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Inclusive diffractive DIS

Inclusive diffractive DIS. Marta Ruspa Univ. of Eastern Piedmont-Novara and INFN-Torino (Italy) XII International Workshop on Deep Inelastic Scattering Strbske Pleso, High Tatras, Slovakia April 14-18, 2004 on behalf of.

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Inclusive diffractive DIS

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  1. Inclusive diffractive DIS Marta Ruspa Univ. of Eastern Piedmont-Novara and INFN-Torino (Italy) XII International Workshop on Deep Inelastic Scattering Strbske Pleso, High Tatras, Slovakia April 14-18, 2004 on behalf of • Diffractive cross section and diffractive structure function • Comparison with colour dipole models • NLO QCD fit

  2. Inclusive diffraction γ*p  Xp Q2 = virtuality of photon = = (4-momentum exchanged at e vertex)2 t = (4-momentum exchanged at p vertex)2 typically: |t|<1 GeV2 W = invariant mass of photon-proton system MX = invariant mass of photon-Pomeron system xIP = fraction of proton’s momentum taken by Pomeron ß = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP e’ Q2 e g* W MX xIP IP p p’ t Exchange of an object with the vacuum q. n.  Proton almost intact after the collision

  3. Diffractive DIS in the Breit frame (Breit frame) • DIS of a pointlike virtual photon off the exchanged object • PDFs HARD SCATTERING FACTORISATION fi/pD(z,Q2,xIP,t): probability to find in a proton, with a probe of resolution Q2, parton i with momentum fraction z, under the condition that the proton remains intact and emerges with small energy loss, xIP, and momentum transfer,t Diffractive Deep Inelastic Scattering probes the diffractive PDFs of the proton relevant when the vacuum quantum numbers are exchanged

  4. Lifetime of dipoles very long due to large γ boost (E γ ~ W2 ~ 1/x  50TeV ! )it is thedipole that interactswith theproton ! • Transverse size of dipoles proportional to  can be so small • that the strong interaction with proton can be treatedperturbatively ! Diffractive DIS in the colour dipole picture We can learn more about the structure of the proton by studying DDIS in a frame in which the virtual photon is faster than the proton (γ* much faster than p) 2 gluon exchange: LO QCD realisation of vacuum q.n.

  5. Diffractive DIS in the colour dipole picture We can learn more about the structure of the proton by studying DDIS in a frame in which the virtual photon is faster than the proton (γ* much faster than p) 2 gluon exchange: LO QCD realisation of vacuum q.n. • BEKW model : at medium β; at small β • saturation model : : as Q2  0, • growth tamed by requiring saturation

  6. Inclusive diffraction γ*p  Xp Exchange of color singlet producing a GAP in the particle flow e p • No activity in the forward direction MX method • Proton suffers only a small energy loss

  7. Selection of events γ*p  Xp with Mx method Properties of Mx distribution: - exponentially falling for decreasing Mx for non-diffractive events - flat vs ln Mx2 for diffractive events Diffr. Non-diffr. Non-diffr. Diffr. • Forward Plug Calorimeter (FPC): • CAL acceptance extended by 1 unit in pseudorapidity from η=4 to η=5 • higher Mx and lower W • if MN > 2.3 GeV deposits EFPC > 1 GeV recognized and rejected! c, bfrom fit n.d. events subtracted contamination fromreaction epeXN

  8. Inclusive diffraction γ*p  Xp Exchange of color singlet producing a GAP in the particle flow e p • No activity in the forward direction MX method • Proton suffers only a small energy loss LPS method

  9. Selection of events γ*p  Xp with LPS Diffractive peak • Free of p-diss background • Low acceptance •  low statistics

  10. 97 LPS sample 0.03 < Q2 < 100 GeV2 25 < W < 280 GeV 1.5 < Mx < 70 GeV xIP< 0.1 Higher xIP region 99-00 FPC sample (Mx method) 22 < Q2 < 80 GeV2 37 < W < 245 GeV Mx < 35 GeV MN < 2.3 GeV Higher β region Data samples

  11. Cross section and structure function diffractiveγ*p cross section • diffractive structure function (assumes )

  12. F2D(3)xIPdependence (LPS) Regge fit (xIP<0.01): with Data agree with Regge factorisation assumptionin the region of the fit xIPdep. of F2D(3) equivalent to W dep. of dσ/dMx(1/xIP ~ W2)

  13. Cross section W dependence (Mx method) p-dissociation events with MN<2.3 GeVincluded MX< 2 GeV: weak W dep. MX> 2 GeV: d/dMX rises with W power-like fit

  14. αIP from diffractive and total γ*p scattering (Mx method) fit to diffractive cross section data: • IPdiff higher than soft Pomeron • Evidence of a rise of IPdiff with Q2  mild Regge factorisation violation . fit to total cross section data: • Similar W dep. of diffractive and total cross section

  15. σdiff/ σtot W and Q2 dependence (Mx method) Regge expectation: BUT ratio ~ flat in W Explained by saturation model [hep-ph 0203258] • low MX :strong decrease of diff/tot with increasing Q2 • high MX :no Q2dependence !

  16. Cross section Q2 dependence (LPS) Transition to a constant cross section as Q20 (similar to total cross section ) Main features of the data described by BEKW parametrization (xIP<0.01) (Bartels, Ellis, Kowalski and Wüsthoff) medium β small β qqg fluctuations dominant at low Q2

  17. F2D(3) Q2 dependence (LPS) (prel.) Data well described by BGK saturation model (xIP<0.01) Positive scaling violation at all values of β QCD fit

  18. NLO QCD fit on LPS+charm data • xIP <0.01 • QCDNUM • Regge factorisation assumption possible for this small data set • DL flux • initial scale Q2=2 GeV2 • zf(z)=(a1+a2z+a3z2)(1-x)a4 • other PDFs parametrisation tried • Thorne-Robert variable-flavour-number-scheme (LPS) QCD fit describes data fractional gluon momentum is at initial scale [F2D(3)cc from DESY-03-094, see N. Vlasov talk]

  19. LPS QCD fit compared to Mxdata ZEUS (MX method) NB: fits scaled by 0.69 to account for p-diss background in Mx data Mx method data described by the fit in the region of overlap LPS-Mxmethod Main discrepancies at high β, where no LPS data available

  20. xIP.F2D(3)/F2Q2 and xBJ dependences (LPS) (LPS) Compare the proton structure function for events with a leading proton and without Nearly the same Q2 dep. (excepthigh β and low xIP) Different behaviour vs x at low xIP

  21. Summary • Recent data from ZEUS with improved precision and extended kinematic range • Data described by colour dipole models (BEKW, saturation) • Data described by a NLO QCD fit  lots of gluons • Possible indication that αIP increases with Q2 in diffraction • W dep. of diffractive and total cross section similar at high Q2

  22. RESERVE

  23. Lifetime of dipoles very long due to large γ boost (E γ ~ W2 ~ 1/x  50TeV ! )it is thedipole that interactswith theproton ! • BEKW model : at medium β; at small β • saturation model : (colour transparency) • as Q2  0, growth tamed by saturating • Transverse size of dipoles proportional to  can be so small • that the strong interaction with proton can be treatedperturbatively ! Diffractive DIS in the proton rest frame We can learn more about the structure of the proton by studying DDIS in a frame in which the virtual photon is faster than the proton (γ* much faster than p) 2 gluon exchange: LO QCD realisation of vacuum q.n.

  24. Inclusive diffraction γ*p  Xp Q2 = virtuality of photon = = (4-momentum exchanged at e vertex)2 t = (4-momentum exchanged at p vertex)2 typically: |t|<1 GeV2 W = invariant mass of photon-proton system MX = invariant mass of photon-Pomeron system xIP = fraction of proton’s momentum taken by Pomeron ß = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP e’ Q2 e g* W MX xIP IP p p’ t Exchange of an object with the vacuum q. n.  Proton almost intact after the collision

  25. Diffractive DIS in the Breit frame (Breit frame) HARD SCATTERING FACTORISATION fi/pD(z,Q2,xIP,t): probability to find in a proton, with a probe of resolution Q2 parton i with momentum fraction z, under the condition that proton remains intact and emerges with small energy loss, xIP, and momentum transfer, t diffractive PDFs are a feature of the proton Diffractive Deep Inelastic Scattering probes the diffractive PDFs of the proton relevant when the vacuum quantum numbers are exchanged

  26. Inclusive diffraction γ*p  Xp Exchange of color singlet producing a GAP in the particle flow e p  No activity in the forward direction  Proton almost intact after the collision diffractiveγ*p cross section • diffractive structure function (assumes )

  27. Cross section and structure function • xIP dependence of F2D(3) and W dependence of dσ/dMX • - extraction of αIP • - Regge factorisation • Q2 dependence of F2D(3) and dσ/dMX • -sensitivity to diffractive • PDFs • comparison to BEKW model and to saturation model diffractiveγ*p cross section • diffractive structure function (assumes )

  28. F2D(3) β dependence (LPS) Different β dep. at low and high xIP Data well described by BGK saturation model (xIP<0.01)

  29. F2D(3) at fixed xIP (Mx method) Maximum near β=0.5 consistent with a β(1- β) behaviour suggesting main contribution from a quark-antiquark state For high β F2D(2) decrease with rising Q2 As β  0 F2D(2) rises. The rise becomes stronger as Q2 increases Evidence for pQCD evolution

  30. MICHELE

  31. r sqq Saturation g* r pQCD npQCD • Connection to high-density QCD, • saturation of parton densities, • Colour Glass Condensate, • geometric scaling, physics of RHIC ~1/Qs small x large x Part III: saturation (how dense is the proton at low x ???) • pQCD: sqq r21/Q2 • (colour transparency) • As Q2  0, sqq  • violation of unitarity • Growth tamed by sqq saturating • at sqq s(rp) • Saturation occurs at • “saturation scale” • Qs2(x)  [xg(x)]  (x0/x)l • with x010-4, l0.3 • (proton denser at small x) cf talks by S. Munier, D. Kharzeev, C. Marquet

  32. Saturation vs data Inclusive DIS: Inclusive diffraction: xIPF2D(3) F2 Diffraction more sensitive to saturation than inclusive: mainly probe intermediate dipole sizes, close to saturation Q2 Golec-Biernat,Wuesthoff, Bartels, Golec-Biernat, Kowalski Also good description of VM, DVCS...

  33. Standard Deep Inelastic Scattering For Q2<< MZ2: In a frame in which the proton is very fast (Breit frame): x = Bjorken’s variable= = fraction of proton’s momentum carried by struck quark  Q2/W2 W = photon-proton centre of mass energy y = W2/s Q2 W F2=Si[ei2 x fi(x,Q2)] DIS probes the partonic structure of the proton R=sL/sT proton PDF

  34. Diffractive Deep Inelastic Scattering e’ Q2 xIP = fraction of proton’s momentum taken by Pomeron = xinFermilab jargon b = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP e g* xIP IP p p’ t F2D(4)  fIP (xIP,t) F2IP (b,Q2) Naively, if IP were particle: [Ingelman, Schlein] Flux of Pomerons “Pomeron structure function”

  35. Diffractive DIS Q2 = virtuality of photon = = (4-momentum exchanged at e vertex)2 t = (4-momentum exchanged at p vertex)2 typically: |t|<1 GeV2 W = invariant mass of photon-proton system MX= invariant mass of photon-Pomeron system xIP = fraction of proton’s momentum taken by Pomeron = x in Fermilab jargon b = Bjorken’s variable for the Pomeron = fraction of Pomeron’s momentum carried by struck quark = x/xIP e’ Q2 e g* W MX xIP IP p p’ t Previous talk: Diffractive Deep Inelastic Scattering probes the diffractive PDFs of the proton, relevant when the vacuum quantum numbers are exchanged N.B. will drop e, e’ from the diagrams in the rest of the talk

  36. (Diffractive) hard scattering factorisation Diffractive DIS, like inclusive DIS, is factorisable[Collins (1998); Trentadue, Veneziano (1994); Berera, Soper (1996)…]: universal partonic cross section diffractive parton distribution functions: evolve according to DGLAP fi/pD(z,Q2,xIP,t): probability to find, with probe of resolution Q2, in a proton, parton i with momentum fraction z, under the condition that proton remains intact, and emerges with small energy loss, xIP, and momentum transfer t – diffractive PDFs are a feature of the proton A new type of PDFs, with same dignity as standard PDFs. Applies when vacuum quantum numbers are exchanged Rather than IP exchange: probe diffractive PDFs of proton

  37. g* X X p p p p + X p Diffractive DIS in the proton rest frame IP 2-gluon exchange: LO realisation of vacuum quantum numbers in QCD ! Cross section proportional to probability of finding 2 gluons in the proton Gluon density in the proton

  38. Part I:The colour dipole approach • The picture discussed in the previous talk emerges in a frame in which the proton is fast (the Breit frame) • Can learn more about the structure of the proton by studying diffraction in a frame in which the virtual photon is faster than the proton. Find out that in exclusive processes • sdiffr [gluon density in proton]2 • Example: exclusive vector meson production • Calculable in QCD ! • Correlations in the proton: Generalised Parton Distributions (GPDs)

  39. g* g* • Lifetime of dipoles very long because of large g boost (Eg 50TeV!) •  it is the dipole that interacts with the proton • Transverse size proportional to 1/  (Q2+ Mqq2) • (for longitudinally polarised photons) • This is why can do diffraction in ep collisions ! Transverse size of incoming hadron beam can be reduced at will. Can be so small that strong interaction with proton becomes perturbative (colour transparency) ! The colour dipole picture Virtual photon fluctuates to qq, qqg states (colour dipoles)

  40. Factorization • QCD Hard Scattering factorization (by Collins;Trentadue, Veneziano; Berera, Soper…:) At fixed xIP and t diffractive Parton Densities evolve according to DGLAP • Regge factorization - “resolved IP model”(IP with partonic structure): (Breit frame) Regge motivated pomeron flux Shape of diffractive pdfs independent of xIP and t

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