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Exploring minijets beyond leading power Piotr Kotko Penn State University based on: supported by: DEC-2011/01/B/ST2/03643 P .K., A. Stasto, M. Strikman DE-FG02-93ER40771 arXiv:1608.00523 San Cristobal de las Casas, 12/01/2016 Introduction

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SLIDE 1

Exploring minijets beyond leading power

Piotr Kotko

Penn State University based on: P .K., A. Stasto, M. Strikman arXiv:1608.00523 supported by: DEC-2011/01/B/ST2/03643 DE-FG02-93ER40771

San Cristobal de las Casas, 12/01/2016

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SLIDE 2

Introduction

Minijets in Pythia

  • The rise of the total cross section with energy in hadron-hadron collision is

due to minijets; in collinear factorization dσ2jet =

  • a,b,c,d

dxA xA dxB xB dˆ σab→cd

  • xA, xB; µ2

fa/A

  • xA; µ2

fb/B

  • xB; µ2
  • dσ2jet is divergent for pT → 0

dσ2jet dp2

T

∼ αs

  • p2

T

  • p4

T

  • phenomenological regularization

[T. Sjostrand, M. van Zijl, Phys.Rev.D 36 (1987) 2019]

dσ′

2jet

dp2

T

∼ αs

  • p2

T + p2 T0 (s)

  • p2

T + p2 T0 (s)

2 , with pT0 (s) = pT0 (s/s0)λ. 1

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SLIDE 3

Introduction

Goal: calculate pT0(s) from some simple approach

  • the pT0 (s) regularization takes the collinear factorization out of the leading

power approximation

  • idea: use frameworks that have power corrections by including transverse

momenta of incoming partons: High Energy (or kT) Factorization (HEF) (or Color Glass Condensate, but saturation is not essential here) 2

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SLIDE 4

Introduction

Goal: calculate pT0(s) from some simple approach

  • the pT0 (s) regularization takes the collinear factorization out of the leading

power approximation

  • idea: use frameworks that have power corrections by including transverse

momenta of incoming partons: High Energy (or kT) Factorization (HEF) (or Color Glass Condensate, but saturation is not essential here) Plan

1 High Energy Factorization 2 Non-leading-power extension of DDT (Diakonov-Dokshitzer-Troyan) formula

for dijet in pp

3 Direct study of minijet suppression 4 Hard dijet observable sensitive to pT0 (s) cutoff 5 Summary

2

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SLIDE 5

High Energy Factorization (HEF)

Gluon production in HEF

[S. Catani, M. Ciafaloni, F. Hautmann, Nucl.Phys. B366 (1991) 135-188] [J.C. Collins, R.K. Ellis, Nucl.Phys. B360 (1991) 3-30]

dσAB→gg = Fg∗/A (xA, kT A; µ) ⊗ dˆ σg∗g∗→gg (xA, xB, kT A, kT B; µ) ⊗ Fg∗/B (xB, kT B; µ)

pA pB kA kB

Fg∗/A Fg∗/B =

kA kB p1 p2 kA kB

[E. Antonov, L. Lipatov, E. Kuraev, I. Cherednikov, Nucl.Phys. B721 (2005) 111-135] [P .K. JHEP 1407 (2014) 128]

Fg∗/H (xH, kT H; µ) – Unintegrated Gluon Distribution (UGD) dˆ σg∗g∗→gg – hard process with off-shell gauge invariant amplitude 3

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SLIDE 6

High Energy Factorization (HEF)

Gluon production in HEF

[S. Catani, M. Ciafaloni, F. Hautmann, Nucl.Phys. B366 (1991) 135-188] [J.C. Collins, R.K. Ellis, Nucl.Phys. B360 (1991) 3-30]

dσAB→gg = Fg∗/A (xA, kT A; µ) ⊗ dˆ σg∗g∗→gg (xA, xB, kT A, kT B; µ) ⊗ Fg∗/B (xB, kT B; µ)

pA pB kA kB

Fg∗/A Fg∗/B =

kA kB p1 p2 kA kB

[E. Antonov, L. Lipatov, E. Kuraev, I. Cherednikov, Nucl.Phys. B721 (2005) 111-135] [P .K. JHEP 1407 (2014) 128]

Fg∗/H (xH, kT H; µ) – Unintegrated Gluon Distribution (UGD) dˆ σg∗g∗→gg – hard process with off-shell gauge invariant amplitude dσAB→gg = 1 64π2

  • d2

kTAd2 kTB

  • z1dz1 z2dz2

(z1 + z2)2

  • dp2

Tdφ

  • z1
  • pT −

KT 2 + z2p2

T

2 Fg∗/A (z1 + z2, kTA) Fg∗/B 1 z2S

  • pT −

KT 2 + 1 z1S p2

T, kTB

  • M
  • 2

g∗g∗→gg

  • z1, z2,

kTA, kTB

  • 3
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SLIDE 7

Unintegrated Gluon Distributions (UGDs)

  • Kimber-Martin-Ryskin (KMR)

[M. Kimber, A. D. Martin, and M. Ryskin, Phys.Rev. D63, 114027 (2001)]

Fg∗/H (x, kT, µ) = ∂ ∂k 2

T

[fg/H (x, kT) Tg (kT, µ)] Tg

  • K 2

T, µ2

– the Sudakov form factor 4

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SLIDE 8

Unintegrated Gluon Distributions (UGDs)

  • Kimber-Martin-Ryskin (KMR)

[M. Kimber, A. D. Martin, and M. Ryskin, Phys.Rev. D63, 114027 (2001)]

Fg∗/H (x, kT, µ) = ∂ ∂k 2

T

[fg/H (x, kT) Tg (kT, µ)] Tg

  • K 2

T, µ2

– the Sudakov form factor

  • Kwiecinski-Martin-Stasto (KMS)

[J. Kwiecinski, Alan D. Martin, A.M. Stasto, Phys.Rev. D56 (1997) 3991-4006]

BFKL + DGLAP corrections + kinematic constraint + running αs

F

  • x, k 2

T

  • = F0
  • x, k 2

T

  • + αsNc

π 1

x

dz z ∞

k2 T 0

dq2

T

q2

T

               q2

TF

x

z , q2 T

  • θ
  • k2

T z − q2 T

  • − k 2

TF

x

z , k 2 T

  • q2

T − k 2 T

  • +

k 2

TF

x

z , k 2 T

  • 4q4

T + k 4 T

               + αs 2πk 2

T

1

x

dz       

  • Pgg (z) − 2Nc

z k2

T k2 T 0

dq2

TF

x z , q2

T

  • + zPgq (z) Σ

x z , k 2

T

      

Fitted to HERA data. [K. Kutak, S. Sapeta, Phys. Rev. D 86 (2012) 094043] 4

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SLIDE 9

Unintegrated Gluon Distributions (UGDs)

  • Kimber-Martin-Ryskin (KMR)

[M. Kimber, A. D. Martin, and M. Ryskin, Phys.Rev. D63, 114027 (2001)]

Fg∗/H (x, kT, µ) = ∂ ∂k 2

T

[fg/H (x, kT) Tg (kT, µ)] Tg

  • K 2

T, µ2

– the Sudakov form factor

  • Kwiecinski-Martin-Stasto (KMS)

[J. Kwiecinski, Alan D. Martin, A.M. Stasto, Phys.Rev. D56 (1997) 3991-4006]

BFKL + DGLAP corrections + kinematic constraint + running αs

F

  • x, k 2

T

  • = F0
  • x, k 2

T

  • + αsNc

π 1

x

dz z ∞

k2 T 0

dq2

T

q2

T

               q2

TF

x

z , q2 T

  • θ
  • k2

T z − q2 T

  • − k 2

TF

x

z , k 2 T

  • q2

T − k 2 T

  • +

k 2

TF

x

z , k 2 T

  • 4q4

T + k 4 T

               + αs 2πk 2

T

1

x

dz       

  • Pgg (z) − 2Nc

z k2

T k2 T 0

dq2

TF

x z , q2

T

  • + zPgq (z) Σ

x z , k 2

T

      

Fitted to HERA data. [K. Kutak, S. Sapeta, Phys. Rev. D 86 (2012) 094043]

  • CCFM
  • ...

4

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SLIDE 10

Non-leading-power extension of DDT

Dokshitzer-Diakonov-Troyan (DDT) formula (leading power)

[Y. Dokshitzer,D. Dyakonov, S. Troyan, Phys.Rep. 58 (1980) 269-395]

dσ2jet dK 2

T

= dxA xA dxB xB dˆ σgg→gg

  • xA, xB; µ2

∂ ∂K 2

T

  • fg/A
  • xA; K 2

T

  • fg/B
  • xB; K 2

T

  • T 4

g

  • K 2

T, µ2

pA

fg/A

. . .

pB

fg/B

pA

fg/A

. . .

pB

fg/B

pA

fg/A

. . . pB

fg/B

pA

fg/A

pB

fg/B

. . .

Tg Tg Tg Tg

Tg

  • K 2

T, µ2

– the Sudakov form factor. DDT applies when µ0 ≪ KT ≪ µ. 5

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SLIDE 11

Non-leading-power extension of DDT

Dokshitzer-Diakonov-Troyan (DDT) formula (leading power)

[Y. Dokshitzer,D. Dyakonov, S. Troyan, Phys.Rep. 58 (1980) 269-395]

dσ2jet dK 2

T

= dxA xA dxB xB dˆ σgg→gg

  • xA, xB; µ2

∂ ∂K 2

T

  • fg/A
  • xA; K 2

T

  • fg/B
  • xB; K 2

T

  • T 4

g

  • K 2

T, µ2

pA

fg/A

. . .

pB

fg/B

pA

fg/A

. . .

pB

fg/B

pA

fg/A

. . . pB

fg/B

pA

fg/A

pB

fg/B

. . .

Tg Tg Tg Tg

Tg

  • K 2

T, µ2

– the Sudakov form factor. DDT applies when µ0 ≪ KT ≪ µ. Improved DDT (IDDT) formula (beyond leading power) [P

.K., A. Stasto, M. Strikman, arXiv:1608.00523]

dσ(IDDT)

2jet

= dσ(IS)

2jet + dσ(FS) 2jet

dσ(IS)

2jet = 2 Fg∗/A (xA, KT, µ) ⊗ dˆ

σg∗g→gg

  • xA, xB,

KT

  • ⊗ fg/B
  • xB, K 2

T

  • ⊗ T 3

g

  • K 2

T, µ2

dσ(FS)

2jet = 2 fg/A

  • xA; K 2

T

  • ⊗ dˆ

σgg→gg∗

  • xA, xB,

KT

  • ⊗ fg/B
  • xB; K 2

T

  • ⊗ Tg
  • K 2

T, µ2

⊗ T 3

g

  • K 2

T, µ2

where Tg

  • K 2

T, µ2

= ∂Tg

  • K 2

T, µ2

/∂K 2

  • T. There is a restriction KT ≤ µ.

5

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SLIDE 12

Direct study of minijet suppression

Inclusive dijets with Pythia: anti-kT with R = 0.5, rapidity [−4, 4] 6

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SLIDE 13

Direct study of minijet suppression

Inclusive dijets with Pythia: anti-kT with R = 0.5, rapidity [−4, 4]

100 10000 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20 5 10 15 20 25 30 d/dpTj [nb/GeV] pTj [GeV] Inclusive dijets pT > 2 GeV

S = 7.0 TeV

Using GRV98 PDFs gg->gg channel

S = 14.0 TeV (x103) S = 20.0 TeV (x106) S = 30.0 TeV (x109)

pythia PS (soft QCD) pythia PS+HAD (soft QCD) LO Collinear Factorization

6

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SLIDE 14

Direct study of minijet suppression

Inclusive dijets with HEF and IDDT

100 10000 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20 5 10 15 20 25 30 d/dpTj [nb/GeV] pTj [GeV] Inclusive dijets pT > 2 GeV

S = 7.0 TeV

Using GRV98 PDFs gg->gg channel

S = 14.0 TeV (x103) S = 20.0 TeV (x106) S = 30.0 TeV (x109)

HEF (KMR) IDDT LO Collinear Factorization

7

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SLIDE 15

Direct study of minijet suppression

Inclusive dijets with HEF and IDDT

10000 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20 1e+22 2.5 3 3.5 4 4.5 5 d/dpTj [nb/GeV] pTj [GeV] Inclusive dijets pT > 2 GeV

S = 7.0 TeV

Using GRV98 PDFs gg->gg channel

S = 14.0 TeV (x103) S = 20.0 TeV (x106) S = 30.0 TeV (x109)

HEF (KMR) IDDT LO Collinear Factorization

7

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SLIDE 16

Direct study of minijet suppression

Inclusive dijets with Pythia ’hard’

10000 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20 1e+22 2.5 3 3.5 4 4.5 5 d/dpTj [nb/GeV] pTj [GeV] Inclusive dijets pT > 2 GeV

S = 7.0 TeV

Using GRV98 PDFs gg->gg channel

S = 14.0 TeV (x103) S = 20.0 TeV (x106) S = 30.0 TeV (x109)

pythia PS (hard QCD) pythia PS+MPI (hard QCD) LO Collinear Factorization

8

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SLIDE 17

Direct study of minijet suppression

Inclusive dijets with Pythia ’hard’

100 10000 1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18 1e+20 5 10 15 20 25 30 d/dpTj [nb/GeV] pTj [GeV] Inclusive dijets pT > 2 GeV

S = 7.0 TeV

Using GRV98 PDFs gg->gg channel

S = 14.0 TeV (x103) S = 20.0 TeV (x106) S = 30.0 TeV (x109)

pythia PS (hard QCD) pythia PS+MPI (hard QCD) LO Collinear Factorization

8

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SLIDE 18

Direct study of minijet suppression

Summary:

  • HEF/IDDT do not produce significant small pT suppression, despite the

internal gluon kT

  • The suppression is very similar to the one produced by Pythia with the ’hard’

events (this is actually quite intuitive)

  • For larger pT the enhancement in HEF (but not IDDT) with respect to

collinear result is very similar to Pythia with MPIs ⇒ MPIs are power corrections which are present in HEF (where this enhancement comes from KT > pT), where pT = (pT1 + pT2)/2 9

slide-19
SLIDE 19

Direct study of minijet suppression

Summary:

  • HEF/IDDT do not produce significant small pT suppression, despite the

internal gluon kT

  • The suppression is very similar to the one produced by Pythia with the ’hard’

events (this is actually quite intuitive)

  • For larger pT the enhancement in HEF (but not IDDT) with respect to

collinear result is very similar to Pythia with MPIs ⇒ MPIs are power corrections which are present in HEF (where this enhancement comes from KT > pT), where pT = (pT1 + pT2)/2 Idea: study sensitivity to large dijet imbalance to look for MPI effects

  • define τ = KT/pT and simply consider dσ/dτ
  • pT of dijets > 25 GeV (to be within the hard regime)
  • study an impact of MPIs (by playing with pT0 (s))

9

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SLIDE 20

Indirect study of minijet suppression

(1/σ) dσ/dτ in Pythia

0.01 0.1 1 10 0.5 1 1.5 2

(1/tot) d/d = 2 qT/(pT1+pT2)

Inclusive dijets pT > 25 GeV PYTHIA with GRV98

no MPI

gg->gg channel

7 TeV 14 TeV 20 TeV 30 TeV

10

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SLIDE 21

Indirect study of minijet suppression

(1/σ) dσ/dτ in Pythia

0.01 0.1 1 10 0.5 1 1.5 2

(1/tot) d/d = 2 qT/(pT1+pT2)

Inclusive dijets pT > 25 GeV PYTHIA with GRV98

MPI

gg->gg channel

pT0(s) = 2.28 GeV

7 TeV 14 TeV 20 TeV 30 TeV

10

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SLIDE 22

Indirect study of minijet suppression

(1/σ) dσ/dτ in Pythia

0.01 0.1 1 10 0.5 1 1.5 2

(1/tot) d/d = 2 qT/(pT1+pT2)

Inclusive dijets pT > 25 GeV PYTHIA with GRV98

MPI

gg->gg channel

pT0(s) = 2.28 (s/7.0 TeV)0.215 GeV

7 TeV 14 TeV 20 TeV 30 TeV

10

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SLIDE 23

Indirect study of minijet suppression

(1/σ) dσ/dτ in Pythia

0.01 0.1 1 10 0.5 1 1.5 2

(1/tot) d/d = 2 qT/(pT1+pT2)

Inclusive dijets pT > 25 GeV PYTHIA with GRV98

MPI

gg->gg channel

pT0(s) = 2.28 (s/7.0 TeV)0.5 GeV

7 TeV 14 TeV 20 TeV 30 TeV

10

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SLIDE 24

Indirect study of minijet suppression

Bimodality coefficient for Pythia b = γ2 + 1 κ , where γ = µ3 σ3 , κ = µ4 σ4 with µn central moments 11

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SLIDE 25

Indirect study of minijet suppression

Bimodality coefficient for Pythia b = γ2 + 1 κ , where γ = µ3 σ3 , κ = µ4 σ4 with µn central moments

0.4 0.5 0.6 0.7 0.8 0.9 1 10 15 20 25 30

b(s) s [TeV]

bimodality coefficient

PYTHIA

pT0(s) = 2.28 (s/7 TeV)0.215 GeV pT0(s) = 2.28 (s/7 TeV)0.5 GeV pT0(s) = 2.28 GeV no MPIs

11

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SLIDE 26

Indirect study of minijet suppression

(1/σ) dσ/dτ in HEF

0.001 0.01 0.1 1 10 0.5 1 1.5 2

(1/tot) d/d = 2 qT/(pT1+pT2)

Inclusive dijets pT > 25 GeV

HEF with KMR (GRV98)

gg->gg channel

7 TeV 14 TeV 20 TeV 30 TeV

12

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SLIDE 27

Indirect study of minijet suppression

(1/σ) dσ/dτ in HEF

0.001 0.01 0.1 1 10 0.5 1 1.5 2

(1/tot) d/d = 2 qT/(pT1+pT2)

Inclusive dijets pT > 25 GeV

HEF with CCFM

gg->gg channel

7 TeV 10 TeV 14 TeV 20 TeV 30 TeV

12

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SLIDE 28

Indirect study of minijet suppression

(1/σ) dσ/dτ in HEF

0.001 0.01 0.1 1 10 0.5 1 1.5 2

(1/tot) d/d = 2 qT/(pT1+pT2)

Inclusive dijets pT > 25 GeV

HEF with KMS-HERA

gg->gg channel

7 TeV 14 TeV 20 TeV 30 TeV

12

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SLIDE 29

Indirect study of minijet suppression

Bimodality coefficient for HEF

0.4 0.5 0.6 0.7 0.8 0.9 1 10 15 20 25 30

b(s) √s [TeV]

bimodality coefficient

HEF

KMR (GRV98) CCFM KMS-HERA

13

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SLIDE 30

Conclusions

  • The τ distribution is sensitive to MPIs
  • The suppression of MPIs can be characterized by the bimodality coefficient

which reflects the behavior of the pT0 cutoff

  • HEF contains power corrections mimicking MPIs
  • The energy dependence of the minijet pT cutoff is related to the small x

evolution of unintegrated gluon distribution 14