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

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

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 x g effects where x g is a longitudinal momentum fraction carried by gluon. b ) a) To go to low x g safely we need to consider off-shell gluon... DIS, London, 07-11.04.08 3

QCD Compton in k T 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

Details of kinematics The Sudakov decomposition is: k = x g p A + z g p B + k T q = x q p A k ′ = x g ′ p A + z g ′ p B + k ′ T q ′ = z q ′ p A + x q ′ p B + q ′ T k Mandelstam variables are: k ′ s = ( p 1 + p 2 ) 2 s = ( k + q ) 2 ˆ q ′ q u = ( k − q ′ ) 2 ˆ ˆ t = ( k − k ′ ) 2 We are interested in configuration where: p B s, ˆ ˆ t, ˆ u< <s DIS, London, 07-11.04.08 5

Hard matrix element After squaring amplitude we obtain: � � x 2 g s 2 ( x 2 q + x 2 q ′ ) s (8 x q + x q ′ ) − ˆ ˆ u (8 x q ′ + x q ) | M | 2 = − (4 π ) 2 α 2 + k 2 u ˆ s x q − x q ′ 18ˆ s ˆ t • In collinear limit k 2 → 0 one obtains QCD Compton • Symmetry ˆ s → − ˆ u , x q ′ → x q DIS, London, 07-11.04.08 6

Some properties of the off-shell ME Angle between icoming gluon and outgoing quark is far from zero 11 10 k g =20GeV Dimensionless off−shell ME 9 10 on−shell ME 7 10 5 10 k g q’ q 5 10 15 20 25 0 q’[GeV] q • off-shell ME allows for larger q ′ q DIS, London, 07-11.04.08 7

Some properties of the off-shell ME Angle between incoming 11 gluon and outgoing quark is zero 10 k g =20GeV off−shell ME 9 10 on−shell ME Dimensionless 7 10 5 10 k g q’ q 0 5 10 15 20 25 q’[GeV] q • at 0 angle there is a singularity at k ′ q = k g DIS, London, 07-11.04.08 8

Cross-section for 2 jets Cross-section for 2-jet production: T , µ ) ⊗ | M | 2 ⊗ f q ( x q , k 2 σ ∼ f g ( x g , k 2 T 2 , µ ) • f g ( x g , k 2 T , µ ) unintegrated gluon density ← CCFM • f q ( x q , k 2 T , µ ) unintegrated valence quark density (needed for technical reasons) ← CCFM-like. Initial valence quark distribution is provided by CTEQ 6.1 • α s → α s ( k 2 T ) • cut on momenta of outgoing jets → p T > 2 . 5 GeV The result for the total x-section is roughly: 10 mb For comparison total pp x-section at LHC energies is roughly 80 mb DIS, London, 07-11.04.08 9

Results - x distribution before collision 3 3 10 10 × × qg → qg qg → qg 3500 x of quark - kt x of gluon - kt 6000 3000 x of quark - col x of gluon - col 5000 ) [nb] ) [nb] 2500 4000 q g 2000 /dlog(x /dlog(x 3000 1500 σ σ 2000 d d 1000 1000 500 0 0 -7 -6 -5 -4 -3 -2 -1 0 -7 -6 -5 -4 -3 -2 -1 0 log(x ) log(x ) g q • Incoming off-shell gluon carrying low momentum fraction • Incoming on-shell quark carrying large momentum fraction DIS, London, 07-11.04.08 10

Results - pseudo-rapidity distribution of produced jets qg → qg qg → qg 3 3 10 10 × × 1200 1200 rapidity of gluon jet rapidity of quark jet 1000 1000 800 800 [nb] [nb] g q 600 600 /dy /dy σ σ d d 400 400 200 200 0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 y y g q • valence quark ( m q = 0 ) is slightly deflected • produced jets are well separated in rapidity DIS, London, 07-11.04.08 11

Results - p T spectra of produced jets 6 6 10 10 qg → qg qg → qg p of quark jet p of gluon jet 5 5 10 10 ] ] -1 -1 [nb GeV [nb GeV 4 10 10 4 fq fg /dp 3 /dp 3 10 10 σ σ d d 2 2 10 10 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160 p [GeV] p [GeV] fq fg DIS, London, 07-11.04.08 12

Conclusions and outlook • We obtained matrix element in k T factorisation which allow for studies of low x g effects at the LHC • CCFM-like equation for unintegrated quark distribution has been incorporated in Monte Carlo framework → CASCADE • p T 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 k T 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

Back up slides 3 10 × qg qg → 1000 y - kt ∆ qg y - col ∆ qg 800 [nb] 600 qg y ∆ /d 400 σ d 200 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 y ∆ qg • Rapidity difference between produced jets DIS, London, 07-11.04.08 14