= ν L. C ν L. = ν R. P ν L. CP ν L. CP Violation. Standard Model contains only left-handed neutrinos and right-handed anti-neutrinos

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1 Phy489 Leture 9 1

2 CP iolation Stanar Moel ontains only left-hane neutrinos an right-hane anti-neutrinos C ν L = ν L harge onjugation not a symmetry of the weak interation P ν L = ν R parity also not onserve in weak interations CP ν L = ν R what about the ombine CP transformation..looks OK?

3 Kaon Osillations (K -K Mixing) K K s s u u u u time K s K s Neutral mesons an osillate bak an forth between partile an antipartile states. [equivalent iagrams mix D with D, B with B ] This (seon-orer) proess mixes states of strangeness = 1, strangeness = -1. Neutral kaons are proue in states of efinite strangeness (i.e. via the strong interation) 3

4 CP Operations on Neutral Kaons Neutral kaons are groun state spin- s mesons, so are pseuosalars [ P = ( 1) +1 ] P K = K P K = K CP K C K = K C K = K = K CP K = K Normalize eigenstates of CP are therefore: K 1 = 1 ( K K ) CP K 1 = + K 1 K = 1 ( K + K ) CP K = K 4

5 Deays of Neutral Kaons If CP is onserve by the weak interation: K 1 eays only to CP = +1 final states K eays only to CP = -1 final states (CP even) (CP o) Neutral kaons are the lightest neutral mesons ontaining a strange quark. Cannot eay via strong interation: M(K ) M(K - ) ~ 4 Me/ << M π Cannot eay eletromagnetially (why not?) Dominant eays are weak eays ( s u transition) into two or three pions System of n pions (without orbital angular momentum) has P = (-1) n K1 ππ M K Me/ M π K πππ M K 3 85 Me/ M π 5

6 Deays of Neutral Kaons Deay of K 1 takes plae 5 times faster than K (phase spae onsierations) Imagine a beam of neutral kaons (proue via the strong interation) 1 ( 1 ) K = K + K Mean eay length (in lab frame) is γβτ (γ the same for K 1 an K ) so mean eay length of K is ~5 times longer that for K 1 K 1 omponent of beam will eay very quikly after proution. Expet to see many K ππ eays near the proution point Far ownstream expet an almost pure beam of K 6

7 CP iolation in Neutral Kaon Deays By going very far ownstream from the K beam proution point, expet an arbitrarily pure beam of K ; if CP is inee onserve by the weak interation will observe only the three π final state very far from the proution point. Cronin an Fith, 1964 (Nobel Prize 198) performe this experiment. Foun small amixture (1/5) of π eays very far from the proution point (no matter how far you go this is the asymptoti value). Long-live neutral kaon state (K Long) is NOT a CP eigenstate: 1 KL = K + K 1+ ε ( ε 1 ) CP is therefore NOT a goo symmetry of the weak interation, although the level at whih it is broken (or violate) is rather small (ε =.3 x 1-3 ). 7

8 Other Manifestations of CP iolation in Kaon System If K L were a CP eigenstate (eg ε = ) then the two eays K L π e + ν e K L π e + ν e Woul our with equal probability: instea BR K e BR K e BR K e BR K e + + ( L π ν e) ( L π ν e) + + ( L π ν e) + ( L π ν e) =.33 8

9 Quark Mixing an the Cabibbo Angle Weak eays of s quarks requires su oupling (i.e. generational transition) unlike in pion eays (for example). Cabibbo introue quark mixing to explain relative branhing ratios weak eays of mesons into leptons: Will see later that we nee form fators to esribe how this takes plae in a boun state µ ν µ µ ν µ W W time u u π + K + s Relative strengths imply smaller oupling at suw vertex than at uw 9

10 Quark Mixing an the Cabibbo Angle Cabibbo s hypothesis (only u,, an s quarks were known at the time). = osθ + s sinθ s = sinθ + s osθ osθ sinθ = s sinθ osθ s θ is the Cabibbo angle ( ~ 13º ) u u s osθ sinθ w + w + Cabibbo-favoure Cabibbo-suppresse π µ ν µ K µ ν µ 1

11 The GIM Mehanism (197) Glashow, Iliopoulos an Maini postulate the existene of a fourth quark (harm) -9 on the basis of the measure branhing fration: BR( K L µ + µ ) = 7 x 1 This is very small. Shoul our at a muh higher rate via the proess: µ µ u u s osθ sinθ ν µ u w+ s w + s osθ sinθ K L w + w + 11

12 The GIM Mehanism (197) Contribution from proess with internal u quark exhange partially anelle by same iagram but with internal quark exhange µ µ µ µ ν µ ν µ u u us ~ sinθ osθ s ~ sinθ osθ s s K L K L If the masses of the u an quarks were iential, these ontributions woul exatly anel. Sine they are not, this merely leas to the (observe) suppression of suh proesses. 1

13 The Kobayashi Maskawa Preition (1973) Later we will see, in the weak interation Lagrangian: u t s b µ 5 (,, ) γ (1 γ ) quark mixing matrix omplex N x N matrix has N real free parameters Unitarity eliminates N N (number of quarks) an be absorbe into the phases in the quark wavefuntions. Not sensitive to an overall phase, so this eliminates N-1 This means N -N+1 = (N-1) are require to parametrize the mixing matrix N(N-1)/ real mixing angles + (N-1)(N-)/ omplex phases A omplex phase in the quark mixing matrix allows for CP violation in the SM However, nee N> for this. Base on this, Kobayashi an Maskawa preite a thir generation in

14 Cabibbo Kobayashi Maskawa Matrix u us ub s = s s b b t ts tb b CKM mixing matrix for three generation of quarks 1,,3 label mixing angles, δ is the phase s 1 = sin(angle 1), 1 = os(angle 1) et s s + s s s s e s s e iδ iδ s1 1 3 ss3e 1 s3 s3e iδ iδ = 1 1 s1 1 1 s s s3 iδ s 1 e s3 3 Three rotations an a phase 1 λ λ Aλ 3 (ρ iη) λ 1 λ Aλ 3 Aλ 3 (1 ρ iη) Aλ O(λ 4 ) Wolfenstein parametrization emphasizes the magnitues of the off-iagonal elements λ = ~.5 sinθ 14

15 Experimental Determination of CKM Matrix Elements u us ub s b t ts tb = λ λ Aλ ( ρ iη ) 1 λ λ Aλ 3 Aλ (1 ρ iη ) Aλ 1 λ = sinθ ~.5 15

16 CP iolation in the K System s us u K u u u t us s ts ub b tb u K s us There are also equivalent iagrams with an t quarks replaing the u quarks in the loop (an iagrams with the quarks going aross an the Ws going up see slie 3). 16

17 CP iolation in the K System s s K u t us s ts ub b tb s K s 17

18 CP iolation in the K System ts t s K t t u t us s ts ub b tb t ts K s 18

19 Unitarity Constraints * * * u t u us ub 1 * * * us s ts s b = 1 * * * ub b tb t ts tb λ λ Aλ ( ρ iη ) 1 λ λ Aλ 3 Aλ (1 ρ iη ) Aλ = * * * us u s ts t Unitarity triangle in omplex plane ~ λ * 5 ts t * us u ~ λ This angle is a measure of the egree to whih CP is 5 4 violate in the kaon system ~ λ / λ = λ ~.5 * s ~ λ There are six suh unitarity triangles, but all have the same area 19

20 CP iolation in the B System B B b b u,,t u,,t u,,t u,,t B b B b Mixing of neutral B meson ours in the same way as in the kaon system

21 B CP iolation in the B System ub u b u u u t us s ts ub b tb u ub There are also equivalent iagrams with an t quarks replaing the u quarks in the loop. b B 1

22 B CP iolation in the B System b b u t us s ts ub b tb b b B

23 B CP iolation in the B System tb t b t t u t us s ts ub b tb t tb b B 3

24 CP iolation in the B Meson System * * * u t u us ub 1 * * * us s ts s b = 1 * * * ub b tb t ts tb λ λ Aλ ( ρ iη ) 1 λ λ Aλ 3 Aλ (1 ρ iη ) Aλ = * * * ub u b tb t ~ λ * 3 ub u tb * t ~ λ 3 Unitarity triangle in ρη plane ~ λ * 3 b 3 3 ~ λ / λ = 1 CP iolation expete to be large in the B system. This has been an ative fiel of researh at the so-alle B fatories sine the mi-late nineties (an remains so) 4

25 CP iolation in the B Meson System * = ~ λ * * * ub u b tb t ub u tb * t ~ λ 3 Divie through sies by b * ~ λ * 3 b Unitarity triangle in ρη plane B-fatory experiments (BABAR,BELLE) eiate to over-onstraining this unitarity triangle as a test of the SM. 1 years of running have proue preision measurements but no eviations from the preitions of the SM PDG(6) sinβ =.73 ±.4 PDG(8) sinβ =.678 ±.5 5

26 Current Status of the Unitarity Triangle (6) 6

27 Current Status of the Unitarity Triangle (8) 7

28 CP iolation an Baryon Number Asymmetry Our universe appears to be mae of matter only. Astronomial observations rule out the existene of omains of anti-matter ominane In the Big Bang, matter an antimatter woul have been reate in equal amounts. Nee some mehanism for reating the observe asymmetry Nee CP violation (whih is an asymmetry between matter an anti-matter) Mehanism of CP violation in Stanar Moel not enough to explain this. Also nee baryon number non-onserving proesses (e.g. GUTs) 8

29 Searh for Proton Deay (violates baryon number onservation) SuperKamiokane Detetor, Japan 9

30 Alpha Magneti Spetrometer (on Spae Station) Amongst other stuies, AMS will look for antimatter potentially left over from the Big Bang (or in regions of anti-matter ominane (anti helium nulei or anti-arbon nulei et ) 3

31 Time Reversal Invariane Quantum Fiel Theory (QFT): CPT theorem says that in any theory onsistent with Lorentz invariane, quantum mehanis an the iea that interations are arrie by fiels, the ombine operations of C, P an T (in any orer) form an exat symmetry of any interation. Sine CP is known to be violate by weak interation, T must be as well Experimental tests of this are har: an t easily run a weak interation bakwars (priniple of etaile balane) Instea, look at quantities that are ientially zero if T is onserve Popular example is eletri ipole moment of the neutron Current limit from PDG 8: n < e.9 x 1-5 m 31

32 Question K * K * K * K Why are osillations not observe experimentally? ( is the same as but with spin-1 instea of spin-. ) K s spin M(K ) 498 Me / K * s spin 1 M(K * ) 89 Me / 3