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

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 (Z 0 ) currents

3 Weak Decays: Charged currents e e W   W c s W u d W gWgW gWgW gWgW gWgW ud vertex: allowed us vertex: not-allowed but observed! Have vertices: Assume quarks have similar vertices: Consider observed reactions: d u W --  -- s u W --  K-K-

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 Flavourmass d d’ s s’ θCθC θ C is known as Cabibbo angle

5 Quark mixing: udsc quarks ud’ W gWgW us W g us u d W g ud =+ Flavour states as mixture of mass states: udW preferred to usW

6 Cabibbo-allowed/suppressed decays (2 generations) g us and g cd are Cabibbo suppressed with respect to g ud and g cs e.g. consider Cabibbo-allowed decays of charm quarks, D + : c  s+l+ and c  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 Z u u Z d’ Z l l Z gZgZ gzgz gZgZ gZgZ Why no flavour changing neutral currents (FCNC)? p261 Bettini Charged current W neutral current Z

8 GIM Mechanism: Add in charm u u Z d’ Z gZgZ gZgZ c c Z s’ Z gZgZ gZgZ d’ s’ No flavour changing neutral Currents (FCNC) Glasgow, Iliopoulos, Maiani 1970, used this to suggest another quark was needed (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 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  s 3 g c c u u c c D0D0 D0D0 Not possible energetically for ψ Ψ’’ allowed 24MeV width g c c d d u u Allowed d d π-π- π+π+ π0π0

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

12 Measuring Elements V ud  -decay (u  d) V us K-decays (s  u) V ub B-decays (b  u) rare difficult to measure, B- factories have improved this V cd production of charm of valence quarks in -DIS V cs Semi-leptonic D-decays (c  s) V cb B-decays (b  c) V td top-decay limits V ts top-decay limits V tb top-decays t  Wb See Bettini p265 et seq

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

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