1. An Introduction to HERA Physics
DESY Summer Student Program
16/17 August, 2005
Tobias Haas
DESY, Hamburg
Tobias Haas: Introduction to HERA

2. Tobias Haas: Introduction to HERA
Part 2
Tobias Haas: Introduction to HERA

3. NC Cross Section and Structure Functions
Q2=-q2=-(k-k’)2
x: momentum fraction
of the struck parton
y=Q2/xs
NC Reduced cross section:
NC Cross Section:
Dominant contribution
Sizeable only at high y (y>~0.6)
Contribution only important at high Q2
Tobias Haas: Introduction to HERA

4. Tobias Haas: Introduction to HERA
F2 vs Q2
Note:
Enormous range of data (5 orders in Q2 and 8 orders in x)
Approximate scaling at high Q2
Scaling violations at low Q2
Tobias Haas: Introduction to HERA

5. Tobias Haas: Introduction to HERA
F2 vs xBj
Dramatic rise a low xBj
Note previous picture:
Tobias Haas: Introduction to HERA

6. Structure Function Evolution
Tobias Haas: Introduction to HERA

7. Reminder: Nomenclature/Kinematics
= 0 in the QPM
Z0 Exchange
Tobias Haas: Introduction to HERA

8. What QCD tells about F2(x,Q2) ?
Splitting functions:
Can be calculated in pQCD
DGLAP Equation:
Integral-Differential equation for the dependence of q(x,Q2), g(x,Q2) on Q2
Need an initial condition!
Tobias Haas: Introduction to HERA

9. Tobias Haas: Introduction to HERA
QCD Fits
Make an ansatz at a fixed value of Q2 = Q02
Write F2 simpler:
Ignore F3 and FL (for the moment)
_ _
F2 ~ 4/9 (U+U) + 1/9 (D+D)
with
_ _ _ _ _ _
D = d+s U = u+c
U = u+c D = d+s
Tobias Haas: Introduction to HERA

10. Parton Distribution Functions
QCD fits to structure functions:
_ _
F2 ~ 4/9 (U+U) + 1/9 (D+D)
_ _ Valence quarks:
2 (U-U) (D -D)
_ _ _ _ _ _
D = d+s U = u+c
U = u+c D = d+s
% precision except for gluon :
Tobias Haas: Introduction to HERA

11. … another way to look at it …
Proton Charge radius
Sample F2 data
Hadron-hadron scattering results
hc/Q = fm
F2 x- at small x
Observation of hadron to parton transition
Tobias Haas: Introduction to HERA

12. Tobias Haas: Introduction to HERA
High Q2 and EW
Tobias Haas: Introduction to HERA

13. Tobias Haas: Introduction to HERA
High Q2 NC (γ, Z Exchange)
Note:
Handle on F3:
Valence quarks!
g-Z interference: e- constructive / e+ destructive
Tobias Haas: Introduction to HERA

14. Charged Current Interactions 
Tobias Haas: Introduction to HERA

15. Tobias Haas: Introduction to HERA
NC vs CC 2
ignore FL and xF3
M2W,Z
l = ± 1 for
left/right handed e
~ 1 / Q4
COUPLING PROPAGATOR
NC pa / Q4
CC pa2 /8 sin4 qW / (MW2+Q2)2
similar since similar at
sin2 qW ~ ¼ Q2 > MW2
‘Unification’ of elm. and weak forces
~ 1 / (MW2+Q2)2
Tobias Haas: Introduction to HERA

16. Tobias Haas: Introduction to HERA
CC Cross Section
d2sCC GF
dxdQ px
(e) = (Y+F Y-xF3 - y2FL )  M2
M2 + Q2 W 2 e- e+
s (e-p) > s (e+p)
_ _
--- s (e-p) ~ x (u+c) + (1-y2) x (d+s)
_ _
--- s (e+p) ~ x (u+c) + (1-y2) x (d+s)
Tobias Haas: Introduction to HERA

17. Tobias Haas: Introduction to HERA
Jets and S(Q2)
Tobias Haas: Introduction to HERA

18. Tobias Haas: Introduction to HERA
How do you get Jets?
Outgoing partons described by 3 more variables:
Tobias Haas: Introduction to HERA

19. Tobias Haas: Introduction to HERA 
e+/ GeV
p 820/920 GeV
Tobias Haas: Introduction to HERA

20. Dijet Cross Section in DIS
Note:
Ingredients in these calculations:
NLO QCD calculation
parton densities
strong coupling, αS
hadronization corrections
Make this a test a test for the strong coupling:
take pdfs from inclusive data (F2)
Calculate hadronization using an QCD-inspired MC model (like jetset)
fit
Tobias Haas: Introduction to HERA

21. Practical consideration: Use Dijet Fraction
R2+1 has smaller sensitivity to PDFs
Some experimental errors cancel
Fit:
Tobias Haas: Introduction to HERA

22. S(Q2) from Dijet Production
Tobias Haas: Introduction to HERA

23. Tobias Haas: Introduction to HERA
as (Q2)
QCD fit of F2 scaling violations :
as = ± (expt+fit) ± (scale) H1
as = ± (expt+fit) ± (scale) ZEUS
Jet cross sections: 1, 2, 3 jets
as = ± (exp) ± (theory)
running as (ET)
in one experiment
Tobias Haas: Introduction to HERA