factorisation Michal Deak, Hannes Jung, Krzysztof Kutak DESY, - - PowerPoint PPT Presentation

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factorisation Michal Deak, Hannes Jung, Krzysztof Kutak DESY, - - PowerPoint PPT Presentation

Mar 11, 2023 226 likes •372 views

Valence quarks and k T factorisation Michal Deak, Hannes Jung, Krzysztof Kutak DESY, Hamburg DIS, London, 07-11.04.08 1 Motivation HERA hints that at rapidities y > 3 there can be new kind of dynamics BFKL, CCFM, BK. However,

slide-1
SLIDE 1

Valence quarks and kT factorisation

Michal Deak, Hannes Jung, Krzysztof Kutak DESY, Hamburg

DIS, London, 07-11.04.08 1

slide-2
SLIDE 2

Motivation

  • HERA → hints that at rapidities y > 3 there can be new kind of dynamics → BFKL,

CCFM, BK. However, at HERA we cannot go to the more forward region.

  • LHC will allow for this study. The interesting region can be studied if we consider

QCD Compton scattering:

rapidity gluon at large valence quark at small rapidity stands for additional QCD C diagrams DIS, London, 07-11.04.08 2

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SLIDE 3

Jets at LHC - collinear approach

Jets are initiated by hard subprocesses (a), (b). QCD Compton (a) is the relevant hard process if we want to study low xg effects where xg is a longitudinal momentum fraction carried by gluon.

a) b)

To go to low xg safely we need to consider off-shell gluon...

DIS, London, 07-11.04.08 3

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SLIDE 4

QCD Compton in kT factorisation

Incoming gluon is not collinear to the proton it is off-shell. Valence quark is collinear to the proton. The upper quark line → replaced by gluon distribution after matrix element is calculated All five diagrams are required by gauge invariance.

DIS, London, 07-11.04.08 4

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SLIDE 5

Details of kinematics

The Sudakov decomposition is: k = xgpA + zgpB + kT q = xq k′ = xg′pA + zg′pB + k′

T

q′ = zq′pA + xq′pB + q′

T

Mandelstam variables are: s = (p1 + p2)2 ˆ s = (k + q)2 ˆ u = (k − q′)2 ˆ t = (k − k′)2 We are interested in configuration where: ˆ s, ˆ t, ˆ u< <s

q′ q k k′ pA pB

DIS, London, 07-11.04.08 5

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SLIDE 6

Hard matrix element

After squaring amplitude we obtain: |M|2 = −(4π)2α2

s

x2

gs2(x2 q + x2 q′)

18ˆ sˆ uˆ t

  • ˆ

s(8xq + xq′) − ˆ u(8xq′ + xq) xq − xq′ + k2

  • In collinear limit k2→0 one obtains QCD Compton
  • Symmetry ˆ

s→ − ˆ u, xq′→xq

DIS, London, 07-11.04.08 6

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SLIDE 7

Some properties of the off-shell ME

5 10 15 20 25

5 7 9

  • n−shell ME

10 10 10

11

10

  • ff−shell ME

kg=20GeV gluon and outgoing quark is far from zero Angle between icoming

Dimensionless q’[GeV]

q

kg q’

q

  • off-shell ME allows for larger q′

q

DIS, London, 07-11.04.08 7

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SLIDE 8

Some properties of the off-shell ME

5 10 15 20 25

11 9 7 5

gluon and outgoing quark is zero kg =20GeV

  • n−shell ME
  • ff−shell ME

10 10 10 10

q’[GeV]

q

Angle between incoming Dimensionless

q’

q

kg

  • at 0 angle there is a singularity at k′

q = kg

DIS, London, 07-11.04.08 8

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SLIDE 9

Cross-section for 2 jets

Cross-section for 2-jet production: σ ∼ fg(xg, k2

T, µ) ⊗ |M|2 ⊗ fq(xq, k2 T 2, µ)

  • fg(xg, k2

T, µ) unintegrated gluon density ← CCFM

  • fq(xq, k2

T , µ) unintegrated valence quark density (needed for technical reasons) ←

CCFM-like. Initial valence quark distribution is provided by CTEQ 6.1

  • αs → αs(k2

T)

  • cut on momenta of outgoing jets → pT>2.5GeV

The result for the total x-section is roughly: 10mb For comparison total pp x-section at LHC energies is roughly 80 mb

DIS, London, 07-11.04.08 9

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SLIDE 10

Results - x distribution before collision

)

q

log(x

  • 7
  • 6
  • 5
  • 4
  • 3
  • 2
  • 1

) [nb]

q

/dlog(x σ d

1000 2000 3000 4000 5000 6000

3

10 ×

qg → qg x of quark - kt x of quark - col

)

g

log(x

  • 7
  • 6
  • 5
  • 4
  • 3
  • 2
  • 1

) [nb]

g

/dlog(x σ d

500 1000 1500 2000 2500 3000 3500

3

10 ×

qg → qg x of gluon - kt x of gluon - col

  • Incoming off-shell gluon carrying low momentum fraction
  • Incoming on-shell quark carrying large momentum fraction

DIS, London, 07-11.04.08 10

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SLIDE 11

Results - pseudo-rapidity distribution of produced jets

g

y

  • 10
  • 8
  • 6
  • 4
  • 2

2 4 6 8 10

[nb]

g

/dy σ d

200 400 600 800 1000 1200

3

10 ×

qg → qg rapidity of gluon jet

q

y

  • 10
  • 8
  • 6
  • 4
  • 2

2 4 6 8 10

[nb]

q

/dy σ d

200 400 600 800 1000 1200

3

10 ×

qg → qg rapidity of quark jet

  • valence quark (mq = 0) is slightly deflected
  • produced jets are well separated in rapidity

DIS, London, 07-11.04.08 11

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SLIDE 12

Results - pT spectra of produced jets

[GeV]

fq

p

20 40 60 80 100 120 140 160

]

  • 1

[nb GeV

fq

/dp σ d

2

10

3

10

4

10

5

10

6

10

qg → qg

  • f quark jet

p

[GeV]

fg

p

20 40 60 80 100 120 140 160

]

  • 1

[nb GeV

fg

/dp σ d

2

10

3

10

4

10

5

10

6

10

qg → qg

  • f gluon jet

p

DIS, London, 07-11.04.08 12

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SLIDE 13

Conclusions and outlook

  • We obtained matrix element in kT factorisation which allow for studies of low xg

effects at the LHC

  • CCFM-like equation for unintegrated quark distribution has been incorporated in

Monte Carlo framework → CASCADE

  • pT and rapidity spectra of produced jets have been calculated
  • Consistency check with collinear approach has been done
  • Step towards including multiple interactions for MC generator in kT factorisation

framework

  • Important for testing different models
  • Since gluon is probed at low momentum fraction we are going to include nonlinear

evolution equation to parametrize unintegrated gluon distribution

DIS, London, 07-11.04.08 13

slide-14
SLIDE 14

Back up slides

qg

y ∆

  • 10
  • 8
  • 6
  • 4
  • 2

2 4 6 8 10

[nb]

qg

y ∆ /d σ d

200 400 600 800 1000

3

10 ×

qg → qg

  • kt

qg

y ∆

  • col

qg

y ∆

  • Rapidity difference between produced jets

DIS, London, 07-11.04.08 14