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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 IFIC, Valencia, 3 December 2008 C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 1 Outline The GSI Anomaly Neutrino Mixing? Interference: Double-Slit Analogy arXiv:0801.1465 and arXiv:0805.0435 arXiv:0801.2121 – arXiv:0801.3262 Quantum Beats? Towards the Epilogue? Conclusions C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 2 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 IFIC, Valencia, 3 Dec 2008 3 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 IFIC, Valencia, 3 Dec 2008 4 Praseodymium 140 58+ 140 58+ 59Pr ! 58 Ce + e Cerium [Litvinov et al, PLB 664 (2008) 168] C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 5 Promethium 142 60+ 142 60+ 61Pm !60 Nd + e Neodymium [Litvinov et al, PLB 664 (2008) 168] C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 6 14058+Pr Morethan4particles 4particles Q=3388keVEC 3particles 2particles 14058+ 1particle Ce 13 65 117 169 187.2187.4 187.6 187.8 Time[s] Frequency[kHz]-61000.0 ◮ 140 58+ ­ About six initial 59 Pr ions (f = qB 2 m ) ◮ 140 58+ Two decayed via nuclear electron capture into 58 Ce ◮ Seen because ∆q = 0 µ ∆f f = ∆m m (small) ◮ + µ Other decayed via ¬ decay (∆q = 1 ∆f 150 kHz) or were lost (interactions with residual gas) C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 7 140 58+ 140 58+ 59Pr ! 58 Ce + e 142 60+ 142 60+ 61Pm !60 Nd + e [Litvinov et al, PLB 664 (2008) 168] C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 8 [Litvinov et al, PLB 664 (2008) 168] C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 9 [Litvinov et al, PLB 664 (2008) 168] C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 10 [Litvinov et al, PLB 664 (2008) 168] C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 11 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 IFIC, Valencia, 3 Dec 2008 12 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 IFIC, Valencia, 3 Dec 2008 13 ∆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 IFIC, Valencia, 3 Dec 2008 14 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 IFIC, Valencia, 3 Dec 2008 15 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 IFIC, Valencia, 3 Dec 2008 16 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 IFIC, Valencia, 3 Dec 2008 17 arXiv:0801.1465 and arXiv:0805.0435 H.J. Lipkin ◮ Causality is violated explicitly ◮ Æ arXiv:0801.1465: The difference in momentum p between the two neutrino eigenstates with the same energy produces a small initial momentum change Æ P . ◮ arXiv:0805.0435: Since the time dependence depends only on the propagation of the initial state, it is independent of the final state, which is created only at the decay point. Thus there is no violation of causality. ◮ But in calculation of effect: The phase difference at a time t between states produced by the neutrino mass difference on the motion of the initial ion in the laboratory frame with velocity V = (P E) is 2 Æ ¡ Æ E t =∆m 2E δE E C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 18 arXiv:0801.2121 – arXiv:0801.3262 A. N. Ivanov, R. Reda, P. Kienle – M. Faber ◮ I ! F + decay rate in time-dependent perturbation theory i j i with final neutrino state j = k k ◮ Not even properly normalized to describe one particle: j i Æ µ h j i h j k = jk = = 3 ◮ Different from standard electron neutrino state £ i j i j e = Uek k k C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 19 Time-Dependent Perturbation Theory ¬ ¬ ¬ ¬ 2 ¬ 2 ¬ t t ¬ ¬ ¬ ¬ ¬ ¬ h jÀ j i h jÀ j i F I F I ¬ ¬ F PI! (t)= d ( ) = d ( ) ¬ + W ¬ k W ¬ 0 k 0 ¬ 3 ÀW (t)= d x HW (x) Effective Four-Fermion Interaction Hamiltonian G F 5 5 Ô ­ ­ ­ ­ H W (x)= cos C ¯e (x) (1 )e(x)¯n(x) (1 gA )p(x) 2 G F £ 5 5 Ô ­ ­ ­ ­ = cos C Uek ¯k (x) (1 )e(x)¯n(x) (1 gA )p(x) 2 k £ i∆Ek t jÀ j i h F I k W ( ) = Uek e Tk with ∆Ek = Ek + EF EI t sin(∆E t 2) = i∆Ek t i∆Ek t =2 k i∆Ek t 2 ! Æ d e = e 2 (∆Ek ) e 0 ∆Ek 2 ∆Ek t 1 C. Giunti The GSI Time Anomaly: Facts and Fiction IFIC, Valencia, 3 Dec 2008 20 ¬ ¬ 2 ¬ ¬ ¬ ¬ 2 £ i∆Ek t Æ ¬ ¬ F PI! + (t) = 4 Uek e (∆Ek ) Tk ¬ ¬ k Æ Tk ³ Tj (∆Ek ) satisfied by wave packet ¬ ¬ 2 ¬ ¬ ¬ ¬ £ i∆Ek t » ¬ ¬ F PI! + (t) Uek e ¬ ¬ k Two-Neutrino Mixing ¬ ¬ 2 ¬ ¬ Et i∆E1t i∆E2t ∆ » ¬ ¬ F PI! (t) cos e + sin e = 1+sin2 cos + 2 ∆m2t = 1+sin2 cos 4M ∆m2 ∆E =∆E ∆E = E E = 2 1 2 1 2M C.
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