Experimental verification of CPT symmetry in kaon physics Wojciech Wiślicki, NCBJ 16 May 2014 HEP seminar, University of Warsaw - Caveats: i) we consider CPT only; no discussions of CP or T violation ii) restrict to neutral kaons - C, P and T - the background, notations - Approach: Bell-Steinberger relation CPT and anti-CPT theorems Decoherence - CPT from Bell-Steinberger relation, world data, incl. KLOE - CPT and Lorentz invariance, KLOE measurement - Further discussions on meaning of the results and experimental perspectives Discrete symmetry transformations C, P and T: what they do? Particle ↔ antiparticle Space inversion Time reversal are real phases Effective formalism for pairs of neutral mesons: the Hamiltonian and its symmetries 2x2, time-independent, in basis of flavour eigenstates ( s for K, c for D, b for B etc.) , mass & decay matrices, both Hermitian Conservation of CPT requires (CP requires, in addition ) Parametrize possible violation of CPT by To remind: CP violation is traditionally parametrized by ε From now on assume expecting possible CPT-violating effects to be tiny (if any whatsoever ..) Mass eigenstates are not the flavour eigenstates In pairs of electrically neutral flavoured mesons, flavour eigenstates mix via box diagrams, e.g. for kaons ΔS=2 transitions H eigenstates expressed via H eigenvalues (or CP- and CPT-violation parameters defined by them) and flavour eigenstates CP violation parameter CPT violation parameter ( means CPT not violated) Bell-Steinberger formula (1965) Relation between H eigenstates and decay amplitudes Assumptions - Initial states of K and final decay states belong to orthogonal subspaces -Time evolution is unitary (probability conserved) Thesis (sum over complete final set) Another form Knowing amplitudes at rhs, kaon properties and ε, one determines Im(δ) Note Observation of BS failure entails breakdown of unitarity or incompletness of the set of final states CPT theorem (Schwinger, Lüders, Jost, Pauli, Bell: 1951-57) Important theorem relating CPT invariance to fundamental properties of the theory Assumptions: - Hermitian H - Unitary evolution - Locality, i.e. fields (anti)commute for (half)integer spin fields at spacelike separations - Finite vacuum expectation value of field products - Lorentz invariance Thesis: The theory is CPT-invariant: [CPT,H]=0 Some phenomenological consequences of the CPT theorem (Lüders, Zumino, 1957) - Particles and antiparticles have the same masses - Particles and antiparticles have the same lifetimes (decay widths) - Equality of partial decay widths of mutually CPT-coupled channels - Equality of total reaction rates from initial set of particles and corresponding set of antiparticles with spins reversed Further developments lead to inverse (anti-CPT) theorem (Greenberg 2002) Under general assumptions (hermiticity, unitarity), in field theory of pointlike particles: violation of CPT invariance entails violation of Lorentz invariance Numerous subtleties, depending on formulation of the CPT theorem Clear hint for phenomenology: CPT tests probe also Lorentz invariance Experimental test of Bell-Steinberger formula Major advantage of neutral K system: only a few final states contribute significantly to rhs: main: 2π, much smaller: 2πγ, 3π, πe(μ)ν The rest is negligible Rewrite rhs of BS relation to the form The α's can be always expressed by amplitude ratios η and branching fractions Phases for η should be known (interferometric measurements) The major data contributors (after 1990) - CPLEAR, CERN: proton-antiproton anihilation at rest, closed - NA48, CERN: KL and KS decays in the same detector, closed neutral kaon program - KTeV, Fermilab: similar principle, closed - KLOE, Frascati: φ(1020) → KL KS, finished previous runs, uptaking with upgraded apparatus Recent contributions only from KLOE 2π non-radiative decays World average data 2πγ decays Inner bremsstrahlung Direct emission And much smaller for neutral pions Interferometric measurement of E773 (FNAL) gives Combining with BR Small compared to 2π 3π decays For neutral-pion mode recent improvement from KLOE (factor 5 in BR and accuracy on η, Phys.Lett. B723(2013)54) Semileptonic decays General parametrization of Kl3 matrix elements parametrize CPT parametrize ΔS═ΔQ where determined by KLOE from and determined by CPLEAR from In practice, solution of BS eqn. where The numbers Sole CPLEAR BS At 95% confidence level Much worse knowledge on Re(δ), base only on CPLEAR semi-leptonic data CPT vs. Lorentz symmetry: Intuition support (vague) - x-dependent couplings in Lagrangian density, slowly varying in large scale (e.g. the Galaxy); derivatives select direction in space-time - vector fields with degenerated vacuum Lowest-energy configuration requires non-zero The vacuum contains intrinsic direction violating rotational invariance and thus Lorentz symmetry More specific proposal: extension of the Standard Model by CPT violating terms Kostelecky, Colladay, late 1990's Lagrangian contains additional CPT-violating terms Modified Dirac equation for quark or lepton field CPT-violating terms of SME; couplings a, b, .. are phenomenological at this stage, to be constrained by experiment For experiment's parametrizations consider the simplest case: nonzero first term of SME with 4-vector quantifying CPT violation, depending on flavour (quark's or lepton's); perhaps more fundamental physics behind Fundamental theory still unknown but enables some experimentally testable predictions Sidereal-time variations of observables For system of neutral mesons, e.g. Meson four-velocity in the observer's frame Difference between SME couplings of meson's valence quarks CPT observables are expected to vary with magnitude and orientation of meson momentum Direct calculation gives Since laboratory rotates together with the Earth, there is a sidereal-time („star time”) dependence of the observables Sidereal time is shorter by ~4 mins/24 hrs than solar time, due to the orbital motion of the Earth around Sun Working with sidereal time ensures variations on daily (and not on seasonal) basis At noon, observer on Earth has Sun and a distant star in zenith After 24 hrs Earth moved on its orbit around Sun Observer looking at the same star needs another 4 mins to catch up and let Earth self-rotate to see Sun in zenith again Pict. courtesy Wikipedia Time-dependence of δ in rotating frame Ω is Earth sidereal rotational frequency χ is angle between z Lab axis and Earth's rotation axis Θ, φ – K angles in LAB Neutral kaons produced in coherent entangled state Observable: double-differential spectrum of decay-time difference Event reconstruction in KLOE Two-pion K decays considered K decay vertices reconstructed from π tracks K decay lengths and Φ vertex positions were left free in fits KLOE result, published recently PL B730(2014)89 (all in GeV) Main contributions to systematics: selection cuts, background, uncertainty in experiment's orientation High sensitivity of the method was demonstrated, close to K-Kbar mass difference Other results using the same methodology Babar, PRL 100(2008)131802 FOCUS (FNAL), PLB 556(2003)7 Final remarks on the meaning of results and experimental perspectives Currently, using neutral mesons one can test CPT with sensitivity around We are close to mass scale given by combination If there are effects related to new physics at Planck scale, one might touch them, provided experimental sensitivity and accuracy are improved Sensitivity of interferometric method depends on how accurate one measures the region of first interference peak; subsequent peaks are quenched by exponential terms Experimental resolutions in time are crucial Time resolution in KLOE was >~ 100 ps (of the order of KS lifetime) – that is not good enough! Time resolution in KLOE-2 is going to be ~25 ps - better but still not good enough.. LHCb spectrometer gives overwhelmingly better time resolution This is fine but should be exploited with K, and not B, because frequency of oscillations is higher for heavier quarks For B, better resolution is partially compensated by shorter period of oscillations Should be studied with K at LHCb Needs dedicated trigger for decays Other CPT invariance tests Backups Effect of discrete symmetries 2πγ, determination of form-factors and ratios KTeV data for KL, formulas by Sehgal KTeV measurements are done with cut For small γ energies, the inner bremsstrahlung amplitude becomes singular At E→0, behavior of IB amplitudes is given by F.Low's theorem (1958) Amplitudes of radiative processes are singular in the limit of low energy. However, they can be expressed in terms of non-radiative amplitudes and their derivatives over energy and photon's angles Then Amplitudes' ratios behave thus CPT violation as a dissipative process Two motivations, rooted in basics of quantum mechanics and, again, search for background effects 1. If quantum-mechanical system of entangled fields propagates in a medium, quantum coherence tends to fade away (decoherence effect) 2. In gravitational background of micro black holes decoherence entails loss of information (Hawking 1976) Loss of coherence in medium is expected: interaction (with a medium) destroys interference terms in density matrix (except for special cases, not applicable to KLOE) Evolution of pure into mixed state entails loss of information and irreversibility, hence inverse scattering matrix does not exist in general. Evolution of pure state into mixed state violates CPT invariance ( Theorem proved by R. Wald, Phys. Rev. D21(1980)2742) Far-reaching consequence: if there exists