Cplear Experiment T and CPT Violation

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http://cplear.web.cern.ch/cplear/Welcome.html Physics at CPLEAR, Phys. Rep. 374 (2003), 165-270 T and CPT Measurements with the CPLEAR Experiment Thomas Ruf

Workshop on T violation and CPT tests in neutral-meson systems, Mainz, April 15-16 The CPLEAR experimental setup (Some formalism) for the afternoon The CPLEAR results CP, T and CPT, and others 1 The CPLEAR Experiment PS195

Data taking from ~1990 until 8th July 1996, 08:21:33 Using antiprotons from CERN de-accelarator LEAR 1MHz rate, stopped in hydrogen target, ± Flavour of neutral kaon at production tagged by charge∓ ퟎ 푝̅ 푝푝̅ → 푲 휋 푲 of charged kaon

Thomas Ruf CERN T/CPT Violation with CPLEAR 2 The CPLEAR Experiment PS195

Very sophisticated first and higher level trigger processing at high rates.

7 × 10 > 1 2 × 107 + − 휋 휋 푡 휏푆 1.3 × 106 0 0 휋 휋 5 × 10 6 푒�푒 1.7 × 105 + − 0 휋 휋 휋 4 0 0 0 휋 휋 휋

Thomas Ruf CERN T/CPT Violation with CPLEAR 3 Principle of the Experiment

Strong interaction

Weak interaction

Thomas Ruf CERN T/CPT Violation with CPLEAR 4 Principle of the Experiment

Strong interaction

Tagging after production: Through charge exchange with absorber material. , ퟎ Strong interaction / 푲� 푝, 푛 → 휦푋/ − ퟎ ퟎ ↳−Λ →+ 푝휋 푲� 푲 푝 푛 → 푲 푲 푋

Thomas Ruf CERN T/CPT Violation with CPLEAR 5 2� Final State, Measurement of

+− 휼

is a free parameter in the ( ) = + + fit, ( +) 휶 휺 푲 used as rate− normalization푻 휶 휺 푲 ퟏ ퟒퟒ 휺 휹 in other decay channels

With free in the fit, not assuming CPT, = ( . ± . ± . ) × 횫퐦 ퟕ −ퟏ 횫퐦 ퟓퟓ� ퟎ ퟒ ퟒ ퟑ ퟑ ퟏ� ℏ풔 Thomas Ruf CERN T/CPT Violation with CPLEAR 6

Rate Normalizations

Different charged kaon reconstruction efficiencies due to non-perfect geometry Solved by frequent changes of magnet polarity Different charged kaon reconstruction efficiencies due to strong interaction with matter, usage of threshold Cherenkov counter for kaon ID = × [ + + ] Normalization factor + 휺 푲 extracted from high statistics 2− channel, 휶 휺 푲 ퟏ ퟒퟒ 휺푻 휹 as function of charged kaon momentum.  = CPT violation in π semileptonic = charge asymmetry, external to CPLEAR: allowed풚 amplitudes = + 휟푺 휟푸 퐿  CP violation in = 퐾 forbidden amplitudes − Different휹푳 �ℝ 휺푻 휹and− � 풙− − 풚 efficiencies 풙 휟푺 휟푸 Obtained from− + pure electron+ − and pion samples π π Note, for small푒 asymmetries:푒 =

Thomas Ruf CERN T/CPT퐴 푝푝푝푝Violation with퐴 CPLEAR푚푚푚� − 퐴푑�푑�푑푑푑푑 7 Physics with semileptonic decays

Precise measurement of the oscillation frequency (setting =0) : 횫퐦 and are stronglyℑ 풙− correlated, >0.99. With = ( . ± . ) × obtain − 횫퐦 = ℑ( 풙 . ± . ) × ퟕ −ퟏ 횫퐦 ퟓퟑ� ퟏ ퟏ ퟒ ퟏ� ℏ풔 Thomas Ruf CERN −ퟑ T/CPT Violation with CPLEAR 8 ℑ 풙− −ퟎ ퟖ ퟑ ퟓ ퟏ� T Violation, CPLEAR Result

CPT conservation in semileptonic decay amplitudes is assumed. Δ =Δ forbidden decays allowed.

푆 푄 Thomas Ruf CERN T/CPT Violation with CPLEAR 9 "Direct" Measurement of T Violation

Valid for ( ), ( ) 풕 흉푺 ≫ ℛ 풙− ℑ 풙+ from pure electron/pion samples

( ) from asymmetry: = + + ( +) 휺 푲 − Rewriting�흅 using = 휶 ( 휺 푲+ ퟏ+ ퟒℛ 휺푻): 휹 ± = [ + ] 풍 푻 − ퟏ−휶 휹 𝟐 휺 휹 풚 − 풙 퐴퐾 � 휹풍 � ℛ 풚 − ℜ 풙−

For the final result, CPT violation in semileptonic decay amplitudes, and are set to zero. = ( 0.2 ± 0.3) × 10 From a global fit: − 푦 푥 −3 − Thomas Ruf CERN ℛ 푦 − 푥 −T/CPT Violation with CPLEAR 10

Direct Measurement of CPT Violation

More direct, using normalization from :

2휋

= : Thomas Ruf CERN T/CPT Violation with CPLEAR 11 Δ푆 Δ푄 Some recent criticisms about the CPLEAR measurement of T violation

AT is also violating CP

So what ? 0 T violation of Hweak

becomes퐴 zero푇 ≠ for⇒ = 0 So what ? No T violation in mixing, no measurement 휺푻 ΔΓ AT is independent of decay time ? Don't understand why this is a problem My personal opinions: Only criticism could be about the assumption of CPT conservation in the decay amplitudes. (Which by the way is also assumed in the recent Babar measurement.) However, with a global fit of all measurements, in can be shown that the contribution of direct CPT violation, 4 ( ), is negligible. I find it more interesting to put limits on CPT violation, rather than performing "direct" observations of T violation. Afterℛ 푦all, −the4ℜ real풙 sensation− would be to measure a deviation from CPT invariance.

Thomas Ruf CERN T/CPT Violation with CPLEAR 12 3� Final State

Only the I=1 amplitude contributes to CP violation. By neglecting CPT violation in decay amplitudes:

Thomas Ruf CERN T/CPT Violation with CPLEAR 13 3� Final State CPLEAR Results

Thomas Ruf CERN T/CPT Violation with CPLEAR 14 3� Final State, CP allowed

Thomas Ruf CERN T/CPT Violation with CPLEAR 15 Unitarity, Bell-Steinberger, Indirect test of CPT, ...

Back to CP violation in the channel

휋휋

CP violation through interference of mixing and decay. Major source of CP violation in the B0 system

Thomas Ruf CERN T/CPT Violation with CPLEAR 16 Unitarity, Bell-Steinberger, Indirect test of CPT, ...

Unique in the kaon system, explore additional constraints

by using measurements. Possible, because of limited number of final states. = 2 and direct emmission amplitudes can be neglected

퐼 휋휋휋

= phase difference of = 0 and the mixing amplitudes (Major source of CP violation in the B0 system) 퐼 CPLEAR contributions: improved limits on and and = forbidden decays 000 +−0 Thomas Ruf CERN T/CPT Violation with CPLEAR 휂 휂 17 Δ푆 Δ푄 Putting all together

Adding external measurement of ( ) = ( . ± . ± . ) × 풍 = ( . ± . ± . ) ×휹 −ퟓ 퓡 휺푻 ퟏퟏ� ퟗ � ퟓ풔�풔� ퟎ ퟏ풔풚� ퟏ� = ( . ± . ± . ) × −ퟓ 해 휹 −� ퟒ ퟓ ퟎ풔�풔� ퟎ ퟏ풔�풔 ퟏ� = (0.3 ± 3.0 ± 0.6 ) × 10 −ퟒ 퓡 휹 −� ퟒ � ퟕ풔�풔� ퟎ �풔�풔 ퟏ� ( ) = ( 0.5 ± 3.0 ± 0.3 ) × 10−3 ℛ 푦 𝑠𝑠 𝑠� ( ) = ( 2.0 ± 2.6 ± 0.5 ) × 10 −3 ℛ 푥− − 𝑠𝑠 𝑠� + = ( 0.2 ± 0.3) × 10 −3 ℑ 푥+ − 𝑠𝑠 𝑠� −3 T violationℛ 푦 푥− − established with 66� ! Translating CPTV in mixing to mass and lifetime differences of neutral kaons:

assuming no CPTV in decay amplitudes

Thomas Ruf CERN T/CPT Violation with CPLEAR 18 Arrow of Time

Thomas Ruf CERN T/CPT Violation with CPLEAR 19 CPLEAR Result

Ellis/Mavromatos, private communication: With these limits, our model is not anymore interesting.

Thomas Ruf CERN T/CPT Violation with CPLEAR 20 EPR Correlations

Thomas Ruf CERN T/CPT Violation with CPLEAR 21 EPR Correlations

Strangeness tagging through strong interactions. Does not require any assumptions about CPT violation in decay amplitudes.

Phys.Lett. B 422 (1998), 339

Thomas Ruf CERN T/CPT Violation with CPLEAR 22 Conclusions The kaon system exhibits all kinds of CP violation T and CPT violation in mixing CP violation through interference of decay amplitudes, called direct CP violation, CP violation through interference of mixing and decay amplitudes 휀′ CPLEAR had been the pionneer experiment for precise T & CPT measurements using flavour tagging at production Many textbook measurements Most measurements are still among the world best measurements CPT tests in the kaon system put world's best limits on mass and lifetime differences of particles and antiparticles Other CPLEAR achievements: Strangeness tagging via strong interactions instead of weak decays used to test EPR entanglement in neutral meson system (before B-factories) New method to measure regeneration

Thomas Ruf CERN T/CPT Violation with CPLEAR 23

Formalism

Thomas Ruf CERN T/CPT Violation with CPLEAR 24 Mainly based on:  The Physics of Time Reversal by Robert G. Sachs  Review on CP Violation by T. Nakada Some Formalism  CP and CPT in the neutral Kaon System, TR

Wigner-Weisskopf formalism, + Stationary states |K > and |K > are mass eigenstates of the 푤𝑤푤 𝑠 𝑒 strong and electromagnetic0 interactions:0 ℋ ≪ ℋ+ |ℋK >= |K > � 0 0 ℋ𝑠 ℋ𝑒 푚0

"Effective" Schrödinger equation:

Parametrization of , avoiding unnecessary phase conventions: not adopted by CPLEAR in general

hermitian part = mass matrix, anti-hermitian part = decay matrix Matrix elements are given by:

Thomas Ruf CERN T/CPT Violation with CPLEAR 25 Some Formalism II † Discrete Symmetries CPT invariance of requires: M = M and = [CPT(CPT)=1 2 = ] ℋ푤𝑤푤 Equal masses and lifetimes of and C T T 11 22 Γ11 Γ22 ⇒ 휙 휙� − 휙 ퟎ ퟎ 퐊 푲� From T invariance of follows: | | = | | and = + 푤𝑤푤 identical to sin ℋ = 12 21 C Γ TΛ violationΛ caused휙 by phase−휙 difference푛 ⋅ 휋 between and 휑푴 − 휑횪 ퟎ 횪ퟏ� 퐌12 From CP invariance of follows: | | = | | and = 푤𝑤푤 Which means, if T or CPTℋ is violated, then also CP is violated. Λ12 Λ21 Λ11 Λ22

† To look for a symmetry violation makes only sense if there exists a part of the Hamilton operator which is invariant under this symmetry. This allows to define the symmetry operator. Thomas Ruf CERN T/CPT Violation with CPLEAR 26

Some Formalism III

Time Dependence Solving the "effective" Schrödinger equation Eigenvalues ,

흀푳 푺

For small T and CPT violation, = + it is convenient to write: 12 12 ΔΛ 2푀 푖Γ

In case of :

Γ12 ≪ 푀12 ( ) Thomas Ruf CERN T/CPT Violation with CPLEAR 27 Some Formalism IV

Decay rate into CP eigenstates, ( = + ) example = ( ) and = 𝟐 푪푪 ퟏ ퟎ ퟎ 푨 퐀 푲 → 𝟐 푨� 퐀 푲� → 𝟐

The p/q used by the B-factories extended to account for CPT violation

No assumptions about small CP violation yet

Some 2nd order terms become With small CP violation important for long decay times and [ + ( + )]

CPLEAR휼�흅흅 ≈ ퟏ − ퟒ� 휼흅흅 ≈ 휼흅흅 푩�흅흅 ≈ ퟏ ퟒퟒ 휺 휹 푩흅흅

Most of the work is now to estimate the different contributions to Thomas Ruf CERN T/CPT Violation with CPLEAR 28 휼흅흅 Some Formalism V

Decay Amplitudes for CP eigenstates, CPT conserving and non-conserving: In case of CPT conservation in the decay, and being an eigenstate of strong and electroweak interaction, i.e. one decay amplitude: 푓 = | > = | > = = 0, 푖�푖=∗+1, is CPT violating 퐴̅ 푛퐶퐶푒 퐴 퐶퐶 푓 푛퐶퐶 푓 푖�� ∗ 푓 2휋 퐼 퐶퐶 퐴̅ − 푒 퐴

Otherwise: = ( ) + ( ) 1 푖�2 ∗ ∗ 2 푖�0 ∗ ∗ And then even퐴̅+− in case3 푒 of CPT푎2− 푏conservation2 3 푒 푎0−푏0 4 | | | | = 2 sin sin ( )| || | 0 3 2 2 퐴+− − 퐴̅+− − 훿0 − 훿2 휓0 − 휓2 푎0 푎2 ≠

Thomas Ruf CERN T/CPT Violation with CPLEAR 29

Semileptonic Amplitudes and Rates

Amplitudes

= allowed

= forbidden Δ푆 Δ푄 = Δ푆 Δ푄 forbidden

= allowed Δ푆 Δ푄 Time dependent rates Δ푆 Δ푄

Neglecting terms proportional to = forbidden amplitudes times T-violation in mixing or CPT-violation in mixing 휟푺 휟푸 = forbidden amplitudes squared 휺푻 휹 휟푺 휟푸 !

풏풏CPLEAR풑풑𝒑풑 풄𝒄풄𝒄� 풄𝒄

Thomas Ruf CERN T/CPT Violation with CPLEAR 풙 ↔ �풙 30 풙− ↔ −풙−

The Four Semileptonic Decay Rates

Thomas Ruf CERN T/CPT Violation with CPLEAR 31 "Direct" Measurement of T Violation

Valid for ( ), ( ) 풕 흉푺 ≫ ℛ 풙− ℑ 풙+ from pure electron/pion samples

Direct Measurement of CPT Violation

More direct, using normalization from :

2휋

= : Thomas Ruf CERN T/CPT Violation with CPLEAR 33 Δ푆 Δ푄 Parametrization of direct CP Violation

= allowed: CPT violating

Δ 푆 Δ푄 CPT violating = forbidden: CPT conserving Δ푆 Δ푄

Thomas Ruf CERN T/CPT Violation with CPLEAR 34 Unitarity, Bell-Steinberger, Indirect test of CPT, ...

Back to CP violation in the channel

휋휋

CP violation through interference of mixing and decay. Major source of CP violation in the B0 system

Thomas Ruf CERN T/CPT Violation with CPLEAR 35 More on and

+− ퟎퟎ 휼 휼

Thomas Ruf CERN T/CPT Violation with CPLEAR 36 Backups

Thomas Ruf CERN T/CPT Violation with CPLEAR 37 CPT Invariance

Thomas Ruf CERN T/CPT Violation with CPLEAR 38 T Invariance

Thomas Ruf CERN T/CPT Violation with CPLEAR 39 T/CPT Violation, Systematic Errors

Thomas Ruf CERN T/CPT Violation with CPLEAR 40 Citations

Thomas Ruf CERN T/CPT Violation with CPLEAR 41 PDG Online 2013

Thomas Ruf CERN T/CPT Violation with CPLEAR 42

Thomas Ruf CERN T/CPT Violation with CPLEAR 43

Thomas Ruf CERN T/CPT Violation with CPLEAR 44 Regeneration

Thomas Ruf CERN T/CPT Violation with CPLEAR 45 Formalism applied to B System

with ± = final state with CP= ± 푲 ퟏ

with = with = = = 횫� ퟎ 횫� 휹 휺 ퟎ

with = with = = = 횫� ퟎ Thomas Ruf CERN T/CPT Violation with CPLEAR 횫� 휹 휺 ퟎ46 Formalism applied to B System, cont.

with = with = = = 횫� ퟎ 횫� 휹 휺 ퟎ

with = with = = = 횫� ퟎ 횫� 휹 휺 ퟎ Thomas Ruf CERN T/CPT Violation with CPLEAR 47 CP Asymmetries

Thomas Ruf CERN T/CPT Violation with CPLEAR 48 EPR CP Tagged Rates

Thomas Ruf CERN T/CPT Violation with CPLEAR 49 "T" Violating Asymmetries

Thomas Ruf CERN T/CPT Violation with CPLEAR 50 "CPT" Violating Asymmetries

Thomas Ruf CERN T/CPT Violation with CPLEAR 51 Semiletponic Asymmetries

Thomas Ruf CERN T/CPT Violation with CPLEAR 52