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Deep Inelastic Scattering (DIS) DeepDeep InelasticInelastic ScatteringScattering (DIS)(DIS) Dr. Un-ki Yang Particle Physics Group The University of Manchester [email protected] Un-ki Yang, Frontier of Particle Physics II - DIS 1 Un-ki Yang, Frontier of Particle Physics II - DIS 2 DeepDeep InelasticInelastic ScatteringScattering (DIS)(DIS) Lepton-nucleon scattering • Discovery of quarks • Quark-parton model • Structure Functions Quantum Chromodynamics (QCD) Applications to proton-proton(or antiproton) scattering (Tevatron and LHC) Lecture note:www.hep.man.ac.uk/~ukyang/dis/dis_lec1_09.pdf Un-ki Yang, Frontier of Particle Physics II - DIS 3 Elastic and Inelastic scattering Electron-proton scattering can be described Electron-Proton Scattering as an exchange of a virtual photon. At low Q2 (momentum carried by photon is low), its wavelength is long compared with the size of the proton. It will be the proton as a point. At medium Q2, its wavelength is comparable to the size of proton. Photon begins to resolve the finite size of P the proton. At high Q2, its wavelength is much shorter than the size of proton. Photon resolve the internal structure of the proton. Un-ki Yang, Frontier of Particle Physics II - DIS 4 Elastic electron - proton scattering Electron-Proton Scattering Assumption • Exchange of a single virtual photon • Relativistic electron (E>>me) • Spin-less electron θ • Proton is a point charge For spin-less electron (Rutherford scatt.) d! # 2 = α(=e2 / 4π ) 2 4 $ P d" 4E sin 2 ≈ 1 / 137 For spin ½ electron (Mott scatt.) 2 2 Q = !(k ! k ') d! # 2 cos2 $ = 2 2 2 2 4 $ " d" 4E sin 2 = 4E sin 2 Un-ki Yang, Frontier of Particle Physics II - DIS 5 Elastic electron-proton scattering with a particular charge distribution For an elastic scattering with a particular charge distribution, ρ(r), the scattering amplitude is modified by a form factor. ! ! F(q) = ! d 3reiq•r "(r) Form factor: Fourier transformation of the spatial charge distribution. - For zero momentum transfer, the form factor is one for unit charge. " d 3r!(r) =1 Un-ki Yang, Frontier of Particle Physics II - DIS 6 Inelastic electron-proton scattering Inelastic scattering: energy and angle e(k',E') of the scattered electron are 2 indep. e (k,E) θ variables γ (q) Form Factor: F(Q2 ,ν): Structure N (P,M) W Functions: W1, W2 for two polarization states of the virtual photon (long & transverse) 2 2 ! Q = 4EE' sin 2 W is the mass of the hadronic 2 2 W = (P + q) system = P2 + 2P "q + q2 2 2 2 2 d! # cos $ = M + 2M# ! Q = 2 W (%,q2 ) +W (%,q2 )tan 2 $ ' 2 4 $ [ 2 1 2 ] d"dE 4E sin 2 ν=E-E’ y= /E ν 7 (inelasticity) Un-ki Yang, Frontier of Particle Physics II - DIS Summary for Form Factor Point charge target: F(Q2)=constant photon always see all of it’s charge F Q2 Elastic electron-proton scattering: photon see less charge as Q2 is increased : F(Q2) F Q2 Inelastic electron-proton scattering: F(Q2 ,ν) − structure function Un-ki Yang, Frontier of Particle Physics II - DIS 8 SLAC-MIT e-P inelastic scattering SLAC-MIT group (Bloom et al.) in 1969 performed an experiment with high-energy electron beams (7-18 GeV). Scattering of electrons from a hydrogen target at 60 and 100. Only electrons are detected in the final state - inclusive approach Un-ki Yang, Frontier of Particle Physics II - DIS 9 Unexpected results from SLAC e-P scattering νW2 2 The ratio of σ /σMott : no Q dependence, and very weak W dependence. 2 Structure Function, νW2 has no Q dependence. What does it mean? Scattering against something like pointlike - a point is a point regardless of it’s λ Un-ki Yang, Frontier of Particle Physics II - DIS 10 Quark-Parton Model The nucleon is made of point-like free quarks with spin ½. Scattering off the nucleon is incoherent sum of elastic scattering off quarks: Inelastic electron-proton scattering => elastic electron-quark scattering. The probability, f(x) for a quark to carry momentum fraction x, does not depend on the process or nucleon energy but is intrinsic property for high energy nucleon. This quark-parton model was first proposed by Richard Feynman. This model explains of no Q2 dependence in Structure Functions (“Bjorken scaling”) Un-ki Yang, Frontier of Particle Physics II - DIS 11 Elastic electron-quark scattering Let’s consider the angular dependence for the total spin=0 and 1 cases Before Scattering After Scattering Total spin=0 e q e q +z direction d! Both spin and helicity (-) are conserved: no angular dependence "1 dy Before Scattering After Scattering Total spin=1 e q e q +z direction d! 2 1! cos" Spin is not conserved.: angular dependence " (1# y) , y = dy 2 2 d! 2 2 2 y For a single quark " eq [1+ (1# y) ] / 2 = eq [ + (1# y)] dy 2 Un-ki Yang, Frontier of Particle Physics II - DIS 12 Elastic electron-quark scattering Differential cross section for electron-quark scattering 2 2 2 d ! 4" ME 2 y = eq [ + (1# y)] dxdy Q4 2 Assume that the momentum fraction of the proton carried by quark is x, and the probability for a quark to carry momentum fraction x is f(x) d 2! 4" 2 ME % y2 ( = e2 xf (x) + 1$ y 4 (#i q i )' ( )* dxdy Q & 2 ) Compared with the inelastic electron-proton scattering. d! 4# 2 E 2 cos2 $ = 2 W (%,q2 ) + W (%,q2 )tan2 $ d"dE Q4 [ 2 1 2 ] d 2! 4" 2 ME $ y2 ' MW ->F = 2xF (x,Q2 ) + 1# y F (x,Q2 ) 1 1 4 & 1 ( ) 2 ) νW ->F dxdy Q % 2 ( 2 2 Un-ki Yang, Frontier of Particle Physics II - DIS 13 Parton Model and Scaling 2xF (x,Q2 ) = F (x,Q2 ) = e2 xf (x) 1 2 !i qi i Structure Functions, 2xF1(x,Q2) and F2(x,Q2) only depends on x, but no Q2 dependence (“Bjorken scaling”) according to quark-parton model, which agrees with results from the SLAC-MIT experiment. • Proton consists of many point-like quarks • Quark has a spin ½ • Callan – Gross relation holds : no contribution from longitudinally polarized virtual photon. 2xF1 = F 2 ∗ - 2xF1 ~ γ T ∗ ∗ - F2 ~ ( γ T + γ L) Thus, a point-like quarks can be only probed by the transversely polarized photon. Un-ki Yang, Frontier of Particle Physics II - DIS 14 Callan – Gross relation Phys.Rev.D20:1471,1979. R value is closed to zero No contribution from a longitudinally polarized virtual photon Thus, quark spin cannot be 0, but 1/2 What R value would you expect if quark spin is 0? homework F ! 2xF R = 2 1 2xF1 Un-ki Yang, Frontier of Particle Physics II - DIS 15 Quark distributions inside nucleon valence sea quark-antiquark pair from vacuum Un-ki Yang, Frontier of Particle Physics II - DIS 16 Quark distributions Un-ki Yang, Frontier of Particle Physics II - DIS 17 Nucleon structure functions F (x) = e2 xf (x) 2 !i qi i Proton and neutron structure functions, considering no strange quark • up(x): probability to find a u quark in a proton with momentum fraction x • un(x): probability to find a u quark in a neutron with momentum fraction x How did we know that u and d quarks have fractional electric charges, 2/3 and -1/3 respectively? Proposed by the Gell-Mann quark model, and confirmed by the SLAC-MIT experiment Un-ki Yang, Frontier of Particle Physics II - DIS 18 Quark Model (1964) Gell-Mann et al proposed a quark model to explain many hadrons observed with accelerators in the 1950’s and 1960’s • Hadrons are either baryons (3 quark bound states) or mesons (quark-antiquark pairs) • There are 3 types of quark (up, down and strange; u, d, s) and 3 types of antiquark with opposite electric charge • Quarks (anti-quarks) are spin 1/2 fermions (anti-fermions) • Quarks carry fractional electric charge (u:+2/3 e; d & s: -1/3 e) for example, proton (uud), neutron(ddu) • All hadrons are well specified according to this quark model, and even predicted missing members (like Ω- baryon) • But Gell-Mann was afraid of claiming a quark as a real physical object (no one has every seen a quark!) • Is this quark same as what Feynman’s quark-parton model mentioned? - yes, quark is found to have spin-1/2 and fractional charges given by this model. Un-ki Yang, Frontier of Particle Physics II - DIS 19 Nucleon structure functions • For isospin symmetry under strong interaction (p=uud, n=udd) • From now, we drop the suffix, use quark distributions inside proton • Take separate contributions of the valence and sea Un-ki Yang, Frontier of Particle Physics II - DIS 20 Quark charge? Bodek PhD. MIT 1972 As x0, sea quarks are dominated. en F2 10S eP ! ! 1 F2 10S As x1, valence quarks are dominated (mainly u quark) en F2 4dv + uv 1 eP ! ! F2 dv + 4uv 4 en F2 4dv + uv + 10sea eP = F2 dv + 4uv + 10sea Un-ki Yang, Frontier of Particle Physics II - DIS 21 Sum Rules from Quark-Paron Model GLS sum rule: there are 3 valence quarks 1 (u (x) + d (x))dx = 3 ! v v 0 Gotttfried sum rule 1 (u (x) ! d (x))dx = 1 " v v 0 Other relations 1 " (u(x) ! u(x))dx = 2 0 1 1 dx xf (x) = 1 (d(x) ! d (x))dx = 1 ! "i i " 0 0 1 " (s(x) ! s (x))dx = 0 0 Un-ki Yang, Frontier of Particle Physics II - DIS 22 Gluon? Sum of the momenta of all quarks should be the total proton momentum 1 dx xf (x) = 1 ! "i i 0 But all valence and sea quarks by u an d quarks carry only 50%.
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