Stefan Baeßler
Neutron Beta Decay Correlations:
Part 1: …within the Standard Model
Proton
u
du
Neutron
u
d
d W
-e
Electron
Anti-Neutrinoeν
Thanks for contributions from:
H. Abele, K.Bodek, G. Konrad, B. Märkisch, P. Mumm, J. Nico, S. Paul, D. Počanić, M. Schumann,
T. Soldner, F. Wietfeldt, A. Young
Outline
Part 1: Contributions to the Standard Model
1. Beta Decay: The study of Parity Violation
2. Measurement of the Beta Asymmetry
3. Measurement of the Neutrino Electron Correlation
Part 2: Searches for physics beyond the Standard Model
…
(First) discovery of Parity Violation (1928)
R.T. Cox et al., PNAS 14, 544 (1928):
Assumption: Scattering probability depends on spin orientation (that was known for X
rays). This is correct, but the reason (Spin-Orbit Interaction) was not discovered yet.
Aim: Prove that an electron is a vector particle.
Result: Asymmetry of count rate for 90 deg / 270 deg found, was not deemed to be
important. Later experiments continued with electrons from a hot filament.
The Beta Decay Hamiltonian
Finally: Parity Violation found by Wu et al, 1956
Now: Construction of Parity-Violating
Hamiltonian, which couples leptons and hadrons
'Fweak,elementary
5
5 h.c.2
eµ µ
V A V A
γ γ γ γ γG
u d e γH νµ µ
− −
−− −= +����� �����
Complication: Nucleons aren‘t elementary particles:
ud 5Fweak 5 h.c.
21 µ µ e
GH p γ γ γ n e γ γ γ ν
V µ µλ −= ⋅ − − +
Coupling constants are unknown. Fermi-Transitions: gV = GF·Vud
Gamow-Teller-Transitions: gA = GF·Vud·λ
Properties: Helicity of fermions is –v/c, of antifermions is v/c
60Co
I�
e-
60Co
I�
e-
≠
( ) ( )d
2
eu
2
e
221 3FV
dwG E
dE
πλ ρ= +
ℏ
Observables in Neutron Beta Decay
( ) ( )u
1 2 2
e
2
n d
21 3FG V E−τ + λ
π= ρ∫ℏ
pn
e-
eν
Neutron lifetime
Fermi’s golden rule:
2
weak
2 Decay probability i fw f H i
πρ→ =
ℏ
( ) ( )2 ee
e
e en
e
ee
e
1 3 1
+
a
A
p p
E E
p p p p
E EB
E E
mdw E b
E
D
ν
ν
ν ν
ν ν
σ
λρ
∝ ⋅ + ⋅ + +
⋅ +
⋅
×+
� �
� � � ��
Observables in Neutron Beta Decay
( ) ( )u
1 2 2
e
2
n d
21 3FG V E−τ + λ
π= ρ∫ℏ
pn
e-
eν
n
�σ e
�σ
Neutron lifetime
Jackson et al., PR 106, 517 (1957):
Observables in Neutron beta decay, as a function of
generally possible coupling constants (assuming only
Lorentz-Invariance)
Beta-Asymmetry
Neutrino-Electron-Correlation
2
2
Re2
1 3A
+= −
+
λ λ
λ2
2
1
1 3a
−=
+
λ
λ
The Standard Model Parameters Vud and λ
νe
n
−2
1p
Fermi-Decay:
gV = GF·Vud
Gamow-Teller-Decay:
gA = GF·Vud·λ
p
p
νee- e-
+2
1
e- νe
νeνee- e-
Two unknown parameters, gA and gV, need to be determined in 2 experiments
1. Neutron-Lifetime: ( )1 2 2
n V A3g g−τ ∝ +n 885 sτ ≈
S = 0, mS = 0
S = 1, mS = 0
S = 1, mS = 1
The Standard Model Parameters Vud and λ
νe
n
−2
1p
Fermi-Decay:
gV = GF·Vud
Gamow-Teller-Decay:
gA = GF·Vud·λ
p
p
νee- e-
+2
1
e- νe
νeνee- e-
Two unknown parameters, gA and gV, need to be determined in 2 experiments
1. Neutron-Lifetime: ( )1 2 2
n V A3g g−τ ∝ +n 885 sτ ≈
A = 0
A = 0
A = -1
2
22 0.1
1 3A
λ + λ= − ≈ −
+ λλ = A
V
g
g2. Beta-Asymmetry:
( )n1 cos ,e
vdw A p
c
∝ +
σ
Decrease of Neutron Counts N with storage time t: N(t) = N(0)exp{-t/τeff}
1/ τeff = 1/τβ+1/τwall losses
Neutron Lifetime Measurements
MAMBO
Many new attempts underway, mostly with magnetic bottles:
Under (at least) construction: Ezhov et al. (ILL, PNPI Gratchina), Bowman et al. (LANL),
Paul et al. (TUM, PSI)
Outline
Part 1: Contributions to the Standard Model
1. Beta Decay: The study of Parity Violation
2. Measurement of the Beta Asymmetry
3. Measurement of the Neutrino Electron Correlation
Part 2: Searches for physics beyond the Standard Model
…
Electron Detector (Plastic Scintillator)
Polarized Neutrons
Split Pair Magnet
Decay Electrons
( )n1 cos ,e
vdw A p
c
∝ +
σ
p+
n
e-
eν
Magnetic Field
The Beta Asymmetry: PERKEO II
PERKEO II
( )up down
n
up down
cos ,e
N N vA p Pf
N N c
−= σ
+
Experimental Reality:
• Flip neutron spin, don’t compare
detectors!
• Two detectors still needed to
suppress electron backscattering.
Detector
On the motivation to achieve high polarization
Easiest type of polarization analysis: (just spin flip ratio):
Polarizer P1Analyzer P2
upN
DetectorPolarizer P1Analyzer P2
downN
Spin flipper F
1up
1 21 2down
1 2 1 2
1 1 1Spin flip ratio: (1 ) (1 ) (1 )
1 2 2
PPNR P P f
N PP PP f
−+ = = − + − + − − +
≐
Note: Modification of spin flip ratio if analyzer is He-cell (opposite polarization)
Result: The spin flip ratio sets a lower limit on the efficiency of devices, even if one
couldn’t tell individual numbers for P1, P2 , or f. If this lower limit is close to 100%, the
precision of any scheme used to determine the efficiencies individually doesn’t have to
be high. Most experimental errors (Background, Depolarization) cause the true
polarization to be even higher than the lower limit given by the spin flip ratio.
Experiment
Problems of polarization measurement: Inhomogeneities of polarization and spin flip efficiency
Supermirror: … with position, angle, wavelength
He-3: … with wavelength, time
-8 -6 -4 -2 0 2 4 6 8 100.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
AP
Position [mrad]
Single Analyzer
Crossed Analyzer
Wavelength dependenceAngular dependence
The crossed geometry
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.75
0.80
0.85
0.90
0.95
1.00
1.05
AP
λ [A]
Single Analyzer
Crossed Analyzer
Supermirror polarizer
1 212
1 2
1 2
1
11 (1 )(1 )
2
P PP
PP
P P
+=
+
≈ − − −
Independent devices
M. Kreuz et al., NIM A 547, 583 (2005)
Beam polarization with crossed supermirrors
Neutron beam polarization for PERKEO II
Above: Polarizer, below: Results
1. Beam polarization: Crossed
supermirrors
2. Spin flip through adiabatic fast
passage
3. Polarization analysis behind
experiment with 2nd spin flipper
and black He-3 analyzer
Kreuz et al., NIM A 547, 583 (2005)
Result:
• Spin flip efficiency f = 100.0(1)%
• Beam polarization P = 99.7(1)%
• No position dependence of f or P
• No time dependence of f or P
M. Schumann et al., PRL 99, 191803 (2007)
PERKEO II: Results
Nup
Ndown
Raw data
Data with
subtracted
background
Background (Shutter
behind polarizer)
Calibration: Conversion electron sources
(Nup-N
dow
n)/
(Nup+
Ndow
n)
( )ncos ,e
vA p Pf
cσ
Error Analysis Correction Uncertainty
PERKEO II
Statistical uncertainty 0.26%
Background 0.1% 0.1%
Neutron beam
polarization
0.3 % 0.1%
Spin flip efficiency 0% 0.1%
Magnetic mirror effect 0.11% 0.01%
Edge Effect -0.22% 0.05%
Detector response 0.18%
…
Uncertainty Budget PERKEO II, last run
H. Abele, 2009, preliminary
Beam time Result Publication
1995 A = -0.1189(12) Phys. Lett. B 407, 212 (1997)
1997 A = -0.1189(7) Phys. Rev. Lett. 88, 211801 (2002)
2004 A = -0.1198(5) (preliminary) → λ = -1.2762(13)
d
n = (ddu)
p = (udu)
u
W±
e-
νegV , gA
Coupling Constants in Neutron Decay
W±
e-
νen
p
n + νe↔ p + e-
Primordial Nucleosynthesis
Solar cycle
W±
e+
νe
p + p
2H+
p + p → 2H+ + e+ + νe
Neutrino Detection (SNO, CC)
W±
νe
e-
2H+
p + p
νe + 2H+→ p + p + e-
n → p + e- + νe
Coupling Constants of the Weak Interaction
Start of Big Bang Nucleosynthesis,
Primordial 4He abundance
Start of Solar Cycle, determines amount of
Solar NeutrinosEfficiency of Neutrino Detectors
Unitarity: Situation 2004
-1.28-1.27-1.26-1.25
λ = gA/gV
0.965
0.970
0.975
0.980
Vu
d
τn [PDG2006]
A [PERKEO II]
0+→ 0+
ud u
2
u
2
s b1V V V= − +Unitarity
of the CKM Matrix
Neutron Measurements needed:
• Neutron lifetime τn
• Beta Asymmetry A(λ)
• Neutrino-Electron-Correlation a(λ)
( )21 2
n ud
2 1 3FVGτ λ− ∝ +
2
2
Re2
1 3A
λ λ
λ
+= −
+
2
2
1
1 3a
λ
λ
−=
+
; λ = gA/gV
uV
udA F
dFFermi-Transition:
Gamow-Teller-Transition:
g G
g
V
G V
= ⋅
= ⋅ ⋅λ
Neutron Measurements needed:
• Neutron lifetime τn
• Beta Asymmetry A(λ)
• Neutrino-Electron-Correlation a(λ)
( )21 2
n ud
2 1 3FVGτ λ− ∝ +
2
2
Re2
1 3A
λ λ
λ
+= −
+
2
2
1
1 3a
λ
λ
−=
+
; λ = gA/gV
uV
udA F
dFFermi-Transition:
Gamow-Teller-Transition:
g G
g
V
G V
= ⋅
= ⋅ ⋅λ
ud u
2
u
2
s b1V V V= − +
Unitarity
of the CKM Matrix
τn [PD
G08]
Vud
Nuclear 0+→ 0+ decaysJ.C. Hardy, I.S. Towner, arXiv:0812.1202
τn [S
erebrov2005]
Unitarity 2008
-1.28-1.27-1.26-1.25
λ= gA/gV
0.965
0.970
0.975
0.980
To make A not limiting for neutron-based
determination of Vud: ∆A/A < 0.2% needed
Neutron lifetime discrepancies have to be
sorted out.
A [PERKEO II, 2009]A [PDG08]
PIBETAD. Počanić et al, PRL 93, 181803 (2004)
-1.28
-1.275
-1.27
-1.265
-1.26
-1.255
λ
PERKEO II,
1997 PERKEO II,
2002
Yerozolimskii, 1997
PERKEO, 1986Liaud, 1997
PERKEO II,
2009
UCNA, 2009
Determination of λ = gA/gV from A
Probability of disagreement between beta asymmetry measurements due to statistical fluctuations:
P = 2.7×10-5 (4.2 σ)
Maybe in PDG2010: “The most recent results from PERKEO II are so far from other results that it
makes no sense to include them in the average. It is up to workers in this field to resolve this issue ???
(THIS IS NOT A SERIOUS PROPOSAL!)
PERKEO II
(averaged)
Liaud
Yerozolimskii
PERKEO
UCNA
-1.29 -1.26
λ
PERKEO II
Corrections in Beta asymmetry measurements
Liaud
Yerozolimskii
PERKEO
UCN source
Polarizer /
Spin flipper
Diamond-coated
quartz tube
MWPC
Plastic scintillator
Light guide
Superconducting solenoidal
magnet (1.0 T)
Decay volume
Field Expansion
Region
Detector housing
PMT
Neutron
absorber
New attempts: UCNA (ultracold neutrons)
Test run: A0=-0.1138(46)(21)
A. Young (NCSU), A. Saunders (LANL), et al.
A0
-0.15
-0.1
-0.05
Energy (keV)
Rat
e (1
/50
keV
·s)
00 200 400 600 800 1000
0.1
0.2
0.3
0.4
0.5Signal
A0<P> = -0.1138±0.0046
Background
Be coated
mylar foil
Pattie et al., PRL 102, 012301 (2009)
Continuous beam
Next generation: PERKEO III
detector
(plastic scintillator)
decay volume, 150 mT
beam dump
2 mvelocityselector
chopper
B. Maerkisch, D. Dubbers (Heidelberg), H. Abele (Vienna), T. Soldner (ILL) et al.
coldneutron beam
detector
(plastic scintillator)
preliminary
(Nup-N
dow
n)/
(Nup+
Ndow
n)
channel0 40 80 120
energy [keV]
200 400 600 800
channel
Co
unts
[A
.U.]
0 40 80 120 160
0
10000
20000
30000
40000
50000
60000
70000
200 400 600 800
energy [keV]
preliminary
Data from 24 calendar hours,
Background subtracted
Energy calibration, cuts, detector
response to be revised
New observable: Weak magnetism
Hadronic current at q ≠ 0:
5 p
weak F
n
5
ud
p
...
2
1
ν
µ µ e
H G p γ γ γ i q nm
e γ
V
γ γ ν
µ µ µνµλ σ
µ
−
= ⋅ − + +
⋅ −
−
weak magnetism
1. First determination in mirror nuclei: Slightly different decay rates due to weak magnetism
2. Determination in hyperons: Not always according to Standard Model
3. New: Determination from beta asymmetry spectrum
p
0 WM
n( ) 1 ,
2A E A c a
µλ
µ = + +
−
2%≈
New attempts at SNS: abBA / Nab / PANDA
3HePolarizer
Spin FlipperAdiabatic
Proton Beam 60 Hz
Biological Shield
ShutterChoppers Flux
Monitor
Neutron Guide
Spectrometer
Mercury
Spallation
Target
Collimator
LH2
19.8 MeV
4He
3He+np+t
20.5 MeV20.1 MeVJπ = 0+
Jπ = 0+
Jπ = 1-,2- 21.2 MeV
Γ = 0.27 MeV
Fast, segmented silicon detector:
S. Wilburn (LANL),
D. Bowman (ORNL),
S.B. et al.
Outline
Part 1: Contributions to the Standard Model
1. Beta Decay: The study of Parity Violation
2. Measurement of the Beta Asymmetry
3. Measurement of the Neutrino Electron Correlation
Part 2: Searches for physics beyond the Standard Model
…
Determination of the Coupling Constants
νe
n
−2
1p
Fermi-Decay:
gV = GF·Vud
Gamow-Teller-Decay:
gA = GF·Vud·λ
p
p
νee- e-
+2
1
e- νe
νeνee- e-
Two unknown parameters, gA and gV, need to be determined in 2 experiments
1. Neutron-Lifetime: ( )1 2 2
n V A3g g−τ ∝ +n 885 sτ ≈
a = 1
a = 1
a = -1
λ = A
V
g
g2b. Neutrino-Electron-Correlation a:
2
2
1~ 0.1
1 3
−λ= −
+ λa
( )1 cos ,ee
vdw a p p
cυ
∝ +
-1.28
-1.275
-1.27
-1.265
-1.26
-1.255λ
Determination of λ = gA/gV
• A measurement of a is independent of possible unknown errors in A,
systematics are entirely different.
• Present experiments have ∆a/a ~ 5%, an order of magnitude improvement
is desirable
PERKEO II,
1997
PERKEO II,
2002
Yerozolimskii, 1997
PERKEO, 1986Liaud, 1997
Stratowa, 1978
Byrne, 2002
PERKEO II,
2009
UCNA, 2009
Mostovoi, 2001
Sensitivity of the Proton Spectrum to a:
pn
e-
eν
( )
+∝e
ppc
vadw e υ,cos1
aSPECT (Mainz, Munich, ILL, Virginia)
0 200 400 600
and for a = -0.103 (PDG 2006)
Proton kinetic energy E [eV]
Dec
ay r
ate
w(E
)
Proton spectrum for a = +0.3
Analyzing Plane
Electrode
Proton Detector
Neutron Decay
Protons
Magnetic
field
22
gyr
p p p
2
Adiabatic Invariant:
angular momentum: const.
magnetic momentum: sin ( , )2 2 2
sin ( , ) const.
p
L r p
Epe eL r p p B
m m m B B
B p B
µ ⊥⊥
= × =
= = = =
=
� � �
� �� �
��
Principle of a Retardation Spectrometer
AB
Potential Barrier
eU
Decay Volume
Analyzing Plane
Proton Trajectory
Magnetic Field
( ) ( )( )
0
A 0
0 ;
1 1 1 ; otherwise
1 ; 1
U A
E e
T E e E
E
B B
B B e
U
-
U
U
<
= − − − >
Transmission function TU(E) in the adiabatic limit:
0,0
0,2
0,4
0,6
0,8
1,0
Tra
nsm
issi
on
fu
nct
ion
TU
(E)
0 200 400 600
and for a = -0.103 (PDG 2006)
Proton kinetic energy E [eV]
Dec
ay r
ate
w(E
)
Proton spectrum for a = +0.3
B0 = 1.8 T
BA = 0.35 T
p⊥
||p
p⊥
||p
Transmission function @ U=375V
Pulse height spectrum:
• 470 counts per second at UA = 50 V (one detector pad)
• Statistical sensitivity on a about 2 % per 24 hours measurement time
• Background stable
Integrated Proton Spectrum:Silicon drift detector,
at -15kV
preliminary
Analyzing plane voltage UA [V]
Tota
l p
roto
n c
oun
t ra
te [
s-1]
0 100 200 300 400 500 600 7000
100
200
300
400
500
Simulation for a = + 0.3
and for a = - 0.103(4) (PDG 2008)
Experimental data (offset subtracted)
( ) ( ) ( )UN U T E w E dE∝ ∫Pulseheight [ADC channels]
0 100 200 300 400 500 600 700
Co
un
ts p
er s
eco
nd
0
1
2
3
4
5
6 barrier voltage
50 V
250 V
400 V
500 V
600 V
780 V
barrier voltage
50 V
250 V
400 V
500 V
600 V
780 VCo
unt
rate
[s-1
bin
-1]
2
4
6
5
0
3
1
Pulse height [ADC channels]
7006004002000 100 300 500
First results of 2008 beamtime @ ILL
Neutron
Beam
-30 kV
Proton
Detector
Decay
Volume
Analyzing
Plane
ExB
ExB
Trapped e-
Trapping problems solved
Measurements without neutron beam
new detector -HV electrode,
SDD detectorInternal getter pumpsnew ExB electrode
-15 kV
0
1
2
3
4
5
0 200 400 600 800
Beam time at FRM-II, Munich (2006)
Beam time at ILL, Grenoble (2008)
Analyzing Plane Voltage UA [V]
Bac
kgro
un
d c
ount
rate
[s-1
]
preliminary
aCORN
Tulane (F. Wietfeldt), Indiana, NIST, et al.
pn
e-
eν ( )( ) 1 cos ,ee
vw E a p p
cυ
∝ +
eppν
pp
e,max eEE Eν = −
Magnetic
field
a = -0.103:
“pυ up”
more likely
Aim: ∆a/a ~ 2%, maybe 0.5% after NIST upgrade
aCORN @ IUCF
Magnet+Yoke Collimator
Decay volume electrode
Ee
(MeV)
pp2
(MeV
2/ c
2
electron and proton phase space
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
The cosθeν spectrometer Nab @ SNS
p
n
e-
eν
1 cos e
vdw a
cνθ ∝ +
eνθ
pp2 [MeV2/c2]
pp
2dis
trib
uti
on
0.0 0.5 1.0 1.5
( )2ep
e
1 cos e
pa p
Eνθ+
Ee = 550 keV
( )2
pcos 1
epνθ = −
( )2
pcos 1
epνθ = +
Kinematics:
• Energy Conservation
• Momentum Conservation
2 2 2
e ep 2 cos ep p p p pν ν νθ= + +
e,max eEE Eν = −
cos 1eνθ = +
cos 0eνθ =
cos 1eνθ = −
cut
The cosθeν spectrometer Nab @ SNS
SegmentedSi detectorNeutron beam
decayvolume
TOF region transitionregionacceleration
region
30 kV
0.00 0.02 0.04 0.06 0.08
1/tp2 [1/µs2]
103
Sim
ula
ted c
ount
rate
Ee = 300 keV
104
105
106
107
Ee = 500 keV
Ee = 700 keV
pp2 [MeV2/c2]
pp
2dis
trib
uti
on
0.0 0.5 1.0 1.5
( )2ep
e
1 cos e
pa p
Eνθ+
Ee = 550 keV
( )2
pcos 1e pνθ = −
( )2
pcos 1
epνθ = +
D. Pocanic, S.B. (Virginia),
D. Bowman (ORNL), et al.
• Spectrometer and detector
shared with abBA
• Background suppression
through coincidences
• Aim: a ~ 0.1%
p
p
p pcos ( )
m dzt
p zθ= ∫
Segmented
Si detector
decay volume
(field rB,DV·B0)
30 kV
0-30 kV
0-31 kV
magnetic filter
region (field B0)
Neutron
beam
TOF region
(field rB·B0)
The asymmetric version of Nab @ SNS
Advantages of asymmetric configuration:
• Reduced sensitivity to electrostatic
potential inhomogeneities
• Statistical: Bigger decay volume vs.
Angular acceptance
• Detection function: Improved flight path
length
• Avoidance of deep Penning trap
• Polarized experiment (abBA, PANDA)
still possible
B0
neutron
beam stop
charged decay
productsB1
B2
neutron decay channel
(neutron guide, 8 m long)Neutron
guide
Velocity
selector
Polarizer
+ Spin flipper
Chopper
Analyzing
plane
Proton
Detector
PERC example: B0 = 2 T, B1 = 8 T, B2 = 0.5 T:
count rates: beam time:
70000 s−1, continuous unpolarized n-beam ½ h
14000 s−1, continuous beam polarized to 98% 2 h
6000 s−1, pulsed unpolarized beam 10 h
370 s−1, pulsed beam polarized to 99.7% 4 d
for ~10−4 statistical error
Future in Europe (@ILL or FRM-2): PERC
Dubbers et al., NIM A 596, 238 (2008)
Electron
Detector
Stefan Baeßler
Neutron Beta Decay Correlations:
Part 2: …beyond the Standard Model
Proton
u
du
Neutron
u
d
d W
-e
Electron
Anti-Neutrinoeν
Thanks for contributions from:
H. Abele, K.Bodek, G. Konrad, B. Märkisch, P. Mumm, J. Nico, S. Paul, D. Počanić, T. Soldner, F. Wietfeldt, A. Young
Outline
Part 1: Contributions to the Standard Model
1. Beta Decay: The study of Parity Violation
2. Measurement of the Beta Asymmetry
3. Measurement of the Neutrino Electron Correlation
Part 2: Searches for physics beyond the Standard Model
1. Fierz interference and S,T currents
2. Asymmetries involving protons and right-handed currents
3. Search for Time Reversal Violation
4. Radiative Beta Decay
5. Bound Beta Decay
General Beta Decay Hamiltonian
{ }
F ud 5 5if
V,A,S,T
2 1 1
2 22j j e j j e
j
j j
G V γ γH p n e ν p eL nR ν− −
∈
− += Γ Γ + Γ Γ∑
Left-handed neutrino Right-handed neutrino
V A 5 S T
,with operators: ; ; 1 ;
2 2
i γi γ
µ νµ µ
γγ γ
Γ = Γ = Γ = Γ =
V A S T A S TStandard Model: 1 ; ; 0VL L L L R R R Rλ= = = = = = = =
( )2 2 2 2 2 2 2 2
V A S T V An S TNeutron lifetime: 3 3 3 3L L L L R R R Rτ ∝ + + + + + + +
Standard Model: 1+3λ2 Standard Model: 0
( )2 2 2 2* * * *
A V A T S T A V A T S T
2 2 2 2 2 2 2 2
V A S T V A S T
2ReBeta Asymmetry:
3 3 3 3
L L L L L L R R R R R R
L L L L R R R RA
− − + + + + − −=
+ + + + + + +
2 2 2 2 2 2 2 2
V A S T V A S T
2 2 2 2 2 2 2 2
V A S T V A S T
Neutrino Electron Correlation: 3 3 3 3
L L L L R R R R
L L L L R R R Ra
− − + + − − +=
+ + + + + + +
Glück et al., NPA 593, 125 (1995), Jackson, PR 106, 517 (1957)
More observables: Fierz Interference Term
pn
e-
eν
n
�σ e
�σ
• Signal expected for left-handed scalar and tensor interaction (neutrino is left-handed, electron is
right-handed). Could be caused by leptoquarks or charged Higgs bosons.
• Signal expected for MSSM: b ~ 10-3 (Ramsey-Musolf, 2007)
• Not measured (directly) in neutron beta decay (detector, background), Nab might be able to.
• Tight bound for scalar part from superallowed decays
Jackson et al., PR 106, 517 (1957):
( )* * * *
S V A T S V A T
2 2 2 2 2 2 2 2
V A S T V A S T
2 Re 3 3
3 3 3 3
L L L L R R R R
L L L L R R R Rb
+ + +=
+ + + + + + +
( ) e
e
e e e en
e
e
e e e
e
e
1
+ ...
p p
E E
p
a b
Ap p p
B N
mdW E
Dp
E
E E ER
E E
ν
ν
ν ν
ν ν
σσ σ
ρ⋅
×
∝
×
⋅ + +
+⋅ + + + +
� �
� � � � � �� �
Fierz-Interference Term:
(Time reversal invariance assumed)
Based on P.A. Vetter et al.,
PRC 77, 035502 (2008)
Search for left-handed scalar and tensor currents
0.10
0.05
0.00
0.100.050.00
LS/LV
neutron 1978
neutron 2002
(0+→
0+)
Fie
rz
LT/L
A
• Most stringent limit comes from superallowed nuclear decays (missing energy dependence of partial
lifetime due to Fierz Term:( ) e
e
e
1m
dW EE
bρ
∝ ⋅ +
• Approximation: Extracted correlation coefficients (a, A, …), where the analysis assumes b = 0, are
in general
e e
e e
, ,...
1 1
a A
mb
Eb
m
E+ +
• Better if experimentalists would discuss the non-V-A case (correct electron energy dependence,
possible influence of b on systematics).
Outline
Part 1: Contributions to the Standard Model
1. Beta Decay: The study of Parity Violation
2. Measurement of the Beta Asymmetry
3. Measurement of the Neutrino Electron Correlation
Part 2: Searches for physics beyond the Standard Model
1. Fierz interference and S,T currents
2. Asymmetries involving protons and right-handed currents
3. Search for Time Reversal Violation
4. Radiative Beta Decay
5. Bound Beta Decay
The neutrino asymmetry B
νe
n
−2
1p
Fermi-Decay:
gV = GF·Vud
Gamow-Teller-Decay:
gA = GF·Vud·λ
p
p
νee- e-
+2
1
e- νe
νeνee- e-
gA and gV can be determined with B and τn (as before) but one is not very sensitive
B = 0
B = 0
B = 1
2
22 0.98
1 3B
λ −λ= ≈
+ λλ = A
V
g
gNeutrino Asymmetry:
( )( )n1 cos ,dw B pν σ∝ +
This can be turned around to look for deviations from the Standard Model (e.g.,
right-handed W bosons)
( ) e
e
e e e en
e
e
e e e
e
e
1
+ ...
p p
E E
p
b
B N D R
mdW E a
p p p p
E E
E
E E EA
� �
� � � � � �� �
⋅
×
∝
×+
⋅ + +
⋅ + + + +
ν
ν
ν ν
ν ν
σσ σ
ρ
More observables: Neutrino Asymmetry
pn
e-
eν
n
�σ e
�σ
Neutrino-Asymmetry
Jackson et al., PR 106, 517 (1957):
Signal expected for MSSM at ∆B ~ 10-3 (Ramsey-Musolf, 2007)
( )
( )
2 2 2 2* * * *
A V A T S T A V A T S T
2 2 2 2 2 2 2 2
V A S T V A S T
* * * * * *
S A V T A T S A V T A T e
2 2 2 2 2 2 2 2
eV A S T V A S T
2 Re
3 3 3 3
2 Re 2 2
3 3 3 3
L L L L L L R R R R R R
L L L L R R R R
L L L L L L R R R R R R m
EL L L L R R R
B
R
− + − − + − +=
+ + + + + + +
− − + + + −+ ⋅
+ + + + + + +
The neutrino asymmetry B from PNPI
Neutrons
Mesh
Mesh
Proton detector
Neutron guide
Electrodes
Electrodes
Result: 0.9821(40)B =
Electron detector (MCP)
n
e-
eν
n
�σp
A. Serebrov et al., JETP 86, 1074 (1998)
B < 0
B = 0
nσ�
Background B−n Displacement
The neutrino asymmetry B from PERKEO II
same
N NB B
N N
⇓↑↑ ⇑↑↑
⇓↑↑ ⇑↑↑
−= ∝
+
Result: 0.9802(50)B =
Combine both B values with A (PERKEO II) and τn (own average):
→ Limit on right-handed W boson: m(WR) > 296 GeV/c2
Compare with limits from D0 (assuming left- and right handed coupling constants are equal):
m(WR) > 1000 GeV/c2
M. Schumann et al., PRL 99, 191803 (2007)
V.M. Abazov et al., PRL 100, 031804 (2008)
n-Spin
Magnetic Field Lines
Scintillation Detector
for Electrons
Photomultiplier Tubes
Neutron Beam
Coils in Split Pair
Configuration
Decay Volume
n
e-
eν
n
�σ p
n
e-
eνn
�σ
vs.
p
n
n
�σ
vs.
p
The proton asymmetry C from PERKEO II
n
n
�σ
p
N ⇑↑↑
N ⇓↑↑
N ⇑↓↑
N ⇓↓↑
( ) ( )( ) ( )exp
N N N NC
N N N N
⇑↑↑ ⇑↓↑ ⇓↑↑ ⇓↓↑
⇑↑↑ ⇑↓↑ ⇓↑↑ ⇓↓↑
+ − +=
+ + +
Electron energy [keV]
0 100 200 300 400 500 600 700
Pro
ton
Asy
mm
etry
Cex
p-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
• Result: M. Schumann et al., PRL 100, 151801 (2008); in SM:
(PERKEO-II measurement of B not independent of PERKEO-II measurement of C)
exp e 0.2377(26)C C dE= = −∫ ( )0.27484C A B= − +
Count rate “Spin up, proton up”
Count rate “Spin down, proton up”
The proton asymmetry C from PANDA
V0
~ ~~
+24 kV
Neutron beamInto page
Detector L Detector R
Uniform magnetic field
L
~~
mirror
~ ~~ ~ ~~
0 100 200 300 400 500 600 700
-0.4
-0.3
-0.2
-0.1
0.0
Standard Model
Pro
ton
Asy
mm
etry
Cex
p(E
)
Proton Kinetic Energy E [eV]
C = <Cexp(E)>
A similar measurement is planned with aSPECT
T. Chupp (Michigan), S.B., et al.
Outline
Part 1: Contributions to the Standard Model
1. Beta Decay: The study of Parity Violation
2. Measurement of the Beta Asymmetry
3. Measurement of the Neutrino Electron Correlation
Part 2: Searches for physics beyond the Standard Model
1. Fierz interference and S,T currents
2. Asymmetries involving protons and right-handed currents
3. Search for Time Reversal Violation
4. Radiative Beta Decay
5. Bound Beta Decay
( ) e
e
e e e en
e
e
e e e
e
e
1
+ ...
p p
E E
p
b
B N D R
mdW E a
p p p p
E E
E
E E EA
� �
� � � � � �� �
⋅
×
∝
×+
⋅ + +
⋅ + + + +
ν
ν
ν ν
ν ν
σσ σ
ρ
More observables: Triple correlation
Triple correlation
Jackson et al., PR 106, 517 (1957):
2
Im2
1 3D
λ
λ=
+
• A non-zero D coefficient violates Time reversal symmetry.
→ complex contribution in Hamiltonian. In SM only in high order
• Final state effects give D ~ 10-5
• Serves to restrict leptoquark extensions to the Standard Model
n
e-
eν
n
�σ
Tn
e-
eν
n
�σ
Measurement of the D coefficient with TRINE-β
Principle Setup
e0,p0 e0,p000
e0,p0 e0,p0
D
N ND
N Nα
↑ ↓
↑ ↓
−= =
+Pκ
Real Setup
Result: D = (-2.8±7.1)×10-4T. Soldner et al., PLB 581, 49 (2004)
But: Imperfect alignment gives too high
sensitivity to A and B.
Better use the following combination:
00 01 10 11
004 D
DP
α α α ακ
− − +=
0
0
1
1
( )e e p e pen n n
e e e
p pD
p p pp p
E E E E E ED Dν
ν ν ν
σ σ σ× − − ××
= = −
� � � � �� �� � �
Measurement of the D coefficient with EMIT
Proton Detector
Electron Detector
pp
pe
• Statistically favorable geometry
• Detection of protons with surface barrier detectors
at -28 kV (Earlier: PIN diodes), electrons with
scintillators
• First results published D = (-6±13)×10-4 (EMIT I)
L. Lising et al., PRC 62, 055501 (2000)
• Difficult systematics if beam polarization is not
homogeneous
• EMIT-2 is still being analyzed, result for D at
several times 10-4 expected
nσ�
pp
pe
Extract D from asymmetry with left detector
minus right detector to suppress unwanted
dependencies on other correlations.
( ) e
e
e e e en
e
e
e e e
e
e
1
+ ...
p p
E E
p
b
B N D R
mdW E a
p p p p
E E
E
E E EA
� �
� � � � � �� �
⋅
×
∝
×+
⋅ + +
⋅ + + + +
ν
ν
ν ν
ν ν
σσ σ
ρ
More Pseudo T violation: R/N correlation
pn
e-
eν
n
�σ e
�σ
Electron polarization
Jackson et al., PR 106, 517 (1957):
2
1 ANv
c
= −
• Standard-Model: NSM = 0.07; RSM = 0.0066 ~ 0
• Scalar or Tensor Interactions lead to deviations (Leptoquarks, charged Higgs, Sleptons in
SUSY)
• Of special interest: R, as it is Time-Reversal violating, measures imaginary part of coupling
constants
The Standard Model Parameters Vud and λ
νe
n
−2
1p
Fermi-Decay:
gV = GF·Vud
Gamow-Teller-Decay:
gA = GF·Vud·λ
p
p
νee- e-
+2
1
e- νe
νeνee- e-
N = 0
N = 0
N = 1
( )( )n1 cos ,edw N σ σ∝ +
σe: N gives
up-down asymmetry
pepν
pp
σn
MWPCscintillator scintillator
Pb-foil
Pb-foil
50
cm
R/N correlation
Polarized
n beam
( )
( )
exp
SM
exp
SM( )
0.056(11)(5)
0.066
0.008(15)(5)
0.00066FSI
N
N
R
R
=
=
=
=
Detection of electron polarization through Mott
scattering in Pb foil: The probability of having
a V track is electron spin dependent.
Result:
K. Bodek (Cracow), Villigen, CAEN, Leuven, Kattowice,
Bodek et al., Phys. Rev. Lett. 102, 172301 (2009)
σe: R gives
forward-backward asymmetry
-0.2 -0.1 0 0.1 0.2-0.2
-0.1
0
0.1
0.2
2Re LS/LV
2R
e L
T/L
A
Grey: Other limits from neutrons and nucleons
N. Severijns et al., RMP 78, 991 (2006)
-0.2 -0.1 0 0.1 0.2-0.2
-0.1
0
0.1
0.2
R/N correlation and implications on S/T couplings
2Im LS/LV
2Im
LT/L
A
Based on Bodek et al., Phys. Rev. Lett. 102, 172301 (2009)
Outline
Part 1: Contributions to the Standard Model
1. Beta Decay: The study of Parity Violation
2. Measurement of the Beta Asymmetry
3. Measurement of the Neutrino Electron Correlation
Part 2: Searches for physics beyond the Standard Model
1. Fierz interference and S,T currents
2. Asymmetries involving protons and right-handed currents
3. Search for Time Reversal Violation
4. Radiative Beta Decay
5. Bound Beta Decay
Motivation: Neutron radiative decay
• Previously unmeasured process in a fundamental
semileptonic decay. Testing QED in a weak process.
• Groundwork for other investigations: new correlations,
photon polarization, corrections O(0.5%).
J. Nico et al., Nature 444, 1059 (2006)
RDK I operated at NIST NCNR cold neutron source.
Measured e-ϒ coincidences followed by delayed proton.
BRRDK I = (3.13 ± 0.34) x10-3
BRQED = 2.81 x10-3
Measured branching ratio:
Measurement @ NIST: Neutron radiative decay
Collaboration: NIST, Tulane, Maryland, Michigan, Sussex, Arizona State
Measurement goal of current run: 1%
Outline
Part 1: Contributions to the Standard Model
1. Beta Decay: The study of Parity Violation
2. Measurement of the Beta Asymmetry
3. Measurement of the Neutrino Electron Correlation
Part 2: Searches for physics beyond the Standard Model
1. Fierz interference and S,T currents
2. Asymmetries involving protons and right-handed currents
3. Search for Time Reversal Violation
4. Radiative Beta Decay
5. Bound Beta Decay
Lamb shift
spin-filter
Decay volume
Ionization
Acceleration
Spectroscopy
Detection
Reactor
Neutron decay into hydrogen
p
e-nνe
( ) ( )ep H p ν= −
F = 1, mF = -1
( ) ( )( ) 0, ( )
( ) ( )e
H p HH H H
H p H
σν
σ⋅
= = −⋅
Left-handed anti-neutrino?
Production rate: ~ 4×10-6, only 10% end up in 2s state (needed for spin state analysis)
Other application: Search for scalar and tensor couplings, which influence occupation
numbers of spin states
Magnetic field
W. Schott et al., EPJ A 30, 603 (2006)
• Rich experimental program with the study of neutron decay
correlations
• New physics might be found with precision measurements.
Maybe soon!
• Main problem: Neutron lifetime disagreement
Thank you for your interest !!
Summary