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PHYS 5326 – Lecture #3

PHYS 5326 – Lecture #3. Monday, Jan. 29, 2007 Dr. Jae Yu. Neutrino-Nucleon DIS n -N DIS Formalism Proton Structure Function and Parton Distribution Functions (PDFs). Neutrino Nucleon Deep Inelastic Scattering.

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PHYS 5326 – Lecture #3

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  1. PHYS 5326 – Lecture #3 Monday, Jan. 29, 2007 Dr. JaeYu • Neutrino-Nucleon DIS • n-N DIS Formalism • Proton Structure Function and Parton Distribution Functions (PDFs) PHYS 5326, Spring 2007 Jae Yu

  2. Neutrino Nucleon Deep Inelastic Scattering • DIS (Deep Inelastic Scattering) of lepton-nucleon are traditionally used to probe nucleon structures • Neutrinos (especially ) are excellent probes • Extremely light • Structureless • Weak interaction only  Probes helicity • nmare normally used for these experiments. Why? • Nucleons consist of partons • Structure of nucleon is described by parton distribution functions (PDF)  Constituents’ probability distributions in fractional momentum space • DIS are viewed as neutrino-parton elastic scattering PHYS 5326, Spring 2007 Jae Yu

  3. Structure Function Measurements • A complete set of Lorentz scalars that parameterize the unknown structure of the proton • Properties of the SF lead to parton model • Nucleon is composed of point-like constituents, partons, that elastically scatter with neutrino • Partons are identified as quarks and gluons of QCD • QCD theory itself does not provide parton distributions within the proton • Then what does QCD provide? • The dynamics of strong interactions using color quantum numbers • QCD analysis of SF provides a determination of nucleon’s valence and sea quark and gluon distributions (PDF) along with the strong coupling constant, as PHYS 5326, Spring 2007 Jae Yu

  4. Kinematics of nm-N CC Interactions • DIS is a three dimensional problem • Three kinematic parameters provide full description of a DIS event are • pm: Muon momentum • qm: Angle of outgoing muon • EHad: Observed energy of outgoing hadrons • Neutrino energy becomes • En=EHad+Em+Mp PHYS 5326, Spring 2007 Jae Yu

  5. nm,(`nm) m-, (m+) k k’ pm, qm W+(W-) q=k-k’ q, (`q) } xP EHad P DIS Kinematics Leptonic System Hadron System Why isn’t NC used for SF? PHYS 5326, Spring 2007 Jae Yu

  6. DIS Lorentz Invariant Variables CMS Energy Energy transferred to the hadronic System Four momentum transfer of the interaction Invariant mass of the hadronic system PHYS 5326, Spring 2007 Jae Yu

  7. DIS Lorentz Invariant Variables cont’d Bjorken Scaling Variable = Fractional Momentum of the Struck parton within the nucleon Inelasticity where q* is CMS scattering angle of m PHYS 5326, Spring 2007 Jae Yu

  8. Weak Coupling Constant W (CC) Propagator Lepton Hadron Hadronic Tensor Leptonic Tensor DIS Formalism Matrix element for n-N interaction Inclusive Spin-Averaged Cross section PHYS 5326, Spring 2007 Jae Yu

  9. n-N DIS Cross Sections for SF Extraction Using ratio of absorption xsec for longitudinal and transversely polarized boson, R PHYS 5326, Spring 2007 Jae Yu

  10. Spin 0 partons Parity violating components • Assuming parton model, n-N cross section can be rewritten in terms of point-like particle interactions that exchange a intermediate vector boson Structure Functions and PDF’s • Comparing the parton-neutrino to proton-neutrino SF and PDF’s are related as PHYS 5326, Spring 2007 Jae Yu If no spin 0, 2xF1=F2

  11. Linking to Quark Flavors • n-N scattering resolves flavor of constituents • CC changes the flavor of the struck quark • Charge conservation at the vertex constraints • Neutrinos to interact with d, s, `u, `c • Anti-neutrinos to interact with `d, `s, u, c • For parton target, the quark densities contribute to SF are PHYS 5326, Spring 2007 Jae Yu

  12. How Are PDFs Determined? • Measure n-N differential cross sections, correcting for target • Compare them to theoretical x-sec • Fit SF’s to measured x-sec • Extract PDF’s from the SF fits • Different QCD models could generate different sets of PDF’s • CTEQ, MRST, GRV, etc Fit to Data for SF PHYS 5326, Spring 2007 Jae Yu

  13. Comparisons of Neutrino and Antineutrino cross sections PHYS 5326, Spring 2007 Jae Yu

  14. What can PDF’s depend on? • Different functional forms of PDF and SF’s • Order of QCD calculations • Higher order (NLO or NNLO) calculations require higher order PDF’s • Different assumptions in the protons • No intrinsic sea quarks • Fixed flavors only • Approximation at non-perturbative regime • Different method of approximating low x behavior PHYS 5326, Spring 2007 Jae Yu

  15. Homework Assignments • Provide a method to measure the average valence quark distributions in a n-N scattering experiment • Derive the Lorentz invariant variables of n-N scattering, s, Q2, W2, x and y on pages 6 and 7 of this lecture. • Make at least 8 plots (two - 1d histograms, two - 2d scatter plots, four composite variables) using root • All these are due Monday, Feb. 12 PHYS 5326, Spring 2007 Jae Yu

  16. Homework Assignments • Draw a few additional Feynman diagrams for higher order GSW corrections to n-N scattering at the same order as those on pg 7 in this lecture • Due: One week from today, Wed., Feb. 5 PHYS 5326, Spring 2007 Jae Yu

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