Results on the proton structure from
Shima Shimizu (Univ. of Tokyo) Introduction HERA physics Proton structure
A unique collider at DESY, Hamburg Circumference: 6.3 km Operated since 1992 to 2007 2 collider experiments: H1 & ZEUS ◆ proton 920 GeV electron/positron 27.5 GeV ◆ center of mass energy √s = 318GeV
Resolution @ HERA √s = 318GeV → s ~ 10 5 GeV² Amin
10-18 m HERA can have a resolution of 1/1000 of proton size.
Proton has its subcomponents: partons ◆ Naive parton model u u d quarks: ‘valence’ quarks ◆ QCD quark emits gluon. gluon splits to qq or gg. → Many quarks with lower momentum: ‘Sea’ quarks
ep collision → scattering of electron and a quark. It reflects the proton structure. Cross section of ep scattering = Cross section of eq scattering   ☭   proton structure Details come later, but; F,  : structure function ∞ total charge-squared weighted number of quarks in the proton Q² : momentum transfer → resolution : momentum fraction of a parton to the proton X
Fixed target experiments only. ◆ It was unclear how to describe the proton structure at low-x. − perturbative QCD: quarks are asymptotically free. : partons are confined in the proton hadronic view l 7
◆ HERA has expanded accessible kinematic region largely. 2 orders in both x and Q 2 | steep rise at low x → pQCD descriptions is verified.
◆ Steep rise of F 2 at low x. ◆ higher Q² = finer resolution → more low-momentum quarks are ‘visible’ i.e. Sea quarks ◆ Sea quarks are generated by gluon. Abundant Sea quarks 😉 Abundant gluons Gluon and Sea quarks’ physics is started by HERA. Introduction HERA physics Proton structure
◆ Kinematic variables to describe DIS Q²: Virtuality → probing power x : Bjorken scaling variable → momentum fraction of struck quark y : Inelasticity Q² = −q² = −(k −k')² = sxy
◆ Kinematic variables to describe DIS → momentum fraction of struck ◆   DIS is a convolution of electroweak (EW) physics and the proton structure. –  Good prove to the proton structure –  Sensitive to EW physics from space-like view. ◆   Hadronic final state is also sensitive to QCD. (not covered in this talk) 12
Neutral current (NC) process Y /Z° exchange ep→e’X Charged current (CC) process W+ exchange ep→ v X ◆   Kinematic variables are reconstructed by two of measured variables; scattered electron energy of angle jet (~ struck quark)

◆  1992-2000: HERA-I
(started with E p =820GeV, until 1997) –  measurements go down to low-Q 2 → Make full use of large kinematic region. 1.5GeV²<Q²<3000GeV²
◆  2002-2007: HERA-II
–  High luminosity to collect high-Q² data. (high-Q² ↔ Weak boson exchange) –  lepton beams are polarized. → Increased sensitivity to EW. Some of results will be shown in next slides.
◆  F, is measured over 4 orders of magnitude in (x, Q 2 ). low x → strong dependence on Q 2 “scaling violation” more g Wh is visible.
Weak bosons are heavy. →  ◆ low Q 2 NC:  Y -exchange CC: W-exchange → σ (NC) >> σ (CC) high Q 2 NC: Y /Z CC: W-exchange → σ (NC) ~ σ (CC) Electroweak unification
Weak process = No right-handed current CC is purely weak process → linear dependence on polarization. Introduction HERA physics Proton structure
♦   Parton distribution functions are used to describe the proton structure. q(x,Q²)  q(x,Q²)  g(x,Q²) – Valence quarks: u val (x, Q 2 ) = u(x, Q 2 ) − usea (x, Q 2 ) ,  same for d quark –  Sea quarks: usea (x,Q²) = u (x,Q²) = s(x,Q²) = s(x,Q²)  ... etc. ◆  PDFs evolve with Q². Larger Q² allows to see more quarks. ♦  The Q² evolution is described by DGLAP equation, based on pQCD.
◆  DIS cross sections can be written with structure functions.
cross section with point-like particle Structure functions: they reflect momentum distribution of partons in the proton. Structure functions are sensitive to PDFs. ◆ F, : total number of quarks F 2 = ∑ Aqx(q +q) : longitudinal structure function —→  gluon ◆ FL only sizable at high-y → Details will come up later

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q(x,Q 2 ) ◆   Q² evolution of PDFs can be predicted by perturbative QCD, i.e. by DGLAP equation. g(x,Q²) x-dependence of PDFs can be extracted from fits to measured cross sections. PDFs@ Q ² ←— Input Evolution in Q² : DGLAP＠NLO ↑ PDFs＠ Q² Fit to measured cross sections @ Q² PDFs are parameterized @ Q 2 = 7GeV 2 x f (x) = A x b (1 − x) c (1 + dx)  for xu , xd , xS, xg, xΔ(= xd − xu A: Normalization, b : Low x, c: High x, d : smoothing for middle x Constraints from momentum and number sum rule, etc. → 11 free parameters 21
A single experiment can determine PDFs. ♦ Pure proton target→ Free from target correction, nuclear effect. ♦ Single experiment→ systematic uncertainties are well understood.
F 2 ∞ Sea + valence quark scaling violation of F շ ∂F 2 ∂ln Q 2 ∞ xg        gluon
HERA etp Charged Current b  r CC is charge selective interaction. ♦ positron-induced → negative-charged partons ଠ(e + p) ∞ [(ū + c) + (1 − y)² (d)+ s)] d quark ♦ electron-induced → positive-charged partons ଠັ(e¯p) ∞ [(u + c) + (1 − y)² (d + s)] u quark
Directly sensitive to gluon density Photo-production (Q²~0) dijets
All 547 data points (ZEUS) are fitted simultaneously. → PDF extraction. ◆ Strong rise of gluon PDF at low x. ◆ Sea quarks are also many. (Note: in the plot they are 1/20)
H1/ZEUS difference
• data set (H1 does not have jets, but results from fixed target exp.) • parameterization • systematic uncertainty
Other (and/or more) measurements ◆ NC/CC –  More statistics with polarized beam. ◆   Heavy Flavour production –  Large statistics with the updated detector in HERA-II. ◆ FL –  First direct measurement at the end of HERA. Understanding of systematic uncertainties of measured cross section in HERA-I ◆  Combining cross sections from the H1 and ZEUS experiments.
◆ Increase of electron data NC → More sensitivity to xF 3 i.e. valence quarks (u+d) ◆ Increase of positron data CC → More sensitivity to d quark
◆   Dominant process of heavy quark production: Boson-Gluon-Fusion (BGF) ◆  Two schemes to treat heavy quarks in pQCD; –  massive scheme (FFN) appropriate for Q 2 ~ M 2 Heavy quarks are produced via BGF. → Sensitive to gluon PDFs —  massless scheme (ZMVFN) appropriate for Q² >> M e ² Heavy quarks are massless and exist in the proton if Q 2 is above the mass threshold. → Intrinsic heavy quarks’ PDFs ◆   Cross check for current pQCD description for the proton. HERA F F 2 ◆  F,cc is extracted for large kinematic region. — different methods ● D mesons by slow pions • Impact parameter tagging –  different data sets, theory → In good agreement ◆ Scaling violation is seen. ◆ Well described by NLO-QCD. F  bb ◆ First measurement of F 2 bb at HERA. ◆ Different methods H1: Impact parameter tagging ZEUS: μ +jet ◆ More data to come
♦  Proportional to longitudinal photon interacting with proton. ◆ In naive QPM, proton has co-linear spin ½ quarks only. Longitudinal photon cannot interact with a quark → F r =0 ♦ gluon emission in the proton → F L ≠ 0 i.e. F r  directly reflects gluon dynamics in the proton. gluon PDF
Measurement of F 1  is good test for the current understanding of proton structure and QCD.
F」 ⇒ gluon → Probably HERA is the best place to measure F」. ◆   Why had F L not been measured before the end of HERA? Ans. Technical difficulties –  Needs cross section measurements with different beam energies. –  Needs to tag scattered electrons with lowest energies as possible. ◆ The last 4 months of HERA operation were dedicated to F r measurement. → Operation with lowered proton beam energy.
Successfully done!
◆   Cross section is combination of F 2 and F L .
•  FL ← Comparison of  F  at the same (x, Q 2 ) but different y →different beam energy Sizable only at high-y ⇔  Low energy of scattered electron. ◆   Linear fit on cross sections at each (x, Q 2 ) bin. → slope = F L
◆ The first F L measurement at low x. ◆ The measured F L is consistent with pQCD description.
All HERA-I inclusive DIS cross sections from H1 and ZEUS are combined by averaging. HERA I e *p Neutral Current Scattering – H1 and ZEUS ◆   Averaged each data point by simultaneous χ ² fit. — Assumption: H1 and ZEUS measure the same cross sections. — taking account of correlated systematics within/between experiments. → Cross calibration Reduction of sys. errors. ◆   It is also an consistency check of two experiments. Uncertainty gets improved by more than sqrt(2).
Q² / GeV²

◆   QCD-Fit on combined cross section. –  Good constraint on PDFs. ◆ HERA PDFs have strong impact on W/Z physics at LHC. ♦  Combination is done only for HERA-I. → HERA-II will come.
◆  During its operation over 15 years, HERA provided plenty of physics through electron-proton collision. –  Not only the proton structure, but Electroweak and QCD physics. ◆   Proton structure has been vigorously investigated at HERA. We have precise understanding of the proton structure. –  Steep rise of gluons and Sea quarks at low-x –  Good description by pQCD → Good input to LHC! ◆ Still, many results from HERA will come up. → We can improve our understanding of the proton structure.
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Backup
W R boson
Extrapolation to P e = ±1 → limits on RH σcc
95% CL on heavy W R boson ◆　M WR >208GeV (H1, e+p) ◆　M WR >186GeV (H1, e-p) ◆　M WR >180GeV (ZEUS, e-p) assuming gL=gR and V R is light
Fit for data points (554 of them) m i  = measured cross section in bin i  by exp e μ i  = true cross section in bin i σ f  = statistical uncertainty in bin i  by exp e β ij  = correlated syst. unc. in bin i    by exp e si, r j ~ N(0,1)
Inclusive jet cross sections in NC DIS ZEUS (Phys Lett B 649 (2007) 12) Inclusive-jet cross sections in NC DIS H1 (DESY 07-073) HERA combined 2007 inclusive-jet NC DIS (this analysis) HERA average 2004 (hep-ex/0506035) World average 2006 (S. Bethke, hep-ex/06065) 0.14 ας (M 7 )