over LO

Future studies at LHC energies and for other couplings


Summary

• NNLL resummation / NNLO expansions

• tt production cross section

• top quark pT and rapidity distributions

• single top cross sections and pT distributions

• NNLO approx corrections are very significant

• excellent agreement with LHC and Tevatron data

• tH− associated production

• top-pair associated production with W+, W−, Z

• top quark FCNC processes


Theoretical results for top quark processes · Aliev et al, CPC 182, 1034 (2011) total-pQCD Ahrens...

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Transcript of Theoretical results for top quark processes · Aliev et al, CPC 182, 1034 (2011) total-pQCD Ahrens...