Université de Moncton INT workshop: Gluons and the quark sea at high energies,distributions, polarisation, tomography September 29, 2010 based on work done with J. R. Forshaw, G.Shaw and B. E. Cox (Manchester and CERN)
Outline 1 Basics of the dipole model 2 Saturation at HERA? 3 Probing saturation at the LHC 4 New information on the ρ wavefunction
High energy factorisation γ p z r 1 z b A b : impact parameter r : transverse dipole size z : fraction of photon s plus-momentum carried by quark At high energy (s t, Q 2, MA 2 ), amplitude factorises : ImA(x, Q, ) d 2 rdz{ψ γ Ψ A eizr. } d 2 be ib. N (x, r, b) Overlap of light-cone wavefunctions {...} = Ψ γ (r, z; Q 2 )e izp.r Ψ A (r, z; M2 A )e izp.r Dipole proton scattering amplitude : N (x, r, b) with x = Q 2 s Holds beyond validity of perturbation theory
Forward amplitude γ p z A r 1 z b ImA(x, Q, 0) s t 2 = 0 Assume factorised b-dependence Use optical theorem d 2 rdzψ γ (r, z; Q 2 )Ψ A (r, z; M2 A )ˆσ(x, r)
Low x DIS z 1-z r b A = γ Optical theorem gives F 2 of low x DIS σ γ p X = ImA(x, Q, 0) s Precise and copious F 2 data from HERA used to constrain ˆσ
DVCS and Vector meson production γ z A r 1 z DVCS : A = γ b VMP : A = ρ, φ, J/Ψ, Υ,... p dσ dt = ImA(x, Q, 0) 2 exp( B t ) (1 + β 2 ) β = ReA ImA Estimate real part using dispersion relations B-slope taken from experiment
Light cone wavefunctions Photon γ µ {ūh Ψ γ{λ} h, h,f (k, z; (k) Q2 ) ee f γ µ.ε {λ} v h( k) } z µ φ γ (k, z; Q 2 ) 1 z Sensitive to quark mass as Q 2 0
Light cone wavefunctions Meson γ µ Γ(k, z) {ūh Ψ v{λ} h, h (k, z) (k) γ µ.ε v{λ} v h( k) } z µ φ λ v (k, z; Mv 2 ) 1 z Gaussian form for scalar part φ BG v,λ (r, z) = N λz z exp ( m2 f R2 8z z z = 1 z ) exp ( 2z zr 2 ) R 2 Constraints Leptonic decay width Normalisation condition
Dipole cross-section Cross-section for elastically scattering a dipole off a proton q q + p q q + p ˆσ contains a lot of physics : 1 Perturbative and non perturbative physics 2 pqcd evolution and saturation 3 Pomerons of Regge theory Invariably contains free parameters fitted to F 2 data
Dipole models pqcd Saturation models Different assumed mechanisms for saturation 1 Glauber-Mueller eikonal approach Evolved from the Golec-Biernat and Wusthoff model to include DGLAP evolution and impact parameter dependence (bsat) 2 Exploits solutions of the Balitsky Kochegov equation Evolved from Colour Glass Condensate (CGC) of Iancu et al. to include impact parameter dependence (bcgc) Regge models No assumed mechanism for saturation Hard and soft Pomerons of Regge theory Saturation can be taken into account in a phenomenological way
Regge inspired models J. R. Forshaw and G. Shaw, JHEP 0412 (2004) 052 For r < r 0, hard term (Colour transparency) : σ hard d (x, r) = A H r 2 x λ H For r > r 1, soft term (Regge theory) : σ soft d (x, r) = A S x λ S. Non perturbative saturation for large dipoles r > r 1 Fixed r 0 Regge-type r 0 varying with x saturation radius Linear interpolation for intermediate r 0 < r < r 1
FSRegge fits to F 2 data. FSRegge Cannot fit
FSSat fit to F 2 data FSSat and CGC Good fits
Saturation in F 2 data? Strong hints but... Only true if data points in the low Q 2 region are included Good fits for both FSSat and FSRegge if Q 2 2 GeV 2
Diffractive Deep Inelastic Scattering (F D 2 (3)) x IP F D(3) 2 0.06 0.04 0.02 0.06 0.04 0.02 0.06 0.04 0.02 0.06 0.04 0.02 0.06 0.04 0.02 0.06 0.04 0.02 =0.003 =0.0067 =0.0218 =0.6522 10-4 10-3 10-2 Q 2 = 2.7 GeV 2 =0.0698 =0.2308 10-4 10-3 10 x -2 IP Q 2 = 4 GeV 2 =0.0044 =0.0066 =0.0099 =0.0148 =0.032 =0.0472 =0.1 Q 2 = 6 GeV 2 ZEUS FPC FS04 sat b= 6.8 GeV -2 FS04 no sat b=8 GeV -2 CGC b=6.8 GeV -2 =0.1429 =0.3077 =0.4 =0.7353 =0.8065 10-4 10-3 10-2 10-1 Theoretical uncertainties at low β and large x P Better precision on the measured value of B-slope will help Cannot really discriminate
Diffractive Deep Inelastic Scattering (F D 2 (3)) x IP F D(3) 2 0.06 0.04 0.02 0.06 0.04 0.02 0.06 0.04 0.02 0.06 0.04 0.02 0.06 0.04 0.02 0.06 0.04 0.02 10-4 10-3 10-2 =0.0088 Q 2 = 8 GeV 2 =0.0153 Q 2 = 14 GeV 2 =0.0291 =0.0196 =0.0338 =0.0632 10-4 10-3 10-2 x IP Q 2 = 27 GeV 2 ZEUS FPC FS04 sat b = 6.8 GeV -2 FS04 no sat b = 8 GeV -2 CGC b = 6.8 GeV -2 Q 2 = 55 GeV 2 =0.1209 =0.062 =0.1037 =0.1824 =0.3125 =0.1818 =0.28 =0.4286 =0.6044 =0.4706 =0.6087 =0.75 =0.8594 =0.8475 10-4 10-3 10-2 =0.9067 =0.9494 =0.9745 10-4 10-3 10-2 10-1
Diffractive J/Ψ production σ [nb] σ [nb] 500 400 Q 2 =0 Q 2 = 0.4 400 ZEUS H1 300 FS04 no sat, Gaussian 300 FS04 sat, Gaussian CGC, Gaussian 200 200 100 100 0 100 1000 100 1000 300 Q 2 = 3.1 (ZEUS); 3.2 (H1) 200 100 150 Q 2 =6.8 (ZEUS); 7.0 (H1) 100 50 Agreement within HERA range Large saturation effects at around 1 TeV Can EIC reveal them at lower energies? 100 1000 W [GeV] 0 100 1000 W [GeV]
Diffractive J/Ψ production 80 60 σ [nb] 70 60 50 40 30 20 Q 2 =13 H1 ZEUS FS04 sat, Gaussian FS04 no sat, Gaussian CGC, Gaussian 50 40 30 20 Q 2 =16 Agreement within HERA range σ [nb] 10 0 40 32 24 16 8 Q 2 =22.4 10 0 100 1000 20 15 10 5 Q 2 =33.6 100 1000 Large saturation effects at around 1 TeV Can EIC reveal them at lower energies? 100 1000 W [GeV] 0 100 1000 W [GeV]
Deeply Virtual Compton Scattering 12 σ [nb] 11 10 9 8 7 6 5 4 3 2 1 Q 2 = 8.0 GeV 2 B = 6.02 GeV -2 H1 FS04 no sat FS04 sat CGC 100 1000 W [GeV] Agreement within HERA range Large saturation effects at 1 TeV Can EIC reveal them at lower energies? Can EIC acheive better precision?
Deeply Virtual Compton Scattering 30 σ [nb] 20 10 FS04 sat FS04 no sat CGC ZEUS (e + p) ZEUS (e - p) Q 2 = 9.6 GeV 2 B = 4.0 GeV -2 100 1000 W [GeV] Agreement within HERA range Large saturation effects at 1 TeV Can EIC reveal them at lower energies? Can EIC acheive better precision?
Saturation at HERA? Forshaw, RS, Shaw JHEP 0611 :025 (2006) Conclusion Saturation may well be present at HERA but no evidence in the perturbative domain Go to higher A : EIC Go to higher energies : LHC
Diffractive Upsilon (Υ) production at the LHC B. E. Cox, J. R. Forshaw, RS, JHEP 06 (2009) 034 Also : L. Motyka and G. Watt, Phys. Rev. D78 014023 (2008) pp p + Υ{µ + µ } + p p p p p Protons lose little energy and momentum and remain intact. Exclusive production of Υ decaying to µ + µ pairs detected in the ATLAS or CMS detectors. Proposed low angle protons detectors at the LHC to tag the outgoing protons : FP 420 project
Diffractive Upsilon (Υ) production at the LHC B. E. Cox, J. R. Forshaw, RS, JHEP 06 (2009) 034 Also : L. Motyka and G. Watt, Phys. Rev. D78 014023 (2008) pp p + Υ{µ + µ } + p p p p p Protons lose little energy and momentum and remain intact. Exclusive production of Υ decaying to µ + µ pairs detected in the ATLAS or CMS detectors. Proposed low angle protons detectors at the LHC to tag the outgoing protons : FP 420 project Any one of the protons can radiate the (almost real) photon.
Rapidity distribution and cross-section f γ/p (ξ) is the photon flux Υ s rapidity Rapidity distribution dσ(pp pυp) dy ( ) ξ s Y = ln M Υ = ξf γ/p (ξ) σ γp (W ) + (Y Y )
Rapidity distribution and cross-section f γ/p (ξ) is the photon flux Υ s rapidity ( ) ξ s Y = ln M Υ Rapidity distribution dσ(pp pυp) = ξf dy γ/p (ξ) σ γp (W ) + (Y Y ) f γ/p (ξ) is the integrated photon flux given by α 1 + (1 ξ) 2 ( ln A(ξ) 11 2π ξ 6 + 3 A(ξ) 3 2A 2 (ξ) + 1 ) 3A 3 (ξ) A(ξ) = 1 + µ2 Q 2 min Q 2 min = ξ2 m 2 p
Rapidity distribution and cross-section f γ/p (ξ) is the photon flux Υ s rapidity ( ) ξ s Y = ln M Υ Rapidity distribution dσ(pp pυp) = ξf dy γ/p (ξ) σ γp (W ) + (Y Y ) Adding cross-sections : neglecting interference.
Rapidity distribution and cross-section f γ/p (ξ) is the photon flux Υ s rapidity ( ) ξ s Y = ln M Υ Rapidity distribution dσ(pp pυp) = ξf dy γ/p (ξ) σ γp (W ) + (Y Y ) σ γp (W ) is the photoproduction cross-section with W 2 = ξs
Rapidity distribution and cross-section f γ/p (ξ) is the photon flux Υ s rapidity Rapidity distribution dσ(pp pυp) dy ( ) ξ s Y = ln M Υ = ξf γ/p (ξ) σ γp (W ) + (Y Y ) Cross-section σ(pp pυp) = dy dσ dy
Rapidity distribution and cross-section f γ/p (ξ) is the photon flux Υ s rapidity Rapidity distribution dσ(pp pυp) dy ( ) ξ s Y = ln M Υ = ξf γ/p (ξ) σ γp (W ) + (Y Y ) Di-muon cross-section σ(pp pυ{µ + µ }p) = dy dσ dy B(Υ µ+ µ )
Υ light-cone wavefunctions γ + p Υ(nS) + p HERA cannot resolve between n = 1, 2, 3 Ψ 1S 2 Ψ 2S 2 Ψ 3S 2 2 0.6 0.4 1 0 0 2 r 4 0.4 0.2 z 0.0 0.4 0.2 0.0 0 1 2 r 3 0.4 0.2 z 4 0.0 5 0.2 0.0 0 1 2 r 3 0.4 0.2 z 4 5 0.0
Photon level cross-section σ γ p [pb] 10 4 10 3 10 2 10 1 10 0 ZEUS H1 ZEUS (2009) FSSat (no skew, no real) FSSat (no skew, real) FSSat (skew, real) FSSat (skew, real, x2) Fit 10 2 10 3 10 4 W [GeV] Real part and skewedness corrections important. Dipole models predict too low normalisation NLO corrections important
Predictions for the rapidity distribution dσ/ dy [fb] 20000 15000 10000 5000 Fit FSSat LHC 0-8 -7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 8 Y Very different distributions for FSSat and Fit Very sensitive to the energy dependence of the photoproduction cross-section Hope to constrain the gluon density and saturation models
Rapidity distributions with cuts dσ/ dy [fb] 3000 2000 1000 LHC Fit (muon cuts) FSSat (muon cuts) 0-5 -4-3 -2-1 0 1 2 3 4 5 Y Cuts on the muon s rapidity and transverse momentum to account for the detectors acceptance Strong sensitivity to energy dependence reduced But there is still hope to constrain the theory
Measuring one proton 3000 LHC Fit (muon cuts) FSSat (muon cuts) FSSat(muon cuts + 1p) Fit (muon cuts +1p) dσ/ dy [fb] 2000 1000 severely limits the acceptance of a measurement but helps to control pile up at high luminosities 0-5 -4-3 -2-1 0 1 2 3 4 5 Y
Measuring the γ p cross-section at the LHC Might be possible to measure the γ p cross-section at around 1 TeV by tagging one proton Gap survival issues can complicate matters
Diffractive ρ meson production at HERA γ + p ρ + p 1 New precise data from HERA available ZEUS Collaboration, PMC, Phys. A1 (2007) 6 H1 Collaboration, JHEP 12 (2010) 052 2 Our models are not able to describe satisfactorily the data 3 Meson wavefunction?
Extracting the ρ meson wavefunction from HERA data J. R. Forshaw and RS (2010), arxiv :1007.1990 [hep-ph] Fits done with FSSat dipole model and Gaussian wavefunction ( ) φ BG λ (r, z) = N λ[z z] b λ exp m2 f R2 λ 8[z z] b exp ( 2[z z]b λr 2 ) λ R 2 λ 1 Original BG : b λ = 1, R L = R T fixed 2 Large χ 2 per data point = 234/75 3 Allow b λ and R λ to vary freely 4 Good fit except at low Q 2
Additional end-point enhancement φ λ (r, z) = φ BG λ (r, z) [1 + c λξ 2 + d λ ξ 4 ] Relative momentum fraction ξ = 2z 1 Preference for additional enhancement in transverse wavefunction only Not necessary if B-slope is allowed to increase at Q 2 = 0 Uncertainties in the Q 2 0 limit prevent a positive statement on requirement for additional enhancement
Longitudinal wavefunction L-wavefunction squared at r = 0 Dotted green : Original BG Solid black : BG Fit Dashed red : Improved fit
Longitudinal wavefunction T -wavefunction squared at r = 0 Dotted green : Original BG Solid black : BG Fit Dashed red : Improved Fit
Extracted light-cone wavefunctions for the ρ 0.08 0.06 0.04 0.02 0.0 0 5 r 10 0.0 0.5 z 1.0 L-wavefunction squared Some broadening
Extracted light-cone wavefunctions for the ρ.015 0.01.005 0.0 0 10 r 20 0.0 0.5 z 1.0 T -wavefunction squared Clear enhancement of end-points contributions
Distribution amplitudes Work in progress with J. Forshaw Connection with Distribution Amplitudes (DAs) Predict moments of leading twist DAs to compare with QCD sum rules and lattice predictions
Conclusions Hints of saturation in inclusive structure functions at HERA...but no firm evidence for perturbative saturation HERA data on exclusive diffraction do not yield further evidence May probe saturation at the LHC in ultraperipheral collisions Can EIC probe saturation at lower energies and in a clean way?