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The GSI Time Anomaly: Facts and Fiction
Carlo Giunti
INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Universita di Torino ` mailto://giunti@to.infn.it Neutrino Unbound: http://www.nu.to.infn.it

20 August 2009, Moscow, Russia 14th Lomonosov Conference on Elementary Particle Physics 19-25 August 2009 Moscow State University, Moscow, Russia

C. Giunti



The GSI Time Anomaly: Facts and Fiction



20 August 2009, Moscow, Russia



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The GSI Exp eriment
Schematic layout of the secondary nuclear b eam facility at GSI
Primary beam 508 MeV/u 152Sm Production target 1032 mg/cm2 Be Degrader 731 mg/cm2 Al 400 MeV/u
140

Pr

58+

Injection from UNILAC
[Litvinov et al, nucl-ex/0509019]

SIS: Heavy Ion Synchrotron FRS: FRagment Separator ESR: Exp eriment Storage Ring
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Schottky Mass Sp ectrometry




Stored ions circulate in ESR with revolution frequencies 2 MHz At each turn they induce mirror charges on two electrodes Revolution frequency sp ectra provide information ab out q m: Bq f= = 2 2 m Area of each frequency p eak is prop ortional to numb er of stored ions
0.06
95 99

Rh

45+

59

Ni
37+

28+

Ag
40

47+ 84

A
Zr
40+ 42 20+

A
Ca

Intensity [arb. u.]

78

K

19+ 38+

El El

q q

Mass value unknown Mass value known

Rb

0.04

97

Pd

46+

80

Sr

101 76

ád

48+ 105

Kr

36+ 61

Sn

50+ 86

Cu

29+

Nb

41+

88 31+

Mo

42+ 32+ 92

65

Ga

0.02

67

57

Co

27+

Ge

Ru44+
69

As

33+

0.00 50000

100000

150000

200000

250000

Frequency [Hz]
C. Giunti



[Litvinov et al, nucl-ex/0509019] The GSI Time Anomaly: Facts and Fiction



20 August 2009, Moscow, Russia



3


Praseodymium

Promethium

Cerium

Neodymium

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Electron Capture
140 59 142 61

Pr58+ Pm60+

140 58

Ce58+ + Nd
60+

e e

142 60

+

seen b ecause q = 0 f f =



m m (small)

? + decay
140 59 142 61

Pr58+ Pm60+

140 58

Ce57+ + e + + Nd
59+

e e

142 60

+ e+ +

not seen b ecause q = f
[Litvinov et al, PLB 664 (2008) 168] C. Giunti






1

150 kHz



The GSI Time Anomaly: Facts and Fiction

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[Litvinov et al, PLB 664 (2008) 168] C. Giunti



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[Litvinov et al, PLB 664 (2008) 168] C. Giunti



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(1) (2) = Eq. (1) (2) Eq. (1) (2)
EC

dNEC (t ) = dt dNEC (t ) = dt + ?+ +
loss

EC

N (t ) =

EC

N (0) e
EC



t

EC

(t ) N (t ) =
EC

(t ) N (0) e



t

(t ) =
140 59

EC

[1 + a cos( t + )] DoF 107.2/73 67.18/70 DoF 63.77/38 31.82/35
2 2

Pr a 0.00138(10) 0.00147(10) 0.18(3) Fit parameters of 142 Pm 61 N0 EC a 46.8(40) 0.0240(42) 46.0(39) 0.0224(41) 0.23(4) N0 EC 34.9(18) 35.4(18)

Fit parameters of

da t a 0.89(1) da t a 0.89(3)

T (140 Pr58+ ) = 7 06 59

?

0 08 s a = 0 20

T (142 Pm60+ ) = 7 10 61

?

?

0 22 s

0 02

C. Giunti



[Litvinov et al, PLB 664 (2008) 168] The GSI Time Anomaly: Facts and Fiction



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8


Neutrino Mixing?
[Litvinov et al, PLB 664 (2008) 168]

Ii

If +

e

e

= cos

SOL 1

+ si n

SOL 2 1

PROPOSED EXPLANATION: INTERFERENCE OF Initial Ion: Momentum P = 0, Energy E
å

AND

2

M a s s i ve

k

: Momentum p k , Energy Ek =

2 2 pk + mk

Final Ion: Momentum
2 E1 + M + p1 2M = E

p

k

2 , Energy M + pk 2M

2 E2 + M + p2 2M = E 2 2 m2

E
C. Giunti

E2

E1 Ã

m 2 2M

m



2 m1



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massive neutrino energy difference:
2 m2 = mSOL

E M

E2

E1 Ã Ã

m 2 2M

Ã8?
2 E

10 5 eV

2

Ã

140 amu

130 GeV

E T=

Ã

31

?

10

16

eV

Ã

19 1 s

= 1 43
T
GSI

ab out 3 times larger than

Ã

7s

CAN INTERFERENCE IN FINAL STATE AFFECT DECAY RATE?

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Interference: Double-Slit Analogy
I
NO INTERFERENCE
NO INTERFERENCE

INTERFERENCE = OSCILLATIONS

INTERFERENCE

F


e = c o s 1 + s in

2

Decay rate of I corresp onds to fraction of intensity of incoming wave which crosses the barrier Fraction of intensity of the incoming wave which crosses the barrier dep ends on the sizes of the holes It does not dep end on interference effects which occur after the wave has passed through the barrier Analogy: decay rate of I cannot dep end on interference of which occurs after decay has happ ened ÄÅ CAUSALITY!
C. Giunti







1

a nd

2



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Causality
INTERFERENCE OF COHERENT ENERGY STATES
(
1

AND

2

)

OCCURRING AFTER THE DECAY
(flavor neutrino oscillations)

CANNOT AFFECT THE DECAY RATE


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Cross Sections and Decay Rates are always summed incoherently over different final channels: I F
1

I

F

2

=Å F=

PI

F

=
k

PI

F

k

coherent final state: F

Ak F
k

k

Ë (S
2

1) I

=Å A? Fk S I k
k

Ak = Fk F
?2 ? ? ? ?

Ë

Fk S I
2

PI

F

= FSI

Ë

? ? ? ? ?

Ë
k

Fk S I

=
k

PI

F

k

coherent character of final state is irrelevant for interaction probability!

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arXiv:0801.1465 and arXiv:0805.0435
H.J. Lipkin


Causality is violated explicitly arXiv:0801.1465: The difference in momentum Ö p b etween the two neutrino eigenstates with the same energy produces a small initial momentum change Ö P . . . arXiv:0805.0435: Since the time dep endence dep ends only on the propagation of the initial state, it is indep endent of the final state, which is created only at the decay p oint. Thus there is no violation of causality. But in calculation of effect: The phase difference at a time t b etween states produced by the neutrino mass difference on the motion of the initial ion in the lab oratory frame with velocity V = (P E ) is





Ö

Ö E Å
C. Giunti

t = m2 2E
E E
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arXiv:0801.2121 - arXiv:0801.3262
A. N. Ivanov, R. Reda, P. Kienle


-

M. Fab er

I

F+

decay rate in time-dep endent p erturbation theory =
k k

with final neutrino state



Not even prop erly normalized to describ e one particle: =Ö =Å =3

j

k

jk



Different from standard electron neutrino state
e

=
k

U

ek

?

k



Several more pap ers with same mistake in arXiv. Two published in PRL!
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Time-Dep endent Perturbation Theory PI
F+

(t ) =

? ? ? ?

t

d
0

F

Ð

W

( )I

?2 ? ? ?

=

? ? ? ? ?

t

d
k 0

k

F

Ð

W

( )I

?2 ? ? ? ?

Ð
G äF

W

(t ) =

d3 x HW (x )

Effective Four-Fermion Interaction Hamiltonian HW (x ) = = F
t

2 2

cos cos

C ?e

(x ) (1



? 5 )e (x )n(x ) (1



gA 5 )p (x )

ä
G

F

C k ek

? Uek ?k (x ) (1 ?e
i Ek t



5 )e (x )n(x ) (1 ?



gA 5 )p (x )

k

ÐW

( )I =U =e

T

k

with

Ek = Ek + EF 2 Ö (Ek ) e



EI

de
0

i Ek t

i Ek t 2

sin(Ek t 2) Ek 2

E 1 t
k

i Ek t 2

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PI T
k

F+

(t ) = 4

2?
? ?

? ?

? Uek e
k

i Ek t

Ö (Ek ) T

?2 ? ? k? ?

Ã

T

j

Ö (Ek ) satisfied by wave packet
PI
F+

(t )

Ë

? ? ? ? ?

? Uek e
k

i Ek t ?
? ?

?2 ?

Two-Neutrino Mixing PI
F+

(t )

Ë

? ? ?

cos e

i E1 t

+ si n e

? i E2 t ?2 ?

Et 2 m 2 t = 1 + sin 2 cos 4M = 1 + sin 2 cos E1 = m 2 2M

E = E2



E1 = E2



C. Giunti



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Standard QFT:

PI

F+

=

FSI

2

=

? ? ? ? ?

k k

FSI

?2 ? ? ? ?



S-matrix op erator at first order in p erturbation theory: S=1



i

d4 x HW (x )



Effective four-fermion interaction Hamiltonian: GF ? HW (x ) = ä cos C ?e (x ) (1 5 )e (x )n (x ) (1 gA 5 )p (x ) 2 GF ? = ä cos C ? Uek ?k (x ) (1 5 )e (x )n (x ) (1 gA 5 )p (x ) 2 k FSI =U GF = i ä cos 2?
k F+ ek C



?

Õ

k

with
k
?2 ? ? k? ?

Õ


k

d4 x

? F ?k (x ) (1 5 )e (x )n (x ) (1 gA 5 )p (x ) I different from standard P =
k

PI

=

? ? ? ?

? Uek

Õ

U

ek

2

Õ

k

2

k

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Check: in the limit of massless neutrinos decay probability should reduce to the Standard Model decay probability PSM =

Õ

SM

2

Õ Õ

with
SM

=

G i äF
e

2

cos

C

d4 x

e

? F ?e (x ) (1 5 )e (x )n (x ) (1 gA 5 )p (x ) I

where
k

is the Standard Model massless electron neutrino cos
C

=

i ä2
G
F

d4 x

k

F ?k (x ) (1 5 )e (x )n (x ) (1 gA 5 )p (x ) I ?

PI

F+

=

? ? ? ? ?

Õk 0 Õ m
? Uek
k
?2 ? ? k? ? mk
k

SM 2?
? ? ? ?

Õ 0 Õ
WRONG!

SM

k

?? Uek ? =PSM ?


?2 ?

C. Giunti



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20 August 2009, Moscow, Russia

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Correct normalized final neutrino state (
Ì

e

e

= 1): FSI

Í 12



e

=



j j

FSI

2
Í 12

k

k

Ì

=




U
j

ej

2

Õ



k

j

2 k

U

ek

?

Õ

k

k

Standard decay probability: PI
F+
e

=

e

FSI

2

=
k

k

FSI
F+
e

2

=
k

U

ek

2 2

Õ

k

2

Õk 0 Õ m
k

SM

=Å

PI

0 Õ m
k

SM

= PSM



In exp eriments which are not sensitive to the differences of neutrino masses in production and detection interactions, as neutrino oscillation exp eriments, Õk Ã Õ =Å e = Ue?k k
k
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Time-Dep endent Perturbation Theory? not appropriate b ecause electron capture and decay are interrupted by Schottky Mass Sp ectrometry with ESR revolution frequency 5 2 MHz, i.e. every

?

10 7 s

much smaller than ion lifetime T
12

(140 Pr) 59

Ã

3 39 m

T

12

(142 Pm) 61

and p eriod of anomalous oscillations T interaction time: t t
W

à 40 à 7s

5s

t

W

mW

Ã

6 6 ? 10 22 MeV s 8 0 ? 104 MeV

10 26 s

in Time-Dep endent Perturbation Theory Quantum Field Theory result

Ç

C. Giunti



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Quantum Beats?


GSI time anomaly can b e due to interference effects in initial state Two coherent energy states of the decaying ion =Å Quantum Beats

I = A1I1 + A2I

2 INTERFERENCE (QUANTUM BEATS)

INTERFERENCE (OSCILLATIONS)

F e = cos 1 + sin
C. Giunti

2



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Causality
INTERFERENCE OF COHERENT ENERGY STATES OCCURRING BEFORE THE DECAY CAN AFFECT THE DECAY RATE

C. Giunti



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Quantum b eats in GSI exp eriment can b e due to interference of two coherent energy states of the decaying ion which develop different phases b efore the decay Coherence is preserved for a long time if measuring apparatus which monitors the ions with frequency 2 MHz does not distinguish b etween the two states I(t = 0) = = 1
1





I1 + =Å
e

2

I2
1

( e

1

2

+

2 2

2

= 1)
E2 t

Ã

2

I(t ) = F S I(t )
2



iE1 t

I1 +

e

i

I2
EC

e e



t 2

PEC (t ) = A 2
1 2

= [1 + A cos(Et + Ã)] P P
EC



t

E

E2 E1

=

e

F S I1

2

Ã

t

e

F S I2

2

dNEC (t ) = N (0) [1 + A cos(Et + Ã)] EC e dt
C. Giunti



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dNEC (t ) = N (0) [1 + A cos(Et + Ã)] EC e dt E (140 Pr58+ ) = (8 38 59

t
) = 0 18

?

0 10)

?

10

16

eV eV
2

14 A(590 Pr

58+

?

0 03 0 04

14 E (612 Pm60+ ) = (8 32

?

0 26) A

?

10 2

16

14 A(612 Pm

60+

) = 0 23

?

1



Energy splitting is extremely small Needed ratio of production probabilities:
1 2 2 2

1 99

or

2

2

1

2

1 99



It is difficult to find an appropriate mechanism
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Hyp erfine Splitting smallest known energy splitting

[Litvinov et al, PRL 99 (2007) 262501]

E

1 eV

=Å

T

10

14

s

far too large to explain the GSI anomaly T
GSI

Ã

7s

EGSI = 2 T

GSI

Ã8?

10 16 eV

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26


feeling of smallness of

EGSI

10 15 eV

N

B

?

à 3?

10

12

eV G

1

(0 5 G ) = 1 5

?

10 12 eV

EGSI

10

3

N

B

?

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27


Further Developments
Berkeley Exp eriment - arXiv:0807.0649


EC:

142

Pm

142

Nd +

e

142

Pm in an aluminum foil =Å

no oscillations at a level 31 times smaller than GSI


Reanalysis of old

142

Eu

142

Sm +

e

EC data

no oscillations

Differences with GSI Exp eriment: neutral and stopp ed atoms Munich Group + F. Bosch (GSI) - arXiv:0807.3297

180

180 180 Re in a tantalum foil Re W+ e no oscillations at a level more than 10 times smaller than GSI

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Conclusions


Interference: due to phase difference of two incoming waves Causality: there cannot b e interference of waves b efore they exist The GSI ion lifetime anomaly cannot b e due to interference of decay product b efore the decay product start to exist (neutrino mixing in the final state) The GSI ion lifetime anomaly can b e due to interference of two energy states of the decaying ion: Quantum Beats No known mechanism, b ecause






Energy splitting of the two energy states: E 8 ? 10 16 eV Ratio of production 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
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Lambiase, Papini, Scarp etta - nucl-th/0811.2302 Spin-rotation coupling in non-exp onential decay of hydrogen-like heavy ions 14 Novemb er 2008 We di i n t he arises nuclei scuss a model in which a recently rep orted modulation decay of the hydrogen-like ions 140 Pr58+ and 142 Pm60+ from the coupling of rotation to the spin of electron and (Thomas precession).

! electron and nucleus spins cannot precess indep endently ! ! they are tied by spin-spin interaction, which generates hyp erfine splitting ! ! it is much stronger than precession force ! ! precession is strongly suppressed by hyp erfine splitting !

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30