2 Probing proton structure at very high Q Masahiro Kuze Department of Physics Tokyo Institute of Technology � Introduction � F 2 measurement and PDF fit 2 region, NC and CC � High- Q 2 region � Low- Q � Summary and prospects kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 1
HERA ep Collider at DESY/Hamburg HERA luminosity 1992 – 2000 Integrated Luminosity (pb -1 ) 70 70 2000 60 60 50 50 40 40 1997 1999 e + 30 30 20 20 1999 e - 1996 95 10 10 98 94 93 92 15.03. Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec + or e − ) ⇒ E p =920 GeV ⊗ E e =27.5 GeV (e • s = 318 GeV • 2 colliding experiments and 2 fixed-target experiments -1 e + p, ~15 pb -1 e − p (‘98-’99) for H1 or ZEUS • On-tape luminosity: ~110 pb kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 2
Deep Inelastic Scattering (DIS) • Probe the proton = our most familiar micro-cosmos with a point-like lepton probe. ‘giant electron-microscope’ • 1/ Q (momentum transfer) gives the spacial resolution. • Bjorken x : Fractional momentum of a parton in the nucleon. 2 =sxy • y =(1-cos θ *)/2 (scattering angle in CM system) Q • Neutral or Charged current in t-channel propagator kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 3
Kinematic region probed Q 2 (GeV 2 ) • > 100x larger kinematic reach 10 5 compared to fixed-target DIS H1 experiments at CERN, DESY, 10 4 ZEUS FNAL, SLAC… (if proton is at rest, Fixed Target Experiments: HERA CM energy means E e =54 TeV ) CCFR, NMC, BCDMS, 10 3 E665, SLAC y=1 (HERA √ s=320 GeV) 10 2 2 , probe the validity of • At high Q SM/QCD at smallest distance → 10 Quark structure? New particles? 2 =40,000 GeV 2 → 1/ Q =0.001 fm) ( Q 1 2 , probe the low- x region • At low Q → very soft constituents of proton; -1 10 Saturation? Breakdown of standard -6 -5 -4 -3 -2 -1 10 10 10 10 10 10 1 DGLAP formalism (BFKL) ? x kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 4
The Detectors ZEUS Detector • Uranium-Scintillator calorimeter – σ ( E ) / E = 18% / for electrons E • • for hadrons σ ( E ) / E = 35% / E Central tracking detector – • σ ( p T ) / p T = T ⊕ 0.0065 ⊕ 0.0014 / p 0.0058 p T e → ← p H1 Detector • – Liquid-Ar calorimeter σ ( E ) / E = 12% / E • for electrons for hadrons • σ ( E ) / E = 50% / E Central tracking detector – 2 out of (E e , θ e , E h , θ h ) 2 ) → Reconstruction of ( x, Q kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 5
Cross section & Structure functions NC differential cross section for ep → eX reaction • 2 σ d 2 2 πα ± e p + F 2 ( x, Q 2 ) Y − x F 3 ( x, Q 2 ) − y 2 F L ( x, Q 2 )] [Y = + 2 4 dxdQ xQ F 2 = Σ xq f + ( x, Q 2 )[ e f 2 − 2 e f v f v e P Z + ( v f 2 + a f 2 )( v e 2 + a e 2 ) P Z 2 ] x F 3 = Σ xq f − ( x, Q 2 )[ − 2 e f a f a e P Z + 4 v f a f v e a e P Z 2 ] (f=u,d,c,s,b) ± 2 2 (Parton Distribution Functions) = xq ) ± xq xq f ( x , Q f ( x , Q ) f − 2 2 θ W ⋅ Q 2 /( Q 2 + M Z 2 ) (Z-exchange & γ− Z interference) P Z = sin ± = 1 ± (1 − y ) 2 , e f : quark charge, v i / a i : EW couplings Y F L = F 2 − 2 x F 1 ( → 0 in LO QCD, longitudinal Str. Function) kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 6
Results of F 2 Structure Function HERA F 2 2 Q 2 =2.7 GeV 2 3.5 GeV 2 4.5 GeV 2 6.5 GeV 2 • Strong rise of F 2 as x decreases 1 Soft ‘ sea ’ of quarks in the proton – 0 2 8.5 GeV 2 10 GeV 2 12 GeV 2 15 GeV 2 2 ↑ • Slope of rise gets steeper as Q 1 0 2 18 GeV 2 22 GeV 2 27 GeV 2 35 GeV 2 softer parton smaller resol. em F 2 1 dynamics of quarks and gluons 0 2 45 GeV 2 60 GeV 2 70 GeV 2 90 GeV 2 1 Good agreement with fixed-target • 0 2 -3 -3 120 GeV 2 150 GeV 2 10 1 10 1 experiments at middle - high x ZEUS NLO QCD fit 1 H1 PDF 2000 fit H1 96/97 BCDMS (sea + valence quarks) ZEUS 96/97 E665 0 NMC -3 -3 10 1 10 1 x kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 7
2 F 2 for fixed x , as a function of Q HERA F 2 -log 10 (x) x=6.32E-5 x=0.000102 ZEUS NLO QCD fit x=0.000161 x=0.000253 H1 PDF 2000 fit • At low x , strong scaling violation x=0.0004 em x=0.0005 F 2 5 H1 94-00 x=0.000632 x=0.0008 is seen. H1 (prel.) 99/00 x=0.0013 ZEUS 96/97 g → qq BCDMS Large gluon density + splitting x=0.0021 E665 4 → F 2 increases x=0.0032 NMC x=0.005 • At x ~ 0.1, approximate scaling. x=0.008 3 2 ↑ . • At higher x , F 2 decreases as Q x=0.013 x=0.021 x=0.032 2 x=0.05 • Line = result of QCD fit (next slide) x=0.08 – All data points well described. x=0.13 x=0.18 1 x=0.25 x=0.4 x=0.65 0 2 3 4 5 1 10 10 10 10 10 Q 2 (GeV 2 ) kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 8
Perturbative-QCD fit of F 2 data • Example: ZEUS NLO DGLAP analysis PRD 67 (2003) 012007 2 = Q 2 – At Q 0 , input functional form of PDF ( Q 2 2 ) 0 =7GeV p2 (1-x) p3 (1+p 5 x) for u-valence, d-valence, sea quarks and gluons • xf(x) = p 1 x 2 evolution’ is predicted by – ‘ Q DGLAP (‘Altarelli-Parisi’) Equations 2 = ( α s /2 ʞ ) ʈ f j ⊗ P ij • Ż f i / Ż ln Q P qq P gq P qg P gg – Use world’s precision DIS data + ZEUS F 2 • BCDMS, NMC, E665, CCFR ( µ -p, µ -D, ν -Fe) 2 fit to determine p 1 … p 5 – χ kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 9
PDFs obtained from the fits ZEUS 0.8 1 xf xf(x,Q 2 ) Q 2 =10 GeV 2 ZEUS NLO QCD fit H1 H1 PDF 2000 0.7 2 ) = 0.118 0.9 α s (M Z Q 2 =10 GeV 2 xu v tot. error ZEUS-S PDF ZEUS-S PDF 0.8 0.6 CTEQ 6M xu V 0.7 0.5 MRST2001 0.6 0.4 xg( × 0.05) xg( × 0.05) 0.5 xd v 0.3 0.4 xd V xS( × 0.05) 0.3 0.2 xS( × 0.05) 0.2 0.1 0.1 0 0 -3 -2 -1 -4 -3 -2 -1 10 10 10 1 10 10 10 10 x x (H1 PDF 2000: uses only H1 data) kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 10
Low-x sea and gluon distributions ZEUS 2 ~ 1GeV 2 , gluon becomes valence- • At Q 6 Q 2 =1 GeV 2 2.5 GeV 2 like (and even tends to be negative) ZEUS NLO QCD fit 4 xg xS • Sea quark is still rising 2 ZEUS xS xg 0 (a) xg -2 x=0.001 20 7 GeV 2 20 GeV 2 x=0.0001 20 tot. error tot. error ( α s free) ( α s fixed) uncorr. error xf ( α s fixed) 15 10 ZEUS NLO QCD fit xg xg tot. error ( α s -free) xS xS tot. error ( α s -fixed) 0 10 200 GeV 2 2000 GeV 2 30 x=0.01 “scaling 5 20 violation” xg xg 10 x=0.1 of gluon xS xS 0 0 -4 -3 -2 -1 -4 -3 -2 -1 10 10 10 10 1 10 10 10 10 1 x 2 3 4 1 10 10 10 10 kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 11 Q 2 (GeV 2 )
2 NC cross section Results on high- Q ZEUS 4 xQ 2 • σ ≡ at low Q ˜ + σ ( x , Q ) ≈ F 2 1.5 Q 2 =200 GeV 2 250 GeV 2 350 GeV 2 450 GeV 2 2 2 2 πα Y 1 2 > ~5000 GeV 2 , effect of At Q 0.5 Z -exchange clearly visible. 0 − p) > σ (e + p) due to ± x F 3 • σ (e 650 GeV 2 800 GeV 2 1200 GeV 2 1500 GeV 2 1 2 2 3 ∝ q ( x , Q ) − q ( x , Q xF ) 0.75 sensitive to valence quarks 0.5 0.25 H1 94-00 ZEUS 96-99 SM (CTEQ6D) NC 0.6 ∼ 0 xF 3 σ Q 2 = 1500 GeV 2 Q 2 = 3000 GeV 2 Q 2 = 5000 GeV 2 2000 GeV 2 3000 GeV 2 5000 GeV 2 8000 GeV 2 0.4 0.8 0.2 0.6 0 0.4 -0.2 0.2 0 0.4 Q 2 = 8000 GeV 2 Q 2 = 12000 GeV 2 Q 2 = 30000 GeV 2 -2 12000 GeV 2 20000 GeV 2 30000 GeV 2 10 1 0.6 0.2 ZEUS NLO QCD fit 0.4 tot. error 0 0.2 ZEUS NC e - p 98/99 -1 -1 -1 ZEUS NC e + p 10 10 10 0 96/97 -2 -2 -2 10 1 10 1 10 1 x x kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 12
“Rutherford experiment” on quarks 2 • Single differential xsec in Q 2 = large angle = smaller distance Large Q HERA Neutral Current d σ /dQ 2 (pb/GeV 2 ) 4 fall over 7 orders of magnitude • 1/ Q H1 e - p 10 ZEUS e - p 98-99 • Analogy to nucleon form factor: SM e - p (CTEQ6D) 1 If finite ‘quark radius’ R q , xsec will -1 10 2 grows. decrease as Q -2 σ = σ SM (1 − < R q 2 > Q 2 /6) 2 10 -3 R q < 0.85 × 10 -16 cm 10 H1 e + p 94-00 -4 ZEUS (prel.) e + p 99-00 10 ZEUS SM e + p (CTEQ6D) N/N CTEQ5D -5 ZEUS 94-00 e ± p 1.2 10 10 2 = (0.85 ⋅ 10 -16 cm) 2 R q 1.1 -6 1 2 = -(1.06 ⋅ 10 -16 cm) 2 R q 10 0.9 y < 0.9 0.8 -7 3 4 10 10 10 3 4 10 10 Q 2 (GeV 2 ) 1 ↓ ↓ - Quark Radius Limits h/ Q = 0.02fm 0.002fm 3 4 10 10 Q 2 (GeV 2 ) kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 13
Charged current − flavour sensitive HERA Charged Current + p: only negative-charge quarks • e H1 e - p H1 e + p 94-00 SM e - p (CTEQ6D) ZEUS e - p 98-99 ZEUS e + p 99-00 SM e + p (CTEQ6D) 2 2 σ d 2 G M [ ] + e p 2 = F W u + c + ( 1 − y ) ( d + s ) σ ∼ Q 2 = 280 GeV 2 Q 2 = 530 GeV 2 Q 2 = 950 GeV 2 2 2 2 2 π + Q dxdQ M 2 W 2 ) probed. At high x , mainly d( x , Q 1 − p: only positive-charge quarks • e 2 2 σ d 2 G M [ ] − Q 2 = 1700 GeV 2 Q 2 = 3000 GeV 2 Q 2 = 5300 GeV 2 e p 2 = F W u + c + ( 1 − y ) ( d + s ) 2 2 2 2 π + Q dxdQ M 1 W At high x , mainly u( x , Q 2 ) probed. 0.5 1 2 ) > d( x , Q 2 ), • In addition to u( x , Q Q 2 = 9500 GeV 2 Q 2 = 17000 GeV 2 Q 2 = 30000 GeV 2 0.75 2 in e + p helicity suppression (1- y ) x · u (1-y) 2 x · d 0.5 − p) >> σ (e + p) at high Q 2 ⇒ σ (e 0.25 -2 -1 -2 -1 -2 -1 10 10 10 10 10 10 • Data (not used in the fit) well described x − 1 2 2 by the QCD prediction. G M 2 σ ≡ σ ( x , Q ˜ F W ) 2 2 2 π x + Q M W kuze@phys.titech.ac.jp 20/Feb/2004 SQS04 14
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