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Inclusive Diffraction at HERA

Inclusive Diffraction at HERA. Valentina Sola Torino University. Diffraction in ep scattering Latest inclusive diffractive ep results Direct measurement of F L D at HERA. Diffraction in ep Scattering. vacuum quantum numbers. LRG. IP. IP. IP. Elastic. Single Dissociation.

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Inclusive Diffraction at HERA

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  1. Inclusive Diffractionat HERA Valentina Sola Torino University • Diffraction in ep scattering • Latest inclusive diffractive ep results • Direct measurement of FLD at HERA

  2. Diffraction in ep Scattering Student Seminar - 14/05/2009

  3. vacuum quantum numbers LRG IP IP IP Elastic Single Dissociation Double Dissociation Diffraction in Hadron Scattering Diffraction is a feature of hadron-hadron interactions (30% of σtot)  Beam particles emerge intact or dissociated into low-mass states → Energy ≈ beam energy (within a few %)  Final-state particles separated by large polar angle (or preudorapidity η = - ln[tan(θ/2)] ) → Large Rapidity Gap (LRG)  Interaction mediated by t-channel exchange of object with vacuum quantum numbers (no colour) →Pomeron (IP) Student Seminar - 14/05/2009

  4. Why Diffraction? Optics: Particle Physics: Scattering elastico pp • diffractive maximum • secondary maxima decreasing for increasing energies • b  R2/4 : the t-slope b is related to the target size (R) Student Seminar - 14/05/2009

  5. Q2 e’ e W g* X p p’ p Non-diffractive event Diffractive event ep  e’X ep  e’Xp’ Q2 ’ ’ W X LRG IP t Diffraction at HERA LRG Diffractive events contribute to up to 15% of the inclusive DIS cross section Student Seminar - 14/05/2009

  6. q ~ 1/Q * q ~1/x Why Diffraction at HERA? Real and virtual photons can fluctuate in hadronic states γ* → vector meson, qq, qqg ... — — Q = 'negative mass' of the virtual photon x = Bjorken scaling variable (as seen in the proton rest-frame) At HERA very small x are reached: → long hadronic lifetime of the photon → diffractive photon-proton scattering in perfect analogy with diffractive hadron-hadron scattering Student Seminar - 14/05/2009

  7. Elastic vector meson scattering (VM) Single photon dissociation (γ SD) Single proton dissociation (p SD) Double dissociation (DD) Diffractive Processes at HERA • This seminar will concentrate on single photon dissociaton (γ SD) • → inclusive measurement • This seminar will not cover elastic vector meson scattering (VM) • → exclusive measurement • Proton dissociation (p SD & DD) represents a backgroud in both mesurements Student Seminar - 14/05/2009

  8. Q2 W xIP GAP t Kinematics of diffractive DIS Standard DIS variables: Q2 = virtuality of photon = = (4-momentum exchanged at e vertex)2 x = Bjorken scaling variable y = inelasticity s = Q2/xy = (ep centre-of-mass energy)2 tipically: √s = 318 GeV at HERA Diffractive DIS variables: W = invariant mass of γ*-p system MX = invariant mass of γ*-IP system xIP= fraction of proton momentum carried by IP ß = x/xIP = fraction of IP momentum carried by struck quark t = (4-momentum exchanged at p vertex)2 typically: |t| < 1 GeV2 ´ • N = proton →γ SD event • N = proton dissociative system → DD event represent a relevant background Student Seminar - 14/05/2009

  9. Hard-Scattering QCD Factorisation  Diffractive DIS, like inclusive DIS, is factorisable: [Collins (1998); Trentadue, Veneziano (1994); Berera, Soper (1996) ... ] σ(γ*p → Xp) ≈ fi/p(β,Q2,xIP,t)xσγ*i(β,Q2) σγ*i(β,Q2) = partonic cross section for the hard subprocess between γ* and the parton i  calculable in perturbative QCD fi/p(β,Q2,xIP,t) = diffractive parton distibution function (DPDF), describes the probability to find in the proton a parton of kind i carring a fraction xIPβ of its momentum with a probe of resolution Q2, under the condition that the proton stays intact with a momentum lost quantified by xIP and t  DPDFs are not known from first principles, but can be determined from fits to the data using the DGLAP evolution equations Consistency between the measured cross section for semi-inclusive processes (eg. γ*i→jets, γ*i→cc, ... ) and calculations using these DPDFs represent an experimental proof of the validity of the QCD factorisation hypotesys in diffraction Student Seminar - 14/05/2009

  10.  According to Regge phenomenology: σ(γ*p → Xp) ≈ fIP/p(xIP,t)xfi/IP(β,Q2)xσγ*i(β,Q2) Regge factorisation describes diffraction in terms of the exchange of a factorisable 'pomeron' with univer- sal parton densities fIP/p(xIP,t)= = pomeron flux factor αIP(t) = αIP(0) + αIP'(t) represents the probability that a pomeron with a particular value of xIP and t couples with the proton fi/IP(β,Q2) = parton distibution function of the diffractive exchange (IP), independent on the four-momemtum of the final state proton REMEMBER: β corresponds to the fraction of the pomeron longitudinal momentum carried by the struck quark ( = diffractive Bjorken scaling variable) At large xIP there is another factorisable sub-leading exchange (reggeon - IR) with different xIP dependence and partonic composition Proton Vertex Factorisation Student Seminar - 14/05/2009

  11. ZEUS Leading Proton Spectrometer (LPS) H1 Forward Proton Spectrometer (FPS) X xL = pz’/pz p' e' LPS, FPS PROS: no DD background direct measurement of t, xIP high xIP accessible CONS: low statistics LRG, MX PROS: near perfect acceptance at low xIP CONS: DD background Diffractive Event Selection Mass of the hadronic system (MX) has different shape between non-diffr DIS and diffr-DIS Large Rapidity Gap (LRG) between X and p' reflects in absence of activity in the forward part of the detector The scattered proton into the beam pipe can be detected by forward instrumentation (LPS, FPS) Student Seminar - 14/05/2009

  12. The diffractive cross section ep  e’Xp’as a function of the reduced cross section σrD : andσrD(4)(β,Q2,xIP,t) = F2D(4)(β,Q2,xIP,t) – y2/Y+·FLD(4)(β,Q2,xIP,t) F2D(4)→ constrains quark density → lnQ2 dependence constrains gluon density FLD(4)→ directly related to gluon density At low y (y < 0.5) the FLD(4) contribution to the reduced cross section is negligible and σrD(4)≈ F2D(4) Diffractive Cross Section • When t is not measured: σrD(3)(β,Q2,xIP)=∫σrD(4)(β,Q2,xIP,t)dt Student Seminar - 14/05/2009

  13. Latest Inclusive Diffractive ep Results Student Seminar - 14/05/2009

  14. H1 t Dependence of σ LPS/FPS data Fit to e-b|t|→b = 7.0 ± 0.4  b is independent on Q2, β and xIP Student Seminar - 14/05/2009

  15. xIP Dependence of σrD(4) LPS data From a fit to the data following vertex factorisation hypotesis with αIP(t) = αIP(0) + αIP'•t αIP(0) = + 1.11 ± 0.02 (stat) + 0.01 - 0.02 (sys) αIP' = - 0.01 ± 0.o6 (stat) + 0.04 - 0.08 (sys)  Low xIP: σrD(4) falls with xIP faster than 1/xIP  High xIP: xIPσrD(4) flattens or increases with xIP (IR)  Same xIP dependence in two t bins Student Seminar - 14/05/2009

  16. xIP Dependence of σrD(3) LRG data αIP(0) = 1.108 ± 0.008 (stat+sys)→ Assumption of Regge factorization works  Rise with xIP not visible, as xIP < 0.2 Student Seminar - 14/05/2009

  17. Q2 Dependence of σrD(3) Proton: Pomeron: Positive scaling violations → DPDFs are gluon dominated Student Seminar - 14/05/2009

  18. Q2 Dependence of σrD(3) MX data At fixed β the shape seems to vary with xIP → contraddiction of vertex factorisation hypotesis Data are consistent with BEKW fit, that does not assume factorisation [Bartels, Ellis, Kowalski, Wustoff in NPB 800 (008)]  Data are consistent with Regge factorization in many other tests  Mild violations should not affect QCD fits, which assume factorisation Student Seminar - 14/05/2009

  19. β Dependence of σrD(3) Proton: Pomeron: Different dependence on the scaling variable → different quark densities Student Seminar - 14/05/2009

  20. β Dependence of σrD(3) MX data BEKW fits to data as a function of β, at fixed Q2 and xIP, give informations about the nature of the interacting photon  rise toward β→ 0 γ* → (qqg)T  broad maximum at β~ 0.5 γ* → (qq)T  excess at β≥ 0.95 γ* → (qq)L Student Seminar - 14/05/2009

  21. Reduced cross section constrains qark density lnQ2 dependence constrains gluon density DPDFs Extraction Student Seminar - 14/05/2009

  22. DPDFS are gluon dominated: the inte-grated fraction of exchanged momen-tum carried carried by gluons is ~75% DPDFs Extraction - H1 NLO DGLAP fit: z fi(z,Q20) = Ai zBi (1-z)Ci at fixed Q2 and evolved with NLO DGLAP z = fractional momentum of parton ( 0 < β < z ) Fit A: Bg = 0 fixed Fit B: Bg= Cg = 0 fixed Student Seminar - 14/05/2009

  23. DPDFs Extraction - ZEUS NLO DGLAP fit: z fi(z,Q20) = Ai zBi (1-z)Ci at fixed Q2 and evolved with NLO DGLAP z = fractional momentum of parton ( 0 < β < z ) Regge factorization is assumed Fit S: Bg, Cg fitted Fit C: Bg = Cg = 0 fixed Student Seminar - 14/05/2009

  24. Test of QCD Factorization Use DPDFs extracted from DGLAP fits of σrD to predict cross section for semi-inclusive hard-processes (eg. γ*i cc or γ*i jets) Normalization and shape of data described ok  Hard scattering factorization works in diffractive DIS Student Seminar - 14/05/2009

  25. Direct Measurement ofF2D at HERA Student Seminar - 14/05/2009

  26. Backup Student Seminar - 14/05/2009

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