Experimental studies of QCD 1. Elements of QCD 2. Tests of QCD in e + e -annihilation 3. Studies of QCD in DIS 4. QCD in pp ( p p ) collisions 1. Elements of QCD - SU(3) Theory (i) Quarks in 3 color states: R, G, B (ii) “colored” gluons as exchange vector boson SU 3 : 3×3=8 1 B R Gluons of color octet: B R R B,R G,G B,G R,B G,B R R B 1 R RG G s 2 1 R R G G2B B B B 6 1 R RG G2B B Ninth state = color singlet B 6 B does not take part in interaction 1 R R G G B B 3 To recapitulate the Quantum Electrodynamics previously discussed material. Lagrangian for free spin ½ particle: µ L(x,t) = iψ (x,t)γ ∂ µψ (x,t) − mψ (x,t)ψ (x,t) Applying the Euler-Lagrange formalism leads to the Dirac equation. Invariance under Local Gauge Transformation Demanding invariance under local phase transformation of the free Langrangian ( local gauge invariance ): ψ (x) →ψ (x) = eiα(x)ψ (x) requires the substitution: i∂µ → i∂µ + eA µ (x) If one defines the tansformation of A under local gauge transformation as Aµ (x) → Aµ (x) + ∂µα(x) iα ( x ) one finds L(x) ψ→ψ e →L(x) invariance of L: To interpret the introduced field A µ as photon field requires to complete the Langrangian by the corresponding field energy: µ µ 1 µν L =ψ (iγ ∂µ − m)ψ + eψγ ψ Aµ − Fµν F 4 Fµν = ∂µ Aν − ∂ν Aµ The requirement of local gauge invariance has automatically led to the interaction of the free electron with a field. Quantum Chromodynamics – SU(3) Theory R Lagrangian is constructed with quark wave functions = G B Invariance of the Lagrangian under Local SU(3) Gauge Transformation k x i k x ' x =U x x =e 2 x with any unitary (3 x 3) matrix U(x) . U(x) can be given by a linear combination of 8 Gell-Mann matrices ... [SU(3) group generators] 1 8 requires interaction fields – 8 gluons corresponding to these matrices 1.1 Color factors e1 q q Coupling strength Coupling strength: QED e e QCD 1 1 2 c c q q 2 1 2 s e2 C Examples: F Color factor B B 1 1 2 2 1 R R G G 2B B C F = = 6 2 3 B B 6 6 R R R R 1 1 R RG G R RG G2B B 2 6 1 1 C = R R C = R R F 12 F 4 1 Color factor for qq color singlet state (meson): R R G G B B 3 B B B R B G 1 3× R RG G2B B B R B G 6 B B B R B G 1 1 1 C = C = C F = F F 3 2 2 1 1 1 1 1 4 C =3 = F 3 3 3 2 2 3 In the case of a color Color singlet meson singlet, each initial and is composed of 3 final state carries a different possibilities factor 1 3 Triple and quadruple gluon Vertex Gluons carry color charges: important feature of SU(3) R G R B G B R G Color flow B Color factors ~ N C ~ T F 4 1 = =3 = 3 2 1.2 Evidence of colored spin ½ quarks a) successful classification of mesons and baryons b) clear two-jet event structure in e e hadrons qq d ~1cos 2 d ee hadrons c) R = indicates fractional charges and N =3 had ee C d) Further indications for N C=3: ∆++ Ω ( s) statistic problem: Spin J( ∆++ )=3/2 (L=0), quark content |uuu> ++ → = u u u forbidden by Fermi statistics Solution is additional quantum number for quarks (color) 1 ++ = u u u i , j ,k=color index 6 ijk i j k • Triangle anomaly γ f γ Divergent fermion loops f γ Divergence 2 1 ~ Q =111 N 3 f C [ 3 3 ] f leptons quarks 3 generations of u/d-type quark cancels if N C = 3 1.3 Tests of QCD in different processes Discussed in Section 2 and 3 Tevatron / LHC (optional) 2. Test of QCD in e +e- annihilation 2.1 Discovery of the gluon Discovery of 3-jet events by the TASSO collaboration (PETRA) in 1977: 3-jet events are interpreted as quark pairs with an additional hard gluon. # 3-jet events 0.15~ α is large # 2-jet events s s at √s=20 GeV 2.2 Spin of the gluon Ellis-Karlinger angle Ordering of 3 jets: E 1>E 2>E 3 Measure direction of jet-1 in the θ Gluon spin J=1 rest frame of jet-2 and jet-3: EK .