PHYSICS 489/1489 LECTURE 16: WEAK INTERACTION OF HADRONS

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1 PHYSICS 489/1489 LECTURE 16: WEAK INTERACTION OF HADRONS

2 ANNOUNCEMENTS Problem Set 3 e on Friay 1700 No cla next Teay No office hor Monay, Teay Sorry! Pleae feel free to en me abot qetion, etc. or to et p an appointment at another time. Miterm grae propoal replace miterm grae with final grae if final grae i higher i.e. final i worth 60% of total grae if final > miterm otherwie final i worth 40% an miterm 20%

3 WEAK INTERACTION OF QUARKS Step back to 1960 when we knew of three qark Notice that ecay of trange particle wa mch lower than expecte, We can compare pion/kaon ecay ig w l l 2 2 νl νl m π = MeV m K = MeV = f 2 m 3 g w 4M W (K µ + µ ) ( µ + µ ) = m m K 3 m 2 K m 2 µ 4 m 2 l (m 2 m 2 l ) 2 m 2 m 2 µ 2 ~18

4 CABIBBO ANGLE Experiment fin that thi ratio i more like 1.3, inicating that omething i wrong with or pictre co C ig w 2 2 Cabbibo potlate that: tranition cale by factor of co θ c c tranition cale by factor of in θ c experimentally θ c ~ 13 in C ig w 2 2 Cabibbo wa able to relate a hot of ecay rate for trange an non-trafe particle with a ingle parameter Cabibbo favore : ecay with co θ c factor Cabibbo ppree : ecay with in θ c factor

5 STILL A PROBLEM µ co C ig w 2 2 W νµ W µ in C ig w 2 2 Above proce hol happen a K 0 μ + +μ - bt it rate a mch lower than expecte, even after coniering Cabibbo factor

6 GIM MECHANISM c W µ W µ νµ c νµ co C ig w 2 2 W µ W µ c A 1 in C co C A 2 in C co C co = C in C in C co C Introce a forth qark charm that cancel contribtion from qark c Mixing ma eigentate (conventional name for qark) are linear combination of flavor eigentate a inicate above i efine a tate that cople to via the W boon i efine a tate that cople to c via W boon

7 THE NOVEMBER REVOLUTION 1974: Dicovery of the J/ψ particle evience of a bon tate with a heavy qark Broght together many element of what we call the tanar moel qark, gage theory, etc

8 TOWARDS THREE GENERATIONS νe νµ ντ Prior to the icovery of the Charm qark, Kobayahi an Makawa contemplate the poibility of ix qark (three generation) in 1964 e µ τ c t b Generalize Cabibbo angle to 3x3 matrix relating ma/flavor tate = V V V b V c V c V cb b V t V t V tb b Apply factor of V ab * for a b tranition W νµ µ factor of V ab for b a tranition note that antiqark tranition are complex conjgate relative to qark tranition jt follow the arrow W µ V ig W 2 p 2 V ig W 2 p 2 (1

9 GIM MECHANISM in CKM µ V ig W 2 p 2 V ig W 2 p 2 (1, c, t W νµ V c ig W 2 p 2 V c ig W 2 p 2 (1 W µ V V + V c V c + V t V t V t ig W 2 p 2 V V Vb Vc Vc Vcb Vt Vt Vtb 1 A V t ig W 2 p 2 (1 V V V b V c V c V cb V t V t V tb 1 A In general, flavor changing netral crrent that procee via a loop an two CC tranition will have thi ppreion Natre abhor flavor changing netral crrent U CKM c t b

10 C SYMMETRY Charge conjgation: flip all internal qantm nmber charge, color, lepton nmber, etc. particle trn into anti-particle e.g. electron->poitron, proton->antiproton, photon->photon ince charge conjgating twice give the ame particle the eigenvale mt be ±1 Convention: C γ = - γ ince we have the ecay π 0 γ + γ, the mean that C π 0 = + π 0 Coneqence: π 0 γ + γ +γ hol not happen if C i a ymmetry

11 CP SYMMETRY In tying pion ecay we fon that P i violate e to the V-A copling: µ µ + + µ P µ µ + + µ C C µ µ Hitorically, people wante to ave ome ort of pace inverion ymmetry o that coniere CP ymmetry mirror ymmetry accompanie by charge conjgation retore ymmetry µ P µ µ µ

12 THE NEUTRAL KAONS Two type of netral kaon proct in trong interaction K 0 K 0 A flavor tate, we can proce them a follow + p + K 0 + p n + n + + K p p + K + + K 0 After proction, they live long enogh that the following mixing procee occr,c,t,c,t K 0 W W K 0 K 0 W W K 0,c,t,c,t

13 MIXING Mixing mean kaon proce initially a a flavor tate (i.e. K 0 or K 0 ) i no long a tate of efinite flavor it i a linear combination of K 0 an K 0 Conier the C an P propertie of thee tate: Thomon convention C K 0 i = K 0 i P K 0 i = K 0 i C K 0 i = K 0 i P K 0 i = K 0 i Then we can contrct CP eigentate: K 1 i = 1 p 2 K0 i + K 0 i CP K 1 i = 1 p 2 K0 i + K 0 i =+ K 1 i K 2 i = 1 p 2 K0 i K0 i CP K 2 i = 1 p 2 K0 i K 0 i = K 2 i

14 DECAY MODES Conier final tate of two or three pion: K! C :1 2 P :( 1) 2 CP :+1 +1 = +1 K! C :1 3 P :( 1) 3 CP :+1 1= 1 CP ymmetry mean K 1 can ecay to ππ bt not πππ K 2 can ecay to πππ bt not ππ Thi mean that K 2 ha a longer lifetime than K 1 Experimentally: t 1 = 8.95x10-11 t 2 = 5.11x10-8

15 CP VIOLATION IN KAON DECAY Proce a beam of K 0 propagate ~20 meter to ecay K 1 all that i left i K 2 Do we ee any K ππ ecay?

16 THE THIRD GENERATION νe νµ ντ e µ τ c t b Kobayahi an Makawa contemplate that CP violation come from mixing phae in the mixing will witch ign when coniering qark v antiqark tranition Impoible to generate phae in mixing with only two generation at leat three are neee Firt inication came from the icovery of the τ in 1975 at SLAC bottom qark icovere in 1977 top qark in 1994 ν τ in 2000 Experiment (kaon, B-factorie, etc.) confirm Kobayahi an Makawa explanation for CP violation in qark

17 SUMMARY Three form of weak ecay ppreion overall at low energie (long lifetime, mall cro ection) helicity ppreion Cabibbo ppreion GIM ppreion Symmetry violation Parity i maximally violate for weak CC interaction CP i alo violate

18 REMINDER No cla next Teay No office hor Monay, Teay Sorry! Pleae feel free to en me abot qetion, etc. or to et p an appointment at another time. Pleae rea Chapter 15