1. Precision QCD Tests at HERA
- The Standard Model of Particle Physics
- HERA Machine and Experiments
- Precision QCD Tests at HERA
Summary
Robert Klanner Hamburg
Precision QCD Tests at HERA

2. Ch.1: Standard Model – Building Blocks
In the Standard Model of Particle Physics,
which summarizes 50 years of experimen-
tal and theoretical research:
Elementary building blocks
of known matter:
mass/energy distribution in universe 5% m t e
leptons
(weak IA)
all elementary particles of the SM have been experimentally observed! ne nm nt
missing element of the SM: generation of mass (of elementary particles): Higgs mechanism
quarks
(+strong IA) up
charm
top
down
strange
bottom
mass
Quarks und Leptonen come in 3 families - masses vary by 106 (1012)
Robert Klanner Hamburg
Precision QCD Tests at HERA

3. Standard Model: Forces
In SM forces mediated by the exchange of bosons, which couple to “charges”
The form of the interactions is derived from the symmetry of “local gauge invariance” (e.g. em: arbitrary rotation in U(1) space)
In Nature we know 4 fundamental forces:
boson: photon with spin 1, U(1), electrom. charge
bosons: 8 gluons with spin 1, SU(3), colour charge
unified GSW
bosons: W+ W- Z0 with spin 1, SU(2), weak charge
bosons: graviton with spin 2, mass, not part of SM !
SM is a beautiful theory – one of the greatest achievements of 20th century physics,
but many open questions: many “arbitrary“ parameters, relation quarks – leptons, unification of forces, gravity, … limit of a more general theory
Robert Klanner Hamburg
Precision QCD Tests at HERA

4. Standard Model: QED Why do we believe in “correctness” of SM?
precise predictions directly testing the struc-
ture of the theory, which have been verified
experimentally to high accuracy
Quantum-Electro-Dynamics:
- thanks to smallness of e.m. coupling
a(E~0) =1/ …
and the ingenuity of our theoretical colleagues
perturbative calculations to high accuracy
½(g-2)e = ( ±3.8) meas.
½(g-2)e = ( ±27.1) theo.
½(g-2)m = ( ±.58) meas.
(meas.-theory) (1.19±0.73) 10-9
(Dm (theoretical) dominated by had. contributions!)
Lamb shift, a(m), and many more
Robert Klanner Hamburg
Precision QCD Tests at HERA

5. Standard Model: Electro-Weak Sector
Precision data from LEP,SLC,FNAL, etc test higher order e.w. predictions of SM
Status: Winter 2005
demonstration of e.w. unification at HERA
rate
distance [m]
Open Question: Why does SM work so well ?!
Robert Klanner Hamburg
Precision QCD Tests at HERA

6. Predictive Power of SM (EW)
Quantum fluctuations (Heisenberg: DE*Dt > h/2p) allow access to higher masses and energies: e+ e-
l,q,W+
l,q,W-
virtual heavy particle influences reaction-rates and -properties
e.g. corrections of higher order in the electro-weak force:
 Mass of Top-Quarks was predicted by precision measurements within SM
Robert Klanner Hamburg
Precision QCD Tests at HERA

7. Gravity – Strong Force – Summary Ch. 1
Gravity not part of SM
- F(gravity)/F(em) ~ (major puzzle !)
 so far not relevant for experimental particle physics
- Newton’s law verified only down to ~ 0.1 mm  possible deviations from 1/r2  extra dimensions to accommodate difference in strength of gravity compared to the other interactions (at low energy) ?
Precision tests of the strong force  ch.3
Summary chapter 1:
Standard Model of Particle Physics is an impressive intellectual achievement:
a theory which makes precise and testable predictions
so far all experimental results agree with predictions (sometimes to an incredible accuracy)
but limitations + incomplete  SM is only limiting case of a broader theory
Robert Klanner Hamburg
Precision QCD Tests at HERA

8. Chapter 2: HERA and its Experiments
The world’s only electron/positron - proton storage ring
27.5 GeV polarised electrons (positrons)
920 GeV protons ⇨ 320 GeV in cms
Four experiments H1, ZEUS, HERMES and {HERAb} (≈ 1000 scientists)
data taking: 1992 until mid 2007 when HERA data taking ends
Robert Klanner Hamburg
Precision QCD Tests at HERA

9. HERA machine 2
HERA I ( ): 110 pb-1 e+ and 15 pb-1 e- data for H1 and ZEUS + polarised e- on pol./unpol. gas target for HERMES + pN data for HERAb
HERAII ( 2007): polarised e+/e--p data for H1/ZEUS + data for HERMES upgrade in 2000/01, 2002/03 severe BG problems, now solved and (aging) HERA runs well
Lmax~ cm-2s-1 ;Luminosity aims: ~0.7 fb-1 until end of data taking in mid 2007
Robert Klanner Hamburg
Precision QCD Tests at HERA

10. HERA Collider Detectors - 1
- detectors conceived
in 1985 to 1988
- first data in 1992
- HERA first collider with
short (96 ns) time
between bunches
 trigger/event pipe-lined
% Lumi accuracy
- compared to LEP/D0/CDF:
precision hadron calorimetry
DE(100GeV) ~ 3.5-5%
calibration at 1% level
(essential for precision
physics at HERA)
- HERAb with 20 MHz inter-
action rate: major progress
in trigger + radiation tolerance
H1 Detector
Robert Klanner Hamburg
Precision QCD Tests at HERA

11. HERA Collider Detectors 2
A (fairly typical)
NC ep  e+q(jet)+X event
(Q2=3500GeV2, x=0.05)
events clean  precise reconstruction of kinematics (directly seen underlying Feynman graph) e e e p
p rest q
q  jet
Robert Klanner Hamburg
Precision QCD Tests at HERA

12. Chapter 4: Tests of QCD at HERA
HERA: precision microscope shining (e.m. and weak) light onto the proton
resolution Dx~1/Q can be tuned at HERA down to 10-18m (1/1000 rp)
Q Dx
GeV2 fm
~ /3
~ /10
> <1/10
>105 <1/1000
charge distr.
quarks scaling
scaling violation
sub-struct.?
p momentum fraction of parton (QPM)
resolution power can be tuned
⊕ for Q2  0 g: has a hadronic component (e.g. g  r)
 transition from point-like g/Z-hadron to hadron-hadron scattering
Robert Klanner Hamburg
Precision QCD Tests at HERA

13. Tests of QCD: Structure of photon vs Q2
Is the picture of the “photon structure” vs resolution – 1/Q2 correct?
 2 jet production vs Q2
~ yes
“direct”
xg > 0.8
“resolved”
xg < 0.8
description not perfect qualitatively o.k!
 with increased Q2 – exchanged g getting point-like
Robert Klanner Hamburg
Precision QCD Tests at HERA

14. Tests of QCD: Properties of Exchanged Partons
Is the picture of the “exchange of virtual quarks and gluons” correct?
 2 jet production vs Q2
yes
“direct”
xg > 0.8
“resolved”
xg < 0.8
angular distribution of jets in jet-jet cm system is sensitive to the spin of the exchanged particle:
Spin 1 (gluons):
(like Rutherford)
Spin ½ (quarks): g g q q
Robert Klanner Hamburg
Precision QCD Tests at HERA

15. Test of QCD: The running coupling constant aS
1973 Breakthrough in development of QCD: asymptotic freedom  strong coupling weak at small distances (high energies – scale m)  perturbative calculations possible for precise predictions
m dependence of aS controlled by b-function:
< 0
aS(m) expressed via parameter L[GeV]:
Robert Klanner Hamburg
Precision QCD Tests at HERA

16. Precision Tests of QCD: What are the Problems
1.) aS is small only at small distances (high Q2)
 only*) domain for precision tests using perturbative expansion in aS, e.g.
calculate Ai from Feynman graphs
 divergences have to be regulated in some scheme
 Ai depend explicitly on scale m (infinite sum does not)
if wrong scale m’ is chosen  terms ln(m’/m) appear
choice not obvious (if higher order terms small  confidence that o.k.)
(NB there are also problems with two scales m1,m2  terms ln(m1/m2))
2.) b function changes when m passes quark mass M
some arbitrariness how to treat effect
3.) no free quarks  non perturbative effects
“everywhere” – handled via models (pdfs,
Monte Carlo)  use reactions where effects
not so important (e.g “total cross sections”)
*) Lattice Gauge Theory is start to produce precise results
Robert Klanner Hamburg
Precision QCD Tests at HERA

17. Measurement of aS – Why?  test QCD
Besides masses, aS [L] only free parameter of QCD
Why precise measurements in many different ways?
all strong interaction cross sections depend on aS,
if QCD correct  all measure ments should agree
 test QCD
if disagree problem with QCD ??? (more probably large distance effects)
unification of forces: precision at today’s energies is required for pre cise extrapolation to unification scale
and the physics on the way to there
Robert Klanner Hamburg
Precision QCD Tests at HERA

18. Test of QCD: aS from DIS Structure Functions
Q2 evolution of structure functions q, g:
splitting functions P have been calculated
up to 2nd order – for unpol. 3rd order soon
- theoretically “clean” method,
- HERA alone: correlation gluon -
aS (resolved by fit SF + jets)
- uncertainty on sea quarks: ,
- terms at large x,
- terms at small x,
- photon structure at low Q2.
improvements (experimental + theoretical) are under way  later
(H1: 2000, ZEUS: 2002)
Robert Klanner Hamburg
Precision QCD Tests at HERA

19. Test of QCD: aS from Jet Production
Diagrams contributing to jet production: Example-1: H1 DIS in Breitframe:
deep inelastic scattering:
photoproduction:
- theoretically less clean than DIS
- but measurement of m dependence
running of aS in agreement with QCD prediction observed in single experiment
Robert Klanner Hamburg
Precision QCD Tests at HERA

20. Test of QCD: aS from 2-Jet to 3- Jet Ratio
Example-2: ZEUS ratio of 3-jet to 2-jet production: :
- uncertainty of parton distribution functions cancel (in some approximation)
running of aS in agreement with QCD prediction observed in single experiment
Robert Klanner Hamburg
Precision QCD Tests at HERA

21. Test of QCD: aS from Jet Sub-structure
Example-3: ZEUS from jet structure:
small experimental error
theoretical error ???
integrated jet shape:
fraction jet transverse
energy within cone of
radius r in η, φ plane
ψ(r=0.5) vs ET(jet)
aS(ET)
ψ(r) comparison to theory
running of aS in agreement with QCD prediction observed in single experiment
Robert Klanner Hamburg
Precision QCD Tests at HERA

22. Test of QCD: aS Summary
measurements compatible
combine results for each expt.
many different aS measurements give consistent results
“running of aS as predicted by QCD  major success QCD
Robert Klanner Hamburg
Precision QCD Tests at HERA

23. Test of QCD: Proton Structure (1)
- HERA !
Robert Klanner Hamburg
Precision QCD Tests at HERA

24. Test of QCD: Proton Structure (2)
dr ∝
1/Q2
major success of perturbative QCD
Robert Klanner Hamburg
Precision QCD Tests at HERA

25. Test of QCD: Proton Structure (3)
(use low Q2 fixed target data to constrain high x pdfs)
HERA has provided a precision determination of proton structure  essential input for SM and BSM study at present and future accelerators
Robert Klanner Hamburg
Precision QCD Tests at HERA

26. Proton Structure and Higgs Cross section at LHC
Impact on precision of parton functions on Higgs signal (+background) at LHC
Spread of existing pdf gives already up to 10% uncertainty  improve !
Robert Klanner Hamburg
Precision QCD Tests at HERA

27. Test of QCD: Proton Structure (4)
Use all (>100pb-1) HERAI data (neutral and charged current reaction):
e p data only (no nuclear data !)
Q2/GeV2
HERA has provided a precision determination of proton structure  essential input for SM and BSM study at present and future accelerators
Robert Klanner Hamburg
Precision QCD Tests at HERA

28. Test of QCD: Jets in the Final State
QCD: parton functions universal  the same parton function describes different reactions e.g.
jet production, heavy quark production, single photons, ….
Events with two jets:
- dominant graph (LO) “photon-gluon fusion”
(direct coupling to gluon – in DIS only derivative ∝ (gluon density in p)
- in two jet events momentum of gluon can be reconstructed
Robert Klanner Hamburg
Precision QCD Tests at HERA

29. Test of QCD: Jets in the Final State
Combined fit of proton structure function and s(jet)
 data well described ⊕ improved precision at high x ⊕ no correlation between aS and gluon ⊕ data from a single experiment
simultaneous description  major success for QCD
Robert Klanner Hamburg
Precision QCD Tests at HERA

30. Test of QCD: Heavy Flavour in the Final State
Production of heavy flavour particles: high quark mass provides large scale m
scc/stot=F2cc/F2
first results become available for b-quarks
NLO QCD predicts scharm correctly
Robert Klanner Hamburg
Precision QCD Tests at HERA

31. HERMES: Spin of Nucleon
NLO QCD (MS) analysis/fit of spin data:
Assumptions:
- Flavour symmetric spin dependent sea
- uv and dv constrained by F and D (SU(3) symmetry)
low-x extrapolation questionable !
 results for Q02 = 4 GeV2:
uv  (0.10)
dv  (0.10)
qs 
 
G 
information from high pT had. pairs (HER-MES, COMPASS) and charm (COMPASS)
Data described by NLO QCD fit
(aS(MZ) = )
Robert Klanner Hamburg
Precision QCD Tests at HERA

32. QCD: Diffraction in Deep Inelastic Scattering
HERA 1992: ~ 10% of deep inelastic events have no particle flow between proton and jet (rapidity gap) - (same effect also seen in W-exchange)
Surprise:
- why does p remain intact - confinement?
- are there colour neutral objects in p?
- can process be described by QCD?
 HERA microscope the ideal instru ment for study
define and measure diffractive structure function:
rap. gap
to proton
Robert Klanner Hamburg
Precision QCD Tests at HERA

33. QCD: Diffraction in Deep Inelastic Scattering
systematic measurements
using different methods:
- rapidity gap,
- fit to particle flow,
- measurement of proton.
after hard work results
of measurements in good
agreement
Robert Klanner Hamburg
Precision QCD Tests at HERA

34. QCD: Diffractive Structure Function
comparison diffractive ⇔ proton structure function: H1
diff. SF: positive  gluon dominance; data well described by NLO QCD
Robert Klanner Hamburg
Precision QCD Tests at HERA

35. QCD: Diffractive Final States
using QCD jet and heavy flavour production in diffraction predicted:
charm structure function D* cross sections
good description by NLO QCD
high Q2 diffraction: well described by QCD – relation to basic QCD however unclear
Robert Klanner Hamburg
Precision QCD Tests at HERA

36. Summary
The Standard Model of Particle Physics beautifully summarizes the present experimental results and knowledge of Particle Physics.
QCD, the theory of the strong force, is the least tested part of the SM.
Tests of QCD (and not of models) is so far (essentially) limited to the small distance predictions (perturbative) – but non-perturbative effects are present everywhere and have to be carefully understood.
HERA has put the tests of QCD to a new level of breadth and precision (scaling of structure functions, final states in photo-production and deep inelastic scattering, aS) – sometimes reaching the 2% level.
So far QCD has very well passed the tests + lots has been learned on QCD
These results, interesting in themselves, are also important for understan- ding the much more complex situation at the LHC.
Robert Klanner Hamburg
Precision QCD Tests at HERA