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The GSI Time Anomaly: Facts and Fiction Eserved@D = *@Let@Token The GSI Time Anomaly: Facts and Fiction Carlo Giunti INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Universit`adi Torino mailto://[email protected] Neutrino Unbound: http://www.nu.to.infn.it La Thuile 2009, 3 March 2009 Les Rencontres de Physique de La Vallee d’Aoste Results and Perspectives in Particle Physics 1-7 March 2009, La Thuile, Aosta Valley, Italy C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 1 The GSI Experiment Schematic layout of the secondary nuclear beam facility at GSI Primarybeam Productiontarget Degrader 508MeV/uSm152 1032 mg/cmBe2 731 mg/cm2 Al 400MeV/u140 Pr58+ Injectionfrom UNILAC [Litvinov et al, nucl-ex/0509019] SIS: Heavy Ion Synchrotron FRS: FRagment Separator ESR: Experiment Storage Ring C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 2 Schottky Mass Spectrometry ◮ Stored ions circulate in ESR with revolution frequencies 2 MHz ◮ At each turn they induce mirror charges on two electrodes ◮ Revolution frequency spectra provide information about q m: qB f = = ­ 2 2 m ◮ Area of each frequency peak is proportional to number of stored ions 0.06 99 Ag47+ A El q 95 45+ 59 28+ Massvalueunknown Rh Ni 84 40+ Zr A El q Massvalueknown 40 19+ K 42 20+ 78 Rb 37+ Ca 80 38+ 0.04 97 Pd 46+ Sr 101Ñd48+ 76 36+ 105Sn50+ Kr 86 41+ 88 42+ 61 29+ Nb Mo Cu 31+ 65 Ga 67 Ge32+ 0.02 57 Co 27+ 92 Ru44+ 69 33+ Intensity[arb.u.] As 0.00 50000 100000 150000 200000 250000 Frequency[Hz] [Litvinov et al, nucl-ex/0509019] C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 3 Praseodymium Promethium Cerium Neodymium C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 4 Electron Capture 140 58+ 140 58+ 59Pr ! 58 Ce + e 142 60+ 142 60+ 61Pm !60 Nd + e seen because ∆q = 0 ∆f f = ∆m m (small) + ¬ decay 140 58+ 140 57+ + 59Pr ! 58 Ce + e + e 142 60+ 142 59+ + 61Pm !60 Nd + e + e not seen because ∆q = 1 ∆f 150 kHz [Litvinov et al, PLB 664 (2008) 168] C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 5 [Litvinov et al, PLB 664 (2008) 168] C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 6 [Litvinov et al, PLB 664 (2008) 168] C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 7 dN (t) EC t (1) = N(t)= N(0) e dt EC EC dN (t) EC t (2) = (t) N(t)= (t) N(0) e dt EC EC + = EC + ¬ + loss EC(t) = EC [1 + a cos( t + )] 140 Fit parameters of 59 Pr data 2 Eq. N0 EC a DoF (1) 34.9(18) 0.00138(10) - - 107.2/73 (2) 35.4(18) 0.00147(10) 0.18(3) 0.89(1) 67.18/70 142 Fit parameters of 61 Pm data 2 Eq. N0 EC a DoF (1) 46.8(40) 0.0240(42) - - 63.77/38 (2) 46.0(39) 0.0224(41) 0.23(4) 0.89(3) 31.82/35 140 58+ 142 60+ ¦ ¦ T (59 Pr ) = 706 0 08 s T (61 Pm ) = 7 10 0 22 s i ¦ ha = 0 20 0 02 [Litvinov et al, PLB 664 (2008) 168] C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 8 Neutrino Mixing? [Litvinov et al, PLB 664 (2008) 168] Ii ! If + e e = cos SOL 1 + sin SOL 2 PROPOSED EXPLANATION: INTERFERENCE OF 1 AND 2 Initial Ion: Momentum P = 0, Energy E Õ 2 2 Massive k : Momentum pk , Energy Ek = pk + mk 2 Final Ion: Momentum pk , Energy M + pk 2M 2 2 E1 + M + p1 2M = E E2 + M + p2 2M = E 2 ∆m 2 2 2 ³ ∆E E E ∆m m m 2 1 2M 2 1 C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 9 ∆m2 ³ massive neutrino energy difference: ∆E E E 2 1 2M 2 2 5 2 ¢ ³ ³ ∆m =∆mSOL ³ 8 10 eV M 140 amu 130 GeV 16 ¢ ∆E ³ 3 1 10 eV 2 ³ ­ T = ­ 19 1s = 1 43 ∆E about 3 times larger than TGSI ³ 7s CAN INTERFERENCE IN FINAL STATE AFFECT DECAY RATE? C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 10 Interference: Double-Slit Analogy I NO INTERFERENCE NO INTERFERENCE INTERFERENCE = OSCILLATIONS INTERFERENCE νe = cos ϑν1 + sin ϑν2 F ◮ Decay rate of I corresponds to fraction of intensity of incoming wave which crosses the barrier ◮ Fraction of intensity of the incoming wave which crosses the barrier depends on the sizes of the holes ◮ It does not depend on interference effects which occur after the wave has passed through the barrier ◮ Analogy: decay rate of I cannot depend on interference of 1 and 2 µ which occurs after decay has happened ´ CAUSALITY! C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 11 Causality INTERFERENCE OF COHERENT ENERGY STATES (1 AND 2) OCCURRING AFTER THE DECAY (flavor neutrino oscillations) CANNOT AFFECT THE DECAY RATE C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 12 Cross Sections and Decay Rates are always summed incoherently over different final channels: ! µ I ! F I F F !F 1 2 = PI! = PI k k i j i entangled final state: jF = Ak Fk k i » j i µ » h j j i h j j i jF (S 1) I = Ak Fk (S 1) I = Fk S I j j i hFk S I j i ´µ hF F = 1 Ak = = È 1 2 2 j j ij jhF I j j S ½ ¼ 2 ¬ ¬ 2 È ¬ ¬ 2 j j ij jhF I ¬ ¬ S 2 £ k k j j ij h j j i jhF I F I ¬ ¬ I !F P = S = Ak k S = = È ¬ ¬ 1 2 2 j j ij jhF I k j j S 2 j j ij jhF I I F = k S = P ! k k k coherent character of final state is irrelevant for interaction probability! C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 13 Quantum Beats? ◮ GSI time anomaly can be due to interference effects in initial state ◮ Two coherent energy states of the decaying ion =µ Quantum Beats I = A1I1 + A2I2 INTERFERENCE = QUANTUM BEATS INTERFERENCE INTERFERENCE = OSCILLATIONS INTERFERENCE νe = cos ϑν1 + sin ϑν2 F ◮ Incoming waves interfere at holes in barrier ◮ Causality: interference due to different phases of incoming waves developed during propagation before reaching the barrier C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 14 Causality INTERFERENCE OF COHERENT ENERGY STATES OCCURRING BEFORE THE DECAY CAN AFFECT THE DECAY RATE C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 15 ◮ Quantum beats in GSI experiment can be due to interference of two coherent energy states of the decaying ion which develop different phases before the decay ◮ Coherence is preserved for a long time if measuring apparatus which monitors the ions with frequency 2 MHz does not distinguish between the two states ◮ 2 2 i A j i A j i jA j jA j jI(t = 0) = 1 I1 + 2 I2 ( 1 + 2 = 1) = iE1t iE2t Γt 2 ³ µ j i j i A j i Γ = Γ1 Γ2 = I(t) = A1 e I1 + 2 e I2 e 2 Γt j j ij ³ PEC(t)= jh e F S I(t) = [1+ A cos(∆Et + )] PEC e 2 2 jA jjA j jh j j ij ³ jh j j ij A 2 1 2 ∆E E2 E1 PEC = e F S I1 e F S I2 dN (t) EC Γt = N(0) [1 + A cos(∆Et + ³)] Γ e dt EC C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 16 dN (t) EC Γt = N(0) [1 + A cos(∆Et + ³)] Γ e dt EC 140 58+ 16 140 58+ ¦ ¢ ¦ ∆E(59 Pr ) = (586 0 07) 10 eV A(59 Pr ) = 0 18 0 03 142 60+ 16 142 60+ ¦ ¢ ¦ ∆E(61 Pm ) = (582 0 18) 10 eV A(61 Pm ) = 0 23 0 04 jA jjA j A 2 1 2 ◮ Energy splitting is extremely small ◮ 2 2 2 2 j jA j jA j jA j jA1 2 1 99 or 2 1 1 99 ◮ It is difficult to find an appropriate mechanism C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 17 Hyperfine Splitting smallest known energy splitting [Litvinov et al, PRL 99 (2007) 262501] 6 9 µ ∆E 10 eV = T 10 s f GHz too large to explain the GSI anomaly 16 ³ ³ ¢ TGSI ³ 7s fGSI 0 14Hz ∆EGSI = 2 TGSI 6 10 eV C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 18 16 ¢ feeling of smallness of ∆EGSI ³ 6 10 eV 12 1 12 ³ ¢ ¢ NB¨ 3 10 eV G (0 5G)=1 5 10 eV 4 ³ ¢ ∆EGSI 4 10 NB¨ C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 19 Further Developments Berkeley Experiment – arXiv:0807.0649 ◮ 142 142 142 EC: Pm ! Nd + e Pm in an aluminum foil no oscillations at a level 31 times smaller than GSI ◮ 142 142 µ Reanalysis of old Eu ! Sm + e EC data = no oscillations ◮ Differences with GSI Experiment: neutral and stopped atoms Munich Group + F.
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