QCD at HERA. Hans-Christian Schultz-Coulon Universität Heidelberg CORFU 2005

Transcription

1 QCD at HERA Hans-Christian Schultz-Coulon Universität Heidelberg CORFU 25 Corfu Summer Institute on EPP Corfu, September 9 th, 25

2 ... that means... proton structure F 2 quark- & gluon-pdfs ( LHC), Δα s /α s ~ 1% (NNLO) F 2 at small Q 2, non-perturbative QCD F 3, PDFs at large (HERA II!)... heavy quarks universality of proton structure (gluon-pdf!) fragmentation, production mechanisms, c/b-pdfs... diffraction and low- physics QCD dynamics at high parton densities... structure of diffractive interactions, factorization DVCS parton-parton correlations (GPDs) jet physics universality of proton structure (gluon-pdf!) parton dynamics, measurement of α s spectroscopy pentaquarks...

3 Nobelprize 24 Coloured Quarks D.J.Gross, H.D. Politzer & F. Wilczek Interaction strength QCD Confinement quarks always bound mass of proton! QED Daten von CERN, Cornell, DESY, KEK and SLAC Gluons Asymptotic freedom perturbative QCD quasi-free partons Low energy Large distances High energy Small distances

4 We know: QCD is the theory of the strong interactions! Why then QCD at HERA? and elsewhere...? Because:... the strong coupling α s is the least well known of the coupling constants... we do not understand how partons are put together to make hadrons... we need to understand future high energy eperiments at the LHC...

5 Masses of Bound States Ratio of the mass of the parts to the mass of the whole: Positronium [e + e - ]: kev/122 kev = 1 Bottonium [bb]: GeV/9.5 GeV =.9 Pion [ud]: (3 + 6) MeV/135 MeV =.7 - Proton [uud]: ( ) MeV/938 MeV =.1 Proton mass =! E B Understanding mass needs understanding of IA inside proton

6 Electron HERA: maimum resolution: h/q ~ 1 m Proton Ideal QCD laboratory

7 DIS Kinematics Electron (e ± ) k Q 2 : four-momentum transfer Q 2 [spatial resolution ~ 1/Q] : : fractional momentum : of the struck quark! k Electron (e ± ) Q 2 = -q 2 = -(k-k ) 2 P q y = Pq/Pk: inelasticity fractional energy transfer in proton rest frame P q = P X Proton P Q 2 = sy [ s: cms-energy] [ " " 1; " y " 1]

8 e Electron-Quark scattering (spinless case) q Structure Function F 2 $ e q d! ( eq) dq 2 = 4"# e 2 2 q 4 q Rutherford scattering on pointlike target d! ( ep) dq 2 q() 1/3 4"# = [ 2e2 u + e2 d ] = q 4 Naive QPM p = uud > = 1/3 4"# q 4 With quark-quark interactions q() d! ( ep) ddq 2 = 4"# [ e 2 q 4 u u( ) + e 2 d d( ) + ] = 4"# F ( ) q 4 QPM: Structure Function F 2 independent of Q 2 1/3

9 Electron (e ± ) Electron (e ± ) Cross Section: d! ~ d! eq "F 2 γ q q Proton SF F 2 = # 2 e q q() describes structure of proton probability to find quark with momentum fraction QPM: independent of Q 2. Correct? Proton Remnant

10 Scaling [SLAC 1972] F 2 Q 2 [GeV 2 ]

11 Scaling Violations [199++] SLAC 1972

12 The QCD Picture of Scaling Violation Proton quark dominated: Q 2 F 2 for fied Proton gluon dominated: Q 2 F 2 for fied Q 2 -evolution described by DGLAP equations

13 QCD Improved Parton Model 1 F 2 ( ) = $ # e 2 q d! q (!)"! = $ e 2 q q( ) q q!p QPM QCD z = /! F 2 ( ) $ e q 2 # = ---- d! q (!) " 1 --! % '!& ( ) s P qq -- 2* % '!& ( Q 2 + log µ 1!P k, k T +, - q. qg +, - q. qg / / µ : cutoff parameter ) s P 2* qq ( z) µ 2 Q 2 # dk T k T 2 ) s P 2* qq ( z) log Q µ 2 q(, Q 2 ) = q( ) q(, µ 2 ) = q( ) + + ) s Q 2 1 log * µ 2 # ) s µ 2 1 log * µ 2 # dz P z qq z dz P z qq z ( ) q( z) ( ) q( z) (A) (B) Splitting function: Probability to find quark with momentum fraction z of a parent quark having emitted a gluon with momentum (1-z) q(, Q 2 ) = q(, µ 2 ) + ) s Q 2 1 log * # µ 2 dz P z qq z ( ) q( z) (A)-(B)

14 DGLAP Equations DGLAP: Dokshitzer, Gribov, Lipatov, Altarelli, Parisi DGLAP evolution equations arise from requirement that q(,q 2 ) should not depend on the choice of scale µ: & $ s Q 2 1 dz log P 2% µ 2 z qq ( z) q( z & ) dq(, µ 2 1 ) $ = s d logµ dz P 2% & z qq ( z) q( z) =! q(, Q 2 ) = q(, µ 2 ) dq(, Q 2 ) d logµ 2! " # dq(, µ 2 ) d logµ 2 = $ s 2% & 1 From iteration dz P z qq ( z) q( z, µ 2 ) z 2 1 z [ z2 + ( 1 z 2 )] PDFs ( 1 z) z 6 z z 1 z z( 1 z) z

15 F 2 at Low Bjorken- [Pre-HERA Knowledge] DGLAP: No prediction for the -dependence of F 2 [ecept asymptotic behaviour] A. De Rujula et.al Fied Target Measure!!

16 Q Accessing Lower Bjorken- HERA Eperiments Fied Target Eperiments Q 2 =sy access to highest Q 2 y = 1 [HERA: s ~ 1 5 GeV 2 ] y = 1 [Fied Target: s < 1 3 GeV 2 ] Fied Target: 1 1 accessing lower at fied Q 2 needs higher s s = 2M p E e s = 1 5 GeV! E e = 5 TeV ep-collider: 1-1 access to lowest at very low Q s = 4E p E e E e = 3 GeV E p = 9 GeV! s = 1 5 GeV

17

18 HERA Tunnel

19 The HERA Accelerator Comple [27.6 GeV] e Halle Nord H1 e p 36m R=797m [92 GeV] p Halle Ost HERMES NW e p HERA- Halle West N NO Halle West HERA-B HERA Trabrennbahn 36m s Stadion Stellingen = 32 GeV W Kältehalle PETRA Magnet- Testhalle H -Linac DESY II/III e PIA + e -Linac e --linac p O Proton ring: Energy*: 92 GeV Mag. Field: T Current: ~ 1 ma * before 1998: 82 GeV ZEUS Halle Süd Electron ring: SW Energy: 27.5 GeV Mag. Field:.164 T Current: ~ 4 ma General: Proton bypass SO Energy in cms: 318 GeV Circumference: 6.3 km BX rate: 1.4 MHz Lumi: cm -2 s -1

20 HERA Detectors ZEUS Uranium Calorimeter!(E)/E = 18% E for electrons!(e)/e = 35%/ E for hadrons Central Tracker Resolution!(p t )/p t =.58 p t /GeV ".65 H1 LAr Calorimeter!(E)/E = 12%/ E for electrons!(e)/e = 5%/ E for hadrons Central Tracker Resolution!(p t )/p t =.6 p t /GeV ".2 Central Muon System Forw. Tracking Central Tracking Silicon Detectors [ZEUS Collaboration] e FPS FNC ToF ToF Lumi p Forw. Muon System Toroid Solenoid SpaCal [H1: Schematic View] LAr-Calorimeter

21 TEST Typical DIS-Event [as seen by the H1 detector] Calorimeter Scattered Quark Backward Electrons Forward! Scattered Electron Q 2 Protons Trackers Q 2 = 4E e E e cos 2 (!/2)

22 ep Cross Section [low Q 2 approimation] Rutherford Proton Structure + q F 2 (, Q 2 ) = e 2 q q, Q 2 [ ( ) + q(, Q 2 )] ( ) * Evolution according to DGLAP d 2! = 4"# F ddq 2 Q 4 2, Q 2 1 ( ) $ [ 1 + ( 1 y) 2 ] y 2 F L ( ) * % &' ~ influence small related to gluon density [contribution high y] [LO: F L =] Considering spin e Before spin e Before q q q q After d e After 1 d 11 e M 2 y - J 2 d,,,' pq E p E e ( 1 cos. * ) = = = pk 2E p E e d, = cos. d * 1, 1 = ( 1 cos. * ) M ( 1 y) 2 y-dependence describes helicity structure of interaction

23 Q 2 (GeV 2 ) Structure Function F 2 [Principle of Measurement] ZEUS > 25 Events > 65 Events > 1 Events < 1 Events Basic (simplified) Procedure:! $ 4"# F 2 Q 4 2 % &' ( and! F 2 = = In reality much more difficult as acceptances, backgrounds, higher order corrections etc. have to be taken into account. N L N (L N: Number of events L : Luminosity y=1 y=1-1 y= Kinematic limit 1 Q 2 =15 GeV

24 MRS D,D - : Fit to fied target data only Different assumptions on g(,q 2 ) H1 '92 MRS D - F Q 2 =15 GeV HERA MRS D CTEQ5D MRST99 ZEUS 96/97 H1 96/97 NMC, BCDMS, E Fied Target 2-3% Precision

25 F 2 [!2 i ] =.5, i = 21 =.8, i = 2 =.13, i = 19 =.2, i = 18 =.32, i = 17 =.5, i = 16 =.8, i = 15 =.13, i = 14 =.2, i = 13 =.32, i = 12 =.5, i = 11 =.8, i = 1 =.13, i = 9 =.2, i = 8 =.32, i = 7 H1 e + p =.5, i = 6 ZEUS e + p BCDMS NMC =.8, i = 5 =.13, i = 4 =.18, i = 3 = =.13 =.18 Scaling Violations [HERA & fied target data] Precision: 2-3% [bulk region] For < 1-2 : df 2 dlogq ~ g(,q 2 )." s (Q 2 ) NLO QCD Fits: =.25, i = 2 =.4, i = 1 Quark densities Gluon density Strong coupling " s H1 PDF 2 Etrapolation =.65, i = =.65 Q 2 [GeV 2 ]

26 QCD Fits: Principle Fit Procedure Parametrize parton distribution functions (PDFs) at starting scale Q 2 = Q 2 as function of. Perform QCD evolution using DGLAP equations. [usually NLO, special treatment of heavy quark PDFs] Calculate predictions for eperimental observables. [cross sections, structure functions,...] Determine PDF parameters from! 2 -fit to eperimental data. For p = u v, d v, " ( q + q), g or p = u + d, u d, s: 2 p(, Q ) A p ap ( 1 ) b p = P( ; c p,...) characterizes PDFs at =. [sea: a p <, valence: a p >] characterizes PDFs at = 1. [b p > for all PDFs] weakly -dependent function. [ fine tuning ]

27 QCD Fits: Inputs Fied target data l p! l p: BCDMS, NMC, E Fied target data l p! "p: CCFR, CDHS, BEBC... H1, ZEUS data structure function and cross H1, ZEUS data section measurements Sum rules: # u v ( ) d = 2, # d v ( ) d = 1, ) * # d ' g( ) + $ [ q( ) + q( ) ] ( = 1, % & I # d G ( ) 1 2 = = # d ( u d). 3 3 F 2 lp F 2 ln Other eperimental data: pp! W + X qq! W u, d, u/d "N! µ + µ + X "s! µc s pp, pn! l + l + X qq! l + l d /u hh! + + X qg! q+ g pp! jets ± X gg! gg, qg!... g Valence quarks Momentum sum rule Gottfried sum rule [Eperiment (NMC): I G =.235 ±.26! u > d ]

28 Comparison H1 vs. ZEUS H1! s fit: H1 PDF fit: ZEUS PDF fit: Dedicated to! s and g(). H1 ep NC data (low Q 2 ) & BCDMS µp data. Parametrization of valence, sea quark and gluon. Starting scale: Q 2 = 4 GeV 2.! s = ±.5 Dedicated to PDF-determination. Fit A: H1 data only (NC, CC, low & high Q 2 ). Fit B: H1 data & BCDMS µp data. Parametrization of U, U, D, D and gluon. Starting scale: Q 2 = 4 GeV 2. scale uncertainty ep. & model uncertainty Dedicated to PDF-determination (main goal). Simultaneous fit to strong coupling constant. Data: ZEUS NC data, BCDMS, NMC, E665, CCFR. Starting scale: Q 2 = 7 GeV 2.! s = ±.4 ep. & model uncertainty scale uncertainty

29 2234!! eperimental uncertainty theoretical uncertainty &%,!6 H1: NLO QCD fit [Eur. Phys. J. C 21 (21) 33] ZEUS: NLO QCD fit [Phys. Rev. D 67 (23) 127] S. Bethke: World Average [hep-e/21112] J. Santiago, F.J. Yndurain [hep-ph/12247] α s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

30 !"#$%&'()&*+$+)*','-./'/)*12$*!" # $!% f(,q 2 ) 1..8 H1 PDF 2 ZEUS-S PDF Q 2 =1 GeV 2 &'()#*(+ &'()#*(, u V 1..8 H1 PDF 2 ZEUS-S PDF CTEQ6.1 Q 2 =1 GeV 2 u V.6.6 g(.5) g(.5).4 d V.4 d V S(.5) S(.5) ! !

31 g 2 1 ZEUS NLO QCD fit Q 2 =1 GeV GeV 2 tot. error (α s free) tot. error (α s fied) uncorr. error (α s fied) Eample: ZEUS Fit GeV GeV 2 Low- gluon PDF determined by HERA precision data Fied Target data constrain valence quark distributions 1.5 Uncertainty of gluon PDF: ~ 1% [for Q 2 > 2 GeV 2, 1-4 < < 1-1 ] Simultaneous etraction of PDFs and as! uncertainties larger. 2 2 GeV 2 2 GeV 2 Important input for LHC

32 Possible Impact of d -u Asymmetries H1 + BCDMS H1 + BCDMS [a u, a d, b u, b d constrained] [a u, a d, b u, b d unconstrained] P().8 P() U U!!.6.4 U U.2 u v.2 u v D D!!.6 D D d v.2 d v g PDFs at Q 2 = 4 GeV 2 eperimental errors model uncertainties g PDFs at Q 2 = 4 GeV 2 eperimental errors model uncertainties parton distribution parton distribution Enforce: (d - u " ) a u, a d, b u, b d : free parameters

33 1 9 LHC parton kinematics 1 8 1,2 = (M/14 TeV) ep( ± y) Q = M M = 1 TeV M = 1 TeV LHC Q 2 (GeV 2 ) M = 1 GeV 1 3 LHC needs: 1 2 y = M = 1 GeV 6 knowledge on parton densities 1 1 HERA fied target etrapolation over orders of magnitude

34 The Gluon Density, LHC and the Higgs ~1 GeV ~1 TeV M 2 = 1 2 s =:!s H Gluon-Gluon Luminosity!dL = " g(, Q 2 )g(!, Q 2 ) d d! -----! with Q 2 =!s [gg CMS-Energy]

35 PDFs Are they universal? g() 12 1 NLO QCD fit µ 2 f = 2 GeV 2 H1 jet data for % s (M z ) =.1184 ±.31 gluon from jets CTEQ5M1 MRST99 Botje99 g(,q 2 ) gluon from charm Q 2 =2 GeV 2 µ 2 =25 GeV 2 2 incl. k $ algorithm H1 prel. ep!" thy D* (DIS) D* (#p)

36 Using Jet Data in PDF Determination f gluon fractional error Gluon fractional error Q = 1 GeV 2 2 Q = 7 GeV 2 2 Q = 2.5 GeV without jet data with jet data 2 2 Q = 2 GeV Q = 2 GeV 2 2 Q = 2 GeV.4.2 New PDFs with improved precision for gluon at medium and high α s =.1183 ±.29 ±

37 non-perturbative region phenomenological description [e.g. Regge-Theory] Strength of interaction QCD Transition? QED perturbative QCD Small Q 2 Large Q 2

38 Y3 Small Q 2 small scattering angles lower cms-energy Shifted Verte Backward Calorimeter Special data taking period with shifted verte + ISR QEDC X1 Y1 X2 X3 Y3 Small angle detector [ZEUS BPT]

39 Eperimental Technics [to Access Low Q 2 ] Shifted Verte e Shifted IP Nominal IP 7 cm BST SpaCal smaller scattering angles p l k smaller cms-energy E e E e - E γ p q QED Compton l' (QEDC) Initial State Radiation (ISR) X smaller scattering angles

40 pqcd small ] F 2 ~ -λ with λ ~ ln Q 2 [ DLL-Approimation ] For Q 2 ~ F 2 ~ -.8 [ Regge-Theory ]

41 ALLM97 H1 QCD Fit Q 2 min = 3.5 GeV 2 H1 Collaboration

42 Determination of λ Result: F 2 ~ -λ for <.1

43 Q 2 -Dependence of F 2 -Slope What happens at Q 2 ~.5 GeV 2? parton radiation decreases & becomes independent of resolution corresponds to scale of r h/q.3 fm. proton radius: r.8 fm Evidence for non-partonic substructure within proton? λ =.8 [Regge phenomenology]

44 From hard to soft physics Do we see saturation?

45 Saturation > c c Unitarity consideration: Rise towards small has to stop somewhere Epectation: At some point number of gluons is so large that recombination becomes important Possible observation: Taming of the rise of F 2 at low

46 Structure Function F2 2 Q 2 =2.7 GeV GeV GeV GeV GeV 2 1 GeV 2 12 GeV 2 15 GeV GeV 2 22 GeV ZEUS NLO QCD fit H1 PDF 2 fit H1 96/97 ZEUS 96/97 BCDMS E665 NMC 27 GeV 2 35 GeV GeV 2 6 GeV 2 7 GeV 2 9 GeV No evidence for saturation GeV 2 15 GeV Bjorken

47 ep-scattering Alternative Pictures Infinite momentum frame Proton rest frame Electron Q 2 Electron A colour dipole of variable size r T ~ 1/Q interacts with the proton at high CM energy s γp = W 2 = Q 2 / [ low = high energy scattering! ] Proton γ* ~.1 L 5 fm proton r T ~ 1/Q (dipole size) r T Electron interacts with quark of proton Parton content described by F 2 L ~ 1/ Q 2 ~ 1 GeV 2 r T.2 fm F 2 (,Q 2 ) = F 2 (W 2,Q 2 ) 4πα 2 Q 2 σ γ*p (s γ p,q 2 )

48 The Saturation Model Dipole model γ*p cross section [for small ] σ γ p T,L (, Q2 ) = Saturation model à la GBW: dipole proton -section d 2 r dz ψ T,L(Q, r, z) ˆσ(, r) ψ T,L (Q, r, z), ˆσ(, r) = σ {1 ep { ( dipole wave function ( )} r 2 /4R() 2 Saturation model including gluon evolution: R () average gluon distance at which saturation sets in DGLAP [for small r]: [ R 2 () = 1 GeV 2 ( ) λ ˆσ(, r) π2 3 r2 α s g(, µ 2 ) ] ˆσ(, r) = σ {1 ep ( π2 r 2 α s (µ 2 ) g(, µ 2 ) 3 σ )}

49 ! (mb) 25 2 constant [ saturation ] 15 = ~ r 2 = r (GeV -1 )

50 Parton Saturation ln 1/ saturation region Saturation scale Q s () Number of gluons at specific 1/ perturbative region Resolved spot size non-perturbative region ln Q

51 F Q 2 =.45 Q 2 =.65 Q 2 =.85 H1 & ZEUS Data Saturation model Saturation model w/ DGLAP Q 2 =.11 Q 2 =.15 Q 2 =.2 Q 2 =.25 Q 2 =.3 Q 2 =.4 Three parameters fit [σ,, λ].2 Five parameters fit [σ, g() parameterization].6 Q 2 =.5 Q 2 =

52 F Q 2 =.45 Q 2 =.65 Q 2 =.85 H1 & ZEUS Data Saturation model Saturation model w/ DGLAP Q 2 =.11 Q 2 =.15 Q 2 =.2 Q 2 =2.7 Q 2 =3.5 Q 2 =4.5 Q 2 =6.5 1 Q 2 =.25 Q 2 Q 2 =8.5 Q 2 =1 =.3 Q 2 Q 2 =12 Q 2 =15 = Q 2 =.5 1 Q 2 = Q 2 =18 Q 2 =22 Q 2 =27 Q 2 = Q 2 =45 Q 2 =6 Q 2 =7 Q 2 =

53 !.45.4 H1 ZEUS saturation model with DGLAP evolution saturation model Q 2 (GeV 2 ) Transition to soft physics described!

54 Do we see saturation? Electron Electron diff / tot.6.4 Q 2 = 8 GeV 2 Q 2 = 27 GeV 2 Q 2 = 14 GeV 2 Q 2 = 6 GeV 2 M X 3 GeV Dipole saturation model successfully describes... Colourless echange HFS Signature: rapidity gap.2 describes F 2 in DIS also at small and low Q2 (Fit!) Proton M X 7.5 GeV predicts details of diffractive processes predicts diffractive DIS/DIS = constant Satur. Mod. with evol 7.5 M X 15 GeV W(GeV) No proof of saturation, but... several independent effects described very appealing also very much discussed also within Heavy Ion community (Color Glass Condensate) more theoretical work needed...

55 Concluding Remarks HERA provides the decisive information about parton distributions, especially the gluon content of the proton HERA has delivered data which guide theory to describe low energy QCD, e.g. the transition from hard to soft physics However, despite of large theoretical progress regarding saturation, dynamic QCD evolution, understanding of diffraction low energy QCD is still not understood More work is needed in order to maybe on day get an understanding of what confinement really is