Particle Physics II

1. Particle Physics II 3rd Handout • Heavy Flavour Physics • Weak decays – flavour changing • Mass states & flavour states • GIM mechanism & discovery of charm • CKM matrix Chris Parkes

2. Weak decays • Weak decays are mediated by: • W bosons charged current interactions • Z bosons neutral current interactions • Weak interaction does not respect conservation of flavour flavour changing interactions are possible • Will discuss how this happens and difference between flavour changing charged (W±) currents, and neutral (Z0) currents

3. Weak Decays: Charged currents m e ne nm gW gW W W u d c s gW gW W W K- p- m- m- s d W W u u nm nm Have vertices: Assume quarks have similar vertices: Consider observed reactions: ud vertex: allowed us vertex:not-allowed but observed!

4. Mass States & Flavour states • ‘flavour’ state is a superposition of the ‘mass’ states • Flavour states = states that couple to W • Mass states = states of definite mass, ‘free’ quark states s s’ d’ θC d Flavour mass θC is known as Cabibbo angle

5. Quark mixing: udsc quarks u d’ u s u d gW gus gud W W W Flavour states as mixture of mass states: = + udWpreferred tousW

6. Cabibbo-allowed/suppressed decays(2 generations) • gusand gcdare Cabibbo suppressed with respect to gud and gcs • e.g. consider Cabibbo-allowed decays of charm quarks, D+: • cs+l+nandcs+u+dbar • Charmed meson decays most commonly include strange mesons • Also explains c decays to Kbars (cs+u+dbar) preferred to c decays to K (cd+u+sbar) Example of: (p270 Bettini)

7. Weak decays: neutral currents n n u u gZ gZ Z Z l l d’ d’ gz gZ Z Z neutral current Z Charged current W p261 Bettini Why no flavour changing neutral currents (FCNC)?

8. GIM Mechanism: Add in charm Glasgow, Iliopoulos, Maiani 1970, used this to suggest another quark was needed c u c u gZ gZ Z Z s’ d’ d’ s’ gZ gZ Z Z No flavour changing neutral Currents (FCNC) (at tree level in SM)

9. Discovery of charm • Introduction of charm solved FCNC problem • Cancellation of FCNC predicted mass of charm to be ~1.5-2GeV • Charm observed as J/ψ=cc in 1974 • Ψ: R-measurement in e+e- • J: Hadron production p+BeJ+X

10. Charmonium – charm width D0 c c u g u c D0 c • p+N: Experimental resolution hides small width in mass reconstruction • e+e-: Extract width from line shape of resonance • 91 keV, small width, large lifetime • Strong decay - Why so small width ? • 1 gluon – 2* mass D > m ψ • 2 gluon – ψ C=-1, g C=-1 • 3 gluon allowed but s3 u π+ d c g d π0 d d c π- u Not possible energetically for ψ Ψ’’ allowed 24MeV width Allowed

11. Generalise cabibbo matrix To three generations Generalise mixing to 3 Families: CKM Matrix Kobayashi Maskawa 2008 Nobel

12. Measuring Elements Vudb-decay (ud) Vus K-decays (su) Vub B-decays (bu) rare difficult to measure, B- factories have improved this Vcd production of charm of valence quarks in n-DIS Vcs Semi-leptonic D-decays (cs) Vcb B-decays (bc) Vtd top-decay limits Vts top-decay limits Vtb top-decays tWb See Bettini p265 et seq

13. Example: W decays revisited u u u c c c b s d b d s Vud Vud Vud Vud Vud Vud W W W W W W In branching fraction calculation we assumed Vud=Vcs=1, and neglected others Q) Why did we get answer right ?

14. CKM Unitary Q) If the measurements of these were to add to < 1, how would you interpret this? And six equations of off-diagonal elements=0, e.g. 1st row * 3rd column: For probability elements need only be real, but for CP violation (see next) need to be complex