Parton saturation and diffractive processes Krzysztof Golec-Biernat Institute of Nuclear Physics PAN, Kraków Institute of Physics, University of Rzeszów Diffractive and electromagnetic processes at high energies WE- Heraeus-Summerschool, Heidelberg, September 5-9, 2011 Parton saturation in diffraction p. 1
Outline Introduction Dipole models with saturation in DIS QCD justification of dipole models Dipoles in pp scattering Diffractive W/Z boson production Parton saturation in diffraction p. 2
Diffractive processes L X s t, m 2 X, m2 Y s vacuum quantum number exchange R Y QCD: two gluons in color singlet state DIS: s Q 2, t, m 2 p Q 2 X semihard process s P Y x = Q2 s 1 Q2 Λ 2 QCD perturbative QCD applicable Parton saturation in diffraction p. 3
Soft and hard diffraction Two basic features of diffraction: rising cross sections with energy s large rapidity gaps: η = log tan(θ/2) (color singlet exchange) 2ϑ Y X Soft diffraction (no hard scale): σ s α P(0) α P (t) = 1.08+0.25 t pp p+p γp V(ρ,ω,φ)+p Hard diffraction (with hard scale): 1.2 < α P (0) < 1.4 γ p X +p γ p V +p γp J/ψ +p pp jj +pp Parton saturation in diffraction p. 4
Hera results Parton saturation in diffraction p. 5
Deep inelastic scattering at small x em F 2 1.6 1.4 Q 2 = 15 GeV 2 1.2 1 0.8 H1 96/97 ZEUS 96/97 NMC, BCDMS, E665 CTEQ6D MRST (2001) 0.6 0.4 0.2 0 10-4 10-3 10-2 10-1 1 x H1 Collaboration Power-like rise of F 2 x λ for x = Q 2 /s 0, driven by gluons. Should it be tamed to logarithmic due to gluon recombination? Parton saturation in diffraction p. 6
Back to basics of DIS Infinite momentum frame (P ): pointlike γ resolves partonic constituents of the proton Proton rest frame (P 0): γ develops partonic fluctuations long before the proton target Coherence length: l c = 1 xm p 1 m p 0.2 fm for x 1. Parton saturation in diffraction p. 7
Dipole states Hadron wave function in light-cone quantization approach Ψ = Ψ n n n = α 1...α n ; k T1...k Tn n are partonic states eigenstates of free Hamiltonian. After Fourier transformation to transverse position space α 1...α n ; k T1...k Tn α 1...α n ; r 1... r n Virtual photon wave function γ = Ψ q q q q + Ψ q qg q qg +... Lowest state: q q dipole of size r = r 1 r 2 at impact parameter. b = 1 2 ( r 1 + r 2 ) Parton saturation in diffraction p. 8
q q dipole Light-cone photon wave function, Ψ λ hh (r,α,q 2 ), known from QED. Dipole states are eigenstates of scattering operator. r, b and α are conserved in the high energy scattering. Parton saturation in diffraction p. 9
Color dipole models Universal description (N. N. Nikolaev, B. G. Zakharov, A. H. Mueller) Scattering amplitude for γ p Ap where A = γ,γ,v A(b) = d 2 rdαψ AN q q (r,b,x)ψ γ N q q is the dipole scattering amplitude. Find N q q from the total γ p cross section σ γ p = 1 4π 2 α em F 2 Q 2 Parton saturation in diffraction p. 10
Phenomenological parameterization GB Wüsthoff parameterization with saturation scale Q s (x) = Q 0 x λ } N q q (r,b,x) = S(b) {1 e r2 Q 2 s /4 Local unitarity fulfilled: N q q 1. Physical interpretation (1/Q s - mean distance between partons): DIPOL 00000000000 11111111111 00000000000 11111111111 1100 0100 1100 1100 00 11 1100 1100 1100 1100 1100 1100 1100 01 1100 1100 1100 00 1100 1100 00 00 11 11 11 00 1100 11 1100 1100 11 1100 x=10 2 x=10 6 N q q r 2 Q 2 s N q q 1 Proton structure function F 2 ln(1/x) for x = Q 2 /s 0. Parton saturation in diffraction p. 11
Dipole cross section Proton structure function F 2 Q 2 σ γ p and σ γ p(x,q 2 ) = d 2 bd 2 rdα Ψ γ (r,α,q 2 ) 2 N q q (r,b,x) Dipole cross section σ q q (x,r) = d 2 bn qq (r,b,x) = σ 0 { 1 e r2 Q 2 s /4 } σ (mb) 30 25 20 15 10 5 x=10-5 x=10-4 x=10-3 x=10-2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 r (fm) Parameters σ 0,λ,Q 0 from a fit to F 2 data in DIS. Use σ q q in diffractive DIS. Parton saturation in diffraction p. 12
Diffractive DIS Diffractive DIS cross section dσ D γ p dt t=0 = 1 16π 2 d 2 rdz Ψ γ (r,z,q 2 ) 2 σ 2 qq(r,x) Successful description of DDIS with two component diffractive state q q α,k t α,k t l t l t l t l t p p The only approach which explains constant ratio with energy σ D γ p σ γ p 1 log(q 2 /Q 2 s(x)) Parton saturation in diffraction p. 13
Constant ratio σ diff /σ tot 0.06 0.04 Q 2 = 8 GeV 2 Q 2 = 27 GeV 2 Q 2 = 14 GeV 2 Q 2 = 60 GeV 2 M X < 3 GeV 0.02 0 0.06 3 < M X < 7.5 GeV 0.04 0.02 0 0.06 7.5 < M X < 15 GeV 0.04 0.02 0 40 60 80 100 120 140 160 180 200 220 W(GeV) Parton saturation in diffraction p. 14
Constancy with energy dipole cross section pqcd Saturation Soft r 1/Q 1/Q s 1/ Λ QCD σ γ p ( ) 1 Q 2 + ( ) 1 Q 2 ln Q2 S Q 2 + ( ) 1 Q 2 σ D γ p ( ) 2 1 Q 2 + ( ) 1 Q 2 + ( ) 1 Q 2 Diffraction probes directly saturation (semihard) region: r 1/Q s Parton saturation in diffraction p. 15
Important improvements Small dipole corrections to match perturbative QCD results (Frankfurt, Strikman, McDermott, Bartels, GB, Kowalski, Iancu, Itakura, Munier) N q q (r,b,x) r 2 α s xg(x,a/r 2 )T(b) Realistic b-profile t-dependence of exclusive diffractive processes (Kowalski, Teaney, Motyka, Watt) T(b) = exp( b 2 /2B) Q s (x,b) = Q 0 x λ T(b)l QCD justification - larger dipole sizes? Parton saturation in diffraction p. 16
Effective slopes of F 2 λ 0.5 Effective slopes 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 10-2 10-1 1 10 10 2 Q 2 (GeV 2 ) F 2 x λ(q2) at fixed Q 2. Parton saturation in diffraction p. 17
Mueller s dipole evolution Soft gluon emissions with α g α q Splitting probablity (xy) (xz) +(zy) dp dy = α s 2π ( x y) 2 ( x z) 2 ( z y) 2 d2 z K(x,y,z) Classical branching process (A. H. Mueller). Multi-dipole distributions n k = δk δu kz[u] u=0 k = 1,2,... BFKL growth of dipole number: n 1 e 4ln2ᾱ sy. Unitarity violated? Parton saturation in diffraction p. 18
Balitsky-Kovchegov equation No, if uncorrelated multiple scattering of dipoles N xy = ( γ)n 1 + ( γ) 2 n 2 + ( γ) 3 n 3 +... p p Nonlinear equation justified in case of γ A scattering N xy Y = Local unitarity: N(b) 1. { } d 2 zk(x,y,z) N xz +N yz N xy N xz N yz }{{} BFKL Parton saturation in diffraction p. 19
t-channel picture of BK equation Summation of BFKL pomeron fan diagrams (M. A. Braun) γ* One BFKL pomeron exchange: F 2 x 4ln2α s Fan diagrams summation: F 2 ln(1/x) as x = Q 2 /s 0 Parton saturation in diffraction p. 20
Summary plot ln(1/x) Nonlinear evolution Dense system Saturation scale Non perturbative region Linear evolution Dilute system ln Q Parton saturation in diffraction p. 21
Problems with BK equation No saturation in dipole number density. Missing dipole merging: 2 1 (no pomeron loops) Color quadrupols and higher multipoles neglected. No symmetric description, necessary in pp scattering. Full theory of saturation - Color Glass Condensate. (F. Gelis, E. Iancu, J. Jalilian-Marian, R. Venugopalan, arxiv:1002.0333) Parton saturation in diffraction p. 22
Dipole swing model (E. Avsar, G. Gustafson, L. Lönnblad: arxiv:1103.4321) Proton wave functions develop Mueller s color dipole cascades. Multiple interaction of dipoles: T(b) = 1 exp{ ij f ij}. Scattering of two dipoles with the same color change of color flow Weight for a swing prefers formation of smaller dipoles weight = (x 1 y 1 ) 2 (x 2 y 2 ) 2 (x 1 y 2 ) 2 (x 2 y 1 ) 2 Smaller dipoles have smaller cross sections - suppression of σ tot pp. Parton saturation in diffraction p. 23
Dipole chain scattering Dipole chain splittings and mergings r rapidity Monte Carlo implementation. Parton saturation in diffraction p. 24
Predictions for pp scattering at the LHC (E. Avsar, G. Gustafson, L. Lönnblad) 120 100 σ (mb) 80 60 40 20 σ tot σ diff σ el 0 10 2 10 3 10 4 s (GeV) σ tot = 108 mb, σ el = 26 mb, σ diff = 12 mb Parton saturation in diffraction p. 25
Hard diffraction in pp scattering W/Z boson production with a hard scale for pqcd: µ = M W/Z. W W Inclusive DPE cross sections dσ W + dy = σ W 0 { u(x1 ) d(x 2 )+ d(x 1 )u(x 2 ) } dσ W + dydξ 1 dξ 2 = σ W 0 { u D (x 1,ξ 1 ) d D (x 2,ξ 2 )+ d D (x 1,ξ 1 )u D (x 2,ξ 2 ) } S 2 diffractive parton distributions Parton saturation in diffraction p. 26
Diffractive parton distributions Inclusive PDFs - universal q a (z) = dy e izp+ y P ψa (y )γ + ψ a (0) P Diffractive PDFs - non-universal qa D (z,ξ) = dy e izp+ y P ψa (y )γ + P X P X ψ a (0) P X Parton saturation in diffraction p. 27
Pomeron model of diffractive PDFs Rapidity gap due to vacuum quantum number pomeron exchange with a partonic content (G. Ingelman, P. Schlein, 1985) q D a (z,ξ) = f IP (ξ)q IP a (z/ξ) Pomeron parton distributions - flavour symmetric u IP = d IP = ū IP = d IP W ± rapidity asymmetry sensitive to u/d content A(y) = dσ W +/dy dσ W /dy dσ W +/dy +dσ W /dy = (u 1 d 1 )ū 2 +ū 1 (u 2 d 2 ) (u 1 +d 1 )ū 2 +ū 1 (u 2 d 2 ) A(y) 0 in inclusive case but A(y) = 0 in DPE. but... Parton saturation in diffraction p. 28
Inclusive W rapidity asymmetry W and Z production cross sections at LHC W asymmetry at LHC dσ/dy (nb) 14 12 A(y) 1 0.9 0.8 10 0.7 8 W + W - 0.6 0.5 6 Z 0.4 4 0.3 0.2 2 0.1 0-4 -2 0 2 4 y 0-4 -2 0 2 4 y W rapitdity asymmetry: A(y) = dσ W + /dy dσ W /dy dσ W +/dy+dσ W /dy Parton saturation in diffraction p. 29
3 8 8 3 3 8 8 3 Soft color interaction model Typical and diffractive events differ by final state effects. Soft gluon exchanges neutralize color but do not change momenta. (A. Edin, G. Ingelman, J. Rathsman: hep-ph/9605281) e e e e 3 3 8 8 3 3 p p In this model W asymmetry is like in inclusive case, A(y) 0! Parton saturation in diffraction p. 30
W rapidity asymmetry DPE model W and Z production cross sections at LHC SCI model W and Z production cross sections at LHC dσ/dy (pb) 14 12 dσ/dy (nb) 14 12 10 10 8 6 W +- Z 8 6 W + W - Z 4 4 2 2 0-4 -2 0 2 4 y 0-4 -2 0 2 4 y A D (y,ξ 1,ξ 2 ) = 0 A D (y,ξ 1,ξ 2 ) = A incl (y) Parton saturation in diffraction p. 31
Single diffractive W rapidity asymmetry SPE model W and Z production cross sections at LHC Ratio of W boson asymmetries dσ/dy (nb) 0.5 0.4 x S 2 = 0.09 W + A D (y) / A(y) 1 0.8 0.3 W - 0.6 0.2 Z 0.4 0.1 0.2 0-4 -2 0 2 4 y 0-4 -2 0 2 4 y In SCI model the ratio A D (y,ξ 1 )/A incl (y) = 1 Parton saturation in diffraction p. 32
ratio = 1 2 ( d 3 σ + W dydξ 1 dξ 2 + d3 σ + W W/Z production rate )/ d 3 σ Z dydξ 1 dξ 2 dydξ 1 dξ 2 ratio 2 1.8 1.6 1.4 SCI 1.2 1 DPE 0.8 0.6-4 -2 0 2 4 y W rapidity asymmetry and W/Z production rate discriminate between different mechanisms of diffraction (G-B, Royon, Schoeffel, Staszewski, in progress) Parton saturation in diffraction p. 33
Conclusions Dipole models with saturation are very successful in describing various diffractive data in ep scattering. Dipole approach can be applied to diffractive pp scattering - dipole swing model. Diffractive W/Z production can discriminate between different models of hard diffraction. Parton saturation in diffraction p. 34