Basic Formalism (leading order in EW coupling)

Transcription

1 Dee Inelastic cattering in Leton-Hadron Collisions Probing the Parton tructure of the Nucleon with Letons Basic Formalism (inde. of strong dynamics and arton icture) Exerimental Develoment Fixed target exeriments HERA exeriments Parton Model and QCD Parton Picture of Feynman-Bjorken Asymtotic freedom, factorization and QCD Phenomenology QCD arameters Parton distribution functions Other interesting toics Basic Formalism (leading order in EW couling) Leton-hadron scattering rocess Effective fermion-boson electroweak interaction Lagrangian: EW U()xU(1) gauge couling constants B (B = g, W, Z) 1 Basic Formalism: current oerators and couling Fermion current oerator: cattering Amlitudes Basic Formalism: cattering Amlitudes B V-A coulings: or, Left-right (chiral) coulings: Charge Weak isosin in 1 rojection tensor Leton current amlitude (known): Hadron current amlitude (unknown): Weinberg angle CKM mixing matrix Object of study: * Parton structure of the nucleon; (short distance) * QCD dynamics at the confinement scale (long dis.) 4

2 Cross section Basic Formalism: Cross section (amlitude) hase sace / flux Basic Formalism: tructure Functions Exansion of W µ ν in terms of indeendent comonents Leton tensor (known): Cross section in terms of the structure functions Hadron tensor (unknown): Charged Current (CC) rocesses (neutrino beams): W-exchange (diagonal); left-handed couling only;. Object of study: * Parton structure of the nucleon; * QCD dynamics at the confinement scale ΣX 5 Neutral Current (NC) rocesses (e,µ scat.)---low energy: (fixed tgt): γ-exchange (diagonal); vector couling only; Neutral Current (NC) rocesses (e,µ scat.)---high energy (hera): γ & Z exchanges: G 1, G 1 G, G terms;. 6 Basic Formalism: caling structure functions Basic Formalism: Helicity Amlitudes Kinematic variables E cattering Amlitudes E 1 B caling form of cross section formula: ( ) caling (dimensionless) structure functions P in 1 rotation matrix Leton current amlitude (known): Hadron current amlitude (unknown): 7 Object of study: * Parton structure of the nucleon; * QCD dynamics at the confinement scale 8

3 Basic Formalism: Helicity structure functions Exerimental Develoment λ λ Relations between invariant and helicity.f.s Conversely, Cross section formula: Where at high energies hould have been absorbed into the definition of the scaling.f. s F,! Interesting and comrehensive descrition of the entire history of robing the structure of nuclei from (re-) Rutherford scattering 190 s 50 s (Hofstadter) 60 s, 70 s (LAC), P, Fermilab, HERA Highly recommended! -lecture series by E. Tassi at CTEQ00 htt://www-zeus.desy.de/~tassi/cte00.html where 9 10 The LAC-MIT Exeriment Under the leadershi of Taylor, Friedman, Kendall (Nobel rize, 1990) First LAC-MIT results ~ 1969 Two unexected results 11 1

4 Exerimental Develoment modern exeriments (high Q) The highest energy (anti-) neutrino DI exeriments NuTeV CCFR and NuTeV Fermilab 1 14 Fixed targets results: An overview (PDG) (Neutral Current old results) F : 1< Q < 00 GeV F : 1< Q < 00 GeV The highest energy (anti-) neutrino DI exeriment F L 15 16

5 F Measurement Isoscalar ν-fe F NuTeV F is comared with CCFR and CDHW results - the line is a fit to NuTeV data All systematic uncertainties are included All data sets agree for x<0.4. At x>0.4 NuTeV agrees with CDHW At x>0.4 NuTeV is systematically above CCFR xf xf Measurement Isoscalar ν-fe xf NuTeV xf is comared with CCFR and CDHW results - the line is a fit to NuTeV data All systematic uncertainties are included All data sets agree for x<0.4. At x>0.4 NuTeV agrees with CDHW At x>0.4 NuTeV is systematically above CCFR Martin Tzanov DI005 Aril, Martin Tzanov DI005 Aril, The HERA Collider The first and only e collider in the world Two indeendent storage rings H1 H1 ZEU Colliding beam exeriments Located in Hamburg H1 Zeus e ± 7.5 GeV 90 GeV s = 18 GeV HERA-B HERME HERA-B HERME Uses beam on wire target Goal: B - hysics Euivalent to fixed target exeriment with 50 TeV e ± ZEU Uses e ± beam on gas jet target Both leton and target olarized Measurement of olarized structure functions 19 0

6 The Collider Exeriments H1 Detector Comlete 4π detector with Tracking i-µvtx Central drift chamber Liuid Ar calorimeter î E=E = 1%= E[GeV ] (e:m:) î E=E = 50%= E[GeV ] (had) Rear Pb-scintillator calorimeter îe=e = 7:5%= E[GeV] (e:m:) µ chambers and much more ZEU Detector Both detectors asymmetric Comlete 4π detector with Tracking i-µvtx Central drift chamber Uranium-cintillator calorimeter î E=E = 18%= E[GeV ] (e:m:) î E=E = 5%= E[GeV ] (had) µ chambers and much more 1 Kinematic Regions of DI NC and CC incl. Processes measured at HERA NC : e ± + e ± + X, CC : e ± + ν ( ν ) + e e X NC: missing ν momentum CC: 4

7 Measurement of F γ (x,q ) For Q «M Z xf negligible; F L only imortant at high y; Both F L and xf ~ calculable in QCD Correct for higher order QED radiation Extract F (x,q ) from measurement of d ûσ e dxdq A major finding at Hera: rise of F (x,q) at small x Early fixed-target results: These are difficult measurements: nevertheless recision level has reached: errors of -% 5 F rise towards low-x established with ~0 nb -1 in early Hera run Recent recise determination of F ( data samles) 6 Physical Interretations of DI tructure Function measurements F The Parton Model (Feynman-Bjorken) Theoretical basis of the arton icture and the QCD imroved arton model high energy (Bjorken) limit l 1 l l 1 l H H At high-q still statistics limited riority to the measurements at high-q A X A a X 7 8

8 Features of the DI structure functions due to M coulings For CC rocesses, only one helicity vertex (out of xx=1) is non-zero: In Brick-Wall (Breit) frame: Vector γ couling: Left-handed W couling: ψ Lorentz boost with v = tanh ψ Allowed sin configurations: µ ν u W + d W continued Conseuences on CC Cross sections (arton model level): Leading (diagonal) EM NC scattering rocesses: α l l' F long = 0 no arity violation (y is the hyerbolic angle connecting the leton and hadron vertices.) W Analogous to the familiar angular distribution of scattering of sin ½ elementary articles in the CM frame: These ualitative features were verified in early (bubble chamber) high energy neutrino scattering exeriments. Gargamelle (CERN) Refined measurements reveal QCD corrections to the aroximate naïve arton model results. These are At HERA, the γ-z interference term also contribute, giving rise to more comlicated atterns for the angular (y) distribution. Features of the artonic interactions revealed by DI exeriments have firmly established that the leton robes interact rimarily with sin ½ uark artons inside the nucleons with coulings of the M. embodies in all modern QCD fits and global analyses. 1

9 tructure functions: Quark Parton Model High-Q CC cross section from HERA Quark arton model (QPM) NC Fs for roton target: γ [ F, F [ xf xf xf γz γz CC,W e + CC, F, xf Z Z ] ] = x = x [ [ = x{ u + c + d + s}, xf + = x{ u + c + ( d + s)}, e,e v, v + a xf ]{ + } e a, v a ]{ - } = x QPM CC Fs for roton targets: CC,W e + CC, e -,W- e -,W- = u, d = x{ d + s - ( u + c)} = x{ u + c - ( d [ e a, v a ] v + s)} For neutron targets, invoke (flavor) isosin symmetry: _ u d and u d _ 4 Comaring NC and CC Xsec s at HERA: EW Unification Manifestation of γz interference: xf (NC) at Hera NC cross section sharly decreases with decreasing Q (dominant γ exchange): ~1/Q 4 CC cross section aroaches a constant at low Q ~[M W/(Q +M W)] xf NC ~ = [ σ ~ ( e ) - σ ( e )] Y Needs better e - data! Dramatic confirmation of the unification of the electromagnetic and weak interactions of the M in Dee Inelastic cattering. 5 NC ± d σborn( e ) πα NC NC NC = 4 [ Y+ F ( x, Q ) - y FL ( x, Q ) my- xf ( x, Q )] dxdq xq 6

10 xf γz (NC) Helicity structure NC κq γz κq = - ae xf + (veae)( ) ( Q + MZ ) Q + MZ xf xf Z γz NC xf - F ( Q + M Z ) /( aeκq ) 7 Needs e - data 8 QCD and DI Cf. Introductory course F : caling violation Q-deendence inherent in QCD Renormalization grou euation governs the scale deendence of arton distributions and hard cross sections. (DGLAP) Rise with increasing Q at small-x Flat behavior at medium x µ is the factorization scale. Usually choose µ = Q: that is how f(x,q) acuires Q-de. 9 decrease with increasing Q at high x 40

11 P( x) = a P da d ln µ R QCD evolution Evolution erformed in terms of (1//) non-singlet, singlet and gluon densities: Where (0) ( x) + a P = β ( a ) = l= 0 ± ± ± ln µ F N = P N Σ P = ln µ g P F a (1) l+ µ ( x) β ln P 0 µ l F R β a β + a β 0 1 (0) g ( x) N P P g gg Σ = P g with where and Cf. Introductory course a α ( µ ) R = 4π β = 11 0 N 8 β = 10 N 1 F F 41 Parton Distribution Functions (PDF): most significant hysical results derived from DI (with hel from other hard scattering rocesses) A common misconcetion: Parton distribution functions tructure functions These are the (rocess-de).f.s These are the (universal) PDFs These are the hard Xsecs. There is a convolution integral and a summation over artons here! 4 Parton Distributions: one examle Cf. course on global analysis and PDFs Outline of the course: ummary and Conclusion Basic Formalism (inde. of strong dynamics and arton icture) Exerimental Develoment Fixed target exeriments HERA exeriments Parton Model and QCD Parton Picture of Feynman-Bjorken Asymtotic freedom, factorization and QCD Phenomenology QCD arameters Parton distribution functions Other interesting toics Imortant to know the model inde. foundation of the measured structure functions and their basic roerties. There is a long and distinguished history, dating back to Rutherford These highest energy and highest statistics exts. rovide the basis for modern recision henomenology DI exeriments rovided direct evidence for the arton structure of the nucleon, and confirmed every asect of the U()xU()xU(1) M. Cf. the rest of the ummer chool courses for exciting conseuences of PQCD as well as other modern theories to follow. 4 44