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Nowe kierunki badań struktury nukleonu

Nowe kierunki badań struktury nukleonu. Andrzej Sandacz. Instytut Problemów Jądrowych, Warszawa. Seminarium Fizyki Wielkich Energii, Uniwersytet Warszawski. 12 stycznia 2007. Kierunki tradycyjne. Rozkłady partonów. rozkłady prawdopodonieństw, niezależne od spinu bądź zależne od skrętności.

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Nowe kierunki badań struktury nukleonu

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  1. Nowe kierunki badań struktury nukleonu Andrzej Sandacz Instytut Problemów Jądrowych, Warszawa Seminarium Fizyki Wielkich Energii, Uniwersytet Warszawski 12 stycznia 2007

  2. Kierunki tradycyjne • Rozkłady partonów rozkłady prawdopodonieństw, niezależne od spinu bądź zależne od skrętności dla kwarków o różnych zapachach i dla gluonów dostępne w: DIS, SIDIS, DY, ‘twardych’ oddziaływaniach pp/ppbar, … dla ustalonej ‘twardości’ oddziaływania, zależą tylko od 1 zmiennej: ułamka pedu nukleonu niesionego przez parton(xBj) • Formfaktory nukleonów elektryczne, magnetyczne, aksjalne, dziwności, … zależą tylko od 1 zmiennej: kwadratu przekazu czteropędu (t) w reprezentacji położeniowej odpowiadają rozkładom prawdopodobieństw w płaszczyźnie prostopadłej do osi zderzenia

  3. Nowe kierunki • Uogólnione rozkłady partonów (GPDs) badane w‘twardych’ procesach ekskluzywnych e p → e p γ(DVCS) np. • Zależne od pędu poprzecznego (TMD) rozkłady partonów i funkcje fragmentacji badane poprzez asymetrie rozkładów azymutalnych w ‘twardych’ procesach SIDIS e p↑ → e π+X ==> m.in. Collins and Sieverseffects np. • Rozkłady poprzecznego spinu kwarków (transversity) analog tradycyjnych rozkładów partonów, ale dla spinu poprzecznego obecnie badane w ‘twardych’ procesach SIDIS

  4. Konferencje dot. GPDs and TMDs w 2006 Trento, Italy June 5 - 9, 2006 Villa Mondragone, Monte Porzio Catone Rome, Italy June 12 - 16, 2006 Hard Exclusive Processes at JLab 12 GeV and a Future EIC University of Maryland College Park October 29 - 30, 2006

  5. Plan referatu • Wprowadzenie • Modelowanie GPDs i obliczenia na sieci QCD • Orbitalny moment pędu kwarków • Dane doświadczalne dla DVCS • Tomografia hadronów • Efekt Sieversa • Planowane doświadczenia

  6. PD GPD GPD PDs and GPDs e p → e X e p → e p γ σ(γ*p →X) ~ σ(γ*p →γ p) ~| A(γ*p →γ p) |2 Im A(γ*p →γ*p)t=0 for given Q2 depends only on xB ( ≡ x) A(ξ, t) ξ≈ xB / (2 - xB) , xB = Q2/(2pq)

  7. Generalized Parton Distributions * Q2 >> 1 t = Δ2 low –t process : -t << Q2 x + ξ x - ξ P1,s1 P2,s2 GPD (x, ξ ,t)

  8. –ξ< x < ξ x > ξ x < –ξ out in out out in Properties of GPDs various parton processes embodied in a given single GPD

  9. Properties of GPDs forp = p’recover usual parton densities decouples forp = p’ needs orbital angular momentum between partons Dirac axial Pauli pseudoscalar Ji’s sum rule total angular momentum carried by quark flavour q (helicity and orbital part)

  10. Shorthand notation: Observables and their relationship to GPDs

  11. Other processes related to GPDs • exclusive meson production M = ρ, π, φ, J/ψ, … • meson distribution amplitude (DA) appears • access to different spin and flavour combinations of GPDs of quarks and gluons • 2 π production similar to EMP • crossed channels γ* γ→p pbar, ππ, ρρ, … generalised distribution amplitudes (GDAs) analogs of GPDs DA GDA • wide angle scattering all invariants (s, t, u) large vs. γp→γp, γ* γ→p pbar, …

  12. Diehl, Jakob, Feldmann and Kroll (2005)

  13. Aq, Bq fitted to F1p and F1n Cq, Dq fitted to F2p and F2n (fitting of α’ optional) shape of profile functions motivated by Regge phenomenology (small x and t ) assuming dominance of a single Regge pole:

  14. OAM from QCD Lattice calculations Note: here Hq(x,Δ2) ≡ Hq(x,ξ=0,Δ2) , etc.

  15. OAM from QCD Lattice calculations

  16. QCD Lattice calculations

  17. from QCDSF Collaboration (Lattice) Diehl, Jakob, Feldmann and Kroll (2005) from fits to nucleon formfactors Ju = 0.20 ÷ 0.23 Jd = –0.04 ÷ 0.04 Lu+d = –(0.06 ÷ 0.11 ) Lu-d = –(0.39 ÷ 0.41 )

  18. Deeply Virtual Compton Scattering ep→epg The same final state in DVCS and Bethe-Heitler interferenceI up to twist-3 BMK (2002) P1 (Φ), P2 (Φ) BH propagators ciDVCS, siDVCS, ciI, siI depend on spin orientations of lepton and nucleon Fourier coefs with twist-2 DVCS amplitudes (related to GPDs) c0DVCS, c1I, s1Iand c0I(the last one Q suppresed) interference + structure of azimuthal distributions + Q2 dependence a powerful tool to disantangle leading- and higher-twist effects and extract DVCS amplitudes including their phases

  19. Available experimental data on DVCS (1) lepton charge or single spin asymmetries at moderate and large xB HERMES and JLAB results • beam-charge asymmetry AC(φ) • beam-spin asymmetry ALU(φ) • longitudinal target-spin asymmetry AUL(φ) • transverse target-spin asymmetry AUT(φ,φs) F1and F2 are Dirac and Pauli proton form factors

  20. epg VGG with TM correction Open symbols raw asymmetry Filled symbols asymmetry corrected for p0 Beam SSA after correction for p0 contaminationfrom CLAS Two data sets (e16 at 5.7 GeV,e1f at 5.5 GeV) with different torus field (different kinematic coverage) and beam energy are consistent.

  21. cross section σDVCS averaged over φ for unpolarised protons H1 and ZEUS Available experimental data on DVCS (2) Hsea, Hg at small xB ( < 0.01) Q² dependence: NLO predictions b assumed Q2-independent no intrinsic skewing bands reflect experimental error on b: 5.26 < b < 6.40 - Wide range of Q2 - sensitivity to QCD evolution of GPDs - Difference between MRS/CTEQ due to different xG at low xB

  22. W dependence: NLO predictions 1996-2000 Meaurements of b significantly constrain uncertainty of models Older H1 (prel.) measurement on 2000 data with a b value in the range [4 - 7] GeV-2

  23. Impact parameter representation and probabilistic interpretation Note: hereHq(x,Δ2) ≡ Hq(x,ξ=0,Δ2)

  24. ( η≡ξ)

  25. uV dV

  26. in ┴ polarized proton uV dV

  27. Deformation of quark space distribution in transversely polarised nucleon note:j denotes current (not angular momentum)

  28. up down Final-state interactions Side view Front view photon NOTE: QCD tells us that the FSI has to be attractive, since quark and remnants form a color antisymmetric state Chromodynamic lensing

  29. Sievers effect Deformation of quark distribution in transversely polarised nucleon and Final state interaction kT asymmetry of ejected (unpolarised) quarks

  30. kTandpT

  31. comparison with HERMES identifiedπ’sand K’s COMPASS – pol. deuterons HERMES – pol. protons

  32. Selected projects of future DVCS measurements

  33. CLAS12-DVCS/BH Target Asymmetry e p epg Transversely polarized target Sample kinematics E = 11 GeV Q2=2.2 GeV2, xB = 0.25, -t = 0.5GeV2 DsUT~ sinfIm{k1(F2H– F1E) +…}df AUTx Target polarization in scattering plane AUTy Target polarization perpendicular to scattering plane • Asymmetry highly sensitive to the u-quark contributions to the proton spin.

  34. Recoil detector design ‘‘COMPASS+’’ Goals:Detect protons of 250-750 MeV/c t resolution => sTOF = 200 ps exclusivity => Hermetic detector Design : 2 concentric barrels of 24 scintillators counters read at both sides European funding (127 k€) through a JRA for studies and construction of a prototype ( Bonn, Mainz, Saclay, Warsaw)

  35. E in B (MeV) deuterons protons Outer Layer Inner Layer 15° CH Target B1 A2 A1 B0 i 25cm A0 110cm Measured β Experimental set-up for the recoil prototype test run in 2006 All scintillators are BC 408 A: 284cm x 6.5cm x 0.4cm Equiped with XP20H0 (screening grid) B: 400cm x 29cm x 5cm Equiped with XP4512 Resolution on TOF Center 340ps HV low Center 310ps HV high Expected resolution 280 ps

  36. Projected errors of a planned DVCS experiment at CERN Beam Charge Asymmetry L = 1.3 1032 cm-2 s-1 Ebeam = 100 GeV 6 month data taking 25 % global efficiency 6/18 (x,Q²) data samples 3 bins in xBj= 0.05, 0.1, 0.2 6 bins in Q2 from 2 to 7 GeV2 Model 1 : H(x,ξ,t) ~ q(x) F(t) Model 2 : H(x,0,t) = q(x) / xα’t Good constrains for models

  37. eRHIC HEsetup σ(γ*p →γ p) [nb] Lint = 530 pb-1 (2 weeks) <W> = 37 GeV Q2[GeV2] Precision of DVCS unpolarized cross sections at eRHIC HEsetup:e+/-(10 GeV) + p (250 GeV)L = 4.4 · 1032 cm-2s-1 38 pb-1/day For one out of 6 W intervals (30 < W < 45 GeV) • eRHIC measurements of cross section will provide significant constraints

  38. Podsumowanie From Stone Age to Bronze Age… powerfull tool to study DVCS amplitudes

  39. Backup slides

  40. HERMES Beam spin and charge asymmetry Beam Spin Asymmetry Beam Charge Asymmetry [PRL87,2001] symmetrizationf → |f| (cancel sin f terms from polarized beam) [hep-ex/0605108, subm. to PRL] e+/- p→ e+/- p g (MX<1.7 GeV) ─ P1 + P2 cos f + P3 cos 2f + P4 cos 3f L=140 pb-1 L=10 pb-1 P1 = -0.01±0.02 P2 = 0.06±0.03 P3 = 0.02±0.03 P4 = 0.03±0.03 <-t> = 0.12 GeV2,<xB> = 0.1, <Q2> = 2.5 GeV2

  41. Deep Exclusive experiments Published ….. Preliminary results 2004 2005 ……… ….. 2009 ? … 2010 JLab@ 12GeV HERA 27.5-900 GeV DVCS HERMES 27 GeV DVCS – BSA + BCA + nuclei d-BSA d-BCA ep→epρ σL + DSA ep→enπ+ + …. CLAS 4-5 GeV DVCS BSA CLAS 5.75 GeV DVCS DDVCS ΔDVCS D2VCS Polarized DVCS ep→epρL ep→epωL ep→epπ0/η ep→enπ+ ep→epΦ Hall A 6 GeV DVCS proton neutron ep→epπo CLAS 6 GeV DVCS Proton ep→epπo/η HERMES DVCS BSA+BCA With recoil detector COMPASS DVCS s+BCA With recoil detector EVERYTHING, with more statistics than ever before

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