Dynamics of color in the soft and hard diffractive phenomena inhadron -nucleus collisions .L.Frankfurt , TAU10th International Workshop IWHSS10,Venice March . 14-17, 2010
Outline●Fundamental properties of high energy processes in QCD.●●☛☛☛Fluctuations of strengths of interaction in a projectile w.f. around averagevalue inelastic soft diffractive processes . Experimental facts .QCD factorization theorems for the interaction of spatially small colorlessdipole and hard diffractive phenomena . Experimental facts.Specific properties of hadron states produced in diffractive processes.Measurement of novel GPDs of various hadronsin hadron induced processes of nucleons(nuclei).Conclusions
Fundamental properties of high energy processes in QCD .●Asymptotic freedom: coupling constant is small for the small space-time intervals.α s (Q 2 ) = (4π/b)/ ln(Q 2 /λ 2 QCD)b = 11N c3− 2n f3●At moderately large energies including the ones probed at HERA the interaction of colorneutral, spatially small quark dipole with a hadron(nuclear) target T is unambiguously calculablein QCD =QCD factorization theorems.QCD factorization theorem for the interaction of small size color singlet wavepackage of quarks and gluons.[σ(d, x) = π23 α s(Q 2 eff )d 2 xG N (x, Q 2 eff )+ 2 ]3 xS N (x, Q 2 eff )Q 2 eff = λ/d 2 , λ =4÷ 10 Baym, Blattel, LF, MS, 93, LF,Miller, MS 93
Coherence phenomenon in the soft inelastic diffraction.t minin the inelastic diffraction:h + T → a + rapidity gap + Trapidly decreases with energy.h≠aThe amplitudes characterizing contributions of states “a” are coherent.Equivalent statement is that coherence length is rapidly increasing with energy:L c =2E h /(M 2 a − M 2 h)- uncertainty principle⇓Quark-gluon configurations in the wavefunctions of energetic hadrons are frozen.
Soft inelastic diffraction at =0 in quantum mechanics|h〉 = a 1 |1〉 + a 2 |2〉habsorber withsame absorptionfor “1” and “2”|final〉 = λ(a 1 |1〉 + a 2 |2〉) =λ |h〉honly elastic scattering|h〉 = a 1 |1〉 + a 2 |2〉habsorber withdifferent absorptionfor “1” and “2”|final〉 = λ 1 a 1 |1〉 + 2 a 2 |2〉)h+h’= c 1 |h〉 + c 2 |h ′ 〉elastic scattering+inelastic diffraction
Due to a slow space-time evolution of the projectile wave function one can treat the interaction asa superposition of interaction of configurations of different strengths . This was understood byPomeranchuk & Feinberg(QED); Good and Walker; Pumplin &Miettinen (preQCD). In QCDdifferent strengths are mostly due to different sizes of different configurations.Size/orientation of the color distribution within a wave function of sufficiently energetic hadronvaries leading to the fluctuations of the strengths of its interaction with a target . Illustrations:pNN = 3q + 3qg + 3q+ ! + ...●●●●rtrvs● ●rtrDescription of processes in terms of fluctuations of color is reasonable for total cross sectionsand for the inelastic diffraction at very small t.6
The coherence of contributions of different configurations in the projectile wave function Ph(σ) -probability that projectile interacts with target with cross section σ:∫= P (σ)σ n dσ∫∫P (σ)dσ =1Total cross section :σ tot =< σ >=P (σ)σdσSecond moment is fixed by Miettenen- Pumplin relation (1978):w σ = − < σ > 2< σ > 2➠Soft inelastic diffraction arises due to fluctuations close to average cross section:No fluctuations = no inelastic diffraction!!Further constraints (Baym, Blattel, Frankfurt, Strikman (BBFS) 93)The form of Ph(σ) at small σ follows from QCD :P h (σ) σ→0 ∝ σ n q−1Here nq is the number of valence quarks within the projectile hadron.Sum rule for for p 2 H diffraction
Cross-section probability for pions Pπ(σ) and nucleons PN(σ) as extracted from experimentaldata. Pπ(σ=0) is compared with the perturbative QCD prediction (BBFS93).
If there were no fluctuations of strength - there will be no inelastic diffraction at t=0:dσ(pp→X+p)dtdσ(pp→p+p)dt| t = 0=! tot [mb]!#" !Tevatron! tot!#" !Tevatron! tot! tot! totLHC∫(σ − σtot ) 2 150 P (σ)dσ 150LHC! tot [mb]σ 2 tot10050100≡ ω σTevatronvarianceLHC! tot0.40.30.20.1" !0010 2 10 3 10 4 10 5 0, i.e., the average area repre-10 2 LHC# s [GeV] 10 3 10 4 10 5 0Size of both small andThelargearea ofconfigurations the inner and outer disk at given energy is proportional to(a)sents the average cross section (b) Tevatrongrows with energy - still there is a correlation betweentot, the difference (ring) the range of the fluctuations . (b) Theσ and parton distributions -smaller σ, harder quark distribution.–dependence of the total cross section tot (left –axis) and the dispersion (right –axis), as predicted by a(a)!#" !TevatronFig. 3: (a) Graphical representation of the cross section distributions in diffraction# at s the [GeV] Tevatron and LHC energy.slow variation of the diffractive cross section with energy.The area of the inner and outer disk at given energy is proportional to! tot! totLHC! tot [mb](b)500010 2 10 3 10 4 10 5Tevatron" !Fig. 3: (a) Graphical representation of the cross section distributions in diffraction at the Tevatron and LH(b)15010050(a), i.e., the average area representsthe average cross section tot, the difference 9 (ring) the range of the fluctuations . (b) TheThe area of the inner and outer disk at given energy is proportional to! tot [mb](b)15010050Tevatron# s [GeV]Fig. 3: (a) Graphical representation of the cross section distributions in diffraction at the Tevatron and LHC energy.0010 2 10 3 10 4 10 5Regge–based parametrization of tot  and a parametrization of the inelastic diffractive cross section inel ,measured up to the Tevatron energy . The weak energy dependence of the width of the ring in figure (a) reflects the# s [GeV]! tot" !order–of–magnitude of the effect, as well as its energy dependence. Our basic assumption is thatLHC! tot" !0.40.30.40.220.127.116.11.1" !" !LHC! tot" !0.40.30.20.1, i.e., the average a
→→√ s = 14 T eVP(σ)[ mb −1 ]0.020.0150.01√0.020.02s = 30 GeV0.0150.015→0.01 0.01√ s = 2 TeV0.020.0150.010.020.0150.010.0050.005 0.0050.0050.00500 00 00 10 20 30 0 40 01050 102060 203070 304080 0 40 5010 90 50 60 100 020 60 70 10 110 30 70 80 12040 80 130 90 50 100 90 60 40 100 110 70 50 120 80 110 60 130 90 120 701σ[ mb ]The 30 GeV curve is result of the analysis (Baym et al 93) of the FNAL diffractive pp and pd datawhich explains FNAL diffractive pA data (LF, Miller, Strikman 93-97). The 14 and 2TeV curves areguesses based on matching with fixed target data and collider diffractive data.10
Critical test - coherent diffraction off nucleiσ diff (A) =∫d 2 B[2 ] −[∫] ] 2dσP (σ) [ ∫dσP (σ) ∑ n∫ ∞F (σ, B) = 1 − e − 1 2σT (B)T (B) =−∞ρ A (B, Z)dZHere the direction of the beam is Ẑ and the distance betweenthe projectile and the nuclear center is ⃗R = B ⃗ + ZẐM =∫d 2 Be i⃗q t· ⃗B 〈h | F (σ, B) | X〉dσ diffdt∫(0 ◦ )=π dσP (σ)f 2 (σ) − π∫ (1 f(σ) ≡ BdB − e − σ 2 T (B))[∫dσP (σ)f(σ)] 2
Fluctuations near average strength dominate for all nuclei for total cross section of diffraction ( asignificant enhancement of smaller size contribution for A ~ 200) - need special triggers to look forconfigurations with σ Full expression.σ apprdiff = ω σ〈σ〉 24∫d 2 BT 2 (B)e−〈σ〉T (B)L.F,J.Miller,M.S PRL 93
The cross section of coherent diffraction dissociationof protons and neutrons on nuclei as a function of A. The solidlines are the theoretical prediction based on the above eqn.Total cross section data are from the FNAL emulsion and 4 He jettarget experiments. The FNAL data on the reactionn+A → p π - +A (a small fraction of the total diffractive crosssection) is presented as stars have similar A-dependence for allmasses and provide a good indication of the overall trend of the A-dependence. The theoretical prediction for coherent diffraction on4He is given by the dashed lines.A- dependence for exclusivechannel is reproducedσ(A) ∝ A n ; n(A = 16) ≈ 0.8, n(A = 200) ≈ 0.4 for s~ 400 GeV 2LHC n=0.27 and e.m. contribution dominates Guzey & Strikman 08
A- dependence for exclusivechannel is reproducedσ(A) ∝ A n ; n(A = 16) ≈ 1.05, n(A = 200) ≈ .65
Regime of complete absorptionIf projectile is absorbed with 100/% probability amplitudes of diffractive processes are proportional to theoverlapping integral between wave functions of initial and final states. For the forward scattering theoverlapping integral differs from 0 if initial and final states coincide. Thus elastic scattering off target Tof radius RT with the amplitude A= s(2 π RA 2 ) is allowed only. This physics is analogue of theFraunhofer diffraction off black screen in optics.If color filtering is neglected hadron scattering off heavy nuclei would be close to black disc regime forcentral impact parameters ➙ inelastic diffraction from the projectile scatteringoff nuclear edge ➙ σdiff ∝ A 1/3 reached at the LHC
$.* 7'#$0"/ !.%$%&3B& $.* /*"5'&+ /%+"#'$.6'( "!!#%A'6"$'%& '&, $.* *22*($) %2 IJ@ #"5'"$'%& ("&"+"'& 1* "1)%#1*5 '& $.* "6!/'$05* 2%# $.* )("$$*#'&+ %2 $.* )6"//=)'
H1 and ZEUS observed processes of diffractive electroproduction of vector mesons.γ ∗ + p → V + pV=ω,ρ,φ,J/ψγ ∗ + p → J/ψ + rap gap + XPractically all regularities predicted by QCD factorization theorems and DGLAPapproximation were observed at HERA
HERA data confirm increase of the cross sections of small dipoles predicted by pQCD2(d , x, Q ) (mb)qqN! −454035Hard 30Regime252015105""Matching Region= 4 x = 0.0001= 10x = 0.001x = 0.01SoftRegime000.10.20.30.40.5d (fm)0.60.70.80.91The interaction cross-section, ˆσ for CTEQ4L, x = 0.01, 0.001, 0.0001,λ =4, 10. Based on pQCD expression for ˆσ at small d t , soft dynamics atlarge b, and smooth interpolation. Provides a good description of F 2p atHERA and J/ψ photoproduction.Frankfurt, Guzey, McDermott, MS 2000-200118Provided a reasonable prediction for σL
Motivations for the hard exclusive hadron induced processes with nucleons and nuclei✴Small size colorless wave package of quarks and gluons weakly interacts with hadron(nucleus) targetin a wide interval of energies. Follows from gauge invariance and asymptotic freedom. As a resultcross section for the interaction of this wave package is unambigously calculable in QCD in a widekinematical range. This QCD factorization theorem allows to evaluate cross sections of variety ofhard diffractive processes observed at FNAL, HERA, TJNAF.✴Another important feature is that gluon dipole - N cross section is 9/4 times larger than quarkdipole - N cross section-important for evaluation of BDR at LHC.✴Analysis of hard diffractive processes allows to extract variety of GPDs which containinformation on hadron(nucleus) quark-gluon structure.✴Going beyond one dimensional image of nucleon - GPDs & correlations in the wave functions ofbaryons and mesons✴To investigate the multiparton structure of hadrons and how it is different for mesons and baryons
Discovery of high energy CT=⇒ Need to trigger on small size configurations at high energies.Two ideas:⋄ Select special final states:diffraction of pion into two high transversemomentum jets - an analog of the positronium inelastic diffraction. Qualitatively- from the uncertainty relation d ∼ 1/p t (jet)⋄ ⋄ Select a small initial state - diffraction of longitudinally polarized virtualphoton into mesons. Employs the decrease of the transverse separation betweenq and ¯q in the wave function of γL ∗, d ∝ 1/Q.QCD factorization for these states includes CT .20
π + N(A) → “2 high p t jets ′′ + N(A)Mechanism:Pion approaches the target in a frozen small size q¯q configurationand scatters elastically via interaction with G target (x, Q 2 ).the first analysis for πp scattering Randa(80), nuclear effects - Bertsch, Brodsky,Goldhaber, Gunion (81), pQCD treatment: Frankfurt, Miller, MS (93)❖❖First attempt of the theoretical analysis of πN process - Randa 80 - power law!qq(1-z)PzP!!, kdependence of pt of the jet (wrong power)First attempt of the theoretical analysis of πA process - Brodsky et al 81 -exponential suppression of pt spectra, weak A dependence (A 1/3 )❖ pQCD factorization A(N) theorem - Frankfurt, A(N) Miller, MS 93; elaborated argumentsrelated to factorization 2003A(π + N → 2 jets + N)(z, p t , t = 0) ∝∫d 2 dψ q¯qπ (z, d)σ ”q¯q”−N(A) (d, s) exp(ik t · d),t-ktd = r q t − r ¯q t ,ψ q¯qπ (z, d) ∝ z(1 − z) d→0 is the light-cone q¯q pion wave function.M.Strikman21
pion wave function is equal to the asymptotic change one. inidentities the wave andwhere the function condition isx of 1 ,x the the 2 light finalcone state. fraction Here Mof int the pion momentumvertex for the three gluon interaction, the color neutrality of2Thus the ratio is determined by the color content (m of color carried by an exchangedπ + N(A) → “2 high p t jets ′′ gluon: k+ N(A) 1 /p k 2 /p rec l 2 t . A factor of t l t ispresent t )/(1z) in the numerator, is the with mass 2 t originating of intermediate from the verticesin the WW representation and lstate, .the pion wave function, and the dijet final state. In the derivationit is helpful to use the observation that effectively2flow in the pion wave function and the quarkand color m rec andisbythe invariant Thus we mass arrive of the 2 t from the integrationover quark momenta in the pion wave atfunction. the recoil equation Allsystem in all this in thethe dependence of energy denominators on the fraction ofx 2 2 Feynman amplitude mechanism. suppressed In the by the region factor l 2 t of /( 2 t ) integration 3 . Another casetribute is shown.1zt /. Evidently similar reasoning is applicable in com-l 2 22t /Moccurs2 jet onewhenmayl 2 neglect by M 2 t 2 t . Then this diagram(2 jet)willin be suppressedthe denominatoraspion momentum carried by quarks and gluons. So Pion approaches the target in a frozen m˜ 2kputing amplitudes to leading order in 1t small size q¯q configurations and all ordersMechanism:incompared to T 1 atas compared to l xand scatters 2 least by one power of s without the largeelastically via interaction 1 1 with .k 1 zp 2 m 2G target (x, Q 26q zx 1 •••, 33asymptotic freedom. This is nontrivial since these factor ln 2 2t /(1z). properties So one obtains are T often violated 22 in the literature.t / QCD . But here we restrict ourselves to thewhile that the near-mass-shell ). line b is independent ofthe first analysis for πpdiagramsscattering Fig. 6 is suppressedRanda(80),by a factornuclearl 2 t / 2 t as com-the to Feynman thatall in Fig.effects - Bertsch, Brodsky,found thatpared produced mechanism 1. This theparticlespower-type is a higher insuppressionthe twist intermediateifcorrec-states that 0Goldhaber, Gunion (81), the pionpQCD wave function treatment: is non-perturbative, Frankfurt, and may beMiller, a MS (93) s ln 2 t /l 2 t .T 2 F2 38T 1 F 2 1 1z1z z (1/ 2Repeating the same reasoning as in the estimate of the1z 2 ln z t ) analysis (z,l of 2 LO t )d 2 corrections. l t dz. In this case, another factor ofterms of TIt follows from the requirement of positivity of energies of1a ,T 1b , and remembering that x 2 2 1/ 4 Similar reasoning helps to prove that the contribution oft / we t arises from the integration over z. Hence we haveachieve the estimate T 3 2 s x 1 G A 1z (x 1 ,x 2 ,zln1z 2t )/ 4 t . It is instructiveto investigate whether the Feynman mechanism,tion to the PQCD contribution. The Feynman mechanism 2 . 24 1. We can now calculate m˜ 2 isNLO s correction if the perturbative high momentum taildirectly is in terms of the lightfurther suppressed included in the bypion thewave requirement function. of a lack of collinearwhere the leading quark anti-quark carries a fraction of thecone momenta of (1-z)P the qq¯ , kto pion momentum Another contributionq radiation—see to T 4 arises ! pair in thetintermediate state:Here F 2 (i) for i8,3 is the Casimir operator for octet ! andDominant triplet representations diagram2thefrom discussion the sum of Feynmandiagrams in which the gluon exchange between the qbelow.pion momentum z close to 1 but high momentum jets areof color group SU(3)zPc . The ratio!qm˜ l t 2T 2 /T 1 is 0.5 for z1/2, remains nearly constant for zz k 1tl t 2formed by the action of a final state interaction, may competeand q¯ in the beam occurs during the interaction with theD. Gluontarget, admixture see Figs. to8, the 9, and wave 10. The functions naive expectation of initialisand that finalwith the PQCD description. In this case transverse momenta1k 21z 1t . 27such terms, which amount to having a gluon exchanged duringthe very short interaction time 4 characteristic of the twostates—Tof constituents l t in the pion wave function are expected to.50.3 and increases to 9/8 at z0,1. This term is addi-regime. suppressed For certaintybyletthe us model Sudakov-type the Feyn-formthe factor timeand ordering bygluon exchange process occurring at high energies, must be -kbe equal to the mean transverse momenta of partons in the The Feynman diagram Combining corresponding Eqs. 25,27 to Fig. we7obtaincontainstvery small indeed.non-perturbativetionallyThe intent corresponding of this section is to use the theqq¯ analytic g configuration propertiestor factor for line a is given byinman mechanismthe byform assuming factorthat w 2 —see recoilthe system discussion quark below.of the scattering amplitude to show that2A(N)lTthe pion wave function interacting with t A(N)z the k 1tl t 24 is negligible.quarks inanti-quark with momentum 1z close to 0. Within this1z x theInstead of calculating the sum of the imaginary parts of all offinal state. 1,28the Inamplitudes, taking the we will imaginary prove that part this sum ofvanishes the amplitude, by analyzingthemodel we will obtain FeynmanC. Finaldiagramsstate interactionfor the termofTthe 2 , butqq¯ pair—T intermediate 3state analytic must properties contain of the a hard important on-shell diagrams. quark Each and while a that of line c is given bywith the region of integration defined by the Feynmanconsidered diagram contains a product of intermediatestatequarkhard on-shell gluon.and which, Butanti-quarksuch when propagator.a state using cannotAt Eq. high energies, 5, be produced leads these to bymechanism. A simple The dimensional interactionevaluation with the of target termgluons T may occur beforethe interaction between quarks∫ 3 due a soft almost propagators on-shell are controlled quark inby the initial terms ofstate, highest so power there of is anto the Feynman mechanism within the Gribov representation in dthe 2 finaldψπ q¯q state, and the related(z, d)σ additional x”q¯q”−N(A)suppression (d, s) factor, exp(ik caused t · d),Examplesamplitudes are denoted theas T 3 , seesuppressedFigs. 5 and 6.diagramsx 1 1 by l thet 21 2p•p x 1 , and as to be shown haverapid d = r q t − r ¯q t , ψ q¯q z k poles1tl decrease in thet 2of m 2complex x 2 jetshows that it is suppressed by the powers of t . The contributionof the region l 2 tour of integration. The sign of the term containing () 2the non-perturbative1 plane which are located on one side of the con-pion wave function with increasing x1z 2 . 29t /(1z)M 2 jet has been consideredeach propagator unambiguously follows from the directionsabove—it is additionally suppressed for the Feynman mechanismby the restriction of the region of integration over z.integral is ofThereforethe formThus our next discussion is restricted by the consideration ofthe contribution of the region, l 2 t /(1z)M 2 jet :T 3 1 t2 z,l t 2 1l t 22A(π + N → 2 jets + N)(z, p t , t = 0) ∝π (z, ofd) pion∝ andz(1 target− momenta. z) d→0 If we iscan the showlight-cone that the typical q¯q pion wave function.x 2 1 l t 2 z k 1tl t 21z tz1z 2.M.Strikman30In order for the term T 3a to compete with T 1a we need tohave l t t , k 1t t —otherwise T 3a will be additionallysuppressed by the power of 2 t , s . These kinematics causeEq. 30 to yield the result x 2 2 t shown. /.This argument can be carried out for all combinations of094015-13diagrams represented by Fig. 5. For example, another attachmentof gluons, in which the gluon k 1 is absorbed by thequark, corresponds to interchanging z with 1z, and there-M 2 the proof would be complete.2L. FRANKFURT, int G. M A. MILLER, We now consider the Feynman graphs, starting with Fig.2 jet AND M. STRIKMAN PHYSICAL REVIEW D 65 0940159. Once again we compute the imaginary part of the graph FIG. 8. A contribution to T 4b . The target gluon absorbs a gluonof pion wave function. Only one diagram of the eight that occur is1z d2 l t dz.311dx 1x 1 aix 1 bi ,,0 32FIG. 7. A time ordering that contributes to T 4 . The qq¯ g stateinteracts with the target. Only a single diagram of the eight where agluon interacts with quarks in a pion fragmentation region that con-Calculation accounts for energy-momentum conservation, gauge invariance, QCD evolution andFIG. 4. Contribution to T 2b from the qq¯ g intermediate FIG. 6. state. and Contribution consider theto intermediate T 3b . A gluon state asfrom beingthe on the two-gluon energy fieldIn the aboveforeformulasleadsThe interactiontowethe sameuse of theresultone Brodsky-Lepage targetfor x 2 .gluonEvidentlyfieldconven-tion for the 2 is valid in the leading thiswithresultan exchangedforof the target gluonshell.interacts The propagatorwith theforhighthe linemomentuma has the factorcomponent of thexdefinition the intermediate of wavestates. functions s ln There 2 2t /and QCD approximation also.is also retaina diagram terms in which final qq¯ thepair gluons wave function. Only a single diagram of the eight thatThus we consider the second situation: lmaximally singular fromwhen the target z→1. arePower crossed, counting and 2 t kanother is 2 1t simple: group 2 t . In thisincontribute which theis exchangedshown.case, the initial pion wave function contains a hard quark,and we discussgluonhard radiativeis emittedcorrectionby theinanti-quark.the next orderOnlyofone of 16 diagramsthat contribute is shown.s . This is the typical situation in which there are extra 094015-12 hardlines, as compared with the dominant terms, and one obtainsa suppression factor 1/ 2 t which could be compensated by 094015-11the d 2 k t integral. However, this integral does not produce2ln 2 t / QCD because the region of integration is too narrow.So this contribution is at most the non-leading-order NLOcorrection over s . But we restrict ourselves by the leadingorderLO contribution only.FIG. 5. Contribution to T 3a . The high momentum component ofthe final qq¯ pair interacts with the two-gluon field of the target.Only a single diagram of the eight that contribute is shown.the factor l t 2 /(1z) t 2 is from the gluon exchange in the222x 1 , because the quark momenta in the final state and in thepion wave function are not connected with the target momentum.The propagator of line c has the factork 2 q 1 2 m q 2 x 2 z•••x 1 z•••.34Here q 1 is the momentum of the jet (z, t ) and ••• denotesthe terms which are independent of x 1 . The last equation isobtained from using Eqs. 5,7. The results 33,34 showthat the diagram of Fig. 9 takes on the mathematical form ofthe integral 32. Thus this term vanishes.We also consider the diagram of Fig. 10. In this case thereare three propagators a,b,c that have a term proportionalto x 1 , but the coefficients are not all positive. The propaga-x 1 p k 1 2 x 1 z•••,35k 2 q 2 2 m 2 q x 2 1z•••1zx 1 •••.36At the same time, the coefficient multiplying x 1 in the propagatorb gluon production has no definite sign. Thus for
The final answer isA(π + N → 2 jets + N)(z, p t ,t= 0) ∝∫d 2 dψ q¯qπ σ q¯q−N(A) (d, s) exp(ip t d)d = r q t − r ¯q t ,ψ q¯qπ (z, d) ∝ z(1 − z) d→0is the quark-antiquark Fock component of themeson light cone wave functionPlane wave in the final state - faster onset of scaling than for VM productionProportionality of the amplitude to the gluon nuclear density (actually GPD) which for small x isnot linear in A - change of meaning of CT for high energies. Dependence on t is the same as fordiffractive vector meson production at HERA. Gluon distribution in impact parameter space isnoticeably more narrow than valence quark distribution.23
Predictions A-dependence: A 4/3 [GA (x, k 2 t )AG N (x, k 2 t )] 2where x = M 2 dijet/sdσ(u)du ∝ φ2 π(z) ≈ u 2 (1 − u) 2 where u = E jet1 /E πkt dependencedσd 2 ∝ 1k t ktn,n≈ 8 for x ~ 0.02Absolute cross section is also predicted
E-791 (FNAL) experiment (PRL 2001) at Einc π =500 GeVFirst experimental observation of high energy CT for pion interaction (Ashery 2001):π +A →”jet”+”jet” +A. Confirmed predictions of pQCD (LF,Miller, Strikman93) forA-dependence, distribution over energy fraction, u carried by one jet, dependence on pt(jet), etc♥Coherent peak is well resolved♥♥ Observed A-dependence A 1.61±0.08 [C → P t]FMS prediction A 1.54 [C → P t] for large k t & extra smallenhancement for intermediate k t .For soft diffraction the Pt/C ratio is ∼ 7 times smaller!!(An early prediction Bertsch, Brodsky, Goldhaber, Gunion 81σ(A) ∝ A 1/3 )In soft diffraction color fluctuations are also important leading toσ soft diffr (π + A → X + A) ∝ A .7discussed in the 1stpart of the talkMiller Frankfurt &S, 9325
dσdu ∝ φ2 π (u, Q2 ) = 36u 2 (1 − u) 2 1.0 + a 2 C 3/22 (2u − 1) + a 4 C 3/224 (2u − 1)prediction(π wave funct) 2Q 2 (π f.f.) ∼ 4k 2 t (jet)Squeezing occurs already before thek t :leading term (1-u)u dominates!!!a 2 = a 4 = 0 → Asymptoticstrong squeezing in π form factor forQ 2 =6 GeV 2t : a 2 = 0.30 ± 0.05, a 4 = (0.5 ± 0.1) · 10 −2 → TransitionNote that enhancement of u ➛(0,1) tail for moderate kt may explain the observed by BaBarurs already before the leading term (1-z)z dominatecollaboration slow decrease with Q of the form factor for the process: γ*(Q^2)+γ➙π 0.2616
♥♥♥♥ k −nt dependence of dσ/dk 2 t ∝ 1/k 7.5tfor k t ≥ 1.7GeV/c close to theQCD prediction - n ∼ 8.0 for the kinematics of E971or higher terms inGegenbauer expansion???CT is easier to probe for mesons than for baryons as only two quarks have to come closeMeson is not as much of a rope (camel) as a baryon and can be easier put through a needleDijet production with quantum numbers different from that for projectile can be run by COMPASSusing hydrogen at a couple of energies to measure decrease of \alpha'R for GPDs with increase ofkt as expected in QCD.M.StrikmanCT has been observed also in the diffractive photoproduction of J/ψ at FNAL and smallereffects in the exclusive electroproduction of pions off nuclei at TJNAF.
Implications for fixed target physics.Wide distribution over the sizes in the wave function of energetic hadrons and in thestrength of interactions with a target. Nonzero probability of small size quark-gluonconfigurations has been established experimentally in color transparency phenomena ➙existence of “superstrong” strong interaction follows from the probability conservation.Post-selection. To vary strengths of hadron-hadron (nucleus) _ interactions by triggering forcertain hadronic final states. Example: selection of q q g hadronic state with quantumnumbers 1 -+ enhances the contribution of superstrong strong interaction. Experimentalsignature would be slower dependence on atomic number.Probing QCD in the hard diffractive phenomena where strong interaction becomesweak-color coherence and color screening phenomena. Effective methods ofmeasuring of generalized parton distributions in nucleons and nuclei.
Inelastic diffraction is promising laboratory for the hunt for new hadronic statesIt is impossible to kill infinite number of color multipoles without infinite numberof degrees of freedom. So constituent quark models of a hadron are a oversimplification.How to hunt for the hadrons which can not be described in terms of quark models.● Inelastic forward diffraction is due to color fluctuations i.e. arises from non averagequark-gluon configurations in the projectile w.f. Larger and smaller configurations areenhanced ➜ production of states with nodes is enhanced, quark-gluon structure of hadronicstates produced in the inelastic diffraction should differ from hadronic states typical for quarkmodels of a hadron.●Wave function of diffractively produced state has two but not 3 dimensional rotationalsymmetry since configurations of different transverse size interact differently. Production ofstates with different angular momenta are allowed for the forward scattering. All diffractivestates should have helicity 0, so they are aligned along projectile momentum direction.● A-dependence of resonance production measures average strength of their interaction.σ apprdiff = ω σ〈σ〉 24∫d 2 BT 2 −〈σ〉T (B)(B)e
Varying transverse momenta of produced hadrons ➜postselects size of projectileChange of dependence on atomic number would allow to establish transition from superstrongstrong interaction (larger than average size of projectile -slower dependence on atomic number )to CT regime (small size of projectile faster dependence on atomic number).Uncertainty relation based guess - very small kt - trigger preferentially on larger thanaverage size configurations; large kt on small size configurations. Study using rescaling of ktfor fixed longitudinal fractions. Examples: p →BM (ΛK + ,...), π→3πp B pBMM./"$0!σ(k t ) ∝ A n(k t),)-+12%. 345!/36,++$&'($0+#$!!$%$&'()*" !
Factorization:First quantitative studies: Kumano, MS, andSudoh PRD 09; Kumano &MS arXiv:0909.1299,bt’dbt’dPhys.Lett. 2010GPDc (meson)GPDc (baryon)Ne (baryon)Ne (meson)ttIf the upper block is a hard (2 →2 ) process, “b”,“d”,“c” are in small size configurations as well asexchange system (qq, qqq). Can use CT argument of the proof of QCD factorization of meson exclusiveproduction in DIS (Collins, LF, Strikman 97)⇓M NN→NπB = GP D(N → B) ⊗ ψ i b ⊗ H ⊗ ψ d ⊗ ψ c31
Best bet for testing these ideas in the near future:π − A → π − π + (π − )A ∗●easier to squeeze● Significant rates - observed at FNAL for A=pdlcoh ~60 fm●freezing is 100% effective for pinc > 100 GeV/c -bAc●Hence a high sensitivity to the size (σcluster- N)15 mb10 mbT (A)0.115 mb20 mbσ eff= 25 mbIf two scales in pion w.f. (oneof explanations of γγ*→π 0rates) steps in T(kt π )●0.0310 20 50 100 200 300COMPASS has data on tapeAObservation of CT implies that GPDs can be measured in hadron induced processes forpions, kaons, baryons in the kinematics complementary to DIS studies of nucleon GPDs
Many other interesting channels to explore multiparton structure of nucleon and mesonsqqP-t’P,Δ, N*-t’/s’~1/2πPπP, Δ, N* Λ,ΣGPDN!qqqP,Δ, N*Pqq!, ρ,η, ϕK,K*(N→M)PMPN, Δ, N*-t=constpp → pN + M(π, η, ππ)pp → p∆ + M(π, η, ππ)pp → pΛ + K +π − p → pπ + MGPD (N→B)π − p → π − π − ∆ ++ ,π − p → π − π + ∆ 0 ,π − p → π − π 0 p,π − p → π − p +(π 0 π 0 − forward low p t )33
ConclusionsData on inelastic soft diffraction observed at fixed target at FNAL prefer colorfluctuations around average value. Open way for search for the superstrong stronginteraction , of resonances beyond constituent quark models.Evidence for onset of CT in the diffractive pion production of double jets at FNAL, in J/\psi diffractivemeson production at FNAL , in exclusive meson electroproduction demonstrates fruitfulness of theconcept of spatially small dipole. Observation of CT in reactions with pions (COMPASS),antiprotons/protons would allow studies of Generalized Parton Distributions of various hadrons inhadronic interactionsHaving few handles in the diffractive production of few hadrons by protons and pions will allow toinvestigate transitions between regimes of superstrong strong interaction and squizing of hadronsand CT regime, dynamics of QCD interactions at the interface between hard and soft QCD,explore the quark-gluon structure of various mesons and baryons.