Structure Functions. From HERA to LHC. Hans-Christian Schultz-Coulon Universität Heidelberg

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1 Structure Functions From HERA to LHC Hans-Christian Schultz-Coulon Universität Heidelberg Introduction to high energy particle and nuclear physics Lecture week, Oslo, March 7 th, 6 International Research and Training Group Development and Application of Intelligent Detectors

2 Nobelprize 4 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

3 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 experiments at the LHC...

4 HERA... Today! proton structure F quark- & gluon-pdfs ( LHC), Δα s /α s ~ 1% (NNLO) F at small Q, x non-perturbative QCD xf 3, PDFs at large x (HERA II!)... heavy quarks universality of proton structure (gluon-pdf!) fragmentation, production mechanisms, c/b-pdfs... diffraction and low-x 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...

5 Structure Functions Basics

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

7 !!!!!!!!!!!!!!!!!!!! HERA Kinematics / I7OPQ!M/N -./%#$&!1/ )! k 8!9$4#:;$;/&%4;!%#<&=9/# >=?<%5<.!#/=$.4%5$&!@!AB6C 8! D8!9#<%5$&<.!;$;/&%4;! D8!$9!%E/!=%#4F!G4<#F ( ) k' Q = -(k k')!*+, q P' -./%#$&!1/ )! 3/4%#5&$! H!I!6 H!I! 7 B=D8!J&/.<=%55%H >!=8!;=!/&/#KHC P= xp q ' p "#$%$& -? IL7,!M/N >R/9$#/!ALLS8!- IS7,!M/NC?

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

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

10 Scaling [SLAC 197] F Q [GeV ]

11 Scaling Violations [199++] SLAC 197

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

13 QCD Improved Parton Model 1 F ( x) = x$ # e q d! q (!)" x! = x$ e q q( x) q q!p QPM QCD z = x/! F x ( ) x$ e q # = ---- d! x q (!) " 1 --! % '!& ( ) x s P qq -- * % '!& ( Q + log µ x 1!P x k, k T +, - q. qg +, - q. qg / / µ : cutoff parameter ) s P * qq ( z) µ Q # dk T k T ) s P * qq ( z) log Q µ q( x, Q ) = q( x) q( x, µ ) = q( x) + + ) s Q 1 log * µ # x ) s µ 1 log * µ # x dz P z qq z dz P z qq z ( ) q( x z) ( ) q( x 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( x, Q ) = q( x, µ ) + ) s Q 1 log * # µ x dz P z qq z ( ) q( x z) (A)-(B)

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

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

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

17

18 The HERA Accelerator Complex [7.6 GeV] e Halle Nord H1 e p 36m R=797m [9 GeV] p Halle Ost HERMES NW e p HERA- Halle West N NO Halle West HERA-B HERA Trabrennbahn 36m s Stadion Stellingen = 3 GeV W Kältehalle PETRA Magnet- Testhalle H -Linac DESY II/III e PIA + e -Linac e --linac p O Proton ring: Energy*: 9 GeV Mag. Field: 4.68 T Current: ~ 1 ma * before 1998: 8 GeV ZEUS Halle Süd Electron ring: SW Energy: 7.5 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 - s -1

19 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 = 1%/ E for electrons!(e)/e = 5%/ E for hadrons Central Tracker Resolution!(p t )/p t =.6 p t /GeV ". 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

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

21 ep Cross Section [low Q approximation] Rutherford Proton Structure + q F ( x, Q ) = x e q q x, Q [ ( ) + q( x, Q )] ( ) * Evolution according to DGLAP d! = 4"# F dxdq xq 4 x, Q 1 ( ) $ [ 1 + ( 1 y) ] y 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 y - J d,,,' pq E p E e ( 1 cos. * ) = = = pk E p E e d, = cos. d * 1, 1 = ( 1 cos. * ) M ( 1 y) y-dependence describes helicity structure of interaction

22 Q (GeV ) Structure Function F [Principle of Measurement] ZEUS > 5 Events > 65 Events > 1 Events < 1 Events Basic (simplified) Procedure:! $ 4"# F xq 4 % &' ( and! F = = 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=1-1 Kinematic limit 1 Q =15 GeV x

23 MRS D,D - : Fit to fixed target data only Different assumptions on xg(x,q ) H1 '9 MRS D - F 1.6 Q =15 GeV HERA MRS D.6.4. CTEQ5D MRST99 ZEUS 96/97 H1 96/97 NMC, BCDMS, E Fixed Target x -3% Precision

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

25 High Q Physics Constraining Valence Quarks

26 Electron (e ± ) Electron (e ± ) Neutrino CC data: [W ± exchange] NC data at high Q : [Z exchange] sensitive to vector and axial couplings of quarks to Z γ Z, W ± q,q coupling only to quarks with right charge; sensitive to Fermi coupling G F and W mass q Proton SF Structure functions [additional definitions] Proton Remnant

27 1! 78+9 " #$#%&'()#*+, " /

28 Neutral Current Interactions! " # e e e e q e + * e Z q q * q q q q q Q Q + M Z = Q 4 Q Q + M & Z Q + M ' Z $ % with: * e = v e ++a e * q = v q ++a q + = ±1 (Helicity) = ( ) e Q 4 q q( x) ( ) e Q Q q * e * q q( x) + + M Z ( ) * Q ( + M Z ) e * q q( x)

29 Unpolarized NC Cross Section d! NC ( e ± ) dxdq = "# Y xq 4 + Y F +$ x y F 3 F L Different sign for positrons and electrons ~ { Y ± = ( 1 ± ( 1 y) )} Helicity Structure & i = x [ q F i ( x, Q ) + q i ( x, Q )] % A q & i x = x [ q F 3 i ( x, Q ) q i ( x, Q )] % B q A q = e q e q ( v e )v q ' Z + v e + a e ( )( v q + a q )(' Z ) B q = e q ( a e )a q ' + Z 4( v e a e )v q a q (' Z ) Propagator: Q ' Z ( Q + M Z Pure Photon exchange )Z-Interference Pure Z exchange

30 !"#$%&'(!)$$&*+(!$,--(.&/+,* $ 5 6$ % 7 % $!$" $ %! + $ $ 5 +! % - + $ $ % +! % - + $ $ % + - %! + $ 134 * 56%7-53/:$ 6!53/:$7!53/:$ 6-53/:$7 89! "! ##! $ ; " !&!' " = "# " " () * #- %.! + /" "!! % )" $ ' " "! %, * " " 1<$)=-5>-?1@=!$4)A3/! "! ##! $ % " !&!' " = "# " " () * #- %.! + /" "!! % )" $ ' " "! %, * " " 1<$)=!5>-?1@=!$4)A3/

31 !"#$%&#""#"'())#*+,-.(%) )!*)! " #$+,*%&' " ( A! IJ H1 e p NC CC H1 e + p NC 94- CC 94- H1 PDF!" -./)/1)#3)&4# )&5617,&5#61355#5&6.735# 38&1#4/19&#1/9&#3:#! " ;4&6.13<&/=#>?7:76/.73@ /.#4/19&#! " #A# B " 1-3 & C +*& D +#61355#5&6.735# )7::&1#)?&#.3#)7::&1& y <.9 s = 319 GeV "" ! " #$%&' " ( ###E?/1=#63.17,?.735 ###F&4767.G#5.1?6.?1&#3: ###;H#7.&1/6.735

32 Constraing PDFs using High Q Data

33 DIS Cross High Q Neutral Current: d # e ± ( ) " $F %xf 3 &y F L dxdq +' different contribution from xf 3 for different lepton charge Influence high y e ± e ± (ν,ν - ) Proton γ, Z (W ± ) SF Charged Current: q q Remnant F " x [ q i + q i ]! i xf x q 3 " i q i! i [ ] Use e + p/e p data to extract xf 3 Sensitivity to valence quark density d # e + d # e " ( ) x [(d + u] " ( ) x [ u + (d] Use e + p/e p data to disentangle up-/down-quark content at high x

34 !"#$%&'(%&#")*++#,%(-.*/ σ 1 3 ZEUS e p ZEUS e + p s=318 GeV s=3 GeV e p ZEUS-S e + p ZEUS-S s=318 GeV s=3 GeV $CD!3 E FGA(H(6A(6<(/?(I97(A / 1!" # /*!.?:< " &'!( " = #"% +!!" # 1 " &'!( + " = #"%!!" # )*+, Q (GeV ) $!" # =!" # -! $ % % #" &'!( " " &'!( + " $ $ # =!! B 3% " =!! B 3 % " $ -./1/3 % 4/5( /.9/7:;(6<(/=>:?@/A(651.1(5/ A9J6/.9/!/K/$L G%

35 σ NC 1 Q = 15 GeV Q = 5 GeV Q = 1 GeV s = 319 GeV H1 PDF : e + p e p e + p H1 94- e p H $!" #.5 xf 3. H1 H1 PDF,-.%%/%1345&1& 6)17$894)1 &14)!%5:;3.<%=!!" > #.)?%?6)17$' 5@%13A.1 ' Z = B / ' ' C? D ED $ '. ' + G F *, $ ' *=H.3I&-& x = $!" # % & % # % '$ ( & (!!( ) ( ) " $ & ( '* + '+ % & % # % '+ ( & (!!( ) ( ) " $ & (! "! " )* xf 3 * $ % & % %!" # & ( ' * x E31.)J@1)313!" > # K#L #' Z $ '

36 γ Z xf Data H1 PDF Q = 15 GeV 5 GeV 1 GeV!" #!$ xf γ Z transformed to Q = 15 GeV H1 H1 " = = % % " /D-1EF!1$@@@? x 1 1 "!#! " = " $% & ' & & ( & (,! " = $% ) ' ) * ) + $% + ' + * + = -- % #- #. /$ $ /.)1)341'13' :;<(=>? "

37 !"#$%"#& ''&'()**&+"%,-). σ CC / * 1 3! " = "#! '' 9! '' 6! '' = = #! ''!" / " #5#3 5 # $ + % +! 7 8"!# + *" $ 5 # $ + % +! 7 8"!# + *" $ 1.5 Q = 53 GeV H1 e p ZEUS e p H1 e + p 94- ZEUS e + p 99- SM e p (CTEQ6D) SM e + p (CTEQ6D) H1 e p H1 e + p 94- SM e p (CTEQ6D) ZEUS e p ZEUS e + p 99- SM e + p (CTEQ6D) σ Q = 8 GeV Q = 53 GeV Q = 95 GeV x Q = 17 GeV Q = 3 GeV Q = 53 GeV Q = 95 GeV Q = 17 GeV Q = 3 GeV x u (1-y) x d +".*-,-B-,8&,),-./1,(#%.$3&)'4!"#$%&'(')&')*&+ :;<!=&>>&?@,@A x

38 Global PDF Fits

39 F [x i ] x =.5, i = 1 x =.8, i = x =.13, i = 19 x =., i = 18 x =.3, i = 17 x =.5, i = 16 x =.8, i = 15 H1 e + p ZEUS e + p BCDMS NMC Proton Structure Function [HERA & fixed target data] x =.13, i = x =., i = 13 x =.3, i = 1 x =.5, i = 11 x =.8, i = 1 x =.13, i = 9 x =., i = 8 x =.3, i = 7 x =.5, i = 6 x =.8, i = 5 x =.13, i = 4 Precision: -3% [bulk region] For x < 1 - : df dlogq ~ g(x,q ).! s (Q ) 1 x =.18, i = 3 x =.5, i = NLO QCD Fits: H1 PDF Extrapolation x =.4, i = 1 x =.65, i = Q [GeV] Quark densities Gluon density Strong coupling α s

40 Where HERA Data constrain PDFs Valence Quarks: High Q, high x NC/CC ep cross section [HERA I: statistics limited] Sea Quarks: Low-x: inclusive NC DIS [HERA I data to be published] Gluon: Low-x: scaling violations Mid-x: jet data Mid-x: heavy flavours High-x: momentum sum rules [HERA I statistics limited at high E T ] [HERA II: jets, heavy flavours]

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

42 QCD Fits: Inputs Fixed target data l p! l p: BCDMS, NMC, E Fixed target data l p! "p: CCFR, CDHS, BEBC... H1, ZEUS data structure function and cross H1, ZEUS data section measurements Sum rules: # u v ( x ) d x =, # d v ( x) dx = 1, ) * # dx x ' g( x) + $ [ q( x) + q( x) ] ( = 1, % & I # d G x ( ) 1 = = # dx ( u d). 3 3 F lp F ln Other experimental 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 [Experiment (NMC): I G =.35 ±.6! u > d ]

43 !"#$%&'()&*+$+)*','-./'/)*1$*!" # $!% xf(x,q ) 1..8 H1 PDF ZEUS-S PDF Q =1 GeV &'()#*(+ &'()#*(, xu V 1..8 H1 PDF ZEUS-S PDF CTEQ6.1 Q =1 GeV xu V.6.6 xg(.5) xg(.5).4 xd V.4 xd V xs(.5) xs(.5) ! x !

44 Comparison H1 vs. ZEUS H1! s fit: H1 PDF fit: ZEUS PDF fit: Dedicated to! s and g(x). H1 ep NC data (low Q ) & BCDMS µp data. Parametrization of valence, sea quark and gluon. Starting scale: Q = 4 GeV.! s = ±.5 Dedicated to PDF-determination. Fit A: H1 data only (NC, CC, low & high Q ). Fit B: H1 data & BCDMS µp data. Parametrization of U, U, D, D and gluon. Starting scale: Q = 4 GeV. scale uncertainty exp. & 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 = 7 GeV.! s = ±.4 exp. & model uncertainty scale uncertainty

45 34!! experimental uncertainty theoretical uncertainty &%,!6 H1: NLO QCD fit [Eur. Phys. J. C 1 (1) 33] ZEUS: NLO QCD fit [Phys. Rev. D 67 (3) 17] S. Bethke: World Average [hep-ex/111] J. Santiago, F.J. Yndurain [hep-ph/147] α s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

46 PDFs Are they universal? x g(x) 1 1 NLO QCD fit µ f = GeV H1 jet data for % s (M z ) =.1184 ±.31 gluon from jets CTEQ5M1 MRST99 Botje99 xg(x,q ).5 gluon from charm Q = GeV µ =5 GeV incl. k $ algorithm x H1 prel. exp!" thy D* (DIS) D* (#p) x

47 Parton LHC What do we need? How well do we know them? How to improve?

48 1 9 LHC parton kinematics p x 1, = (M/14 TeV) exp( ± y) Q = M M = 1 TeV p x 1 x M Q (GeV ) M = 1 GeV M = 1 TeV LHC M = x 1 x s i.e. to produce a particle with mass M at LHC energies ( s = 14 TeV) <x> = x 1 x = M/ s [x 1 = x : mid-rapidity] LHC needs: y = M = 1 GeV HERA fixed target 6 knowledge on parton densities extrapolation over orders of magnitude x

49 Gluon Gluon top top top Higgs Simple spread of existing PDFs gives a 5-1% uncertainty on the Higgs cross section.

50 W and Z LHC Q for W/Z LHC energies x =.5 Extrapolation pp W + X pp Z + X Considered as luminosity monitor

51 Jet LHC ATLAS TDR: Inclusive Jet E T d"/de T [nb/gev] <! < 1 1 <! < <! < 3 NLO QCD <! 1 < leading Jet E T [GeV] First plot to be made at LHC Sensitive to: Parton distribution functions Detector performance [Energy scale and resolution] New Physics

52 Relative Uncertainty [compared to CTEQ 6.1M] Inclusive Jet Cross LHC [D.Stump et al., JHEP 1 (3) 46] p T dσ/dp T p T Mid-rapidity: 1 % E T ~ 5 TeV Forw. jets: 1 % E T ~ TeV p T

53 Quark Substructure [Compositeness] Expectation: Enhancement of σ jet at high E T ATLAS TDR: Inclusive Jets

54 Heavy Gluons [Extra Dimensions] σkk = σ - σsm hep ph/ SM ~ /year Heavy Gluons: Kaluza Klein Excitations of normal gluon Mass of g*: Scale of Extra Dimension p T,min (TeV)

55 Heavy Gluons [Extra Dimensions] Ratio σkk/σsm hep ph/ SM Heavy Gluons: Kaluza Klein Excitations of normal gluon Mass of g*: Scale of Extra Dimension p T,min (TeV)

56 HERA Parton Distributions Present Precision Future Perspectives

57 Status Dec. HERA I HERA II H1 Integrated Luminosity / pb -1 1 HERA- 17 pb -1 [deliv.: 1 pb -1 ] electrons positrons Status Nov. HERA I: HERA-1 75 pb -1 [deliv.: 96 pb -1 ] e + p Scattering: ~ 1 pb -1 e p Scattering: ~ pb -1 HERA II: Int. Luminosity: ~ 5-7 pb -1 Lepton Polarisation 6 pb -1 [deliv.: 9 pb -1 ] 4 pb -1 [deliv.: 6 pb -1 ] pb -1 [deliv.: 5 pb -1 ] Days of running Up top now: e + p, P=+1: ~13 pb -1 e + p, P= 1: ~13 pb -1 e p, P=+1: ~15 pb -1 e p, P= 1: ~ 1 pb -1

58 Where HERA Data constrain PDFs Valence Quarks: High Q, high x NC/CC ep cross section [HERA I: statistics limited] HERA II Sea Quarks: Low-x: inclusive NC DIS [HERA I data to be published] Gluon: Low-x: scaling violations Mid-x: jet data Mid-x: heavy flavours High-x: momentum sum rules [HERA I statistics limited at high E T ] [HERA II: jets, heavy flavours] HERA II

59 New H1 Low-Q Results Fractal fit F and dipol F ALLM 97 H1 QCD fit 97 Q min = 3.5 GeV L Q =.35 GeV Q =.5 GeV Q =.65 GeV Precision of -3% down to Q =.35 Q =.85 GeV Q = 1. GeV Q = 1.5 GeV Q = GeV Q =.5 GeV Q = 3.5 GeV F Q =15 GeV Q = 15 GeV CTEQ5D MRST99 ZEUS 96/97 H1 96/97 Precision: -3% NMC, BCDMS, E x

60 Impact of New HERA low-q data gluon fractional error Q = 4 GeV Q = 7 GeV ZEUS Fit to H1 Data High Q NC/CC Data 94- Low Q NC (published) High Q NC/CC Data 94- Low Q NC (estimate) Q = 1 GeV Q = GeV Q = GeV Q = GeV - improved knowledge of gluon at low x and low Q - some reduction also at higher x C.Gwenlan [HERA/LHC Workshop] ZEUS anal. (H ) ZEUS anal. (H1 ) only Moderate impact on xg(x) from extra precision on low Q data x

61 Jet Data Examples: HERA-I high E T jet measurements in DIS and Photoproduction (Q ~ ) dσ/de T,jet B (pb/gev) !"#$%&'()"*+(4789:;4<(/,;(47(=&+ ZEUS ZEUS NLO QCD: Jet energy scale uncertainty (corrected to hadron level) α s (M Z )=.1175 DISENT MRST99 (µ R =E B T,jet ) DISENT MRST99 (µ R =Q) 15 < Q < 5 GeV ( 1 5 ) 5 < Q < 5 GeV ( 1 4 ) 5 < Q < 1 GeV ( 1 3 ) 1 < Q < GeV ( 1) < Q < 5 GeV ( 1) dσ/de T jet1 (pb/gev) !"#$%&'()"*+(,-.%/,(γ1(,(3453%" ZEUS 6 ZEUS x γ obs >.75 NLO (GRV) HAD NLO (AFG) HAD Jet energy scale uncertainty 1 < η jet1 <.4-1 < η jet < (x ) 1 < η jet1 <.4 < η jet < 1 (x 1) 1 < η jet1, <.4 (x ) Q > 5 GeV ( 1) 1-3 < η jet1 < 1-1 < η jet < (x.5) < η jet1, < 1 (x.1) E B T,jet (GeV) < η jet1, < (x.1) <*-B(*%,.+./,./(+E%B'(*).+/'./*,%.%())*,D'-%.%FGGDH =! 1*.%-+.+ E T jet1 (GeV)

62 Impact of Jet Data on Gluon PDF xg Q = 1 GeV without jet data with jet data ZEUS Q =.5 GeV gluon fractional error Q = 1 GeV ZEUS Q =.5 GeV without jet data with jet data Q = 7 GeV Q = GeV.6.4 Q = 7 GeV Q = GeV Q = GeV Q = GeV.6.4 Q = GeV Q = GeV x x Clear improvement of xg(x) at x ~.1 -.1

63 Impact of 5 pb -1 Jet Data xg 1 5 ZEUS-JETS fit Q = 1.5 GeV -1 ZEUS-JETS+5 pb jets Q = 3 GeV gluon fractional error Q = 1 GeV Q =.5 GeV Q = 7 GeV Q = GeV.4.3 Q = 7 GeV Q = GeV Q = GeV Q = GeV.3. Q = GeV Q = GeV ZEUS-JETS fit -1 ZEUS-JETS+5pb jets x x #$%&'()&()$*+,(-,.*/.,),1)/3-4)34'56(&*4(*57)&65)65+3'5+ Further improvement of xg(x) at x ~.1 -.1

64 HERA prospects using jets by optimizing selection cuts )-1 jet1 /dσ zeus /de T jet1 (dσ/de T jet1 jet E T >14GeV, E T >11GeV jet1 jet x γ >.75, 1< η <.4, <η <1 Published All flavors up/down error ZEUS gluon up/down error Data+stat+syst errors Data+energy scale uncertainity jet1 (GeV) E T )-1 jet1 jet E T >15GeV, E T >1GeV jet1 /dσ zeus /de T jet1 (dσ/de T pb -1 data assumed jet1 jet x γ <.75, <η <3, <η <3 Optimised All flavors up/down error ZEUS gluon up/down error Data+stat+syst errors (est) Data+energy scale uncertainity (est) jet1 (GeV) E T Significant improvement seems possible.

65 Impact of HERA II [case study using current running scenario] Data sample L of HERA-I measurement (pb -1 ) l assumed L of HERA-II measurement (pb -1 ) Central values taken from Systematica taken from High-Q NC e existing data existing data High-Q NC e existing data existing data High-Q CC e existing data existing data High-Q CC e existing data existing data Inclusive DIS jets 37 5 existing data existing data Dijets in γp 37 5 existing data existing data Optimised dijets in γp - 5 NLO QCD NOT INCLUDED statistically limited data-sets scale statistical uncertainties on existing data assuming max. 7 pb -1 (equally between e+/e-) systematic uncertainties taken from existing data optimised jet cross sections include simulated data-points from NLO QCD, statistical uncertainties assume 5 pb -1 no systematics included

66 u-valence Uncertainties log-x scale (low-x region) linear-x scale (high-x region)

67 d-valence Uncertainties log-x scale (low-x region) linear-x scale (high-x region)

68 Sea Quark Uncertainties log-x scale (low-x region) linear-x scale (high-x region) most significant improvement from increased statistics at HERA-II

69 Gluon Uncertainties log-x scale (low-x region) linear-x scale (high-x region) most significant improvement from optimized jet analysis

70 Caveats

71 Comparison of H1 and ZEUS xf Q = 1 GeV xf Q = 1 GeV xf Q = 1 GeV 15 ZEUS Data (ZEUS analysis) exp. uncert. 15 H1 Data (ZEUS analysis) exp. uncert. 15 H1 Data (ZEUS analysis) exp. uncert. H1 PDF exp. uncert. 1 xg 1 xg 1 xg total uncert. 5 xs 5 xs 5 xs ZEUS analysis/ ZEUS data x ZEUS analysis/ H1 data x ZEUS analysis/h1 data H1 analysis/h1data x Here we see the effect of differences in the data; recall that the gluon is not directly measured (no jets). The data differences are most notable in the large 96/97 NC samples at low-q. If a fit is done to ZEUS and H1 together the χ for both these data sets rises compared to when they are fitted separately... Here we see the effect due to differences in the analysis choice e.g. parametrization at Q... [Cooper-Sarkar]

72 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] xp(x).8 xp(x) xu xu!!.6.4 xu xu. xu v. xu v xd xd!!.6 xd xd.4.4. xd v. xd v 6 4 xg PDFs at Q = 4 GeV experimental errors model uncertainties x 6 4 xg PDFs at Q = 4 GeV experimental errors model uncertainties x x parton distribution x parton distribution Enforce: x(d - u x " ) a u, a d, b u, b d : free parameters

73 non-perturbative region phenomenological description [e.g. Regge-Theory] low Q Strength of interaction QCD QED perturbative QCD Small Q Large Q

74 Y3 Small Q small scattering angles lower cms-energy Shifted Vertex Backward Calorimeter Special data taking period with shifted vertex + ISR QEDC X1 Y1 X X3 Y3 Small angle detector [ZEUS BPT]

75 Experimental Technics [to Access Low Q ] Shifted Vertex 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

76 Fractal fit F and dipol F ALLM 97 H1 QCD fit 97 Q min = 3.5 GeV L Q =.35 GeV Q =.5 GeV Q =.65 GeV Q =.85 GeV Q = 1. GeV Q = 1.5 GeV Q = GeV Q =.5 GeV Q = 3.5 GeV

77 ALLM97 H1 QCD Fit Q min = 3.5 GeV H1 Collaboration

78 pqcd small x] F ~ x -λ with λ ~ ln Q [ DLL-Approximation ] For Q ~ F ~ x -.8 [ Regge-Theory ]

79 Determination of λ λ Result: F ~ x -λ for x <.1 x

80 Q -Dependence of F -Slope What happens at Q ~.5 GeV? 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]

81 Q -Dependence of F -Slope What happens at Q ~.5 GeV? 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] H1 Collaboration More precision from combined data...

82 From hard to soft physics Do we see saturation?

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

84 Structure Function F Q =.7 GeV 3.5 GeV 4.5 GeV 6.5 GeV GeV 1 GeV 1 GeV 15 GeV 1 18 GeV GeV ZEUS NLO QCD fit H1 PDF fit H1 96/97 ZEUS 96/97 BCDMS E665 NMC 7 GeV 35 GeV 45 GeV 6 GeV 7 GeV 9 GeV No evidence for saturation 1 1 GeV 15 GeV Bjorken x

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

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

87 ! (mb) 5 constant [ saturation ] 15 x = ~ r x = r (GeV -1 )

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

89 F..1 Q =.45 Q =.65 Q =.85 H1 & ZEUS Data Saturation model Saturation model w/ DGLAP Q =.11 Q =.15 Q =. Q =.5 Q =.3 Q =.4 Three parameters fit [σ, x, λ]. Five parameters fit [σ, g(x) parameterization].6 Q =.5 Q = x x x

90 F..1 Q =.45 Q =.65 Q =.85 H1 & ZEUS Data Saturation model Saturation model w/ DGLAP Q =.11 Q =.15 Q =. Q =.7 Q =3.5 Q =4.5 Q =6.5 1 Q =.5 Q Q =8.5 Q =1 =.3 Q Q =1 Q =15 = Q =.5 1 Q = Q =18 Q = Q =7 Q = Q =45 Q =6 Q =7 Q = x

91 !.45.4 H1 ZEUS saturation model with DGLAP evolution saturation model Q (GeV ) Transition to soft physics described!

92 Do we see saturation? Electron Electron diff / tot.6.4 Q = 8 GeV Q = 7 GeV Q = 14 GeV Q = 6 GeV M X 3 GeV Dipole saturation model successfully describes... Colourless exchange HFS Signature: rapidity gap. describes F in DIS also at small x and low Q (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...

93 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

94 Epilogue How to constrain PDFs at LHC [some examples]

95 Vector Boson Production Direct γ-production: Singel W/Z production: q q q W ± Z :$7)"6&%+"'P RD%,&*-)&4(,K>4,)&$S ;$7)"6&%+"'P RD%,&*-)&4(,K>4,)&$S ud # W "! du # W uu # Z dd # Z q At LHC energies these processes take place at low values of Bjorken-x Only sea quarks and gluons are involved At EW scales sea is driven by the gluon, i.e. x-sections dominated by gluon uncertainty Constraints on sea and gluon distributions

96

97 Direct γ Production γ + jet event Sensitive to PDF differences CTEQ - MRST: ± % disagreement Needs good understanding of detector Normalized Number of Events Generator cuts: η = 4. P T = 1 GeV Generator cuts: η = 4. P T = 1 GeV 1 - Algorithm: PT cut 14 GeV on jet and γ ATLAS Algorithm: PT cut 14 GeV on jet and γ Normalised to cross section Normalised to cross section 1-3 Normalized Number of Events : P T in GeV P T in GeV

98 Single W and Z Production '! J V'5 J *K*L "# ****H&MI < 9 = W ± rapidity distribution B)*C+7+%DE * RNS+9::9T8E/ = *U*:K=9 9 *U*:K:::< = *U*:K::A 9 *U*:K::A J W = *U*:K:::< 9 *U*:K=9 S5XX#4(,- : TA T@ T9 : A *5 J!*K*L " ***H&MI E7F 9@ 9< 99 9= 9: =D =C =B =A =; =@ J * E7F 8E/ 88E/ W ± total cross section GH=:I Theoretical uncertainty dominated by PDFs Extra input from LHC measurements

99 Effect on PDFs of LHC W data ds B e/dy ds B e/dy Q = 6488 GeV Q = 6488 GeV ZEUS PDF fit before including W data ZEUS PDF fit after including W data e + CTEQ6.1 pseudo-data e + CTEQ6.1 pseudo-data 35% error reduction y y

100 Data Included in CTEQ Fits 1 DIS (fixed target) HERA ( 94) DY W-asymmetry Direct-γ Jets Q (GeV) /X