# 1 FK7003 Lecture 8 ● CP -violation ● T -violation ● CPT invariance.

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1 FK7003 Lecture 8 ● CP -violation ● T -violation ● CPT invariance

2 FK7003 Recap

3 FK7003 Looking for CP violation via kaons decays Incoming K 2 beam Decay of K 2 into 3 pions   

4 FK7003 Neutral Kaon system Incoming K 2 beam Decay into two pions  

5 FK7003 Explaining the Cronin/Fitch Experiment

6 FK7003 CP -violation CP

7 FK7003 Which one is the ”particle” ? Produce in strong interaction Weak interactions break the degeneracy.

8 FK7003 CP Lear Experiment Compare rates for the two processes CP transformations of each other. CPLEAR Experiment at CERN ( pp interactions) Consider two strong reactions e+e+ e-e- e K0K0 K0K0   W-W- W+W+ d u d s d u d s e

9 FK7003 CP-Lear Experiment Measurement made of an asymmetry A T K 0 K 0 and K 0 K 0 do not occur at the same rate This ”drives” the CP violation observed in kaon decays (we believe). Result and experiment to be discussed further in the context of time reversal. (8.05)

10 FK7003 Question The CP-Lear experiment measures events in which a K 0 or a K 0 is produced. After a certain time it is checked if the kaon has decayed to two pions. They measure a difference in the amount of. Is this observation consistent with CP -violation ?

11 FK7003 Another CP -violating process If no CP -violation then CP transforms (a) to (b) CP non-violation would imply equal rates. But, positron decay more likely by a fractional amount  3.3x10 -3 Unequal production of matter-antimatter!! Could CP violation in the early universe be responsible for today’s asymmetry ?

12 FK7003 C,P and CP in the weak force ● C and P are maximally violated ● CP violation is rarely seen in weak processes. It is small effect which dominantly arises from neutral meson states which can convert into each other: K 0 K 0, B 0 B 0 ● CP -violation with B -mesons not covered – similar mathematics as for the kaons presented here. Not seen!!

13 FK7003 Implications beyond particle physics Communicating with aliens. Originally from Feynman  Imagine communicating with aliens. You want to describe humans and human behaviour.  You describe human height with wavelengths of light.  You describe human age by ticks of an atomic clock  How do you communicate the custom of shaking right hands ? What is right and left ? Need to use P and CP violation.

14 FK7003 Parity violation ● Try to use parity violation to provide a fundamental definition of left and right. ● Could be useful if we need to send a message to an alien with no knowledge of human convention!   Message to alien: Study   decays (charge of pion the same as the atomic electron). (1) Look at decays in which the charged particle goes up (against gravity - he/she is standing on a planet in a lab.) (2) Consider the situation when you are looking at a plane consisting of the pion, muon and neutrino. (3) The muon is ”rotating” from left to right ( – we choose a ”vertical” z-axis.)   decays z

15 FK7003 Be careful! ● The alien extends his/her left hand for a shake and annihilates your right hand. ● His/her galaxy is made of antimatter and in his/her world the muon is spinning in the opposite direction to ours. ● Why ? ● How do we let the alien know in advance if he/she is living in an antimatter world ?      

16 FK7003 What we can tell the alien. ● With CP violation we can define:  Matter and anti-matter ● Antielectrons are favoured in K L decays ● The alien goes away and checks if the most favoured lepton in a K L decay is the same particle found in an atom on his/her world.  Positive and negative charge ● positive leptons are favoured in K L decays. ● Now the alien knows our charge definition we use parity violation to define:  Left and right ● The muon from the negative pion decay ”spins” from left to right.

17 FK7003 Conserved quantities/symmetries QuantityStrongWeak Electromagnetic Energy Linear momentum Angular momentum Baryon number Lepton number Isospin -- Flavour (S,C,B) - Charges (em, strong and weak forces) Parity (P) - C-parity (C) - G-parity (G) -- CP - T - CPT Coming up

18 FK7003 T symmetry Do the laws of physics work exactly the same way in reverse if the time direction is changed t -t ? If we consider a + b c + d could we tell by looking at the reaction rate if the process was going forward or backward in time ?

19 FK7003 Checking T symmetry t t Apply T transformation

20 FK7003 T symmetry Take into account initital momenta. T invariance demonstrated so far for the strong and electromagnetic forces. Best em limit from neutron’s electric dipole moment What about the weak force ? Detailed balance experiments difficult since Study T invariance with reactions such as :

21 FK7003 Did this earlier! T violation in the weak force Compare rates for the two weak processes Oscillations easier to study than ”detailed balance” experiments. CPLEAR Experiment CERN ( pp interactions) Consider two strong reactions e+e+ e-e- e K0K0 K0K0   W-W- W+W+ d u d s d u d s e

22 FK7003 Observation of T violation Measurement made of an asymmetry A T There is a difference in rates for forward and reversed versions of the same reaction. T is violated in the weak force. K 0 K 0 and K 0 K 0 do not have the same rates! Could be deduced from CP violation. Necessary that neutral kaons show CP and T violations. (8.09)

23 FK7003 T violation and CPT ● A small amount of T -violation in the weak force is a consequence of CP -violation. T -violation also occurs due to mixing. Many weak processes respect T - symmetry. ● The combined symmetry CPT is always respected in the weak (and em and strong) forces. ● CPT symmetry required for any quantum field theory in which signals do not propagate faster than light! CPT is believed in!

24 FK7003 CPT symmetry

25 FK7003 Tests and consequences of CPT invariance Consistent particle and anti-particle masses imply CPT symmetry. + CPT invariance implies particles and anti- particles have the same lifetime. + CPT invariance also implies that if CP and T are violated then there must be at least 3 quark generations. ( )

26 FK7003 More CPT tests M. Sozzi, Discrete Symmetries and CP violation Finding a violation of CPT would be of greater importance than discovering the Higgs or supersymmetry (IMO). Ps  positronium (covered in next lecture) Penning trap: Device for storing charged particles with constant B and non-uniform E - field.

27 FK7003 Conserved quantities/symmetries QuantityStrongWeak Electromagnetic Energy Linear momentum Angular momentum Baryon number Lepton number Isospin -- Flavour (S,C,B) - Charges (em, strong and weak forces) Parity (P) - C-parity (C) - G-parity (G) -- CP - T - CPT

28 FK7003 Lecture summary ● C and P are symmetries respected by the strong and electromagnetic forces but are maximally violated by the weak force. ● CP is violated in the neutral kaon system by a small amount by the weak force. This is dominantly caused by mixing. ● P violation allows a left-right distinction to be made. ● CP violation allows a distinction to be made between matter and anti-matter. ● CPT symmetry is observed by all forces. ● We are now able to tell an alien which hand should be shaken without fear of annihilation.

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