Energies and Mandelstan Variables s [ ] ( ) ( ) • Total Energy = + θ + − θ E x x 1 cos 1 cos e a b 4 • Longitudinal Energy s [ ] ( ) ( ) = + θ − − θ E x x 1 cos 1 cos L a b 4 M • Transversal Energy = θ E W sen T 2 • Mandelstan variables of the process s ˆ ( ) ( ) a c = − = − − θ t p p 2 ˆ 1 cos c a 2 2 − A 1 s θ = ± ˆ ( ) ( ) cos = − = − + θ u p p 2 ˆ 1 cos A c b 2 d b = + = = s p p M A M E 2 2 ˆ ( ) / 2 a b W W T 22
W (Z) Diffractive cross sections • W +(�) diffractive cross section σ d V G t u 2 2 ˆ 2 2 ˆ ( ) = ∑ ∫ ∫ dx g x dE f x f x ab F ( ) ( ) ( ) IP IP T a IP a b η Γ d / b p s M / − 6 A 2 1 a b − + W W , e e ( ) • Z 0 diffractive cross section π σ → dx dx dx C Z G M d ab ZX 2 ˆ 2 ( ) = ∑ ∫ ∫ ∫ σ µ µ IP b a f x f x f x ab F Z 2 2 ( ) ( , ) ( , ) IP a IP a b x x x / b p d t ˆ / s 3 2 a b IP b a , • f a/IP is the quark distribution in the IP parametrization of the IP structure function (H1) • g (x IP ) is the IP flux integrated over t 0 ∫ ∞ = f x f x t dt ( ) ( , ) IP IP p IP / − − θ + θ Z C e e 2 2 4 1 / 2 2 | | sin 4 | | sin qq q W q W ' • θ is the Weinberg or weak�mixing angle W 23
W + and W � Cross Sections IS + GSP models Tevatron [ sqrt (s) = 1.8 TeV ] Pseudo- Data R(%) Inclusive W + rapidity (%) ± ± 0 . 715 0 . 045 CDF 1 . 15 0 . 55 η < Diffractive W - | | 1 . 1 e ± ± 1 . 08 0 . 25 0 . 715 0 . 045 1.8 < η < ± ± 1 . 5 | | 2 . 5 0 . 64 0 . 24 1 . 7 0 . 875 e TeV D0 W → e ν ± ± 0 . 89 0 . 25 Total 0 . 735 0 . 055 ± ± → e + − Z e 0 . 71 0 . 05 Total 1 . 44 0 . 80 (*) GSPs GSP is an average of KMR (S 2 = 0.09) and GLM (S 2 = 0.086) estimations η • Tevatron, without GSP – 7.2 % ∫ + − σ W + σ W | η e | < 1.1 diff diff • Ranges − η = R η 1.5< | η e |<2.5 ∫ + − σ W + σ W * | η |<1.1 inc inc 24 − η
Quarkonium production in NRQCD 25 MBGD, M. M. Machado, M. V. T. Machado, PLB 683, 150-153 (2010)
Diffractive hadroproduction o Focus on the following single diffractive processes ( ) ( ) pp → p + + + X → Υ γ pp p + J + + X ψ γ / o Diffractive ratios as a function of transverse momentum p T of quarkonium state o Quarkonia produced with large p T easy to detect o Singlet contribution o Octet contributions o Higher contribution on high p T 26
J/ ψ + γ production � Considering the Non-relativistic Quantum Chromodynamics (NRQCD) � Gluons fusion dominates over quarks annihilation � Leading Order cross section convolution of the partonic cross section with the PDF � MRST 2001 LO no relevant difference using MRST 2002 LO and MRST 2003 LO NLO expansions in α s � Non-perturbative aspects of quarkonium production one virtual correction and three real corrections • Expansion in powers of v � v is the relative velocity of the quarks in the quarkonia 27
T. Mehen, Phys. Rev. D55 (1997) 4338 NRQCD Factorization � Negligible contribution of quarks annihilation at high energies J/ ψ rapidity 9.2 GeV 2 is the center mass energy (LHC = 14 TeV ) 28
T. Mehen, Phys. Rev. D55 (1997) 4338 NRQCD factorization � ( ) is the momentum fraction of the proton carried by the gluon invariant mass of J/ ψ + γ system � Cross section written as Coefficients are computable in perturbation theory Matrix elements of NRQCD operators 29
T. Mehen, Phys. Rev. D55 (1997) 4338 Matrix elements Q Q Bilinear in heavy quarks fields which create as a pair Quarkonium state e c = 2 3 α s running 30
E. Braaten, S. Fleming, A. K. Leibovich, Phys. Rev. D63 (2001) 094006 F. Maltoni et al ., Phys. Lett. B638 (2006) 202 Matrix elements (GeV 3 ) 1.16 10.9 e b = − 1 3 1.19 x 10 -2 0.02 m = GeV 4 . 5 b 0.01 0.136 m Υ = 9 . 46 GeV/c 2 0.01 x m 2 0 c 31
Diffractive cross section Momentum fraction carried by the Pomeron Squared of the proton's four-momentum transfer Pomeron flux factor Pomeron trajectory 32
Variables to DDIS Cuts for the integration over x IP Scales ( ) 2 p + m 2 = Λ 2 = 2.5 GeV 2 Q 0 0.2 T ψ = � 2 QCD F 4 33
Results for J/ ψ + γ • Predictions for inclusive and diffractive cross sections • LHC, Tevatron and RHIC • Diffractive cross sections considering GSP (<|S| 2 >) • B = 0.0594 is the branching ratio into electrons ≤ ≤ p 1 20 at LHC T 34
Results for ϒ + γ • Predictions of inclusive cross section • LHC , Tevatron and RHIC -1 < |y| < 1 • B = 0.0238 is the branching ratio into electrons 35
Results for J/ ψ + γ at LHC • B = 0.0594 • Absolute value cross section strongly dependent Quark mass NRQCD matrix elements Factorization scale • Diffractive cross sections (DCS) without GSP (<|S| 2 >) • Comparison between two different sets of diffractive gluon distribution (H1)
Results for ϒ + γ at LHC • B = 0.0238 • Absolute value cross section strongly dependent Quark mass NRQCD matrix elements Factorization scale • Diffractive cross sections (DCS) without GSP (<|S| 2 >) • Comparison between two different sets of diffractive gluon distribution (H1) 37
Diffractive ratio at LHC ** C. S. Kim, J. Lee and H. S. Song, Phys Rev D59 (1999) 014028 This work Ref ** � Slightly large diffractive ( ) = E � 2 p + m 2 T ψ = F T � F ratio in comparison to ** 4 <|S| 2 >=0.06 Renormalized Pomeron flux � Could explain the p T dependence Q 2 evolution in the gluon No Q 2 evolution in the gluon in our results density density [ σ ] = pb 38 considering FIT A
Heavy quark production MBGD, M. M. Machado, M. V. T. Machado, PRD. 81, 054034 (2010) MBGD, M. M. Machado, M. V. T. Machado, PRC. 83, 014903 (2011) 39
M. L. Mangano et al, Nucl. Phys. B 373, 295 (1992) Heavy quark hadroproduction ( ) X ( ) X o Focus on the following single diffractive processes pp → p + b b + pp → p + c c + o Diffractive ratios as a function of energy center-mass E CM → g + g Q + Q o Diagrams contributing to the lowest order cross section 40
M. L. Mangano, P. Nason, G. Ridolfi Nucl. Phys. B373 (1992) 295 Total cross section LO � = s x x s x 1,2 are the momentum fraction 1 2 are the parton distributions inner the hadron i=1 and j=2 Partonical cross section ( ) � F � factorization (renormalization) scale R 41
M. L. Mangano, P. Nason, G. Ridolfi Nucl. Phys. B373 (1992) 295 NLO Production → g + g Q + Q + g Running of the coupling constant n 1f = 3 (4) charm (bottom) 42
P. Nason, S. Dawson, R. K. Ellis Nucl. Phys. B303 (1988) 607 NLO functions a 0 0.108068 a 4 0.0438768 Auxiliary functions a 1 -0.114997 a 5 -0.0760996 a 2 0.0428630 a 6 -0.165878 a 3 0.131429 a 7 -0.158246 43
Diffractive cross section Pomeron flux factor β = x x IP Pomeron Structure Function (H1) KKMR model <|S| 2 > = 0.06 at LHC single diffractive events Parametrization of the pomeron flux factor and structure function H1 Collaboration 44
Heavy quarks production at the LHC Heavy quarks cross sections in NLO to pp collisions GSP value decreases the diffractive ratio (<|S| 2 > = 0.06) Inclusive nuclear cross section at NLO A PbPb = 208 (5.5 TeV); 40 (6.3) TeV 45
pA cross sections @ LHC = S 2 0 . 0287 GAP Similar results that B. Kopeliovich et al , 0702106 [arXiv:hep-ph] (2007) � Suppression factor 46 σ pA ~ 0.8 mb (charm)
Diffractive cross sections @ LHC Inclusive cross section Nucleus-Nucleus collision A Pb = 240 � Coherent Diffractive cross sections Pomeron emmited by the nucleus → A + A X + A + [LRG] + A � Predictions to cross sections possible to be verified at the LHC 47 Very small diffractive ratio
Diffractive cross sections @ LHC � Incoherent Pomeron emmited by a nucleon inner the nucleus → * A + A X + A + [LRG] + A � No values to <|S| 2 > for single diffractive events in AA collisions � Estimations to central Higgs production <|S| 2 > ~ 8 x 10 -7 � Values of diffractive cross sections possible to be verified experimentally A Pb = 240 48
DPE results at LHC pp collisions LHC (14 TeV) Ingelman-Schlein Bialas-Landshoff AA collisions LHC CaCa (6.3 TeV) 49 PbPb (5.5 Tev) Ingelman-Schlein > Bialas-Landshoff
Higgs production MBGD, M. M. Machado, G. G. Silveira, PRD. 83, 074005 (2011) 50
Higgs production b -jet � Standard Model (SM) of Particle Physics has unified the Eletromagnetic interaction and the weak interaction; gap gap H η η η η � Particles acquire mass through their � � interaction with the Higgs Field; � Existence of a new particle: the Higgs boson b -jet � The theory does not predict the mass of H; � Predicts its production rate and decay modes for each possible mass; � Exclusive diffractive Higgs production pp → p H p : �������� � Inclusive diffractive Higgs production p p → p + X + H + Y + p : ��������� Albert de Roeck X BARIONS (2004) 51
Tevatron cuts � LHC opens a new kinematical region: � CM Energy in pp Collisions: 14 TeV 7x Tevatron Energy � Luminosity: 10 – 100 fb -1 10 x Tevatron luminosity � Evidences show new allowed mass range excluded for Higgs Boson production � Tevatron exclusion ranges are a combination of the data from CDF and D0 52 The TEVNPH Working Group, 1007.4587 [hep-ph]
D. Graudenz et al. PRL 70 (1993) 1372 Gluon fusion o Focus on the gluon fusion o Main production mechanism of Higgs boson in high-energy pp collisions o Gluon coupling to the Higgs boson in SM triangular loops of top quarks Lowest order to gg contribution 53
M. Spira et al. 9504378 [hep-ph] Gluon fusion � Lowest order partonic cross section expressed by the gluonic width of the Higgs boson Quark Top gg invariant energy squared � dependence 54
LO hadroproduction � Lowest order two-gluon decay width of the Higgs boson PDFs � Gluon luminosity MSTW2008 � Lowest order proton-proton cross section � Renormalization scale 55 � s invariant pp collider energy squared
Virtual diagrams � Coefficient contributions from the virtual two-loop corrections � Regularized by the infrared singular part of the cross section for real gluon emission � Infrared part � Finite τ Q dependent piece � Logarithmic term depending on the renormalization scale � 56
Delta functions o Contributions from gluon radiation in gg , gq and qq scattering renormalization scale � o Dependence of the parton densities factorization scale M o Renormalization scale QCD coupling in the radiative corrections and LO cross sections 57
d functions F + : usual + distribution Considering only the heavy-quark limit Region allowed by Tevatron combination 58
NLO Cross Section � Gluon radiation two parton final states � Invariant energy in the channels � New scaling variable supplementing and � The final result for the pp cross section at NLO � Renormalization scale in α s and the factorization scale of the parton densities to be fixed properly 59
Diffractive processes Single diffractive Double Pomeron Exchange 60
Diffractive cross sections Single diffractive Double Pomeron Exchange Momentum fractions: pomeron and quarks β = x Normalization x IP Gluon distributions in the proton MSTW (2008) H1 parametrization (2006) 61 Pomeron flux Gluon distributions ( i ) in the Pomeron IP
FIT Comparison :: SD vs. DPE 62
SD production as M H function (NLO) 63 GLM KKMR
Exclusive Higgs boson production MBGD, G. G. Silveira, Phys. Rev. D 78, 113005 (2008) MBGD, G. G. Silveira, Phys. Rev. D 82, 073004 (2011) 64
Khoze, Martin, Ryskin, EPJB 401, 330 (1997) Diffractive Higgs Production → + + pp p H p • The reaction • • Protons lose small fraction of their energy :: scattering in small angles • Nevertheless enough to produce the Higgs Boson 2 M σ = d Durham π dy b Model 2 3 2 16 ≡ − Q Q 2 2 G F is the Fermi constant and T T ���$����� ��� �%������� �����&���� ��������������� ��������� 65
J.R. Forshaw, arXiv:0508274[hep-ph] 2-gluon emission • The probability for a quark emit 2 gluon in the t-channel is given by the integrated gluon distribution ( ) ( ) ≡ ∂ ∂ f x Q K G x Q Q 2 , , ln • The factor K is related to the non-diagonality of the distribution 2 σ α d G d Q 2 2 ( ) ( ) ∫ ≈ s F T f x Q f x Q , , T T 1 2 dy b Q 2 4 9 T 66
J.R. Forshaw, arXiv:0508274[hep-ph] Sudakov form fators • The former cross section is infrared divergent ! • The regulation of the amplitude can be done by suppression of gluon emissions from the production vertex; • The Sudakov form factors accounts for the probability of emission of one gluon • The suppression of several gluon emissions exponentiate • Then, the gluon distributions are modified in order to include S 67
Cross section I :: Sudakov 30x 2 σ α d G d Q 2 2 ~ ~ ( ) ( ) ∫ ≈ s F T f x Q f x Q , , T T 1 2 dy b Q 2 4 9 68 T
Cross section II :: PDFs 69
Photoproduction mechanism • The Durham group’s approach is applied to the photon-proton process; • This is a subprocess of Ultraperipheral Collisions ; • Hard process: photon splitting into a color dipole, which interacts with the proton; Dipole contribution 70
γ p cross section 71
Ultraperipheral Collisions • Photon emission from the proton with photon fluxes • The photon virtuality obey the Coherent condition for its emission from a hadron under collision 72
Photoproduction cross section pp M H = 120 GeV Cross section = 1.77-6 fb Estimations for the GSP in the LHC energy 73
pA collisions Process Events/yr BR(H → bb-bar) = 72% 74
Conclusions � GFPAE has been working in hard diffractive events � Use of IS with absorptive corrections (gap survival probability) describe Tevatron data for W +� and Z 0 production rate production for quarkonium + photon at LHC energies R (J/ ψ ) R ( Υ ) SD = 0,8 – 0,5 % SD = 0,6 – 0,4 %(first in literature) predictions for heavy quark production (SD and DPE) at LHC energies possible to be verified in AA collision (diffractive cross section in pp, pA and AA collisions ) C C B B A = Lead and Calcium Higgs predictions in agreement with Hard Pomeron Exchange 75 Cross sections of Higgs production 1 fb ( DPE ); 60-80 fb ( SD )
Conclusions � Exclusive photoproduction is promising for the LHC strong suppression of backgrounds cross section prediction ��� fb expecting between 1 and 6 events per year additional signature with the H γ associated production High event rates for pA collisions σ = 1 pb pPb collisions 76
Next DIFFRACTION IN NUCLEAR COLLISIONS � Gap survival probability for nuclear collisions � Dijets in hadronic and nuclear collisions � ... 77 77
BACKUP 78 78
Predictions (LHC – 14 TeV) High diffractive ratio 1 ∫ σ diffractiv e = = R − 1 0 . 311 KMR 1 ∫ σ inclusive − 1 Large range of pseudorapidity − ≤ η ≤ 6 6 79
A. Bialas and W. Szeremeta, Phys. Lett. B 296, 191 (1992) Bialas-Landshoff approach + → + + p p p Q Q p Double Pomeron Exchange nucleon form-factor Differential phase-space factor 80 mass of produced quarks
Bialas-Landshoff approach Sudakov parametrization for momenta two-dimensional four-vectors describing the transverse component of the momenta momenta for the incoming (outgoing) protons momentum for the produced quark (antiquark) momentum for one of exchanged gluons 81
A. Bialas and W. Szeremeta, Phys. Lett. B 296, 191 (1992) Bialas-Landshoff approach Square of the invariant matrix element averaged over initial spins and summed over final spins effect of the momentum transfer dependence of the non-perturbative gluon propagator 82
Processes in channels s and t • Two body scattering can be calculated in terms of two independent invariants, s and t, Mandelstam variables ( ) ( ) = + = + s A B 2 C D 2 Square of center-of-mass energy ( ) ( ) where = − = − t A C 2 B D 2 Square of the transfered four momentum s A C A t B B C D D ( ) ( ) = A s t A t s , , by crossing symmetry AB → CD → A C B D g 2 ( ) ≈ A s t , pion exchange − m t 2 π g coupling constant t = m 83 83 2 Singularity (pole) in non-physical region t > 0 in s-channel diagram π
Regge Theory • At fixed t, with s >> t • Amplitude for a process governed by the exchange of a trajectory α (t) is A ( s,t ) • No prediction for t dependence •Elastic cross section •Total cross section considering the optical theorem 84 84
Diffractive scattering Consider elastic A B A B 2 2 A A A A σ d X 1 1 α (t) ∑ s α − ≈ t 2 ( ) 2 ≈ ≈ el dt s s 2 2 X B B B B ( ) 1 ( ) 1 ������� ������� AB α − σ AB ≈ ≈ A s 0 Im tot el = t o s A A A A A 1 1 1 ∑ ∑ σ = = ≈ α (0) tot X s s s 2 2 X X B B B B B vacuum trajectory by Regge Apparent Pomeron α IP (t) contradiction vacuum quantum numbers α ≈ + ε α ≤ 85 85 ( 0 ) 1 , ( 0 ) 0 . 5
Diffractive scattering α = + t t (p p, p p ) ( ) 1 . 085 0 . 25 IP The interactions described by the exchange of a IP are called diffractive so σ AB β β d t t 2 2 ( ) ( ) α − ≈ s tot AIP BIP 2 2 IP π dt 16 Pomeron coupling with external particles β iIP t → ∞ → Valid for s , 0 s High s α − σ AB ≈ β β s 1 ( 0 ) ( 0 ) IP tot AIP BIP 86 86
Froissart limit � No diffraction within a black disc ( ) ∝ R s � It occurs only at periphery, b ~ R in the Froissart regime, ln � Unitarity demands i.e. � Donnachie�Landshoff approach may not be distinguishable from logarithmic growth Any s λ power behaviour would violate unitarity At some point should be modified by unitarity corrections 87 87 • Rate of growth ~ s 0.08 would violate unitarity only at large energies
����� !��������$��" ���'(� o Elastic amplitude mediated by the Pomeron exchange ∝ A el (t) What is the Pomeron? o A Regge pole: not exactly, since α IP (t) varies with Q 2 in DIS o DGLAP Pomeron specific ordering for radiated gluon and o BFKL Pomeron no ordering no evolution in Q 2 88 88 o Other ideas?
Studies of diffraction o In the beginning hadron�hadron interactions SOFT low momentum transfer o Exclusive diffractive production: ρ, φ, J/ψ, Y, γ HARD high momentum transfer Gluon exchange o Cross section o δ expected to increase from soft (~ 0.2 is a “soft” Pomeron) to hard (~ 0.8 is a “hard” Pomeron) o Differential cross section 89 89
Some results � Many measurements in pp � Pomeron exchange trajectory � Pomeron universal and factorizable applied to total, elastic, diffractive dissociation cross sections in ep collisions 90 90
Diffractive Structure Functions � DDIS differential cross section can be written in terms of two structure functions D F D ( 4 ) F ( 4 ) and 1 2 � Dependence of variables x, Q 2 , x IP , t � Introducing the longitudinal and transverse diffractive structure functions = − = D D D D D F F xF F xF ( 4 ) ( 4 ) ( 4 ) ( 4 ) ( 4 ) 2 2 L T 2 1 1 � DDIS cross section is σ γ D d = πα ( ) y 2 2 4 * p − + D em y F x Q x t [ ] ( 4 ) 2 ( ) 1 , , , IP + D dxdQ dx dt xQ R x Q x t 2 2 4 ( 4 ) 2 2 1 , , , IP IP D F ( 4 ) is the longitudinal�to�transverse ratio � D = R L ( 4 ) 91 91 D F ( 4 ) T
Diffractive Structure Functions � Data are taken predominantly at small y � Cross section little sensitivy to R D(4) for β < 0.8 – 0.9 neglect R D(4) at this range << D D F F � ( 4 ) ( 4 ) L T σ γ D d = πα ( ) y 2 2 4 * p − + D em y F x Q x t ( 4 ) 2 1 , , , IP 2 dxdQ dx dt xQ 2 4 2 IP proportional to the cross section for diffractive γ *p scattering � D F ( 4 ) 2 σ D d ( ) Q 2 γ * p D = F x Q x t ( 4 ) 2 , , , IP πα 2 dx dt 2 4 em IP � D F ( 4 ) dimensional quantity 2 D D F 2 dF x Q x t 2 ( , , , ) is dimensionless D ≡ F IP ( 4 ) 2 92 92 2 dx dt IP
Diffractive Structure Functions � When the outgoing proton is not detected no measurement of t � Only the cross section integrated over t is obtained σ γ D d = πα ( ) y 2 2 4 * p − + D em y F x Q x ( 3 ) 2 1 , , IP dxdQ dx xQ 2 2 4 2 IP D F � The structure function ( 4 ) is defined as 2 ( ) ( ) ∞ ∫ D = D F x Q x d t F x Q x t ( 3 ) 2 ( 4 ) 2 , , | | , , , IP IP 2 2 0 93 93
Diffractive Parton Distributions � Factorization theorem holds for diffractive structure functions � These can be written in terms of the diffractive partons distributions � It represents the probability to find a parton in a hadron h , under the condition the h undergoes a diffractive scattering D � QCD factorization formula for is F 2 D ξ µ i dF x Q x t df x t x 2 2 = ∑∫ ( , , , ) ( , , , ) ^ x IP ξ µ d F Q IP i IP 2 2 2 , , 2 ξ dx dt dx dt x i IP IP ξ µ is the diffractive distribution of parton i � df x t dx dt 2 ( , , , ) / i IP IP � Probability to find in a proton a parton of type i carrying momentum fraction ξ � Under the requirement that the proton remains intact except for a momentum transfer quantified by x IP and t 94 94
Diffractive Parton Distributions � Perturbatively calculable coefficients x ˆ F i Q 2 � 2 , , 2 ξ X 2 = M 2 � Factorization scale � Diffractive parton distributions satisfy DGLAP equations � Thus df x t ∂ ξ � 2 df x t d ξ � ς ξ 2 ( , , , ) ( , , , ) ∑∫ 1 j IP = P i IP α � , ( ) ij s ∂ dx dt dx dt � 2 ς ς ln ξ j IP IP � “ ����� �� � ������ ” is a diffractive parton distribution integrated over t df x df x t ξ � 2 ξ � 2 ( , , ) ∞ ( , , , ) ∫ = i IP d t i IP 2 2 x m dx dx dt IP N − 95 95 x IP IP 1 IP
Partonic Structure of the Pomeron IP F 2 � It is quite usual to introduce a partonic structure for � At Leading Order Pomeron Structure Function written as a superposition of quark and antiquark distributions in the Pomeron ∑ β = β β IP IP F Q e q Q 2 2 2 ( , ) ( , ) q 2 q q , x β = � interpreted as the fraction of the Pomeron momentum x IP carried by its partonic constituents q IP β � Q probability of find a quark q with momentum fraction β 2 ( , ) inside the Pomeron � This interpretation makes sense only if we can specify unambigously the probability of finding a Pomeron in the proton and assume the Pomeron to be a real particle (Ingelman, Schlein, 1985) 96 96
Partonic Structure of the Pomeron � Diffractive quark distributions and quark distributions of the Pomeron are related β df Q x t 2 ( , , , ) 1 q IP − α = t IP β g t x q Q 2 2 ( ) 2 | ( ) | ( , ) IP IP IP π dx dt 2 16 IP • Introducing gluon distribution in the Pomeron g IP β Q 2 ( , ) • Related to by df dx dt g / IP β df Q x t 2 ( , , , ) 1 g IP − α = t IP β g t x g Q 2 2 ( ) 2 | ( ) | ( , ) IP IP IP π dx dt 2 16 IP •At Next�to�Leading order, Pomeron Structure g IP β Function acquires a term containing Q 2 ( , ) Representation of D* diffractive production in the 97 97 infinite-momentum frame description of DDIS
Diffractive processes � Hadronic processes can be characterized by an energy scale Soft processes – energy scale of the order of the hadron size (~ 1 fm) pQCD is inadequate to describe these processes Hard processes – “hard” energy scale ( > 1 GeV 2 ) can use pQCD “factorization theorems” Separation of the perturbative part from non�perturbative � Most of diffractive processes at HERA !"��� �����""�"# 98 98
Pomeron as composite • Considering Regge factorization we have ( ) ( ) = β D IP F x Q x t f x t F Q ( 4 ) 2 2 , , , , ( , ) IP IP IP 2 2 p IP IP flux Structure function see MBGD & M. V. T. Machado 2001 Data Good fit with added Reggeon for HERA Pomeron as gluons •Elastic amplitude neutral exchange in t�channel • Smallness of the real part of the diffractive amplitude nonabeliance Born graphs in the abelian and nonabelian (QCD) cases look like 99 99
The Pomeron o From fitting elastic scattering data IP trajectory is much flatter than others α ≈ α ≈ − GeV ( 0 ) 1 o For the intercept ' 2 total cross sections implies 0 . 25 IP IP o Pomeron dominant trajectory in the elastic and diffractive processes o Known to proceed via the exchange of $�� � % ��� ��� ����" in the t �channel ( ) ( ) α = α + α t t Regge�type 0 ' First measurements in h�h scattering σ d ( ) [ ] α + = t W b t W 2 2 ( ) 2 ( ) exp IP 0 dt � α(0) and α’ are fundamental parameters to represent the basic features of strong interactions σ d = + α b b W 4 ' ln( ) = α − W W bt 4 ( 0 ) 4 ( ) exp( ) 0 dt 100 100 � α’ energy dependence of the transverse system
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