Quantum Chromo-Dynamics (QCD)

Presentation on theme: "Quantum Chromo-Dynamics (QCD)"— Presentation transcript:

1 Quantum Chromo-Dynamics (QCD)
“Strong Interactions” Underlying field theory is a renormalizable non-abelian gauge theory named Quantum Chromo-Dynamics (QCD) QCD Lagrangian: with ψ Dirac field and Aμ vector field and a,b,c color indices, others understood covariant derivative (makes Dirac-vector field interaction locally gauge-invariant) non-abelian theory t = generators of gauge transformations f = fine structure constants 19-Mar-13

2 QCD Lagrangian ⇒ trilinear and quadrilinear couplings
Consequence? “Maxwell” eqs. for vector fields for  = 0 “Gauss” law for color charge a distributed with density a and generating color electric field Eai = Fa0i 19-Mar-13

3 density from pointlike color charge a=1
vacuum fluctuation “sink” of field E 3 dipole charge a=1 pointing to source getting away from source the color charge a=1 looks stronger! antiscreening 19-Mar-13

4 QCD : screening + antiscreening (≫)
QED : screening QCD : screening + antiscreening (≫) confinement ? asymptotic freedom (only non-abelian 4-dim. gauge field theories display it) ~ ΛQCD 19-Mar-13

5 ΛQCD ≪ : perturbative regime, calculable with techniques mutuated
Regimes ΛQCD ≪ : perturbative regime, calculable with techniques mutuated from QED ΛQCD ≲ : non-perturbative regime, not directly calculable Structure of hadrons realized at scale ~ ΛQCD hadrons cannot be deduced directly from the Lagrangian describing the forces that make them ! Alternative: compute QCD on lattice statistical approach, no direct access to dynamics Hadronic Physics : study hadronic systems using effective approaches induced by QCD ✦ spectroscopy ✦ dynamical structure ☜ 19-Mar-13

6 Historical origin End of ‘60’s: famous SLAC experiment of Deep Inelastic Scattering (DIS) on proton targets at 7 ≲ Q2 ≲ 10 (GeV/c)2 and 6o < e < 10o ☛ scaling = the target response does no longer depend on momentum transferred ☛ isolated events of diffusion at very large angles ☛ the proton behaves like an ensemble of pointlike scattering centers, each one moving independently from the others ☛ birth of the Quark Parton Model (QPM) Bloom et al., P.R.L. 23 (69) 930 Feynman, P.R.L. 23 (69) 1415 Friedman, Kendall,Taylor NOBEL laureates 19-Mar-13

7 Scattering lepton -- hadron
(electron, neutrino, muon) (nucleon, nucleus, photon) Quantum ElectroDynamics (QED) known at any order leptonic probe explores the whole target volume em ~ fine structure constant is small → perturbative expansion Born approximation (exchange of one photon only) works well virtual photon (* ): (q,) independent, two different * polarizations (longitudinal and transverse) → two different target responses 3 independent 4-vectors k, k’, P + spin S e scattering angle prototype reaction e+p -> e’+X 19-Mar-13

8 definitions and kinematics
e- ultrarelativistic me ≪ |k|, |k’| Target Rest Frame (TRF) kinematical invariants 19-Mar-13

9 (cont’ed) elastic limit final invariant mass anelastic limit 19-Mar-13

10 Q is our “lense” Q [GeV]  ~ 1/Q [fm] target 0.02 10 nuclei 0.1 2 0.2
mesons / baryons partons …… ?? N.B. 1 fm = (200 MeV)-1 19-Mar-13

11 Frois, Nucl. Phys. A434 (’85) 57c nucleus MA nucleon M
unaccessible domain 19-Mar-13

12 Cross Section no events per unit time, scattering center, solid angle no incident particles per unit time, area J  flux phase space scattering amplitude 19-Mar-13

13 Leptonic and Hadronic Tensors
2 J  = leptonic tensor hadronic tensor 19-Mar-13

14 Inclusive Scattering  X hadronic tensor
cross section for inclusive scattering (general formula) large angles are suppressed ! 19-Mar-13

15 Inclusive Elastic Scattering
W ’=(P+q)2=M2 hadronic tensor  ↔ Q : scaling various cases 19-Mar-13

16 target = free scalar particle
2 independent 4-vectors: R=P+P ’, q=P-P ’ ⇒ J  » F1 R  + F2 q  F1,2(q2,P 2,P ’2) = F1,2 (q2) current conservation q J  = 0 ⇒ define : N.B. for on-shell particles q•R = 0 ; but in general for off-shell 19-Mar-13

17 Inclusive elastic scattering on free scalar target
elastic Coulomb scattering on pointlike target target recoil target structure 19-Mar-13

18 Breit frame → target form factor
P = - q/2 R = (2E, 0) q = ( 0, q)  = 0 J = (J0, 0) ≈ (2E F1(Q2), 0) P’ = + q/2 F1(Q2) → F1(|q|2) = ∫ dr (r) e i q∙r form factor for charge matter ….. distribution of charge matter ….. works only in the non-relativistic limit in fact, ρ is a static density, while Breit frame changes with Q2=q2 : boost makes | P’=+q/2 > ≠ | P=−q/2 > ⇒ density interpretation is lost 19-Mar-13

19 target = pointlike free Dirac particle
Example: e- + - → e-’ + - spin magnetic interaction with  * 19-Mar-13

20 target = free Dirac particle with structure
3 independent 4-vectors P, P ’,  (+ parity and time-reversal invariance) current conservation q J = 0 Dirac eq. 19-Mar-13

21 Gordon Decomposition (on-shell)
proof flow-chart from right handside, insert def. of  use Dirac eq. use {,} = 2 g use Dirac eq. → left handside namely R ⇔ 2M  – i  q 19-Mar-13

22 …… target = free Dirac particle with structure cross section
internal structure (not easy to extract) 19-Mar-13

23 Rosenbluth formula Define Sachs form factors
(Yennie, 1957) N.B. reason: in Breit frame + non-rel. reduction → charge / magnetic target distribution easier to handle 19-Mar-13

24 Rosenbluth separation
at large e (large Q2) → extract GM small e (small Q2) → extract GE by difference Rosenbluth plot linear transverse polarization of * measurements at different (E, e) → plot in  at fixed Q2 crossing at =0 → GM slope in  → GE 19-Mar-13

25 Rosenbluth plot pQCD scaling JLAB data Q2 ~ 10 (GeV/c)2 not yet
(obtained with more precise e- N → e- N ) Q2 ~ 10 (GeV/c)2 not yet perturbative regime?? → → 19-Mar-13