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CPT Symmetry, Quantum Gravity and Entangled Neutral Kaons Antonio Di Domenico Dipartimento Di Fisica, Sapienza Università Di Roma and INFN Sezione Di Roma, Italy

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CPT Symmetry, Quantum Gravity and Entangled Neutral Kaons Antonio Di Domenico Dipartimento Di Fisica, Sapienza Università Di Roma and INFN Sezione Di Roma, Italy CPT symmetry, Quantum Gravity and entangled neutral kaons Antonio Di Domenico Dipartimento di Fisica, Sapienza Università di Roma and INFN sezione di Roma, Italy Fourteenth Marcel Grossmann Meeting - MG14 University of Rome "La Sapienza" - Rome, July 12-18, 2015 MG Meetings News MG Meetings News Scientific Objectives Press releases The Previous Registration Meetings Internet connections Satellite meetings MG Awards MG14 Booklet MG14 Summary The MG Awards Important dates Previous MG Awards Location Publications Public Lectures Click to download the preliminary poster Titles & Abstracts Social Events Proceedings Accompanying Secretariat/registration open from 8:00am to 1:30pm from wednesday Persons Activities Payment of registration fee after Wednesday 1pm o'clock will be General Information possible only by cash Photos Information about We thank ICTP, INFN, IUPAP, NSF for their support! Rome Scientific Committees Live streaming of Plenary and Public Lectures Transportation International photos of the meeting available here Meals Organizing Hotels Local Organizing International Organizing Committee chair: Remo Ruffini, University of Rome and ICRANet Participants International International Coordinating Committee chair: Robert Jantzen, Villanova University Coordination Local Organizing Committee chair: Massimo Bianchi, University of Rome "Tor Vergata" Preliminary List Scientific Program The Fourteenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Contacts Relativity, Gravitation, and Relativistic Field Theory will take place at the University of Rome Sapienza July 12 - 18, Plenary Invited Contact us Speakers 2015, celebrating the 100th anniversary of the Einstein equations as well as the International Year of Light under the aegis of the United Nations. Plenary Program Links For the first time, in addition to the main meeting in Rome, a series of satellite meetings to MG14 will take place. Chairpersons of The registration to MG14 will also cover participation in one additional satellite meeting. ICRA Homepage Parallel Sessions Preregistration will take place Sunday July 12 from 10am to 6pm at the Department of Physics, and the official ICRANet Homepage Parallel Sessions opening of the meeting Monday morning, July 13. During the six day conference a wide variety of topics will be discussed in the morning plenary sessions beginning with mathematical topics on Monday, quantum aspects of Sponsors Parallel Sessions by gravity on Tuesday, precision tests of general relativity on Wednesday, relativistic astrophysics on Thursday, Day cosmology and astroparticle physics on Friday and the latest scientific news and the history of physics Saturday. There will be five plenary lectures each morning and up to twenty parallel sessions in the four weekday afternoons Global Program excluding Wednesday, which is left free for a trip and the evening conference banquet. IUPAP Declaration (http://www.iupap.org/): Freedom of Movement for Scientists. The Marcel Grossman Meetings were founded with the premise that scientists of all nations have a right to meet to exchange knowledge independent of national borders. As such we affirm the IUPAP declaration: "To secure IUPAP sponsorship, the organizers have provided assurance that MG14 will be conducted in accordance with IUPAP principles as stated in the IUPAP resolution passed by the General Assembly in 2008. In particular, no bona fide scientist will be excluded from participation on the grounds of national origin, nationality, or political considerations unrelated to science." Contact email: mg14[AT]icra.it CPT: introduction The three discrete symmetries of QM, C (charge conjugation: q ! -q), P (parity: x ! -x), and T (time reversal: t ! -t) are known to be violated in nature both singly and in pairs. Only CPT appears to be an exact symmetry of nature. CPT theorem : R. Jost J. Schwinger (1957) G. Lüders (1951) (1954) W. Pauli J. Bell (1952) (1955) Exact CPT invariance holds for any quantum field theory (like the Standard Model) formulated on flat space-time which assumes: (1) Lorentz invariance (2) Locality (3) Unitarity (i.e. conservation of probability). Testing the validity of the CPT symmetry probes the most fundamental assumptions of our present understanding of particles and their interactions. A. Di Domenico 14th Marcel Grossmann meeting July 12-18, 2015 Rome 2 CPT: introduction The three discrete symmetries of QM, C (charge conjugation: q ! -q), P (parity: x ! -x), and T (time reversal: t ! -t) are known to be violated in nature both singly and in pairs. Only CPT appears to be an exact symmetry of nature. Intuitive justification of CPT symmetry [1]: For an even-dimensional space => reflection of all axes is equivalent to a rotation e.g. in 2-dim. space: reflection of 2 axes = rotation of π around the origin In 4-dimensional pseudo-euclidean space-time PT reflection is NOT equivalent to a rotation. Time coordinate is not exactly equivalent to space coordinate. Charge conjugation is also needed to change sign to e.g. 4-vector current jµ. (or axial 4-v). CPT (and not PT) is equivalent to a rotation in the 4-dimensional space-time [1] Khriplovich, I.B., Lamoreaux, S.K.: CP Violation Without Strangeness. A. Di Domenico 14th Marcel Grossmann meeting July 12-18, 2015 Rome CPT: introduction Extension of CPT theorem to a theory of quantum gravity far from obvious. (e.g. CPT violation appears in several QG models) huge effort in the last decades to study and shed light on QG phenomenology ⇒ Phenomenological CPTV parameters to be constrained by experiments Consequences of CPT symmetry: equality of masses, lifetimes, |q| and |µ| of a particle and its anti-particle. Neutral meson systems offer unique possibilities to test CPT invariance; e.g. taking as figure of merit the fractional difference between the masses of a particle and its anti-particle: −18 m 0 m 0 m 10 neutral K system K − K K < −14 m 0 m 0 m 10 neutral B system B − B B < proton- anti-proton −8 mp −mp mp <10 Other interesting CPT tests: e.g. the study of anti-hydrogen atoms, etc.. A. Di Domenico 14th Marcel Grossmann meeting July 12-18, 2015 Rome 4 The neutral kaon: a two-level quantum system 0 Since the first observation of a K0 (V- K 0 K particle) in 1947, several phenomena ππ observed and several tests performed: S=+1 S=-1 • strangeness oscillations s d s d • regeneration • CP violation • Direct CP violation € € € • precise CPT tests • … € € One of the most intriguing physical systems in Nature.€ T. D. Lee € Neutral K mesons are a unique physical system which appears to be created by nature to demonstrate, in the most impressive manner, a number of spectacular phenomena. ........ If the K mesons did not exist, they should have been invented “on purpose” in order to teach students the principles of quantum mechanics. Lev B. Okun A. Di Domenico 14th Marcel Grossmann meeting July 12-18, 2015 Rome 5 The neutral kaon system: introduction The time evolution of a two-component state vector Ψ = a K 0 + b K 0 0 0 in the { K , K } space is given by ∂ K 0 K 0 (Wigner-Weisskopf approximation): i Ψ(t) = HΨ(t) ππ d s d ∂t s H is the effective hamiltonian (non-hermitian), decomposed into a Hermitian € € € € € part (mass matrix M) and an anti-Hermitian part (i/2 decay matrix Γ) : € € i € $ m11 m12 ' i $ Γ11 Γ€12 ' € H = M − Γ = & ) − & ) 2 % m21 m22 ( 2% Γ21 Γ22 ( Diagonalizing the effective Hamiltonian: eigenstates eigenvalues 1 K 1 K 0 1 K 0 i S,L = [( +εS,L ) ± ( −εS,L ) ] λ €= m − Γ 2 1+ εS,L S,L S,L 2 S,L ( ) |K1,2> are −iλS,L t 1 K t = e K 0 CP=±1 states S,L ( ) S,L ( ) = [ K1,2 +εS,L K2,1 ] (1+ εS,L ) τS ~ 90 ps τL ~ 51 ns € ∗ -3 KL →ππ violates CP KS KL ≅εS +εL ≠ 0 small CP impurity ~2 x 10 € A. Di Domenico 14th Marcel Grossmann meeting July 12-18, 2015 Rome 6 € € € CPT violation: standard picture CP violation: T violation: ε H − H −iℑM − ℑΓ 2 S ,L = ε ±δ ε = 12 21 = 12 12 2(λS − λL ) Δm +iΔΓ / 2 CPT violation: m 0 − m 0 − i 2 Γ 0 − Γ 0 H11 − H22 1 ( K K ) ( )( K K ) δ = = 2(λS − λL ) 2 Δm + iΔΓ/2 • δ ≠ 0 implies CPT violation Δm = mL − mS , ΔΓ = ΓS − ΓL • ε ≠ 0 implies T violation −15 • ε ≠ 0€ or δ ≠ 0 implies CP violation Δm = 3.5 ×10 GeV 2 m 7 10−15 GeV (with a phase convention ℑ Γ 12 = 0 ) ΔΓ ≈ ΓS ≈ Δ = × A. Di Domenico 14th Marcel Grossmann meeting July 12-18, 2015 Rome 7 € neutral kaons vs other oscillating meson systems <m> Δm <Γ> ΔΓ/2 (GeV) (GeV) (GeV) (GeV) K0 0.5 3x10-15 3x10-15 3x10-15 D0 1.9 6x10-15 2x10-12 1x10-14 0 -13 -13 -15 B d 5.3 3x10 4x10 O(10 ) (SM prediction) 0 -11 -13 -14 B s 5.4 1x10 4x10 3x10 A. Di Domenico 14th Marcel Grossmann meeting July 12-18, 2015 Rome “Standard” CPT tests A. Di Domenico 14th Marcel Grossmann meeting July 12-18, 2015 Rome 9 CPT test at CPLEAR e+ Test of CPT in the time evolution of K0 K0 neutral kaons using the semileptonic π- τ=0 τ asymmetry ν ⎧ R+ (τ ) −αR− (τ ) R− (τ ) −αR+ (τ ) ⎪Aδ (τ ) = + R ( ) R ( ) R ( ) R ( ) ⎪ + τ +α − τ − τ +α + τ ⎪ 0 +(−) −(+) ⎨R+(−) (τ ) = R (K t=0 → (e π v)t=τ ) ⎪ 0 −(+) +(−) R ( ) R K t 0 (e v) ⎪ −(+) τ = ( = → π t=τ ) ⎪ ⎩α =1+ 4ℜε L Aδ (τ >> τ S ) = 8ℜδ ℜδ = (0.30 ± 0.33 ± 0.06) × 10-3 CPLEAR PLB444 (1998) 52 A. Di Domenico 14th Marcel Grossmann meeting July 12-18, 2015 Rome The Bell-Steinberger relationship (1965) J.
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