Download presentation

Presentation is loading. Please wait.

Published byDario Smerdon Modified over 2 years ago

1
: Section 3: Mixing and CP violation in (mostly) neutral mesons

2
State evolution in neutral mesons Neutral meson states P o, P o –Could be K o, D o, B o With internal quantum number F –Such that F=0 emag/strong, F 0 for H weak Obeys time dependent Schrödinger eqn M, Hermitian 2x2 matrices, mass matrix and decay matrix, H 11 =H 22 from CPT (mass/decay particle = anti- particle)

3
Solve Schrödinger for Eigenstates of H w From characteristic equation If E 1 =M 1 -i 1 /2, E 2 = M 2 -i 2 /2 and M=M 2 -M 1, = 2 - 1 Complex coeff. p,q obey |q| 2 +|p| 2 =1

4
Eigenvector Eqn Eigenstates have time evolution: then with

5
Finally probabilities… With The oscillations depend upon the parameter x the speed of oscillations c.f. lifetime Where = ( 1 + 2 )/2 Interference term

6
Mixing probabilities x in B s not yet measured >19 Probability of finding P o from initial pure P o beam

7
CP in decay CP in mixing CP in interference between mixing and decay Types of CP violation P f f P f f P P f f P PP P f f P PP P + +

8
1) CP Violation in mixing Indirect CP Violation Mass eigenstates being different from CP eigenstates Mixing rate P o P o is different to P o P o If conserved CP|P 1 > = +1 |P 1 > CP|P 2 > = -1 |P 2 > with If violated Such asymmetries usually small Need to calculate M, , involve hadronic uncertainties Hence, tricky to relate to CKM parameters

9
2) CP Violation in decay direct CP Violation Two types of phase –Weak phase: due to weak interactions (complex CKM elements) –Strong phase: contribution from intermediate states, CP conserving (same sign in both) f is final state common to both decays occurs for both charged and neutral states P

10
3)CP violation in the interference of mixing and decay Choose state* f, P o f, P o f Two possible decay chains, with or w/o mixing CP can be conserved in mixing and in decay and still be violated ! *Not necessary to be CP eigenstate Interference term depends on Can putand getbut

11
: Section 4: Neutral Kaon system

12
K o K o system Kaon mesons in two isospin doublets K + = us K o = ds K - = us K o = ds S=+1S=-1 Part of pseudo-scalar J P =0 - meson octet with , I 3 =+1/2 I 3 =-1/2 Kaon production K o : - + p o + K o But from baryon number conservation: K o : + + p K + + K o + p Or K o : - + p o + K o + n +n Requires higher energy Much higher S 0 0 -1 +1 S 0 0 +1 -1 0 S 0 0 +1 -1 0 0

13
Kaon oscillations So say at t=0, pure K o, –later a superposition of states d s u, c, t WW WW _ s d _ d s WW WW _ s d _ _ _ _ K0K0 K0K0

14
K o Decay In that case CP=+1 CP=-1 K s o o K s + - K L + - o K L o o o CP=+1 CP=-1 K S branching fractions: 69%, 31% K L branching fractions: 21%, 13%, 66% mass eigenstates KSKS KLKL show Assume CP

15
Time dependent probabilities for the neutral kaon case. t (1/ )

16
K o Regeneration Start with Pure K o beam –After time all K s component decayed Introduce slab of material in beam –reactions 1) Elastic scatttering2) Charge exchange 3) Hyperon production Hence K o absorbed more strongly i.e. K s regenerated

17
Discovery of CP Violation K 1 o o K 1 + - K 2 + - o K 2 o o o CP=+1 CP=-1 So if K L =K 1 CP eigenstate, Observe no two pion component But if broken get: Where quantifies degree of CP violation BUT Can one find K L decaying into + - ?

18
K L X K L p = p + p = angle between p KL and p If X = 0, p = p KL : cos = 1 If X 0, p p KL : cos 1 cos KLKL m ( ) < m K J.H. Christenson et al., PRL 13,138 (1964) Discovery of CP violation m ( ) = m K m ( ) > m K Mass and angular spectrum

19
So CP symmetry is violated in the neutral kaon system. Mass eigenstates (K S and K L ) CP eigenstates Both K S and K L could decay into + - -. Experimentally well known: The majority of K S decays into - and K L into - - . Small but with profound implications In K L

20
Decay final state at time t -- Spin( ) = 0 L - = 0 Initial state at t = 0 S = 0 CP( - i.e. CP eigenstate K 0 at t = 0 decays into vs K 0 at t = 0 decays into any difference = CP violation CPLEAR revisited Tag K o /K o from charged pion/kaon

21
K0K0 K0K0 _ CPLEAR R +- (t) and R +- (t) _ CP violation

22
CPLEAR CP asymmetry A (t) = R +- (t) R +- (t) R +- (t) R +- (t) _ _ large difference! CP violation in mixing The two mass eigenstates are not CP eigenstates

23
Kaons: CP violation in Decay CP violation first through existence of certain decay modes ~2.3x10 -3 If CP violation is only in mixing, i.e. independent of decay So, put channel independent term and channel dependent ’ Hence, by measuring only rates: get

24
So, two expts in the 80’s did it: NA31 (CERN) E731 (Fermilab) Ambiguous result! So, two expts did it again…….

25
NA48

26
KTeV

27
Measure and at the same time: NA31, NA48 K S is regenerated from K L : E731, KTeV No normalization is required, but efficiencies, acceptances etc. have to be corrected… Normalisation constants

28
Effort over 30 years! Note; 3 Re = | / | i.e. Re 0 Not easy to compare with SM theory

29
CKM parameters with CP conserving parameters |Vud| : nuclear Beta decay 0.9734 0.0008 |Vus| : semileptonic Kaon and hyperon decay (CCFR) 0.2196 0.0026 |Vcd| : Neutrino and anti-neutrino production of charm off valence d quarks 0.224 0.016 |Vcs| : W decays (LEP/me!) 0.996 0.013 |Vcb| : semileptonic inclusive and exclusive B decays (LEP/CLEO) 0.0412 0.0020 |Vub| end point spectrum in semileptonic B decays(LEP/CLEO) 0.0036 0.0007 B o mixing x d, + lattice gauge inputs |Vtb*Vtd| 0.0079 0.0015 Can use Unitarity constraints

Similar presentations

Presentation is loading. Please wait....

OK

Shu-Yu Ho Date : 2010/9/20 QFT study group

Shu-Yu Ho Date : 2010/9/20 QFT study group

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on regular expression c# Ppt on health effects of air pollution in delhi Ppt on regular expression File type ppt on cybercrime prevention Ppt on pin diode phase Ppt on automobile industry in india free download Seminar report and ppt on google glasses Ppt on earth dam breach Download ppt on strings in c language Ppt on google driverless cars