Exclusive Reactions at High Momentum Transfer Jefferson Lab, Newport News, VA May 21-24, 2007 Imaging the Proton via Hard Exclusive Production in Diffractive pp Scattering Charles Earl Hyde Old Dominion University, Norfolk VA 23529 USA Université Blaise Pascal, Clermont-Ferrand, France chyde@odu.edu L.Frankfurt, Ch.E.H., M. Strikman, Ch.Weiss, Phys.Rev. D75 054009 (2007). Ch.E.H., L.Frankfurt, M. Strikman, Ch.Weiss, DIS2006: hep-ph/0608312
Quark & Gluon Imaging Example of Deeply Virtual Compton Scattering (DVCS) ep ep JLab, HERMES q q + HERA, COMPASS EIC? Large Virtuality q 2 =Q 2 : Factorization of perturbative sub-process. Longitudinal momentum transfer: 2 = 2x Bj /(2x Bj ) = skewness = difference of initial and final momentum fractions = 0: Densities; > 0: Wigner functions = (q-q ), 2 = t 2 t min t Fourier conjugate to impact parameter, b. Parton Tomography: Correlation of parton longitudinal momentum and transverse position May 2007 CEH Exc2007 1
Idea of pp Diffractive Production p 1 +p 2 p 3 + gap + H + gap + p 4 H = Higgs, di-jet, Upsilon, J/, di-hadron, di-lepton, di-photon M H 2 = 1 2 s << s: Phase space for rapidity gaps M H 2 >> 2 QCD : Perturbative mechanism t 1 =(p 3 -p 1 ) 2 ( 1 ) 2 t 2 =(p 4 -p 2 ) 2 = ( 1 ) 2 1,2 : Fourier Conjugate to impact parameters b 1,2 of hard scattering process pp impact parameter b = b 2 b 1 P 1 P 1 (1-1 )+ 1 Irreducible soft interactions: Convolute hard and soft contributions to 1,2 Measure/compute soft interaction effects? Does hard scattering measure properties of ground state or of soft collisional excited state? P 3 P 2 (1-2 )+ 2 May 2007 CEH Exc2007 2
Gribov Picture of Fast Projectiles hep-ph/0006158 Large-x partons (x>0.01) confined to a volume: R 2 R 2 Low-x partons (x1/). Transverse diffusion R 2 ln( x 0 / x) PM Longitudinal spread Invariant longitudinal size. x x R 2 R 2 May 2007 CEH Exc2007 3
Elastic Scattering & Black Disk Limit Impact Parameter (b) Representation P 1μ =M (1,0,0,) s =(P 1 +P 2 ) 2 =4M 2 2 b b 1/(M) b is a good quantum # P 2μ =M (1,0,0,-) Elastic Scattering Amplitude T El, for -Momentum Transfer : Elastic scattering = diffraction pattern of b-dependent absorption i(b,s). T El (,s) =[is/(4)] 2 b e i b (b,s) Center of Proton is Black: Black Disk Limit (BDL) = Pure Absorption (0,s) = 1 (stevatron) Stabilizes numerical estimates May 2007 CEH Exc2007 4
Elastic, Inelastic, and Total Scattering Cross Sections Impact Parameter Representation: d 2 El (s) = d 2 (2 ) 2 d 2 be ib 2 (b; s) El (s) Tot (s) = d 2 b Inel (s) 1-(b;s) 2 = Probability of no inelastic scattering at impact parameter b. Elastic S-matrix: (b; s) 2 [ ] 2 (b; s) 1 1(b; s) 2 [ ] S El (, s) = e ib d 2 b 1(b, s) [ ] May 2007 CEH Exc2007 5
pp Total Cross Sections Fit adapted from Donnachie and Landshoff, hep-ph/92-09205 SPS RHIC pp2pp2007? TOTEM 2007 Threshold for BDL? May 2007 CEH Exc2007 6
Behavior of Total & (b;s) Gaussian model: (b,s) = exp[b 2 /B(s)]. Total = 4B(s) Regge Fit Total 0 (s/s 0 ) 0.08 + B(s) = B 0 (s/s 0 ) 0.08. B = 21.8 GeV -2 BDL: 1(0,s) = 0 s = (14 TeV) 2 : LHC. (b,s) is a slowly varying function of s at high energy. M. Islam, et al, PLA18, 743, 2003. Model of Kaidalov, Khoze, Martin, and Ryskin gives similar results Ultraperipheral: (s)=0 May 2007 CEH Exc2007 7
Diffractive High Mass Production t << R (x 1,b 1 ) b = b 2 b 1 (x 2,b 2 ) Soft interactions for R t R Hard interactions for t R/ t > +R (x 2,b 2 ) b H (x 1,b 1 ) Time scales of hard and soft interactions differ by factor. May 2007 CEH Exc2007 8
Hard Scattering Kinematics, s=(p 1 +P 2 ) 2 P 1 P 2 Gluon GPD at scale Q 2 k 1 k 2 H P 3 P 1 (1 1 ) +p 3 P 4 P 2 (1 2 ) +p 4 k 1 x 1 P 1 + k 1 k 2 x 2 P 2 + k 2 k = (x 1 1 )P 1 + k ( x 2 2 )P 2 k Post Selection of Rapidity Gap Suppression of gluon bremsstrahlung: Loop Virtuality: k 2 1 ~ k 2 2 ~ k 2 ~ Q 2. Kinematic Hierarchy: 2 QCD << Q 2 << M H 2 << s 2 x 1 x 2 s M H (x i i ) << x i i << 1 May 2007 CEH Exc2007 9
Factorization of Hard & Soft Scattering T Diff = <p 3 p 4 S Soft (,0)V Hard (H)S Soft (0,) p 1 p 2 > V Hard : Diagonal in impact parameter Time scale = R/ << R = Time scale of S Soft Does not mix Fock sub-spaces in diffractive production. Conserves parton helicity [V Hard, S Soft ] 0 T. Diff = P 3 P 4 S Soft (,) X X V Hard (H) P 1 P 2 Broken by transverse correlations of hard and soft partons V Hard and S Soft populate orthogonal inelastic intermediate states. Excitation of low mass N* by S Soft suppressed at LHC energies (Goulianos hep-ph/0510035). T Diff P 3 P 4 S Elastic (,) p' p" p' p"v Hard (H) P 1 P 2 May 2007 CEH Exc2007 10
Scattering Amplitude in Impact Parameter Space GPD h g in impact parameter space. h(x,, ) = d 2 (2 ) 2 ei H(x,,t = 2 ) Scattering amplitude [ ] T Diff ( 1,p 3, 2,p 4 ) = d 2 1 d 2 2 e i 1 p 3 + 2 p 4 ( 1, 2 )h(x 1, 1, 1,Q 2 )h(x 2, 2, 2,Q 2 ) [ 1( 2 1,s)] Soft Scattering b= 2-1 b 1 2 Hard Scattering Beam-pipe view : One projectile coming towards us, one moving away. May 2007 CEH Exc2007 11
S 2 : Rapidity Gap Survival Probability for Hard Exclusive Production Surface Peaking: Integrand = gluon density [1-] BDL integrand S 2 DD (Full) DD (no_soft : = 0) = d 2 bp hard (b)1(b,s) 2 Rapidity Gap Survival probability S 2 May 2007 CEH Exc2007 12
Diffractive images in transverse plane (p 3y =0) Optical analog:{ H(,)= fourier transform of Diffraction Grating, [1-(21)] = single slit profile of each grating p4y p 4x May 2007 CEH Exc2007 13
Azimuthal Distribution of p 4 vs p 3 = 4 3. 0 + production (g μ ) maximizes p 3 p 4 = : both projectiles recoil in same direction 0 production ( μ ) maximizes E 1 p 2 (p 3 p 4 ) =/2: projectiles recoil at right angles. Sensitivity to parity of new particles 0 + production: 140 GeV Higgs at 7 TeV May 2007 CEH Exc2007 14
Correlations of soft and hard partons in transverse plane Hard Scattering of parton at impact parameter 1 in projectile 1 on parton at impact parameter 2 in projectile 2. Local density of soft partons in each projectile near 1,2 is greater than average density in each projectile. Partons are clustered in hadrons Sources of parton clustering: Pion-cloud for < m /M 6% reduction of S 2. Constituent Quarks: Size = (600 MeV) -1 from Instantons Previous estimate of S 2 is upper bound May 2007 CEH Exc2007 15
Conceptual Conclusions: Rapidity Gap Survival in Central Hard Diffraction Generalized Parton Distributions: Unifying Concept for Hard Exclusive Reactions: ep, pp, Impact Parameter representation gives physical picture Quantum Numbers (parity) of new particles [Approximate] factorization of hard & soft interactions Transverse-spatial imaging of [quark &] gluon distributions Model independent Parameterization of Soft Interactions Black Disk Limit at b=0, stevatron highly constrains numerical estimates P T distributions (spatial distribution of gluons) Depend on Rapidity Correlations of Hard and Soft partons in impact parameter Complicates separation of hard and soft scattering Examples: Pion-cloud, constituent-quarks, instantons: Diffraction may provide new tool for observation of correlations. Bound on Rapidity Gap Survival: S 2 0.03. May 2007 CEH Exc2007 16
Experimental Outlook RHIC: pp2pp @ STAR s=200 GeV Si tracker at 60 m 2007 Elastic polarized pp scattering amplitude Constrain onset of Black Disk Limit? Si tracker at 20 m 2008 Rapidity gap events with central production in STAR s=500 GeV 2010? LHC TOTEM (CMS 2007): Si tracker at 200 m Elastic Scattering, total cross section, Re/Im ratio at t=0. Rapidity gap tagging for 0.01<<0.1 LHC420 ( 2008): Si tracker at 420 m Rapidity gap tagging for 0.001 < < 0.01 May 2007 CEH Exc2007 17
Additional Transparencies May 2007 CEH Exc2007 18
Evolution and Parton model H (x,, 2,Q 2 ) P 3 H ( x,0, 2 2,Q 0 ) P 1 x x- Q 2 >> Q 0 2 x x = x x x P 3 P 1 (1)+ x- 0 x x = x x = x << x, << x x <<1 Example: p=7 TeV M H = 100 GeV x 10 2 << x <<1 Virtuality Q 2 : evolution local in impact parameter space, May 2007 CEH Exc2007 19
Hard Scattering Amplitude: Un-integrated Generalized Parton distributions P 1 x 1 P 1 ' P 1 (1 1 )+ 1 x 2 H Perturbative kernel for gluon(x 1 )+gluon(x 2 ) H Soft matrix elements of projectiles Gluon +Proton -> Gluon +Proton Compton amplitude for gluons of virtuality Q 2 QCD 2 << Q 2 << M H2. Virtuality Q 2 : evolution is local in impact parameter space May 2007 CEH Exc2007 20
Scattering Amplitude in Momentum Transfer Space pqcd kernel Gluon GPDs of Projectiles T Diff ( 1,p 3, 2,p 4 ) = d 2 (2 ) 2 ( 1, 2 )H g (x 1, 1,t 3,Q2 ) H g (x 2, 2,t 4,Q 2 ) (2 ) 2 (2) ( )+ 4i s T El (s,t) dx 1dx 2 S Soft t = 2 t 3 = (p 3 ) 2 t 4 = (p 4 + ) 2 May 2007 CEH Exc2007 21
Gaussian Model H g (x,, 2 ) = H 0 (x,)e 2 Bg() T El = d 2 be ib (b,s) (b, s) = e b2 /B J/ Photoproduction, B g 3.24 GeV 2 << B22 GeV 2 Transverse size B g of hard gluons is smaller than hadronic radius B. GPD(x0.05, Q 0 2 3 GeV 2 ) dominates determination of GPD(x=0.01, Q 2 20 GeV 2 ) M H =140 GeV @ LHC T Diff = e B g ( 1 )p 3 2 +B g ( 2 )p 2 4 /2 1 B Tot = B g ( 1 )+B g ( 2 )+B [ ] B [ e B g ( 1 )p 3 +B g ( 2 )p 4 ] 2 / 2B Tot B Tot May 2007 CEH Exc2007 22
Rapidity Dependence Rapidity y of Higgs 0 = [ 1 2 ] 1/2 = M H /s 1,2 = 0 e ±y B g ( 1,2 ) B g ( 0 ) + g ln[ 1,2 / 0 ] B g ( 1,2 ) B g ( 0 ) ± y g Forward backward asymmetry depends only on g A = d( 1, 2 ) d ( 2, 1 ) d( 1, 2 )+ d ( 2, 1 ) y g r = (p 3 p 4 ) P = (p 3 + p 4 )/2 May 2007 CEH Exc2007 23
Rapidity Gap Survival Probability: S 2 S 2 not an observable, but a useful statistic DD = total Double Diffractive cross section. DD ( 1, 2 ) d 2 p 3 (2 ) 2 d 2 p 4 (2 ) 2 T Diff ( 1,p 3 ) 2 d 2 1 d 2 2 2 2 h (1 g, 1 )h (2 g, 2 )1( 2 1, s) 2 S 2 DD (Full) DD (no_soft : = 0) = d 2 bp hard (b)1(b, s) 2 P hard (b) = d 2 1 d 2 2 (2) (b + 1 2 ) 2 h (1, g 1 ) d 2 2 'h (1,') g May 2007 CEH Exc2007 24 S 2 depends on hard sub-process h 2 (2, g 2 ) d 2 2 "h (1,") g
Effect of Rapidity Gap Survival Probability T diff 2 = Full Diffractive calculation H g 4 H g 4 = T diff 2 with S soft = 1 (=0, No soft absorption) r = (p 3 p 4 ) P = (p 3 + p 4 )/2 May 2007 CEH Exc2007 25
Sensitivity to form of Gluon Distribution H g Exponential and Dipole forms H g (x,, 2 ) = 1 1+ 2 2 /m g e 2 Bg()/2 [ ] 2 May 2007 CEH Exc2007 26