The GSI Time Anomaly: Facts and Fiction

Carlo Giunti INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Universit`adi Torino mailto://[email protected] 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 Promethium

Cerium Neodymium

C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 4 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

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 = = 1 2

2

j j ij

jhF I

j j S

2

2

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 =

=

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 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 + )] 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 + )] 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

Munich Group + F. Bosch (GSI) – arXiv:0807.3297

◮ 180 180 180 Re ! W+ e Re in a tantalum foil

no oscillations at a level more than 10 times smaller than GSI

C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 20 Conclusions

◮ Interference: due to phase difference of two incoming waves

◮ Causality: there cannot be interference of waves before they exist

◮ The GSI ion lifetime anomaly cannot be due to interference of decay product before the decay product start to exist (neutrino mixing in the final state)

◮ The GSI ion lifetime anomaly can be due to interference of two energy states of the decaying ion: Quantum Beats

◮ No known mechanism, because

◮ 16 ¢ Energy splitting of the two energy states: ∆E  6 10 eV ◮ Ratio of probabilities of the two energy states: 1/99

◮ GSI group is trying to measure EC of different hydrogen-like ions, EC of +

helium-like ions and decay of hydrogen-like ions

C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 21 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 La Thuile 2009, 3 March 2009 22 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 La Thuile 2009, 3 March 2009 23

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 La Thuile 2009, 3 March 2009 24

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. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 25

2

◮ 2

j j ij h j j i

jh F I F I

F 

Standard QFT: PI! + = S = k S k

◮ S-matrix operator at first order in perturbation theory: 4 S = 1 i 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

◮ £

j j i Å

h F I k S = Uek k with G

F 4 5  5

Ô

h j j i

Å F I k = i cos C d x k ¯k (x)  (1 )e(x)¯n(x) (1 gA )p(x)

2

2

◮ £ 2 2

Å j j jÅ j

I F 

P ! + = Uek k different from standard P = Uek k

k k

C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 26 ◮ Check: in the limit of massless decay probability should reduce to the Standard Model decay probability

2 j PSM = j ÅSM

with G

F 4 5  5

Ô

h j j i

Å F I SM = i cos C d x e ¯e (x)  (1 )e(x)¯n(x) (1 gA )p(x) 2

where e is the Standard Model massless electron neutrino G

F 4 5  5

Ô

h j j i

Å F I k = i cos C d x k ¯k (x)  (1 )e(x)¯n(x) (1 gA )p(x)

2

! Å Åk SM

mk !0

2 2

£

£ 2

Å ! jÅ j 6

I F 

P ! + = Uek k SM Uek =PSM

m !0 k k k

WRONG!

C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 27

◮

j i

Correct normalized final neutrino state (h e e = 1):

=

1 2

2



i jh j j ij j i h j j i j e = j F S I k k F S I

j k

=

1 2

2 2 £



j jÅ j Å j i = jUej j Uek k k j k

◮ Standard decay probability:

2 2 2 2

j j ij jh j j ij j j jÅ j

jh F I F I F  PI! + e = e S = k S = Uek k

k k

!

I F  P ! + e PSM

mk !0 ◮ In experiments which are not sensitive to the differences of the neutrino

masses, as experiments,

£

³ Å µ j i j i Åk = e = Uek k

k

C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 28 Time-Dependent Perturbation Theory? not appropriate because and decay are interrupted by

Schottky Mass Spectrometry

with ESR revolution frequency  2 MHz, i.e. every

7 ¢  5 10 s

much smaller than ion lifetime

140 142

³ ³ = T1=2( 59Pr) 3 39 m T1 2( 61Pm) 40 5s

and period of anomalous oscillations T ³ 7s

22 ¢ ~ 66 10 MeVs

26

³  t 

interaction time: W 4 10 s ¢ mW 80 10 MeV

t  tW in Time-Dependent Perturbation Theory ·

Quantum Field Theory result

C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 29 Lambiase, Papini, Scarpetta – nucl-th/0811.2302

Spin-rotation coupling in non-exponential decay of hydrogen-like heavy ions 14 November 2008 We discuss a model in which a recently reported modulation in the decay of the hydrogen-like ions 140Pr58+ and 142Pm60+ arises from the coupling of rotation to the spin of electron and nuclei (Thomas precession).

! electron and nucleus spins cannot precess independently ! ! they are tied by spin-spin interaction, which generates hyperfine splitting ! ! it is much stronger than precession force !

! precession is strongly suppressed by hyperfine splitting !

C. Giunti The GSI Time Anomaly: Facts and Fiction La Thuile 2009, 3 March 2009 30