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Lecture 12 – Asymptotic freedom and the electrodynamics of quarks ● ● Asymptotic freedom and the running of coupling ”constants”. Testing the theory of the quarks and strong force in e- e+ reactions. FK7003 1 The theory of the strong force QCD Its a bit embarrassing. We talk about quarks and gluons but we haven't even attempted a calculation/estimate for a process using Feynman diagrams. q q αs q q αs Problem is that α S >> 1 for most of the processes we've been interested in. However, α S can be low depending on how close the quarks are to each other. Easiest to see how this all works by first considering electromagnetic interactions. FK7003 2 Capacitors Field in capacitor with vacuum between Q plates : E0 = Aε 0 Dielectric between plates is polarised (+- dipoles produced) Field in capacitor between plates: Q E= εr < E0 Aε 0 εr > 1 The presence of +- dipoles lowers the field. Plate area =A FK7003 3 What is the charge of a particle ? +ve charged particle q in a dielectric. The material surrounding the particle is composed of molecules which become polarised by the electric field of q. Produce a dipole field which reduces the electric field from q. q q εr E= → (12.01) 4πε 0 r 2 4πε 0 r 2 Anyone making a measurement of q in the dielectric would see a screened charge q . Screening reduced as εr measurement is made closer to the particle than molecular separation. FK7003 4 Screening in a dielectric qeff q/εr Intermolecular separation r The effective charge increases at small distances FK7003 5 Vacuum polarisation The "vacuum" consists of virtual particles fluctuating into and out of existence. An electron is surrounded by virtual particles which act to shield the charge as in a polarised dielectric. eg e − , e + pairs (lightest and easiest to make). Feynman diagram formalism shown as photon coupling to e − , e + pairs. Screening reduced for distances shorter than λc = λc = h (12.02) me h = Compton wavelength=2.43 ×10−12 m (12.03) me e- e- e- e- e+,e+ e+,e- e- e- e+,ee- FK7003 e6 Screened charges Electromagnetic force (QED) Electric charge screened: distance > Compton wavelength λc α Strong force (QCD) e2 = Implications: coupling constant at vertex: (1.24) Effective colour α charge grows at larger distances. 4πε 0 Small charge over distances < fm lead to asymptotically free If the charges are screened then coupling, α changes according to interaction distance. quarks in hadrons. Alternatively interaction distance d ∼ 1 1 ∼ (12.04) momentum exchange Q ⇒ α depends on interaction distance or momentum exchange. FK7003 7 The electromagnetic coupling 4πε 0 = 2 α e 1 Barely changes ~(Momentum transfer=Q)2 /GeV2 Interaction distance FK7003 8 What about the strong force ? q q q q q q q q q,q + other higher order diagrams q,q q,q q q q q q q q q Similar story as for electromagnetism except that gluons can self-interact (they carry colour - the photon carries no charge!) This turns out to be critical..... FK7003 9 Asymptotic freedom Strong force (Quantum chromodynamics: QCD) Effective colour charge grows at larger distances. Small charge over distances < fm lead to quasi-free quarks in hadrons. Asymptotic freedom! Nobel prize (2004) for Gross, Politzer and Wilczek. ( 33 − 2 N f ) Q α s ( Q ) = α s ( M Z ) 1 + α s ( M Z ) ln 6π MZ N f = number of quark flavours αs −1 (12.05) α s ( M Z ) = 0.118 ± 0.002 (12.06) Varies strongly with momentum!! αs Q αs Momentum transfer, Q (GeV) Interaction distance FK7003 10 Running of the coupling ”constants” Similar story for weak force. If interactions occur over distance scales which suppress screening The three forces would be of (roughly) the same size Measurements Predicted behaviour (tested with measurements at lower energies) The coupling strengths of the strong,electromagnetic, and Weak forces converge at higher energies. Is this evidence that they are part of a single force ? Later lecture. FK7003 11 Consequences 2 From lecture 11 : F2 constant with Q at fixed x. Quasi-free quark is struck by photon. ⇒ Bjorken scaling. 1 Short distance/time interaction ∆t ∼ Q QCD corrections imply scaling violations. FK7003 12 Scaling violations Described by QCD over several orders of magnitude in Q2. FK7003 13 OZI suppression In OZI-suppressed processes, the gluons carry all of the momenta of some or all of the final particles and there is consequently a lower probability of emitting such ”hard” gluons in comparison with ”soft” gluons in non-OZI suppressed reactions. FK7003 14 Testing what we know about the quarks and their interactions Use what we've learned from hadron properties and DIS on a totally different reaction: e − + e + → hadrons. Study electomagnetic quark interactions (quark electrodynamics) and strong interactions.. Show (1) 3 colours 2 1 (2) Quarks (+ antiquarks) with charges ± e and ± e. 3 3 (3) QCD makes precise predictions for short distance reactions. Also discuss how long-distance effects produce the observed hadrons FK7003 15 Ratio of hadronic to muonic production in e+e- collisions R= σ ( e− e+ → hadrons ) σ (e e → µ µ − + − + ) ∼ . Centre-of-mass energy ECM (GeV) 16 Understand the features of the graph. (1) e − e + → hadrons ≡ e− e+ → qq (bound state -resonance)+ e − e + → qq (non-bound state) ≡ + Resonance : Ecm = resonance rest mass . Particle must be produced at rest in c.m frame. eg e− e + → ρ ; ρ mass ∼ 770 MeV , width ∼ 200 MeV ⇒ Mass-localised peak around Ecm ∼ 770 MeV FK7003 Bound + non-bound states Non-bound states Centre-of-mass energy ECM (GeV) Five quarks and three colours Away from the resonance region 15 < Ecm < 40 GeV σ ( e− e + → hadrons ) = σ ( e− e+ → qq ) = N C ea2 ( e − e + → µ − µ + ) (12.08) NC = number of colours. Five quarks u, d , s, c, b can be produced (top is too heavy): 11 NC 9 11 No. colours N C = 3 ⇒ R = 3 Five quarks and three colours! R = N C ( eu2 + ed2 + es2 + ec2 + eb2 ) = R = 5 ⇔ 6 quarks,3 colours Bound + non-bound states Non-bound states R= 11 ⇔ 5 quarks,3 colours 3 R= 11 ⇔ 5 quarks,1 colour 9 Centre-of-mass energy ECM (GeV) FK7003 18 Taking a closer look QCD demands a correction to (12.08) by taking into account an additional diagram (gluon emission) Gluon momentum >> 1 GeV ⇒ α S << 1 GeV ⇒ use QCD. with correction without correction Bound + non-bound states Non-bound states Centre-of-mass energy ECM (GeV) FK7003 19 ”Observing” gluon emission Gluons and quarks carry colour so are never seen. jet The process by which they convert into hadrons is known as hadronisation/fragmentation. High energy quarks and gluons convert into jets of hadrons. Models of hadronisation exist but are simply very good jet "best guesses". We don't yet understand the process jet by which quarks are confined and therefore the process through which jets are formed. An example of how we think hadronisation is given in the next lecture when the jet top quark discovery is discussed. Computer visulation of 3 jets jet reconstructed in an e − e + reaction jet at the PETRA collider (1979). First measurement of gluon-jets. FK7003 20 Summary ● Vacuum polarisation makes the couplings of the fundamental forces ”run” with energy − ● ● Asymptotically free quarks! At high energies QCD makes precise calculations − Scaling violations − Hadronic to muonic ratio Tested our picture of quarks, gluons and the strong force on e- e+ interactions. FK7003 21