Diffraction in ep and pp collisions

Transcription

1 Diffraction in ep and pp collisions Anna Stasto RIKEN BNL & Penn State U. & INP Krakow 05/5/00 RHIC Spin: The Next Decade, Iowa State University

2 Outline Diffraction in ep(a) (EIC) Inclusive case Exclusive processes (vector mesons) Diffraction in pp (RHIC) elastic, single-diffractive, double diffractive Central exclusive processes

3 Diffractive events Characteristic feature is the existence of the rapidity gap. L X s t, m X,m Y s vacuum quantum number exchange R Y QCD: two gluons in color singlet state Q X DIS: s Q Λ QCD, t, m p s semihard processes: x = Q /s P Y perturbative QCD applicable 3

4 Two basic features of diffraction: Soft and hard diffraction rising cross sections with energy s large rapidity gaps: η = log tan(θ/) (color singlet exchange)! Y X Soft diffraction (no hard scale): σ s α P (0) α P (t) = t pp p + p γp V (ρ, ω, φ) + p Hard diffraction (with hard scale):. < α P (0) <.4 pp jj + pp γ p X + p γ p V + p γp J/ψ + p In general, theoretical description very difficult: Soft diffraction: phenomenology based on Regge models Hard diffraction: difficulty of combining soft (gap) + hard(pqcd evolution) 4

5 W p t Diffraction in ep p Proton stays intact and separated by a rapidity gap M gap diffractive mass t = (p p ) momentum transfer η = ln /xip Rapidity gap : Kinematic variables relevant for diffractive DIS. momentum fraction of the Pomeron with respect to the hadron eneral can only be used for diffractive processes in the ep deep inelass, the scale of nonuniversality can be estimated by applying them to momentum fraction of the struck parton with respect to the Pomeron the color dipole approach with the qq and qqg diffractive components escription was studied in detail in [30]. In short, after extracting the pproach provides Q -independent quark and gluon DPD. In addition, Bjorken x was computed assuming strong ordering between transverse momenta air, gives the first step in the Q -evolution of the gluon distribution. hich is based on the DGLAP evolution equations, extends 5the two by taking into account more complicated diffractive final state. In

6 an analogue of the Bjorken variable for the diffractive system. Experimentally ing ton, Q an t = analogue (p p ) <,M of 0the is the Bjorken square variable of four-momentum x for the diffractive system. Experimentally Q,M,thust,thust can can be be neglected neglected in the the above above formulas. formulas. F D(3) tmax, M is invariant diffractive mass and W is invariant energy,l (β,q Finally, Finally,,x IP )= the the Bjorken Bjorken variable variable of the γ p system. The Bjorken variable x B = x IP β. For most of the diffracti dt F much smaller then other scales, thus it can be neglected in eqs.,l(β,q D,x (3). The IP,t) diffra iable x t B = x IP β. For most of the diffractive events t is min Q functions are measured in a limited range of t, thustheintegratedstructurefuncti s it can be Q neglected in eqs. (3). The diffractive structure is defined in a similar way. Diffraction in ep tmax r ange = Q of Diffractive + W = β x IP. (3) Q t, thustheintegratedstructurefunctionsaredefined + W cross = β section x IP. The reduced cross section σ D(3) (3) F D(3) d 4 σ D dβ dq dx IP dt = πα (,L (β,q,x { IP )= dt F,L(β,Q D },x IP,t), tmax em β Q 4 +( y) ) F D t y over the min x +( the y) F L ter averaging over the azimuthal angle of the scattered proton, the diffractive D IP )= dt F,L(β,Q D,x IP,t), (4) cross cross t min. Twist contribution tion n is is characterizedby by two The dimensionful integrated reduced diffractive cross section structure σr D(3) functions is defined in F D(4) Fa similar D(4) way. σr D(3) is defined in a similar way.,l,l Diffractive structure functions In the QCD {[ {[ +( y) ] approach based on collinear factorisation, the diffractiv. decomposed Twist F D(4) contribution into the leading and higher twist contributions d 4 σd 4D σ D dx IP dt = em dq dx 4 IP dt = πα em xq 4 y F D(4) },, (4) (4) In the QCD approach based on collinear F,L D factorisation, = F D(tw),L full a full analogy to inclusive DIS. They depend on four variables: (x, (x, Q Q + the F D(tw4),L diffractive +... structur. linear factorisation, the diffractive ; x Dimensionless diffractive decomposed structure into functions the leading are and higher twist contributions ; x IP,t). IP,t). After After her integration twist contributions structure over over function t t (if (ifttisis not The measured), twist part the is dimensionless given in terms of structure the diffractive functions parton are are distributio tained. Due Dueto tothe the kinematical factor in (4), we neglect F,L D = Fthe D(tw),L thelongitudinalstructure + F D(tw4),L F D(tw) collinear factorisation formulae [3,3 34]. In next-to-leading logar,l + F D(tw4) ctionf D(4) F D(4),L (5) L L in inthe the following. have f the diffractive parton distributions The twist throughpart the standard is given in terms of the diffractive parton distributions throug The e leading leadingtwist twist description collinear of of diffractive factorisationdis formulae is isrealized using usingdiffractive parton parton disbutions distions (DPD) (DPD) qi D qi D F D(tw) [3,3 34]. In the next-to-leading logarithmic app (x, Q,x IP,t)=S D + α { Collinear factorization works diffractive processes. J.C. Collins 34]. In the next-to-leading logarithmic approximation we s C S S D + C G,wherei,wherei have enumerates quark flavour, flavour, in in terms terms of of which π which N f N f ) (4) = = e e i β { qi D (x IP,t; β,q )+q D i (x IP,t; β,q ) i β { qi D (x IP,t; β,q )+q D i (x F D(tw) (x, IP,t; β,q ) } Q,x IP,t)=S D + α } s Collinear approach (NLO): F {C D(tw) S S D + C G D L (x, Q,x IP,t)= α { },t)=s D + α } s {C s S S D + C G G D (6) π twist, π CL S π S D + CL G (5) G D, (5) i= i= F D(tw) L (x, Q,x IP,t)= α { },t)= α { } s C s L S π S D + CL G G D (7) where α CL S π S D + CL G G s is the strong coupling constant and C S,G D,L are coefficients functi DIS [35, 36]. The integral convolution is performed for the longitudina ant and C S,G,L are coefficients functions function where α known s is the from strong inclusive coupling constant and C S,G,L are coefficients functions known n is performed for the longitudinal momentum fraction DIS [35, 36]. The integral convolution is performed for the longitudinal momentu (C F )(β) = dz C (β/z) F (z). β )(β) = dz C (β/z) F (z). (8) β (C F )(β) = dz C (β/z) F (z). 6 β 4 L

7 Collinear factorization, diffractive parton distributions S D = N f f= e f β G D = βg D (β,q,x IP,t) { } q f D (β,q,x IP,t)+q f D (β,q,x IP,t) g D q f D diffractive parton distributions β = x/x IP plays the role of the Bjorken variable in diffractive DIS One can interpret the DDIS parton distributions as conditional probabilities for finding a parton with small fraction of momentum x in the proton, provided that the proton stays intact and it looses fraction of its momentum given by DGLAP evolution with respect to the variable Q (x IP,t) are external parameters with respect to the DGLAP evolution x IP Regge factorization ansatz often used q f D (β,q,x IP,t)= f IP (x IP,t) q f IP (β,q ) P P g D (β,q,x IP,t)= f IP (x IP,t) g IP (β,q ). Diffractive scattering occurs through the exchange of the Pomeron, parametrized by the flux, and the hard scattering of the photon on the quark which is in the Pomeron, and carries a fraction of its momentum β = x/x IP 7

8 Color dipole models Universal description in the leading order in log(s) (N. N. Nikolaev, B. G. Zakharov) Scattering amplitude (A = γ, γ,v) A(γ + p A + p) = d rdz Ψ A N q q Ψ γ Factorization at small x N q q (r, b, Y =ln(/x)) is the dipole scattering amplitude Find N q q from σ tot Im A(γ + p γ + p) and test in DDIS processes. 8

9 Universality of dipole amplitude Inclusive Diffractive! * -z! * r z q -z z r q p p p p σ tot = r,z Ψ(r, z, Q) ˆσ q q (x, r) dσ dif = dt t=0 6π r,z Ψ(r, z, Q) ˆσ q q(x IP,r) x Q W x IP Q + M W Dipole cross section: ˆσ q q (x, r) = d b ( S(x, r, b)) 9

10 Q = 0.8 GeV Diffraction and saturation d!t/dr Inc (b) 3 Golec-Biernat,Wuesthoff overlap function in the dipole model 30 d!t/dr Inc /Q 5 d!t/dr (a) 3! (mb) d!t/dr Q = 0 GeV 0 3 r [R0] /Q Inc DD dipole cross section /Q -5.5 Inc r [R0] x=0-4 x=0-3 x=0 - x= DD r (fm) 0 r [R0] R0 = Qs 0.5 /Q.5 r [R0] Inclusive: dominated by relatively hard component Diffractive: dominated by the semi-hard momenta contribution of different dipole sizes 0

11 Q = 0.8 GeV Diffraction and saturation d!t/dr Inc (b) 3 Golec-Biernat,Wuesthoff overlap function in the dipole model 30 d!t/dr Inc /Q 5 d!t/dr (a) 3! (mb) d!t/dr Q = 0 GeV 0 3 r [R0] /Q Inc DD dipole crossdiffraction section /Q -5 Inc r [R0] x=0-4 x=0-3 x=0 - x= DD is a collective phenomenon /Q Explore relation with saturation..5 r (fm) r [R0] r [R0] R0 = Qs Inclusive: dominated by relatively hard component Diffractive: dominated by the semi-hard momenta contribution of different dipole sizes 0

12 Diffractive to inclusive ratio in ep Constant ratio naturally explained in the saturation model. Golec-Biernat, Wuesthoff

13 Diffraction in ea Two possibilities for the diffractive events in nuclei: e e e e A gap A A A p n gap Coherent No-breakup Incoherent With breakup into nucleons The gap is still there Challenge for the experiment : measure the breakup, forward neutrons.

14 Diffractive to inclusive ratio in ea Predictions give 0%-40% for in the regime down to 0 6 σ diff /σ tot Cazaroto,Carvalho, Goncalves, Navarra Kowalski, Lappi, Venugopalan 3

15 Exclusive diffraction of VM Exclusive diffractive production of VM is an excellent process for extracting the dipole amplitude Suitable process for estimating the blackness of the interaction. t-dependence provides an information about the impact parameter profile of the amplitude. Differential cross section for exclusive VM production Amplitude for elastic scattering Elementary amplitude for elastic scattering Optical theorem 4

16 Impact parameter profile Munier,Stasto,Mueller Kowalski, Teaney t-dependence vs impact parameter dependence. What is the characteristic size of the proton in strong interactions? Profile extracted from the HERA data Extrapolations of the S matrix towards lower values of x S probability that a dipole passing the proton will induce an inelastic reaction at the given impact parameter Models indicate significant blackness for central impact parameter Q 5 GeV 5 x =

17 Diffraction in pp General (soft) processes with rapidity gaps at hadron-hadron colliders Elastic scattering Single diffractive scattering Double diffractive scattering Difficulty: no hard scale... Gribov Regge-Pomeron theory: multiple exchanges and interactions of Pomerons (σ el +σ SD + σ DD )/σ tot For Tevatron and LHC M X M X M X (a) (b) (c) (d) (e) single Pomeron exchange multiple Pomeron exchange. unitarization proton excitations in the intermediate states High mass diffraction. Single diffraction dissociation. Double diffractive dissociation 6

18 Diffraction in pp Unfortunately, no complete solution to the Gribov Pomeron calculus so far... What we know up to now: Partonic description of hard Pomeron at small coupling (BFKL Pomeron) Triple Pomeron vertex Resummation of certain classes of fan diagrams (fan diagrams, BK equation) Gribov- Pomeron calculus does indeed emerge from QCD (Kovner-Lublinsky) Difficulties: Hard Pomeron valid for pqcd regime, unknown how to continue to strong coupling Large higher order corrections, need of resummation beyond leading log/x Needs to resum a complete set of diagrams (loops) Couplings to target and projectile particles... One needs to rely on many model assumptions 7

19 Diffraction in pp: phenomenology (E. Avsar, G. Gustafson, L. Lönnblad, [hep-ph]) Dipole evolution at small x Include Pomeron loops Include constraints from kinematics Model confinement Monte-Carlo framework Simultaneous description of deep inelastic data and hadron-hadron cross sections (total, elastic, diffractive) C B A! "* p tot (µb) DIS Q (GeV ) (a) With swing No swing H ZEUS W (GeV ) Hadron-hadron r 80 rapidity! (mb) 60! tot! diff! el 40 Also: Khoze, Martin, Ryskin; Levin et al; Kaidalov et al; Ostapchenko; "s (GeV)

20 Diffraction and the shape of proton Diffractive/elastic scattering gives important information about the shape of the proton and its change with the increasing energy Need precise measurement of the elastic slope B(t) = d(ln dσ el/dt) dt Small t region is responsible for periphery of the proton. Opacity(density) is small hence large contribution to the survival probability of gaps. Determination of ratio of real/imaginary part of the scattering amplitude Large t region is crucial for understanding what happens in the centre of the interaction region: how dense the system is, how close to the unitarity is the amplitude. RHIC could give us information about the B slope in the energy between low energy measurements and Tevatron/LHC range. pp vs ppbar differences? Should in principle vanish at higher energies. RHIC can help us answer these questions. 9

21 Central exclusive production in diffraction Khoze,Martin,Ryskin Harland-Lang, Khoze, Ryskin, Stirling Pasechnik, Szczurek,Terayev pp( p) p + X + p( p), h h x x At higher energies, LHC, one can study new states (Higgs, SUSY) produced exclusively via such mechanism x q 0 q q x P X At lower energies, Tevatron and RHIC, crucial test of theoretical framework of QCD Tevatron measured central exclusive production with various states (talk by Christina Mesropian) h h Test of energy dependence, RHIC-Tevatron-LHC Particularily interesting is production of heavy quarkonia χ c χ b Valuable tool for analysing NRQCD, physics of bound states etc... 0

22 Harland-Lang, Khoze, Ryskin, Stirling General framework T = π d Q M Q (Q p ) (Q + p ) f g(x,x,q,µ ; t )f g (x,x,q,µ ; t ), Q T factorization assumed gg X M is the amplitude for sub-process ( ) ( ) f g unintegrated skewed parton (here gluon) distributions in the proton Factorized t-dependence f g (x, x,q,µ ; t) =f g (x, x,q,µ ) F N (t), Proton form factor, phenomenological parametrization F N (t) =exp(bt/), with b =4GeV.

23 dσ dy X = Survival factors d p d p T (p, p )) 6 π 5 S eik (p, p ), Harland-Lang, Khoze, Ryskin, Stirling p T,p T transverse momenta of the protons Survival factor in impact parameter space S eik (b t)=exp( Ω(s, b t )). Slow variation with the energy χ c0 χ c χ c η c Tevatron LHC (7 TeV) LHC (0 TeV) LHC (4 TeV) RHIC Need to include survival factor due to the enhanced graphs

24 Cross section estimates for central exclusive production c c s (TeV) dσ (pp pp(j/ψ + γ)) dy χ c dσ( + ) dσ(0 + ) dσ( + ) dσ(0 + ) Harland-Lang, Khoze, Ryskin, Stirling Table 3: Differential cross section (in nb) at rapidity y χ = 0 for central exclusive χ cj production via the χ cj J/ψγ decay chain, summed over the J =0,, contributions, at RHIC, Tevatron and LHC energies, and calculated using GRV94HO partons, as explained in the text. Interesting prediction: the energy increase by factor 0 only gives a moderate increase in the cross section. Compensating effects: Higher energy: increase of the gluon density at small x This comes at a price: survival factors drop down Larger rapidity gap, larger enhanced absorption RHIC can pin down the magnitude of these effects at lower energies. Comparison with Tevatron can constrain the models for the absorption. 3

25 Summary Diffraction is a very intriguing phenomenon in QCD collisions. Theoretical description very difficult: diffraction involves soft physics. Collective phenomenon: proton stays intact; large distance scales involved; factorization breaking when going from ep to pp. Interplay between saturation physics and diffraction. Possibilities for EIC: Inclusive diffraction on nuclei. Diffractive to total ratios. Exclusive vector meson production. Is the energy dependence (x dependence) for VM in ea the same/different as in ep? Measurement of t dependence in exclusive vector meson production provides an insight into the impact parameter profile of the target. Possibilities for RHIC: Standard questions: t- slope of elastic cross section. What about t=0? Extraction of rho parameter. Central exclusive production. Especially heavy quarkonia. Pin down the theoretical uncertainties on the survival probabilities. Other: search for the Odderon? Importance of the spin in diffraction: not much is known here, anything that will be measured will provide valuable information about the nature of diffraction (for example: are asymmetries vanishing?). 4