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

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

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

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

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

Structure Function Evolution Tobias Haas: Introduction to HERA

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

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

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

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

… another way to look at it … Proton Charge radius Sample F2 data Hadron-hadron scattering results hc/Q = 6.3 2.0 0.6 0.2 0.06 0.02 fm F2 x- at small x Observation of hadron to parton transition Tobias Haas: Introduction to HERA

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

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

Charged Current Interactions   Tobias Haas: Introduction to HERA

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 2pa2 1 / Q4 CC pa2 /8 sin4 qW 1 / (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

Tobias Haas: Introduction to HERA CC Cross Section d2sCC GF dxdQ2 4 px (e) = (Y+F2 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

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

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

Tobias Haas: Introduction to HERA   e+/- 27.5 GeV p 820/920 GeV Tobias Haas: Introduction to HERA

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

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

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

Tobias Haas: Introduction to HERA as (Q2) QCD fit of F2 scaling violations : as = 0.1150 ± 0.0019 (expt+fit) ± 0.0050 (scale) H1 as = 0.1166 ± 0.0052 (expt+fit) ± 0.0040 (scale) ZEUS Jet cross sections: 1, 2, 3 jets as = 0.1224 ± 0.002 (exp) ± 0.004-5 (theory) running as (ET) in one experiment Tobias Haas: Introduction to HERA