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