Jet production at the LHC in NNLO QCD Jo ao Pires The Latsis - - PowerPoint PPT Presentation

SLIDE 1

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

Jet production at the LHC in NNLO QCD

Jo˜ ao Pires The Latsis Symposium 2013 June 5, 2013

• in collaboration with A. Gehrmann-De Ridder, T. Gehrmann, N.Glover

SLIDE 2

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

INCLUSIVE JET AND DIJET CROSS SECTIONS

◮ look at the production of jets of hadrons with large transverse energy in

◮ inclusive jet events

pp → j + X

◮ exclusive dijet events

pp → 2j

◮ cross sections measured as a function of the jet pT, rapidity y and dijet

invariant mass mjj in double differential form

(GeV)

T

Jet p

200 300 1000 2000

d|y| (pb/GeV)

T

/dp σ

2

d

• 5

10

• 1

10

3

10

7

10

11

10

13

10

)

4

10 × |y| < 0.5 ( )

3

10 × 0.5 < |y| < 1.0 ( )

2

10 × 1.0 < |y| < 1.5 ( )

1

10 × 1.5 < |y| < 2.0 ( ) 10 × 2.0 < |y| < 2.5 (

CMS

= 7 TeV s

• 1

L = 5.0 fb R = 0.7

T

anti-k

T

= p

F

µ =

R

µ NP Corr. ⊗ NNPDF2.1

SLIDE 3

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

INCLUSIVE JET AND DIJET CROSS SECTIONS

state of the art:

◮ dijet production is completely known in NLO QCD [Ellis, Kunszt, Soper ’92],

[Giele, Glover, Kosower ’94], [Nagy ’02]

◮ NLO+Parton shower [Alioli, Hamilton, Nason, Oleari, Re ’11] ◮ threshold corrections [Kidonakis, Owens ’00]

Goal:

◮ obtain the jet cross sections at NNLO accuracy in double differential form

d2σ dpTd|y| d2σ dmjjdy∗ this talk:

◮ NNLO inclusive jet and dijet cross section (gluons only, leading colour)

SLIDE 4

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

THEORETICAL VS EXPERIMENTAL UNCERTAINTIES

(GeV)

T

Jet p

200 300 400 1000 2000

Cross section uncertainty

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3

|y| < 0.5 Total PDF Nonpert. Scale

NNPDF2.1

= 7 TeV s R = 0.7

T

anti-k

relative theoretical uncertainties for the inclusive jet production (NLO theory input) [CMS, arXiv:1212.6660]

(GeV)

T

Jet p

200 300 400 1000 2000

Cross section uncertainty

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4

|y| < 0.5 Total JES Unfolding Luminosity

CMS

= 7 TeV s

• 1

L = 5.0 fb R = 0.7

T

anti-k

relative experimental uncertainties for the inclusive jet production [CMS, arXiv:1212.6660]

◮ residual uncertainty due to scale choice at NNLO expected at ≈ few percent

level

◮ jet energy scale uncertainty has been determined to less than 5% for central

jets → expect steady improvement with higher statistics

◮ theoretical prediction with the same precision as the experimental data →

need pQCD predictions at NNLO accuracy

SLIDE 5

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

INCLUSIVE JET AND DIJET CROSS SECTIONS

(GeV)

T

Jet p

200 300 400 1000 2000

Ratio to NNPDF2.1

0.6 0.8 1 1.2 1.4 1.6

|y| < 0.5 Data CT10 HERA1.5 MSTW2008 ABKM09

CMS

= 7 TeV s

• 1

L = 5.0 fb R = 0.7

T

anti-k

• Exp. Uncertainty
• Theo. Uncertainty

(NLO theory input) [CMS, arXiv:1212.6660]

(GeV)

jj

M

200 300 400 1000 2000 3000

Ratio to NNPDF2.1

0.5 1 1.5

< 0.5

max

|y| Data CT10 HERA1.5 MSTW2008 ABKM09

CMS

= 7 TeV s

• 1

L = 5.0 fb R = 0.7

T

anti-k

• Exp. Uncertainty
• Theo. Uncertainty

(NLO theory input) [CMS, arXiv:1212.6660] Phenomenological applications with NNLO:

◮ data can be used to constrain parton distribution functions ◮ size of NNLO correction important for precise determination of PDF’s ◮ inclusion of jet data in NNLO parton distribution fits requires NNLO corrections to

jet cross sections

◮ αs determination from hadronic jet observables limited by the unknown higher order

corrections

SLIDE 6

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

pp → 2j AT NNLO: GLUONIC CONTRIBUTIONS

A(0)

6 (gg → gggg)

A(1)

5 (gg → ggg)

A(2)

4 (gg → gg)

[Berends, Giele ’87], [Mangano, Parke, Xu ’87], [Britto, Cachazo, Feng ’06] [Bern, Dixon, Kosower ’93] [Anastasiou, Glover, Oleari, Tejeda-Yeomans ’01],[Bern, De Freitas, Dixon ’02] dˆ σNNLO =

• dΦ4

dˆ σRR

NNLO +

• dΦ3

dˆ σRV

NNLO +

• dΦ2

dˆ σVV

NNLO

◮ explicit infrared poles from loop integrations ◮ implicit poles in phase space regions for single and double unresolved gluon

emission

◮ procedure to extract the infrared singularities and assemble all the parts in a

parton-level generator

SLIDE 7

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

NNLO IR SUBTRACTION SCHEMES

◮ sector decomposition: expansions in distributions, numerical integration

[Binoth, Heinrich ’02], [Anastasiou, Melnikov, Petriello ’03]

◮ pp → H [Anastasiou, Melnikov, Petriello ’04] ◮ pp → V [Melnikov, Petriello ’06]

◮ qT-subtraction for colorless high-mass systems [Catani, Grazzini ’07]

◮ pp → H

[Catani, Grazzini ’07]

◮ pp → V

[Catani, Cieri, Ferrera, de Florian, Grazzini ’09]

◮ pp → VH

[Ferrera, Grazzini, Tramontano ’11]

◮ pp → γγ

[Catani, Cieri, de Florian, Grazzini ’11]

◮ sector decomposition combined with subtraction

[Czakon’ 11], [Boughezal, Melnikov, Petriello ’11]

◮ pp → t¯

t [Baernreuther, Czakon, Fiedler, Mitov ’13]

◮ pp → Hj (gluons only) [Boughezal, Caola, Melnikov, Petriello, Schulze ’13]

◮ antenna subtraction [Gehrmann-De Ridder, Gehrmann, Glover ’05]

◮ e¯

e → 3j [Gehrmann-De Ridder, Gehrmann, Glover, Heinrich ’07], [Weinzierl 08]

◮ pp → 2j (gluons only) [Gehrmann-De Ridder, Gehrmann, Glover, JP ’13]

SLIDE 8

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

NNLO ANTENNA SUBTRACTION

dˆ σNNLO =

• dΦ4
• dˆ

σRR

NNLO − dˆ

σS

NNLO

• +
• dΦ3
• dˆ

σRV

NNLO − dˆ

σT

NNLO

• +
• dΦ2
• dˆ

σVV

NNLO − dˆ

σU

NNLO

• ◮ dˆ

σS

NNLO: real radiation subtraction term for dˆ

σRR

NNLO

◮ dˆ

σT

NNLO: one-loop virtual subtraction term for dˆ

σRV

NNLO

◮ dˆ

σU

NNLO: two-loop virtual subtraction term for dˆ

σVV

NNLO

◮ subtraction terms constructed using the antenna subtraction method at NNLO

for hadron colliders → presence of initial state partons to take into account

◮ contribution in each of the round brackets is finite, well behaved in the

infrared singular regions and can be evaluated numerically

SLIDE 9

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

pp → 2j AT NNLO

[A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, JP] Implementation checks (gluons only channel at leading colour):

◮ subtraction terms correctly approximate the matrix elements in all unresolved

configurations of partons j, k dˆ σRR,RV

NNLO ∀{j,k},{j}→0

− − − − − − − − → dˆ σS,T

NNLO

◮ local (pointwise) analytic cancellation of all infrared explicit ǫ-poles when integrated

subtraction terms are combined with one, two-loop matrix elements Poles

• dˆ

σRV

NNLO − dˆ

σT

NNLO

• = 0

Poles

• dˆ

σVV

NNLO − dˆ

σU

NNLO

• = 0

◮ process independent NNLO subtraction scheme ◮ singularities in intermediate steps cancel analytically ◮ allows the computation of multiple differential distributions in a single program run

SLIDE 10

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

NUMERICAL SETUP

[A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, JP]

◮ jets identified with the anti-kT jet algorithm ◮ jets accepted at rapidities |y| < 4.4 ◮ leading jet with transverse momentum pt > 80 GeV ◮ subsequent jets required to have at least pt > 60 GeV ◮ MSTW2008nnlo PDF ◮ dynamical factorization and renormalization central scale equal to the leading

jet pT (µR = µF = µ = pT1)

SLIDE 11

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

NUMERICAL SETUP

[A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, JP]

◮ jets identified with the anti-kT jet algorithm ◮ jets accepted at rapidities |y| < 4.4 ◮ leading jet with transverse momentum pt > 80 GeV ◮ subsequent jets required to have at least pt > 60 GeV ◮ MSTW2008nnlo PDF ◮ dynamical factorization and renormalization central scale equal to the leading

jet pT (µR = µF = µ = pT1) Integrated cross section results (gluons only channel) with scale variations

σ8TeV−LO

incl.jet

(pb) σ8TeV−NLO

incl.jet

(pb) σ8TeV−NNLO

incl.jet

(pb) µ = 0.5pT1 (12.586 ± 0.001) × 105 (11.299 ± 0.001) × 105 (15.33 ± 0.03) × 105 µ = pT1 (9.6495 ± 0.001) × 105 (12.152 ± 0.001) × 105 (15.20 ± 0.02) × 105 µ = 2.0pT1 (7.5316 ± 0.001) × 105 (11.824 ± 0.001) × 105 (15.21 ± 0.01) × 105 ◮ NNLO result increased by about 25% with respect to the NLO cross section

SLIDE 12

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

INCLUSIVE JET pT DISTRIBUTION

[A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, JP]

(GeV)

T

p

2

10

3

10 (pb/GeV)

T

/dp σ d

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1 10

2

10

3

10

4

10

5

10

LO NLO NNLO

=8 TeV s R=0.7

T

anti-k MSTW2008nnlo

T1

= p

F

µ =

R

µ

(GeV)

T

p

2

10

3

10 1 1.2 1.4 1.6 1.8

NLO/LO NNLO/NLO NNLO/LO

◮ NNLO effect stabilizes the NLO k-factor growth with pT

SLIDE 13

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

INCLUSIVE JET pT DISTRIBUTION

[A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, JP]

T1

/p µ 1 (pb)

T

/dp σ d 20 30 40 50 60 70 80 90

3

10 ×

LO NLO NNLO

=8 TeV s R=0.7

T

anti-k MSTW2008nnlo µ =

F

µ =

R

µ < 97 GeV

T

80 GeV < p

◮ flat scale dependence at NNLO

SLIDE 14

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

INCLUSIVE JET pT DISTRIBUTION R = 0.7

◮ double differential inclusive jet pT distribution at NNLO (gluons only)

(GeV)

T

p

2

10

3

10 d|y| (pb/GeV)

T

/dp σ

2

d

• 7

10

• 5

10

• 3

10

• 1

10 10

3

10

5

10

7

10

9

10

11

10

13

10

15

10

)

6

|y|<0.3 (x10 )

5

|y|<0.8 (x10 ≤ 0.3 )

4

|y|<1.2 (x10 ≤ 0.8 )

3

|y|<2.1 (x10 ≤ 1.2 )

2

|y|<2.8 (x10 ≤ 2.1 )

1

|y|<3.6 (x10 ≤ 2.8 ) |y|<4.4 (x10 ≤ 3.6

=8 TeV s R=0.7

T

anti-k MSTW2008nnlo

T1

= p

F

µ =

R

µ

(GeV)

T

p

2

10

3

10 1 1.2 1.4 1.6 1.8 2 |y|<0.3

NLO/LO NNLO/NLO NNLO/LO

(GeV)

T

p

2

10

3

10 1 1.2 1.4 1.6 1.8 2 |y|<0.8 ≤ 0.3

NLO/LO NNLO/NLO NNLO/LO

(GeV)

T

p

2

10

3

10 1 1.2 1.4 1.6 1.8 2 |y|<1.2 ≤ 0.8

NLO/LO NNLO/NLO NNLO/LO

double differential k-factors

◮ NNLO result varies between

25% to 12% with respect to the NLO cross section

◮ similar behaviour between

the rapidity slices

SLIDE 15

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

INCLUSIVE JET pT DISTRIBUTION R = 0.4

◮ double differential inclusive jet pT distribution at NNLO (gluons only)

(GeV)

T

p

2

10

3

10 d|y| (pb/GeV)

T

/dp σ

2

d

• 7

10

• 5

10

• 3

10

• 1

10 10

3

10

5

10

7

10

9

10

11

10

13

10

15

10

)

6

|y|<0.3 (x10 )

5

|y|<0.8 (x10 ≤ 0.3 )

4

|y|<1.2 (x10 ≤ 0.8 )

3

|y|<2.1 (x10 ≤ 1.2 )

2

|y|<2.8 (x10 ≤ 2.1 )

1

|y|<3.6 (x10 ≤ 2.8 ) |y|<4.4 (x10 ≤ 3.6

=8 TeV s R=0.4

T

anti-k MSTW2008nnlo

T1

= p

F

µ =

R

µ

(GeV)

T

p

2

10

3

10 1 1.2 1.4 1.6 |y|<0.3

NLO/LO NNLO/NLO NNLO/LO

(GeV)

T

p

2

10

3

10 1 1.2 1.4 1.6 |y|<0.8 ≤ 0.3

NLO/LO NNLO/NLO NNLO/LO

(GeV)

T

p

2

10

3

10 1 1.2 1.4 1.6 |y|<1.2 ≤ 0.8

NLO/LO NNLO/NLO NNLO/LO

double differential k-factors

◮ NNLO result varies between

20% to 5% with respect to the NLO cross section

◮ similar behaviour between

the rapidity slices

SLIDE 16

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

INCLUSIVE JET pT DISTRIBUTION

80GeV< pT < 96GeV 1148GeV< pT < 1388GeV

◮ inclusive jet cross section versus R ◮ can the NNLO cross section describe data for different values of R

simultaneously at low and high jet pT?

SLIDE 17

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

EXCLUSIVE DIJET MASS DISTRIBUTION R = 0.4

◮ double differential dijet mass distribution at NNLO (gluons only)

(GeV)

jj

m

3

10 dy* (pb/GeV)

jj

/dm σ

2

d

• 12

10

• 9

10

• 6

10

• 3

10 1

3

10

6

10

9

10

12

10

15

10

17

10

) y*<0.5 (x10 )

2

y*<1.0 (x10 ≤ 0.5 )

4

y*<1.5 (x10 ≤ 1.0 )

6

y*<2.0 (x10 ≤ 1.5 )

8

y*<2.5 (x10 ≤ 2.0 )

10

y*<3.0 (x10 ≤ 2.5 )

12

y*<3.5 (x10 ≤ 3.0 )

14

y*<4.0 (x10 ≤ 3.5 )

16

y*<4.5 (x10 ≤ 4.0

=8 TeV s R=0.4

T

anti-k MSTW2008nnlo

T1

= p

F

µ =

R

µ

(GeV)

jj

m

3

10 0.5 1 1.5 2 y*<0.5

NLO/LO NNLO/NLO NNLO/LO

(GeV)

jj

m

3

10 0.5 1 1.5 2 y*<1.0 ≤ 0.5

NLO/LO NNLO/NLO NNLO/LO

(GeV)

jj

m

3

10 0.5 1 1.5 2 y*<1.5 ≤ 1.0

NLO/LO NNLO/NLO NNLO/LO

double differential k-factors

◮ NNLO corrections up to 20%

with respect to the NLO cross section

◮ corrections increase slightly

for large y∗ = 1/2|y1 − y2|

SLIDE 18

MOTIVATION NNLO CALCULATIONS ANTENNA SUBTRACTION NUMERICAL RESULTS

CONCLUSIONS

◮ antenna subtraction method generalised for the calculation of NNLO QCD

corrections for exclusive collider observables with partons in the initial-state

◮ non-trivial check of analytic cancellation of infrared singularities between

double-real, real-virtual and double-virtual corrections

◮ proof-of principle implementation of the gg → gg contribution to pp → 2j at

NNLO in the new NNLOJET parton-level generator

◮ computation of multiple differential distributions at NNLO in a single

program run → experimentalists input welcome Future work:

◮ go beyond gluons only leading colour approximation ◮ include remaining partonic subprocesses

◮ 4g2q processes [Currie, Glover, Wells ’13] ◮ 2g4q processes ◮ 6q processes