Deep Inelastic Scattering (DIS) Un-ki Yang Dept. of Physics and Astronomy Seoul National University Un-ki Yang - DIS

Transcription

1 Deep Inelastic Scattering (DIS) Un-ki Yang Dept. of Physics and Astronomy Seoul National University Un-ki Yang - DIS 1

2 Elastic and Inelastic scattering Electron-Proton Scattering P Electron-proton scattering can be described as an exchange of a virtual photon. Ø At low Q (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. Ø At medium Q, its wavelength is comparable to the size of proton. Photon begins to resolve the finite size of the proton. Ø At high Q, its wavelength is much shorter than the size of proton. Photon resolve the internal structure of the proton. Un-ki Yang - DIS

3 Elastic electron - proton scattering Electron-Proton Scattering P θ Q = (k k ') = 4E sin θ Ø Assumption Exchange of a single virtual photon Relativistic electron (E>>m e ) Spin-less electron Proton is a point charge Ø For spin-less electron (Rutherford scatt.) dσ dω = α 4E sin 4 θ Ø For spin ½ electron (Mott scatt.) dσ dω = α cos θ 4E sin 4 θ α (=e / 4π ) 1 / 137 Un-ki Yang - DIS 3

4 Elastic electron-proton scattering with a particular charge distribution Ø For an elastic scattering with a particular charge distribution, ρ(r), the scattering amplitude is modified by a form factor. F( q) 3 iq = d re r ρ( r) Ø Form factor: Fourier transformation of the spatial charge distribution. - For zero momentum transfer, the form factor is one for unit charge. d 3 rρ(r) =1 Un-ki Yang - DIS 4

5 Inelastic electron-proton scattering e (k,e) N (P,M) Q = W = = P M e(k',e') γ (q) = ( P + q) + P q + q + Mν Q θ θ 4EE' sin ν=e-e y=ν/e (inelasticity) W Ø Inelastic scattering: energy and angle of the scattered electron are indep. variables Ø Form Factor: F(Q,ν): Structure Functions: W 1, W for two polarization states of the virtual photon (long & transverse) Ø W is the mass of the hadronic ystem dσ = α cos θ dωde ' 4E sin 4 θ W (ν,q ) +W 1 (ν,q )tan θ [ ] Un-ki Yang - DIS 5 s

6 Summary for Form Factor Ø Point charge target: F(Q )=constant photon always see all of it s charge F Q Ø Elastic electron-proton scattering: photon see less charge as Q is increased : F(Q ) F Q Ø Inelastic electron-proton scattering: F(Q,ν) - structure function Un-ki Yang - DIS 6

7 SLAC-MIT e-p inelastic scattering Ø SLAC-MIT group (Bloom et al.) in 1969 performed an experiment with high-energy electron beams (7-18 GeV). Ø Scattering of electrons from a hydrogen target at 6 0 and Ø Only electrons are detected in the final state - inclusive approach Un-ki Yang - DIS 7

8 Unexpected results from SLAC e-p scattering νw Ø The ratio of σ /σ Mott : no Q dependence, and very weak W dependence. Ø Structure Function, νw has no Q dependence. Ø What does it mean? Scattering against something like pointlike - a point is a point regardless of it s λ Un-ki Yang - DIS 8

9 Quark-Parton Model Ø The nucleon is made of point-like free quarks with spin ½. Ø Scattering off the nucleon is incoherent sum of elastic scattering off quarks: Inelastic electron-proton scattering => elastic electron-quark scattering. Ø 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. Ø This quark-parton model was first proposed by Richard Feynman. Ø This model explains of no Q dependence in Structure Functions ( Bjorken scaling ) Un-ki Yang - DIS 9

10 Quark distributions inside nucleon valence sea quark-antiquark pair from vacuum Un-ki Yang - DIS 10

11 Quark distributions Un-ki Yang - DIS 11

12 Nucleon structure functions F (x) = i e qi xf i (x) Ø Proton and neutron structure functions, considering no strange quark u p (x): probability to find a u quark in a proton with momentum fraction x u n (x): probability to find a u quark in a neutron with momentum fraction x Ø How did we know that u and d quarks have fractional electric charges, /3 and -1/3 respectively? Proposed by the Gell-Mann quark model, and confirmed by the SLAC-MIT experiment Un-ki Yang - DIS 1

13 Quark Model (1964) Ø 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/ fermions (anti-fermions) Quarks carry fractional electric charge (u:+/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/ and fractional charges given by this model. Un-ki Yang - DIS 13

14 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 - DIS 14

15 Quark charge? Bodek PhD. MIT 197 Ø As xà 0, sea quarks are dominated. en F F 10S ep 10S 1 Ø As xà 1, valence quarks are dominated (mainly u quark) F en F ep 4d v + u v d v + 4u v 1 4 en F F = 4d + u + 10sea v v ep d v + 4u v + 10sea Un-ki Yang - DIS 15

16 Sum Rules from Quark-Paron Model Ø GLS sum rule: there are 3 valence quarks 1 0 (u v (x) + d v (x))dx = 3 Ø Gotttfried sum rule 1 0 (u v (x) d v (x))dx = 1 Ø Other relations (u(x) u(x))dx = (d(x) d (x))dx = 1 (s(x) s (x))dx = dx xf i (x) = 1 i Un-ki Yang - DIS 16

17 Gluon? Ø Sum of the momenta of all quarks should be the total proton momentum 1 dx xf i (x) = 1 0 i Ø But all valence and sea quarks by u an d quarks carry only 50%. Basically, integrals of F P and F n didn t add up to 1. Missing mom entum is carried by neutral parton gluon. F p F n x x Un-ki Yang - DIS 17

18 Summary Ø Feynmann s parton model was very successful in describing nucleon structure. Ø Parton was identified as quark which was proposed by Gell-Mann. Ø The valence quarks are the simple quark model constituents, and the sea quarks are concentrated at small x. o The integral of F (x) over all x gives the total momentum fraction carried by the valence and sea quarks is only 0.5. Ø Evidence for neutral parton ( gluon ) inside nucleon, which couples to quarks. Ø All lead to Quantum Chromodynamics (QCD) Un-ki Yang - DIS 18