Partículas Elementares (2015/2016)

Transcription

1 Partículas Elementares (015/016) 11 - Deep inelastic scattering Quarks and Partons Mário Pimenta Lisboa, 10/015 pimenta@lip.pt

2 Elastic scattering kinematics (ep) Lab 1 θ 3 Only one independent variable! Feynman diag 4 p 1 p 3 q p p 4 p 1 = (E, p 1 ) p = (M p, 0 ) p 3 = (E ', p 3 ) p 4 = (E 4, p 4 ) (p ) = (p 4 ) =(M p )

3 Elastic scattering kinematics (ep) Lab 1 θ 3 Only one independent variable! Feynman diag 4 p 1 p 3 q p p 4 p 1 = (E, p 1 ) p = (M p, 0 ) p 3 = (E ', p 3 ) p 4 = (E 4, p 4 ) (p ) = (p 4 ) =(M p ) q = (p 1 p 3 ) q = (p 1 p 3 ) = (p 4 p 3 ) = - Q q - 4 E E sin (θ/)

4 Elastic scattering kinematics (ep) Lab 1 θ 3 Only one independent variable! Feynman diag 4 p 1 p 3 q p p 4 p 1 = (E, p 1 ) p = (M p, 0 ) p 3 = (E ', p 3 ) p 4 = (E 4, p 4 ) (p ) = (p 4 ) =(M p ) q = (p 1 p 3 ) p 4 = p + q (p 4 ) = (p + q) = (p ) + q + p q q = (p 1 p 3 ) = (p 4 p 3 ) = - Q q = - p q = - M p (E- E ) q - 4 E E sin (θ/) q = - M p ν x Q p q Q M P 1

5 Point Particles elastic scattering d E Q (1 sin ( / )) 1 tan 4 d 4E sin ( / ) E M Rutherford Mott Recoil Rosenbluth Coulomb field Spin 1/ Finite mass target Spin ½ target

6 Electron-proton elastic scattering Rosenbluth formula McAllister and R. Hofstadter (1956)

7 Electron-proton elastic scattering Rosenbluth formula McAllister and R. Hofstadter (1956) Experimental parameterization Finite size proton GE and GM describes the charge and current distribution inside the proton if GE = GM = 1 the Rosenbluth formula is recovered (Q 0, λ ) Experimentally: GE (0) = 1 but GM (0) = μp.79! magnetic anomalous momentum

8 Q 4 M p

9 Dipole proton form factor Mc Allister and Hofstadter 1955 At high Q d d elastic d d Mott 1 q 6

10 Dipole proton form factor Mc Allister and Hofstadter 1955 At high Q d d elastic d d Mott 1 q 6 In the Lab frame the interpretation of the form factors is not simple due to the nuclei recoil, but in the non-relativistic approximation (and in the Breit frame) the form factors are the Fourier transformation of the charge and magnetic momentum distribution inside the proton if F( q ) br ( r) 0 e 1 q F(0) / b a 1/ b 0. fm

11 Dipole form factor Show that an electric dipole form factor F( q ) F(0) 1 q / b corresponds to an exponential charge distribution ( r) 0 Note that e br iq. r 3 4 ( r) e d r ( r) q r sin( qr) dr If (r) has spherical symmetry

12 Deep inelastic scattering: Inelastic kinematics Center-of-mass energy Lab Energy loss W inelasticity inelastic x Q 1 M P Two independent variables! E, ϴ - Experiment (q, ν), (Q, x) - Theory Bjorken/Feynman x variable

13 e p deep inelastic scattering Kinematics Consider the e p deep inelastic elastic scattering and deduce the following formula: a) Q = 4 E E sin (θ/) b) Q = M ν c) Q = x y (s -y )

14 Electron-proton inelastic scattering W 1, W structure functions Extended particles q,w 1 e W 0

15 Bjorken scaling (1967) In the limit of infinite Q with At large Q, interactions with point-like constituents

16 Deep inelastic scattering

17 Deep inelastic scattering : the detector

18 Electron-proton cross-section M = W E and θ fixed Δ +

19 Differential cross section normalized to the Mott cross-section Mott cross-section: Elastic scattering of an electron in a Coulomb field d d Mott 4k 4 E (1 sin 4 sin ( / ) 4 ( / )) For high W the ratio is constant! The proton is not a point particle but it behaves as it would have point-like constituents

20 Validation of the Bjorken scaling F = ν W Measurements at different scattered energies and angles x = 0.5

21 Feynman Quark-Parton model The nucleons are composed by point-like constituents, the partons, which at high Q behave basically as free particles but are, however, confined inside the nucleon. The structure functions for the electron-parton elastic scattering are :

22 Callan-Gross relation The partons are indeed spin-half Dirac particles!

23 Parton Distribution Functions (PDFs) f i (Z i ) density probability to find a parton carrying a fraction of momentum Z i

24 Inside one proton Three (valence) quarks interacting through the strong field (gluons) and a sea of virtual quark/antiquark pairs Then and

25 Proton PDFs x f i (x) % carried momentum There are three valence quarks! Only about half of the proton momentum is carried by the valence quarks!

26 Gottfried Sum rule Deduce in the framework of the quark parton model the T Gottfried sum rule: 1 x ep en F F dx u ( x) d ( x) dx x x and comment the fact that the value measured in e p and e d deep inelastic elastic scattering experiments is around 0.5.

27 Q dependence of the PDFs What one see depends on its momentum! Guido Altarelli Q 1 Q Q > Q 1 DGLAP equations (Dokshitzer-Gribov-Lipatov-Altarelli-Parisi)

28 Scaling violations F (x, Q ) = x e i f i (x, Q ) HERA electron-proton collider 3 km ring, 7.5 GeV electrons, 80 (or 90) GeV protons H 1 e p

29 Chapter bibliography An introduction to particle and Astroparticle Physics, Alessandro De Angelis, Mário Pimenta - sections 5.5 Modern Particle Physics, Mark Thomson Chapter 8

30 A função ᵟ de Dirac