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Factorization and factorization breaking in non-diffractive scattering at HERA Bruce Straub, University of Oxford Representing the ZEUS and H1 Collaborations XXXV International Symposium on Multiparticle Dynamics ˇ rı ˇ Kromeˇ´z, Czech Republic, 9-15 August 2005 • When Should Factorization Apply? • Tests of Factorization • Parton Densities: Can NLO QCD ﬁts describe ep, γp and p¯ ? p • Fragmentation Functions: Compare NC DIS (Breit frame) and e+e− • Factorization Breaking • Underlying event studies in tagged photoproduction • Forward Neutron Production • Sketch of the Dipole Model of DIS • Conclusions Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 1 When Should Factorization Apply? • Incident particles have high momentum • Hadrons are Lorentz contracted along the direction of ﬂight, so the interaction time is decreased. • Interactions internal to hadrons are time dilated, so the lifetime of the partonic state is increased. • Long distance interactions of partons within the hadron can be neglected during the (short-distance) hard interaction, so the partons can be treated as free particles. • The partons can be assigned a fraction x of the hadron’s longitudinal momentum. The momentum distribution of parton species i within hadron H in x can be described by a universal parton density fi/H(x) with 0 < x < 1. • The density of partons should not be too high, so that the collision can be described by a single hard scattering Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 2 Factorized Cross Sections • The Neutral Current DIS cross section can be factored into a sum over quark densities and a hard scattering cross section d2σ(ep) 2πα2 = (1 + (1 − y)2) e2fi/p(x, Q2) i dxdQ2 Q4 i • The direct γp cross section can be written σdir (ep → e + N jets + X) = fγ/e (y, Q2) fi/p(x, µ2)dˆ (γi → N jets) σ Ω i • The resolved γp cross section can be written σres (ep → e+N jets+X) = fγ/e (y, Q2) fi/p(x, µ2)fj/γ (xγ , µ2 )dˆ (ij → N jets) p γ σ Ω ij Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 3 Factorization in the Final State • After the hard scatter, hadron formation occurs over a much longer time scale, so it can be described independently of the hard process, again by a universal function gH/i(z) which gives the density in z, the fraction of the parton momentum carried by the hadron for hadrons of species H produced in the fragmentation of parton species i. Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 4 ZEUS NLO QCD Fit Compared to ZEUS NC DIS Data ZEUS ZEUS σNC σNC 2 Q = 2.7 GeV 2 3.5 GeV2 4.5 GeV2 6.5 GeV 2 1.5 2 Q = 200 GeV 2 250 GeV2 350 GeV 2 450 GeV 2 ~ ~ 1.5 1 1 0.5 0.5 0 8.5 GeV2 10 GeV2 12 GeV2 15 GeV2 1.5 0 650 GeV2 800 GeV2 1200 GeV2 1500 GeV2 1 1 0.8 0.5 0.6 0 0.4 18 GeV2 22 GeV2 27 GeV2 35 GeV2 1.5 0.2 1 0 2000 GeV2 3000 GeV2 5000 GeV2 8000 GeV2 0.5 0.8 0 0.6 2 2 2 2 45 GeV 60 GeV 70 GeV 90 GeV 1.5 0.4 1 0.2 0.5 0 12000 GeV2 20000 GeV2 30000 GeV2 10-2 10-1 1 0 0.6 -3 -2 -1 -3 -2 -1 ZEUS-JETS 120 GeV2 150 GeV2 10 10 10 1 10 10 10 1 1.5 tot. uncert. 0.4 1 ZEUS-JETS tot. uncert. ZEUS NC e+p 99-00 0.2 0.5 ZEUS NC e-p 98-99 ZEUS NC e+p 96-97 ZEUS NC e+p 96-97 0 0 10-3 10-2 10-1 1 10-3 10-2 10-1 1 10-2 10-1 1 10-2 10-1 1 10-2 10-1 1 x x DESY-05-71, submitted to European Physical Journal C Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 5 CTEQ61 Compared to CDF Jet Data 2 10 2.5 [nb/(GeV/c)] Data / Theory KT D=0.7 0.1<|Y|<0.7 KT D=0.7 0.1<|Y|<0.7 10 Data Systematic errors Data 1 NLO: JETRAD CTEQ61 2 Systematic errors -1 10 corrected to hadron level NLO uncertainties JET -2 µ R = µ F = max PJET / 2 d σ / dY dPT T 10 NLO uncertainties -3 1.5 CDF Run II Preliminary 10 10-4 2 -5 10 1 -6 10 CDF Run II Preliminary -7 10 -1 s =1.96 TeV L=385 pb -8 0.5 10 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 JET JET PT [GeV/c] PT [GeV/c] CTEQ61 also gives an excellent description of the HERA DIS data Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 6 ZEUS NLO QCD Fit Compared to Direct Photoproduction Data e+ dσ/dET (pb/GeV) ZEUS γ 10 6 xobs > 0.75 γ ZEUS-JETS tot. uncert. 105 ZEUS dijet γ p 96-97 jet1 Jet energy scale uncert. 104 p 103 e+ 102 1<ηjet1,2<2.4 γ (× 20000) 10 1 1<ηjet1<2.4 p 0<ηjet2<1 1<ηjet1<2.4 (× 100) 10-1 -1<ηjet2<0 (× 20) e+ 10-2 γ 10-3 0<ηjet1,2<1 0<ηjet1<1 (× 0.01) -1<ηjet2<0 10-4 (× 0.0005) p -1<ηjet1,2<0 (× 0.00001) 10-5 20 30 40 50 60 70 Ejet1 (GeV) T Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 7 ZEUS NLO QCD Fit Compared to Resolved Photoproduction Data ZEUS γ d σ /dE T (pb/GeV) xγ 6 10 x OBS < 0.75 γ ZEUS 96-97 ( γ p data) Jet Energy Scale Uncertainty 5 10 NLO QCD (AFG-PH) × δhad: ZEUS-JETS (prel.) 94-00 4 total uncertainty p jet1 10 3 10 2 γ 10 1< η jet1,2<2.4 10 ( × 5000) 1 1< η <2.4,0< η jet1 jet2 <1 p ( × 100) -1 1< η <2.4,-1< η jet1 jet2 10 <0 ( × 20) -2 10 0< η jet1,2 <1 γ -3 10 ( × 0.01) -4 10 -1< η jet1,2<0 0< η <1,-1< η -5 jet1 jet2 ( × 0.00001) <0 10 ( × 0.0005) -6 p 10 20 30 40 50 60 jet1 ET (GeV) The data lies above the NLO QCD calculations, especially at high E T Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 8 Resolved Photoproduction Data Compared to NLO Predictions Cross section/theory ZEUS 2 1<η < 2.4 jet1,2 1 CTEQ5M1 parton densities for the proton 2 1<η < 2.4 jet1 1.5 The hatched theory error band includes: 0<η <1 jet2 1 · Renormalization and factorization scales µ varying between ET /4 and ET 3 1<η jet1 < 2.4 · Hadronization uncertainty -1 < η <0 jet2 2 · αs(Mz ) = 0.116 ± 0.003 1 2 0<η jet1,2 <1 High ET excess especially pronounced for forward jets 1 4 0 < ηjet1< 1 -1 < ηjet2< 0 2 1.5 -1 < ηjet1,2< 0 ZEUS 1996-97 xγ < 0.75 obs 1 NLO (GRV) ⊗ HAD NLO (AFG) ⊗ HAD 0.5 Jet energy scale uncertainty 20 30 40 50 60 jet1 ET (GeV) European Physic. Journal C23 (2002) 4, 615-631 Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 9 NC DIS Breit Frame Current Region Scaled Momentum Spectra European Physical Journal C 11 (1999) 2, 251-270 ZEUS 1994-7 2 0 q = (0, 0, 0, −Q) is the 2 virtual photon momentum. 0 0 5 2 Max momentum of 0 particles in the current 2 region is Q/2 0 2 For particle with 0 momentum p, 0 5 2 xp = 2p/Q 0 2 0 2 0 0 2.5 5 2 0 0 2.5 50 2.5 5 Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 10 Breit Frame Current Region Multiplicity in Bands of Scaled Momentum Open Symbols are e+e− multiplicities (divided by 2) plotted at Q2 = s Q2 variation = scaling violation e+ e− and NC DIS data agree well Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 11 Compare Shape of the NC DIS Scaled Momentum Spectra to e+e− Parameterize the ln(1/xp ) distribution with mean l and width w as a distorted Gaussian in δ = (ln(1/xp ) − l)/w: (2+k)δ 2 sδ 3 kδ 4 “ ” k sδ f (δ) = exp 8 − 2 − 4 + 6 + 24 e+e− and NC DIS data agree well Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 12 Event Characteristics for Tagged Photoproduction Z. Phys. C70 (1996) 17 Q2 < 0.01 GeV2 dσ/dET [nb/GeV] 10 Tagged electron with 8 < E e < 1 20 GeV 10 -1 0.25 < y < 0.7 10 -2 150 < W < 251 GeV 20 25 30 35 40 45 50 ET [GeV] Better description using simulations 12 with multiple interactions (PHOJET, <dET/dη > [GeV] 10 PYTHIA mia) * 8 6 4 2 0 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 η * Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 13 Tagged Photoproduction Underlying Event ET density vs. xγ jet Require 2 jets with ET > 7 GeV and −2.5 < η ∗ < 0.5 1.4 xjets is the fraction of the photon’s <ET>/(∆η∆φ) [GeV/rad] γ longitudinal momentum carried by 1.2 the dijet system 1 jets (E − Pz )jet1 + (E − Pz )jet2 xγ = 0.8 (E − Pz )γ 0.6 Plot shows the (η, φ) ET density in the central region |η ∗| < 1 excluding 0.4 cones of radius 1.3 centered on the 2 highest ET jets 0.2 Low xjets (resolved) γp interactions γ 0 0 0.2 0.4 0.6 0.8 1 have ∼ 2× as much ET density as jets xγ direct γp. Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 14 Photoproduction ET Spectrum Compared to NLO QCD H1 inclusive jet photoproduction dσep /dE jet [nb/GeV] NLO results corrected by H1 data Q2 ≤ 0.01 GeV2 ( × RF ) 2 1 + δhadr = (1 + δfrag )(1 + δue) 10 H1 data Q2 ≤ 1 GeV2 10 NLO (1+ δhadr.) 1 + δfrag corrects for fragmentation. T NLO 1 GRV,CTEQ5M The underlying event correction -1 10 1 + δue is deﬁned as the ratio of cross -2 sections with and without a simulated 10 underlying event which was tuned -3 10 incl. k⊥ algor. (D=1) to describe the energy ﬂow between -4 -1 ≤ η jet ≤ 2.5 jets. 10 164 ≤ Wγ p ≤ 242 GeV -5 1+δue 10 2 (σ-σTheory)/σTheory NLO (1+ δhadr.) 1.8 0.4 0.2 LO (1+ δhadr.) 1.6 0 1.4 -0.2 1.2 -0.4 1 -0.6 , H1 data 0.8 10 20 30 40 50 60 70 10 20 30 40 50 60 70 ETjet European Physical Journal C29 (2003) 497-513 E jet [GeV] T Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 15 Forward Neutron Production in DIS and γP ZEUS 20 18 16 14 12 10 xL = Pn/Pp 8 6 Probability of producing a neutron is about 1/2 that observed in pp 4 collisions at the ISR. 2 γp collisions are 20-30% less likely to produce a neutron compared to 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 NC DIS, although no Q2 dependence is observed for Q2 > 4. Nucl. Physics B637 (2002) 3-56 Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 16 Forward Neutron Production in DIS and γP ZEUS 1.4 Small γ = High Q2, No Rescatter, n detected 1.2 1 0.8 0.6 0.4 0.2 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.06 Large γ = Low Q2 −→ Rescatter. fln=σ2j+n/σ2j H1 data RAPGAP-π/PYTHIA-MI rnπ smaller at lower xL −→ Rescatter 0.05 PYTHIA/PYTHIA (*0.6) 0.04 γp 0.03 0.02 0.01 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 jet xγ Eur. Phys. J. C41 (2005) 273-286 Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 17 Dipole Model of Deep Inelastic Scattering 2 γ * γ * Detector γ* γ* p p Y γ * p a p p 1 γ γ * * Detector The Optical Theorem relates the amplitude for elastic γ ∗p scattering (no cut) to the inclusive γ ∗p cross section (with the cut). p p p γ * Y The total cross section is a sum of all b diagrams with all possible Pomeron (gluon 2 ladder) exchanges. Diagram (a) above right γ* γ* Detector gives the leading term to the diffractive cross section. p p Y γ * p J.Bartels, M.Salvadore, G.P.Vacca,Eur.Phys.J. C42 (2005) 53-71 c H.Kowalski, D.Teaney, Phys.Rev. D68 (2003) 114005 Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 18 Dipole Model of Deep Inelastic Scattering The γ ∗p cross section for k-cut Pomerons 10 F2 F2 vs. impact parameter b is 1 1 dσk Ω(b)k -1 10 -1 = exp(−Ω(b)), where 10 d2 b k! 10 -2 -2 π2 2 2 2 10 Ω= r αs(µ ) xg(x, µ ) T (b) NC 10 -3 10 -5 10 -4 10 -3 10 -2 10 -3 10 -5 10 -4 10 -3 10 -2 is the Opacity written in terms of the dipole x x radius r, the gluon density xg(x, µ2 ) and Contributions to F2 from k-cut Pomerons (H.Kowalski). the transverse shape of the proton T (b). ratio ratio To get the total cross section, F2, average 1 1 the dipole cross secctions over the photon wave function ψ(r, z) and integrate over the 10 -1 10 -1 impact parameter Q2 dz ∗ dσk Z Z Z -2 -2 10 10 k 2 2 -5 -4 -3 -2 -5 -4 -3 -2 F2 = d r ψ ψ d b 2 . 10 10 10 10 x 10 10 10 10 x 4π 2 αem 4π d b Fraction of F2 due to single Pomeron exchange, multiple Pomeron exchange, and diffraction. Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 19 Conclusions • Factorization holds very well in non-diffractive interactions of protons with point-like photons • Universal parton densities can describe ep, direct γp, and hard p¯ p interactions • Fragmentation functions measured in DIS are quite compatible with those measured in e+e−. Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 20 Conclusions • In resolved photoproduction, which is a hadron-hadron collision, multiple- interaction models describe the data better than LO models without multiple interactions. • The underlying event produces about twice as much ET in resolved photoproduction compared to direct • Resolved γp cross sections exceed NLO QCD predictions, at high ET • HERA experiments should measure event shapes and energy ﬂow in γp more systematically, instead of focusing entirely on jets • The probability to produce a forward neutron is process dependent, highest in pp collisions, and lowest in γp interactions. • The dipole model relates the cross section for multiple gluon exchange to the diffractive cross section. Even at the relatively high Q2 of 40 GeV2, the model predicts that multiple gluon exchange makes up 6-8% of the DIS cross section Factorization and factorization breaking in non-diffractive scattering at HERA/ Bruce Straub/ ISMD 2005 21

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