Deep Inelastic Scattering in Lepton-Hadron Collisions Probing the Parton Structure of the Nucleon with Leptons Basic Formalism (indep. of strong dynamics and parton picture) Experimental Development Fixed target experiments HERA experiments Parton Model and QCD Parton Picture of Feynman-Bjorken Asymptotic freedom, factorization and QCD Phenomenology QCD parameters Parton distribution functions Other interesting topics
Basic Formalism (leading order in EW coupling) Lepton-hadron scattering process B Effective fermion-boson electroweak interaction Lagrangian: (B = g, W, Z) EW SU()xU(1) gauge coupling constants
Basic Formalism: current operators and coupling Fermion current operator: V-A couplings: or, Left-right (chiral) couplings: Charge Weak isospin Weinberg angle CKM mixing matrix
Scattering Amplitudes Basic Formalism: Scattering Amplitudes B Spin 1 projection tensor Lepton current amplitude (known): Hadron current amplitude (unknown): Object of study: * Parton structure of the nucleon; (short distance) * QCD dynamics at the confinement scale (long dis.)
Basic Formalism: Cross section Cross section (amplitude) phase space / flux Lepton tensor (known): Hadron tensor (unknown): Object of study: * Parton structure of the nucleon; * QCD dynamics at the confinement scale ΣX
Basic Formalism: Structure Functions Expansion of W µ ν in terms of independent components Cross section in terms of the structure functions Charged Current (CC) processes (neutrino beams): W-exchange (diagonal); left-handed coupling only;. Neutral Current (NC) processes (e,µ scat.)---low energy: (fixed tgt): γ-exchange (diagonal); vector coupling only; Neutral Current (NC) processes (e,µ scat.)---high energy (hera): γ & Z exchanges: G 1, G 1 G, G terms;.
Basic Formalism: Scaling structure functions Kinematic variables E E 1 Scaling form of cross section formula: ( ) Scaling (dimensionless) structure functions P
Scattering Amplitudes Basic Formalism: Helicity Amplitudes B Spin 1 rotation matrix Lepton current amplitude (known): Hadron current amplitude (unknown): Object of study: * Parton structure of the nucleon; * QCD dynamics at the confinement scale
Basic Formalism: Helicity structure functions λ λ Relations between invariant and helicity S.F.s Conversely, Where at high energies Should have been absorbed into the definition of the scaling S.F. s F,3! Cross section formula: where
Experimental Development Interesting and comprehensive description of the entire history of probing the structure of nuclei from (pre-) Rutherford scattering 1930 s 50 s (Hofstadter) 60 s, 70 s (SLAC), SPS, Fermilab, HERA Highly recommended! -lecture series by E. Tassi at CTEQ003 http://www-zeus.desy.de/~tassi/cte003.html
The SLAC-MIT Experiment Under the leadership of Taylor, Friedman, Kendall (Nobel prize, 1990)
First SLAC-MIT results ~ 1969 Two unexpected results
Experimental Development modern experiments (high Q) NuTeV
The highest energy (anti-) neutrino DIS experiments CCFR and NuTeV Fermilab
The highest energy (anti-) neutrino DIS experiment
Fixed targets results: An overview (PDG) F : 1< Q < 00 GeV F 3 : 1< Q < 00 GeV F L
The HERA Collider The first and only ep collider in the world Located in Hamburg H1 Zeus e ± p 7.5 GeV 90 GeV s = 318 GeV Euivalent to fixed target experiment with 50 TeV e ±
Two independent storage rings H1 H1 ZEUS Colliding beam experiments HERA-B HERMES HERA-B Uses p beam on wire target Goal: B - physics ZEUS HERMES Uses e ± beam on gas jet target Both lepton and target polarized Measurement of polarized structure functions
The Collider Experiments H1 Detector Complete 4π detector with Tracking Si-µVTX Central drift chamber Liuid Ar calorimeter p î E=E = 1%= E[GeV ] (e:m:) p î E=E = 50%= E[GeV ] (had) Rear Pb-scintillator calorimeter p îe=e = 7:5%= E[GeV] (e:m:) µ chambers and much more
ZEUS Detector Complete 4π detector with Tracking Si-µVTX Central drift chamber Uranium-Scintillator calorimeter p î E=E = 18%= E[GeV ] p î E=E = 35%= E[GeV ] (e:m:) (had) µ chambers Both detectors asymmetric and much more
Kinematic Regions of DIS
NC and CC incl. Processes measured at HERA NC : e ± + p e ± + X, CC : e ± + p ν ( ν ) + e e X NC: missing ν momentum CC:
Measurement of F γ (x,q ) For Q «M Z xf 3 negligible; F L only important at high y; Both F L and xf 3 ~ calculable in QCD Correct for higher order QED radiation Extract F (x,q ) from measurement of d ûσ ep dxdq These are difficult measurements: nevertheless precision level has reached: errors of -3%
A major finding at Hera: rise of F (x,q) at small x Early fixed-target results: F rise towards low-x established with ~0 nb -1 in early Hera run Recent precise determination of F (1996-97 data samples)
F At high-q still statistics limited priority to the measurements at high-q
Physical Interpretations of DIS Structure Function measurements The Parton Model (Feynman-Bjorken) Theoretical basis of the parton picture and the QCD improved parton model high energy (Bjorken) limit l 1 l l 1 l H H a A X A X
Features of the DIS structure functions due to SM couplings For CC processes, only one helicity vertex (out of xx3=1) is non-zero: In Brick-Wall (Breit) frame: Vector γ coupling: Left-handed W coupling: ψ Lorentz boost with v = tanh ψ Allowed spin configurations: µ ν u d W + W +
continued Conseuences on CC Cross sections (parton model level): These ualitative features were verified in early (bubble chamber) high energy neutrino scattering experiments. Gargamelle (CERN) Refined measurements reveal QCD corrections to the approximate naïve parton model results. These are embodies in all modern QCD fits and global analyses.
Leading (diagonal) EM NC scattering processes: l W l' α Analogous to the familiar angular distribution of scattering of spin ½ elementary particles in the CM frame: F long = 0 no parity violation (y is the hyperbolic angle connecting the lepton and hadron vertices.) At HERA, the γ-z interference term also contribute, giving rise to more complicated patterns for the angular (y) distribution. Features of the partonic interactions revealed by DIS experiments have firmly established that the lepton probes interact primarily with spin ½ uark partons inside the nucleons with couplings of the SM.
)} ( - { )}, ( { )} ( - { }, { - - 3, CC, 3,, s d c u x xf s d c u x xf c u s d x xf s d c u x xf CC e e CC e CC e + + = + + + = + + = + + + = + +,W- Structure functions: Quark Parton Model Quark parton model (QPM) NC SFs for proton target: = = = + + = d u v Z γz Z γz γ a v a e x a v a e x xf xf a v v e e x F F F, 3 3 ], [ } - ]{, [ ], [ } ]{,, [ ],, [ QPM CC SFs for proton targets: 3,W + 3,W-,W + For neutron targets, invoke (flavor) isospin symmetry: u d and u d
High-Q CC cross section from HERA
Comparing NC and CC Xsec s at HERA: EW Unification NC cross section sharply decreases with decreasing Q (dominant γ exchange): ~1/Q 4 CC cross section approaches a constant at low Q ~[M W/(Q +M W)] Dramatic confirmation of the unification of the electromagnetic and weak interactions of the SM in Deep Inelastic Scattering.
Manifestation of γz interference: xf 3 (NC) at Hera xf NC 1 - + - ~ 3 = [ σ ~ ( e p) - σ ( e p)] Y Needs better e - data! d NC ± σborn( e p) πα NC NC NC = 4 [ Y+ F ( x, Q ) - y FL ( x, Q ) my- xf3 ( x, Q )] dxdq xq
xf 3 γz (NC) NC κq γz κq 3 = - ae xf3 + (veae)( ) ( Q + MZ ) Q + MZ xf xf3 γz NC xf3 - F3 ( Q + M Z ) /( aeκq Z )
Helicity structure Needs e - data
QCD and DIS Cf. Introductory course by Sterman µ is the factorization scale. Usually choose µ = Q: that is how f(x,q) acuires Q-dep.
F : Scaling violation Q-dependence inherent in QCD Renormalization group euation governs the scale dependence of parton distributions and hard cross sections. (DGLAP) Rise with increasing Q at small-x Flat behavior at medium x decrease with increasing Q at high x
QCD evolution P ln ln = = = ± ± ± g P P P P g P gg g g F NS NS NS F Σ Σ µ µ F F S S l l l S S R S R S S R F S S N N a a a a d da a x P x P a x P a x P 3 38 10 and 3 11 where ) ( ln 4 ) ( with ) ( ln ) ( ) ( ) ( 1 0 1 3 0 0 (0) 0 (1) (0) = = + = = = + = = + β β β β β β µ π µ α µ µ β Evolution performed in terms of (1//3) non-singlet, singlet and gluon densities: Where Cf. Introductory course by Sterman
Parton Distribution Functions (PDF): most significant physical results derived from DIS (with help from other hard scattering processes) A common misconception: Parton distribution functions Structure functions These are the hard Xsecs. These are the (process-dep) S.F.s These are the (universal) PDFs There is a convolution integral and a summation over partons here!
Parton Distributions: one example Cf. course on global analysis and PDFs
Outline of the course: Summary and Conclusion Important to know the model indep. foundation of the measured structure functions and their basic properties. Basic Formalism (indep. of strong dynamics and parton picture) Experimental Development Fixed target experiments HERA experiments Parton Model and QCD Parton Picture of Feynman-Bjorken Asymptotic freedom, factorization and QCD Phenomenology QCD parameters Parton distribution functions Other interesting topics There is a long and distinguished history, dating back to Rutherford These highest energy and highest statistics expts. provide the basis for modern precision phenomenology DIS experiments provided direct evidence for the parton structure of the nucleon, and confirmed every aspect of the SU(3)xSU()xU(1) SM. Cf. the rest of the Summer School courses for exciting conseuences of PQCD as well as other modern theories to follow.