1 Particle Physics Dr M.A. Thomson e+ q √α γ S g √α √α Qq 1 e- q2 q Part II, Lent Term 2004 HANDOUT III Dr M.A. Thomson Lent 2004 2 QCD QUANTUM ELECTRODYNAMICS: is the quantum theory of the electromagnetic interaction. ★ mediated by massless photons ★ photon couples to electric charge, Ô ★ À » « Strength of interaction : . ¾ « QUANTUM CHROMO-DYNAMICS: is the quantum theory of the strong interaction. ¾ Õ ★ mediated by massless gluons, i.e. ½ propagator ★ gluon couples to “strong” charge ★ Only quarks have non-zero “strong” charge, therefore only quarks feel strong interaction Basic QCD interaction looks like a stronger « « Å version of QED, Ë QED q QCD q √α Q √α S q q q α 2 π α 2 π = e /4 ~ 1/137 γ S = gS /4 ~ 1 g « ( subscript em is sometimes used to distinguish the Ñ « of electromagnetism from Ë ). Dr M.A. Thomson Lent 2004 3 COLOUR In QED: ★ Charge of QED is electric charge. ★ Electric charge - conserved quantum number. In QCD: ★ Charge of QCD is called “COLOUR” ★ COLOUR is a conserved quantum number with 3 VALUES labelled “red”, “green” and “blue” Quarks carry “COLOUR” Ö Anti-quarks carry “ANTI-COLOUR” Ö ¦ ¼ Ï Leptons, ­ , , DO NOT carry colour, i.e. “have colour charge zero” DO NOT participate in STRONG interaction. Note: Colour is just a label for states in a non-examinable SU(3) representation ¼ ¼ ½ ¼ ½ ¼ Ö ½ ¼ ¼ Dr M.A. Thomson Lent 2004 4 GLUONS In QCD: ★ Gluons are MASSLESS spin-1 bosons Consider a red quark scattering off a green quark. Colour is exchanged but always conserved. q q r g gluon r g q q g r UNLIKE QED: ★ Gluons carry the charge of the interaction. ★ Gluons come in different colours. Expect 9 gluons (3 colours ¢ 3 anti-colours) Ö Ö Ö Ö , , , , , Ö Ö , , However: Real gluons are orthogonal linear combinations of the above states. The ½ Ô ´Ö · · µ combination Ö is colourless ¿ and does not take part in the strong interaction. Dr M.A. Thomson Lent 2004 5 Colour at Work Õ EXAMPLE: Õ Annihilation q q rr g q q g g Normally do not show colour on Feynman diagrams - colour is conserved. QED POTENTIAL: « V É Ö QCD POTENTIAL: At short distances QCD potential looks similar « Ë V É ¿ Ö apart from colour factor. ¿ Note: the colour factor (4/3) arises because more than one Õ gluon can participate in the process Õ . Obtain colour factor from averaging over initial colour states and summing over final/intermediate colour states Dr M.A. Thomson Lent 2004 6 SELF-INTERACTIONS At this point, QCD looks like a stronger version of QED. This is true up to a point. However, in practice QCD behaves very differently to QED. The similarities arise from the fact that both involve the exchange of MASSLESS spin-1 bosons. The big difference is that GLUONS carry colour “charge”. GLUONS CAN INTERACT WITH OTHER GLUONS: g g g g g g g 3 GLUON VERTEX 4 GLUON VERTEX EXAMPLE: Gluon-Gluon Scattering + + e.g.rrrrgg + bb→ + Dr M.A. Thomson Lent 2004 7 CONFINEMENT NEVER OBSERVE: single FREE quarks/gluons ★ quarks are always confined within hadrons ★ This is a consequence of the strong self-interactions of gluons. Qualitatively, picture the colour field between two quarks. The gluons mediating the force act as additional sources of the colour field - they attract each other. The gluon-gluon interaction pulls the lines of colour force into a narrow tube or STRING. In this model the string has a ‘tension’ and as the quarks separate the string stores potential energy. Energy stored per unit length constant. Î ´Ö µ » Ö ★ Requires infinite energy to separate two quarks. Quarks always come in combinations with zero net colour charge: CONFINEMENT. Dr M.A. Thomson Lent 2004 8 How Strong is Strong ? QCD Potential between quarks has two components: « Ë ★ “COULOMB”-LIKE TERM : ¿ Ö Ö ★ LINEAR TERM : · α 1 -4 s V = 3r +kr (GeV) 0 -4α V = s QCD 3r -1 V α =0.2 -2 s k=1 GeV/fm -3 0 0.2 0.4 0.6 0.8 1 r(fm) Force between two quarks at separated by 10 m: « Ë Î · Ö É Ö ½ Î with fm « Î Ë · ¾ Ö Ö ½¼ ½ ¢ ½¼ Æ at large r ½ ½¼ ½ ¼¼¼¼ Æ Equivalent to the weight of approximately 65 Widdecombes. Dr M.A. Thomson Lent 2004 9 JETS · Õ ÕÕ Consider the Õ pair produced in : e+ q γ qq e- q 1 -4α V = s+kr As the quarks separate, the 3r (GeV) 0 energy stored in the colour -4α V = s QCD 3r field (‘string’) starts to in- -1 crease linearly with separa- V α =0.2 tion. When ×ØÓÖ -2 s k=1 GeV/fm ¾Ñ ÕÕ Õ new pairs can be created. -3 0 0.2 0.4 0.6 0.8 1 r(fm) q q q q q q q q as energy decreases... hadrons freeze out Dr M.A. Thomson Lent 2004 10 Õ As quarks separate, more Õ pairs are produced from the potential energy of the colour field. This process is called HADRONIZATION. Start out with quarks and end up with narrowly collimated JETS of HADRONS q π+ q (ud) q q etc... q q SPACE q q π+ q q 0 - -π +π q π K π+ q π0π0 π0 TIME p e+ q q γ e- e+ - e q q · ÕÕ Typical Event The hadrons in a quark(anti-quark) jet follow the direction of the original quark(anti- quark). Consequently · ÕÕ is observed as a pair of back-to-back jets of hadrons Dr M.A. Thomson Lent 2004 11 aside..... DALI Run=56698 Evt=7455 ALEPH 3 Gev EC 6 Gev HC Y" 1cm 0 −1cm −1cm 0 1cm X" Filename: DC056698_007455_000830_1723.PS Made on 30-Aug-2000 17:24:02 by konstant with DALI_F1. Z0<5 D0<2 RO TPC (φ −175)*SIN(θ) x xo o o−xo−oxx−− o x o x o o − − o x − −− o xo−x x xoo− − x x o − o x o x x o − − x o − − x − o xo − o − − oo− o − x o o x − x − x o x ox − x −−o − x 15 GeV θ=180 θ=0 ★ You will now recognize the “Higgs” event from the cover of Handout I as · ÕÕÕÕ something Dr M.A. Thomson Lent 2004 12 « Running of Ë ★ « Ë specifies the strength of the strong interaction ★ « BUT just as in QED, Ë isn’t a constant, it “runs” ★ In QED the bare electron charge is screened by a cloud of virtual electron-positron pairs. ★ In QCD a similar effect occurs. In QCD quantum fluctuations lead to a ‘cloud’ of Õ virtual Õ pairs q one of many (an infinite set) q q q such diagrams analogous to q those for QED. q q In QCD the gluon self-interactions ALSO lead to a ‘cloud’ of virtual gluons g one of many (an infinite set) such diagrams. Here there is no g g q analogy in QED, photons don’t have self-interactions since they g q don’t carry the charge of the in- q teraction. Dr M.A. Thomson Lent 2004 13 Colour Anti-Screening ★ Due to the gluon self-interactions bare colour charge is screened by both virtual quarks and virtual gluons ★ The cloud of virtual gluons carries colour charge and the effective colour charge INCREASES with distance ! ★ « At low energies (large distances) Ë becomes large can’t use perturbation theory (not a weak perturbation) α α EM QED S QCD 1/128 M 1/137 Z Mp High EnergyMZ Low Energy High Energy Low Energy s 1 s 1 α α MZ Mp 0 0 0246-20 -18 -16 2 2 log10(q /GeV ) log10(r/m) ★ « At High energies (short distances) Ë is small. In this regime treat quarks as free particles and can use perturbation theory ASYMPTOTIC FREEDOM Ô ★ × ½¼¼ Î « ¼ ½¾ At , Ë . Dr M.A. Thomson Lent 2004 14 Scattering in QCD EXAMPLE: High energy proton-antiproton scattering Jet along u √α u beam direction p S g g 1 q2 p √α Visible jet u S u in direction of q ¾ ½ ´« µ Ô Ô Ë Å « « µ Ë Ë ¾ Õ ª ×Ò ¾ The upper points are the Geiger and Marsden data (1911) for the elastic scatter- ing of « particles as they traverse thin gold and silver foils. The lower points show the angular distribution of the quark jets observed in proton-antiproton scattering ¾ ¾ ¾¼¼¼Î at Õ Both follow the Rutherford formula for elastic scatter- ing: ×Ò . ¾ Dr M.A. Thomson Lent 2004 15 · Ô EXAMPLE: ÔÔ vs scattering p π+ g g p p · ´ÔÔµ ´ Ôµ Calculate ratio of total to total ★ QCD does not distinguish between quark flavours, only COLOUR charge of quarks matters. At high energy (E bind- ing energy of quarks within hadrons) ratio of ÔÔ and Ô total cross sections de- pends on number of pos- sible quark-quark combina- tions. Predict ´Ôµ ¾¢¿ ¾ ´ÔÔ µ ¿¢¿ ¿ Experiment ´Ôµ ¾ Ñ ´ÔÔµ ¿ Ñ ¼ ¿ Dr M.A. Thomson Lent 2004 16 · QCD in Annihilation Direct evidence for the existence of colour comes · from Annihilation. · · · ÕÕ ★ Compare , : · ´ ÖÓÒ× µ Ê · · ´ µ e+ µ+ e+ q γ γ √α √α √α √α Qq 1 1 e- q2 µ- e- q2 q If we neglect the masses of the final state quarks/muons then the ONLY difference is the É ½ É Õ charge of the final state particles ( , ¾ ½ = · or ) ¿ ¿ Start by calculating the cross section for the · ´ µ process .( represent a · ÕÕ fermion-antifermion pair e.g.