# CP violation Lecture 6

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### Transcript of CP violation Lecture 6

Niels Tuning (*)CP violation

Lecture 6N. Tuning

Niels Tuning (*)

Diagonalize Yukawa matrix YijMass termsQuarks rotateOff diagonal terms in charged current couplingsNiels Tuning (*)Recap

Niels Tuning (*)CKM-matrix: where are the phases?Possibility 1: simply 3 rotations, and put phase on smallest:Possibility 2: parameterize according to magnitude, in O():

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This was theory, now comes experimentWe already saw how the moduli |Vij| are determinedNow we will work towards the measurement of the imaginary partParameter: Equivalent: angles , , .

To measure this, we need the formalism of neutral meson oscillationsNiels Tuning (*)

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Meson DecaysFormalism of meson oscillations:

Subsequent: decay

Classification of CP Violating effectsCP violation in decay

CP violation in mixing

CP violation in interferenceNiels Tuning (*)

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Classification of CP Violating effectsCP violation in decayExample:

CP violation in mixingExample:

CP violation in interferenceExample:Niels Tuning (*)B0J/Ks

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Remember!Necessary ingredients for CP violation:Two (interfering) amplitudes Phase difference between amplitudesone CP conserving phase (strong phase)one CP violating phase (weak phase) Niels Tuning (*)

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Remember!Niels Tuning (*)

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NextCP violation in decay

CP violation in mixing

CP violation in interference

Niels Tuning (*)Why bother with all this?CKM matrix has origin in LYukawaIntricately related to quark massedBoth quark masses and CKM elements show intriguing hierarchy

There is a whole industry of theorist trying to postdict the CKM matrix based on arguments on the mass matrix in LYukawa

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KaonsNiels Tuning (*)Different notation: confusing!K1, K2, KL, KS, K+, K-, K0

Smaller CP violating effects

But historically important!Concepts same as in B-system, so you have a chance to understand

Niels Tuning (*)

Neutral kaons 60 years of history the 0 must be considered as a "particle mixture" exhibiting two distinct lifetimes, that each lifetime is associated with a different set of decay modes, and that no more than half of all 0's undergo the familiar decay into two pions. 1947 : First K0 observation in cloud chamber (V particle)1955 : Introduction of Strangeness (Gell-Mann & Nishijima) K0,K0 are two distinct particles (Gell-Mann & Pais)

1956 : Parity violation observation of long lived KL (BNL Cosmotron)1960 : Dm = mL-mS measured from regeneration1964 : Discovery of CP violation (Cronin & Fitch)

1970 : Suppression of FCNC, KLmm - GIM mechanism/charm hypothesis1972 : 6-quark model; CP violation explained in SM (Kobayashi & Maskawa)

1992-2000 : K0,K0 time evolution, decays, asymmetries (CPLear) 1999-2003 : Direct CP violation measured: e/e 0 (KTeV and NA48)From G.CaponNiels Tuning (*)

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Intermezzo: CP eigenvalueNiels Tuning (*)Remember: P2 = 1 (x -x x)C2 = 1 ( ) CP2 =1 CP | f > = | f > Knowing this we can evaluate the effect of CP on the K0CP|K0> = -1| K0>CP| K0> = -1|K0 >CP eigenstates:|KS> = p| K0> +q|K0>|KL> = p| K0> - q|K0>

|Ks> (CP=+1) p p (CP= (-1)(-1)(-1)l=0 =+1)|KL> (CP=-1) p p p (CP = (-1)(-1)(-1)(-1)l=0 = -1)

( S(K)=0 L()=0 )

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Niels Tuning (*)Decays of neutral kaons Neutral kaons is the lightest strange particle it must decay through the weak interactionIf weak force conserves CP then decay products of K1 can only be a CP=+1 state, i.e. |K1> (CP=+1) p p (CP= (-1)(-1)(-1)l=0 =+1) decay products of K2 can only be a CP=-1 state, i.e. |K2> (CP=-1) p p p (CP = (-1)(-1)(-1)(-1)l=0 = -1)

You can use neutral kaons to precisely test that the weak force preserves CP (or not)If you (somehow) have a pure CP=-1 K2 state and you observe it decaying into 2 pions (with CP=+1) then you know that the weak decay violates CP( S(K)=0 L()=0 )

Niels Tuning (*)Designing a CP violation experimentHow do you obtain a pure beam of K2 particles?It turns out that you can do that through clever use of kinematicsExploit that decay of K into two pions is much faster than decay of K into three pionsRelated to fact that energy of pions are large in 2-body decay t1 = 0.89 x 10-10 sec t2 = 5.2 x 10-8 sec (~600 times larger!)Beam of neutral Kaons automatically becomes beam of |K2> as all |K1> decay very early onInitial K0 beamK1 decay early (into pp)Pure K2 beam after a while! (all decaying into ) !

Niels Tuning (*)The Cronin & Fitch experimentIncoming K2 beamDecay of K2 into 3 pionsIf you detect two of the three pions of a K2 ppp decay they will generally not point along the beam lineEssential idea: Look for (CP violating) K2 pp decays 20 meters away from K0 production point

Niels Tuning (*)The Cronin & Fitch experimentIncoming K2 beamDecay pionsIf K2 decays into two pions instead of three both the reconstructed direction should be exactly along the beamline (conservation of momentum in K2 pp decay)Essential idea: Look for K2 pp decays 20 meters away from K0 production point

Niels Tuning (*)The Cronin & Fitch experimentIncoming K2 beamDecay pionsResult: an excess of events at Q=0 degrees!K2 pp decays (CP Violation!) Essential idea: Look for K2 pp decays 20 meters away from K0 production pointK2 ppp decaysNote scale: 99.99% of K ppp decays are left of plot boundaryCP violation, because K2 (CP=-1) changed into K1 (CP=+1)

"for the discovery of violations of fundamental symmetry principles in the decay of neutral K mesons"Val Logsdon Fitch 1/2 of the prize Princeton University Princeton, NJ, USA b. 1923 James Watson Cronin 1/2 of the prize University of Chicago Chicago, IL, USA b. 1931The discovery emphasizes, once again, that even almost self evident principles in science cannot be regarded fully valid until they have been critically examined in precise experiments. Nobel Prize 1980Niels Tuning (*)

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Cronin & Fitch Discovery of CP violationConclusion: weak decay violates CP (as well as C and P)But effect is tiny! (~0.05%)Maximal (100%) violation of P symmetry easily follows from absence of right-handed neutrino, but how would you construct a physics law that violates a symmetry just a tiny little bit?

Results also provides us with convention-free definition of matter vs anti-matter.If there is no CP violation, the K2 decays in equal amounts to p+ e- ne (a) p- e+ ne (b)Just like CPV introduces K2 decays, it also introduces a slight asymmetry in the above decays (b) happens more often than (a)Positive charge is the charged carried by the lepton preferentially produced in the decay of the long-lived neutral K mesonNiels Tuning (*)

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Intermezzo: RegenerationDifferent cross section for (p K0) than (pK0)Elastic scattering: sameCharge exchange : sameHyperon production: more for K0 !

What happens when KL-beam hits a wall ??Then admixture changes: |KL> = p| K0> - q|K0>Regeneration of KS ! Could fake CP violation due to KS+-

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KS and KLKL and KS are not orthogonal:Usual (historical) notation in kaon physics:Modern notation used in B physics:Regardless of notation:Niels Tuning (*)

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Three ways to break CP; e.g. in K0 +-Niels Tuning (*)

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Classification of CP Violating effectsCP violation in decay

CP violation in mixing

CP violation in interferenceNiels Tuning (*)

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Time evolutionNiels Tuning (*)

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B-system 2. CP violation in mixing K-systemCPLear (2003)BaBar, (2002)CPLEAR, Phys.Rep. 374(2003) 165-270

B-system 2. CP violation in mixing K-systemNA48, (2001)L(e) = (3.317 0.070 0.072) 10-3BaBar, (2002)Niels Tuning (*)

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B-system 3.Time-dependent CP asymmetryB0J/KsBaBar (2002)Niels Tuning (*)

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B-system 3.Time-dependent CP asymmetry K-systemp+p- rate asymmetryCPLear (PLB 1999)K0-+B0J/Ks~50/50 decay as Ks and KL + interference!BaBar (2002)K0K0_

The Quest for Direct CP ViolationIndirect CP violation in the mixing: Direct CP violation in the decay: A fascinating 30-year long enterprise: Is CP violation a peculiarity of kaons? Is it induced by a new superweak interaction?Niels Tuning (*)

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B system 1. Direct CP violation K systemDifferent CP violation for the two decays Some CP violation in the decay! B0K+- 0B0K-+ K0-+ K000K0-+K000Niels Tuning (*)

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Niels Tuning (*)Hints for new physics?1) sin2sin2 ?4th generation, t ?3) s0.04 ?2) ACP (B0K+-)ACP (B+K+0) ?4) P(B0sB0s) P(B0sB0s)

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Present knowledge of unitarity triangleNiels Tuning (*)

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The Unitarity triangleWe can visualize the CKM-constraints in (r,h) plane

Present knowledge of unitarity triangle

I) sin 2

I) sin 2

II) and the unitarity triangle: box diagramCP violation in mixing

II) and the unitarity triangle: box diagram

II) and the unitarity triangle: box diagramIm(z2)=Im( (Rez+iImz)2)=2RezImz

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