neutron decay data are useful

Schleching 2008 4.1Präzisionsphysik mit Neutronen / 4. Experimente diesseits SM

Many processes have the same Feynman diagram as neutron decay:

Primordial element formation n + e+ ↔ p + ν'e σν ~ 1/τ

(2H, 3He, 4He, 7Li) p + e− ↔ n + νe σν ~ 1/τ

n ↔ p + e− + ν'e τ

Solar cycle p + p ↔ 2H + e+ + νe

p + p + e− ↔ 2H + νe etc. ~ (gA/gV)5

Neutron star formation p + e− ↔ n + νe

Pion decay π− ↔ π0 + e− + ν'e

Neutrino detectors ν'e + p ↔ e+ + n

Neutrino forward scattering νe + n ↔ e− + p etc.

W and Z production u' + d ↔ W− e− + ν'e etc.

… precision data of weak interaction parameters

today only from neutron decay

Neutron decay data are useful

u e−

W

d νe

e− νe

W

d u'

d νe

W

u e−


calculated gains in neutron count rates

ILL-Millenium program

Mean gain in ILL total efficiency

0

2

4

6

8

10

12

14

16

18

19

99

20

01

20

03

20

05

20

07

20

09

Year

Instr.+GuideRenewal

Instr. RenewalOnly


2001 S-DH GmbH: Neutron optics, H. Häse

2006 CASCADE GmbH : large fast n-detectors, M. Klein, C. Schmidt

Start-ups

http://pi1.physi.uni-heidelberg.de/physi/cascade/images/new_detektor2.jpg


Temperature kT = 10+19 GeV Planck scale

10+16 GeV Grand Unification Inflation ... ... wenn H = å/a ≈ const. Chiral phase transition Nucleon freeze out Electroweak transition Nuclear freeze out Atomic freeze out

Galactic freeze out 10-11 GeV (T = 2.726 K) Big Bang 10-43 s 10-35 s 10-12 s 1 s 105 y 109 y today

Time

…

t

History of the universe: a succession of phase transitions

TP NP AP FKP


n-decay rate: τ −1 = const (|gV|2 + 3|gA|2) = const GF2 |Vud|2 (1+3|λ|2)

Only 2 parameters needed: CKM matrix element Vud,

(GF from muon decay) ratio of c.c. λ = gA/gV

Only few Standard Model parameters in n-decay

… but many n-decay observables:

data? Hνn plus , ,, :spinelectron involving nscorrelatio n correlatio- tripleViolating-T

)11(238.0 31

4 0.2748 :asymmetry p

)4(981.0 31

)1(2 :asymmetryν

)13(1173.0 31

)1(2:asymmetryβ

)4(103.0 31

1 :correl. e

s 8)(885.7 ),31(const ratedecay

2

2e

2

2

2

e

22

ud1

...GNR,D,

C

B

A

a

V

problem is overdetermined: many tests of Standard Model


Standard model:axial to vector coupling c.c. λ = gA /gV CKM- matrix element |Vud| unitarity test of CKM-matrix Δ = Vud

2 + Vus2 + Vub

2 1 = 0 ?weak magnetism μp − μn

all ν - p, ... weak cross-sections σνp/Eν = 0.67·10−38 cm2/GeVnumber of ν-families Nν = 2.5(6)baryonic matter in universe ρ/ρcrit = 3.3(7) %

beyond Standard model:mass of right-handed boson m(WR) > 300 GeV/c2 (90% c.l.)left-right mixing angle 0.20 < ζ < 0.07 (90% c.l.)scalar weak interaction amplitudes gS

tensor weak interaction amplitudes gT

Fiertz interference amplitude bsecond class amplitudesneutrino helicity < 1? (semileptonic decays) T-viol. amplitudes ... and others

Aim: measure all these parameters to the highest precision possible

Many derived quantities from n-decay


. · · . · · . . . · · . . .

· . · . UCN

best measured with stored ultracold-neutrons ('UCN', Tn ~ 1mK)

short history:

neutrons 'in-beam': 1960: τ = (101030) s1982: τ = (92511) s

stored UCN: 1989: τ = (8883) s2004: τ = (885.70.8) s

N = Noexp(– t/τ)

→ decay rate: τ−1 = const × |Vud|2 (1 + 3λ2)

History of neutron lifetime τ

R. Picker, Mo Abend


History: λ = gA/gV:

derived from β-asymmetry A:

λ =gA/gV = −1.19 ±0.02 1960

= −1.25 ±0.02 1975

= −1.261 ±0.004 1990

= −1.2695±0.0039 2005

= −1.2739±0.0015 2006


-0,005

0,000

0,005

0,010

0,015V

ud from:

n: Nucl: :

DEVIATION FROM UNITARITY

upper row, combined: Δ = 0.0040 ± 0.0012

first column, with Vcd, Vtd:Δ' = 0.0015±0.0054

Unitarity tests of upper row of CKM matrix

upper row, with:

Vud= 0.9717±0.0013 nVud= 0.9740±0.0005 NucleiVud= 0.9728±0.0030 π

Vus= 0.21960±0.0023 KVub= 0.0036±0.0009 Bif Δ due to right-handed currents:

phase ζ = 0.0020 ± 0.0006

|Vud|2 + |Vus|2 + |Vub|2 = 1 − Δ Standard Model: Δ = 0

↑0.0000i.e. test of cos2θC + sin2θC

Aim: all entries in CKM matrix from particle decays


Nuclear super-allowed 0+→0+ β-transitions

2ud

2 VG

Kft

F

(plus corrections)

with half life t,

phase space factor f

J.C. Hardy, I.S. Towner,

PR C 71, 055501 (2005)

before nuclear corrections:

after nuclear corrections:

1σ band→

(from > 100 measurements)


new neutron lifetime measurement

1988 1990 1992 1994 1996 1998 2000 2002 2004 2006870

875

880

885

890

895

900

new value

Neutron Lifetime, recent results

all previous

neut

ron

lifet

ime

(s)

Year

reestablishes unitarity when using old Vus … Δ ≈ 0 ± 0.001


= by-product of ε'/ε-analysis:

2002↓ ↓2005

B.R. KL→ π e ν, π μ ν

reestablishes unitarity when using old τn:

PDG 2006, all measurements: Δ = 0.0008 (5)ud (9)us

Other strategy: assume unitarity to hold → strong-interaction physics

New Vus value


planned: PERC

bright: ~ 106 neutron-decays/sec/m of beam

clean: under well defined conditions:

spectral distortions ≤ 10−4, background/signal ≤ 10−4, …

versatile: vary width and divergence of emerging p+, e− beam

without change of spectral properties

collect charged decay products from within a long piece of cold n-guide:

n-guide = source of neutron decay products:

"Proton-Electron Radiation Channel" PERC

neutron puls in long piece of n-guide

B ~Tesla e−

p+


example for setup:

example: B0=2T, B1=8T, B2=½T:

count rates:6104 s−1 for a continuous unpolarized n-beam; 1104 s−1 for a continuous beam polarized to 98%; 3103 s−1 for a pulsed unpolarized beam;3102 s−1 for a pulsed beam polarized to 99.5%.

beam time for ~10−4 statistical error:½ h for continuous unpolarized, 3 h for continuous polarized,10 h for pulsed unpolarized, 4 d for pulsed polarized

10m

ILL user


Error budget of PERC (not all measurements sensitive to all errors) correction error

orifice: in units of 10−4

1. non-uniform neutron beam profile over orifice 0.6 0.2

2. finite thickness of orifice eliminated

3. electron escape from orifice 1 0.2

solid angle of p+, e− emission:

4. non-uniformity of B0-field 1 0.3

5. non-adiabatic variation of B1-field; adiabatic decoupling from B2-field 0.5 0.5 (M-C- req.)

background:

6. from neutron guide 4 1

7. from n-beam shutter, pulsed neutron beam non-existent

from n-beam shutter, continuous neutron beam 1 1 (exp. study req.)

8. from n-beam stop, pulsed neutron beam non-existent

from n-beam stop, continuous neutron beam 2 1

e−/p+ backscattering:

9. from beam window 1 0.2

10. from electron/proton beam dump 2 0.4

11. from electron/proton detector (user's responsibility) 6 1

neutron polarization:

12. polarisation measurement 5 5

13. depolarisation in non-magnetic supermirror guide ≤5

At present (for β-asymmetry A, total, D. Mund (2005)): present: 34 present: 39


magnetic mirror limits beam divergence:

θcrB0

example:

magnetic field: 2Tesla 8Tesla ½Teslagyration radius: 2mm ½mm 4mmcritical angle: 300 900 150

beam width can be traded against beam divergence, with negligible spectral distortion

B1

n-guide magn. mirror → to experiment

= 'keyhole'

B2

~10m


… of variable beam divergence:

guide field B0

magnetic mirror field

B1

high divergence

low divergence n-decay products


neutron beamstop:

Charged neutron decay products can be guided anywhere (electro-)magnetically

Example:

50 0 50 100 150 200zcm

7.55

2.50

2.55

7.510

xmc

MAGNETICFIELD LINES

↑ n-guide ↑ n and γ e and p ↑ absorbers

window frame

B0=2T B1=8T B2=0.5T

50 0 50 100 150 200zcm

7.55

2.50

2.55

7.510

xmc

MAGNETICFIELD LINES

↑ n-guide ↑ n and γ e and p ↑ absorbers window frame

B0=2T B1=8T B2=0.5T

cm

cm

Scale×10


EXAMPLES

a) e− spectroscopy (from pol., unpol. n's):

orifice energy sensitive detector

e−B2


b) magnetic p+, e− spectroscopy: MAGNETICSPECTROMETER

e−

B2 B3

window- ↑ frame p+

γ-shielding ↑ ↑ position- sensitive detectors

Fig. 6: Sketch of a magnetic spectrometer for neutron decay products installed at the end of the beam line.


c) aSPECT retardation spectrometer:

↑ aSPECT

↑orifice

p+


d) Mott scattering:

MOTT

SCATTERING

APPARATUS

↑orifice

e−

test of:

electron helicity He ~ υe/c in hadron decay


Error sources

thin orifice: no angular or spectral distortion of the p+, e− beam

B

n-guide

orifice→

1

0.

50

0.5

1LA

TER

AL

POSI

TIO

Nxx 2

0.2

0.4

0.6

0.81

T e

FRA

ME

TR

AN

SMIS

SIO

N

Transmission profile of the absorbing frame:

thin orifice: in 1st order no edge effect


2nd order error sources of orifice:

1. neutron beam not uniform over edge of orifice:

error 6·10−5 at Eβmax for 10% change of n-flux over 1cm width

2. particles hit inner face of orifice:

solution: oblique edge angle >θ2

3. non-perfect absorption near edges: error 4·10−3 × 0.1 "active edge"

N.B.: electron scattering effects can be calculated reliably to better than 10%

2mm


b) effect of mag. mirror field B1 on p+, e−:

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

A/A

0

c) ASYMMETRY

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

NA

2

d) EFFICIENCY

0 0.2 0.4 0.6 0.8 10

20

40

60

80

c0

a) CRITICAL ANGLE

0 0.2 0.4 0.6 0.8 1B0/B1

0

0.2

0.4

0.6

0.8

1

N/N

0

b) COUNTRATE

B0/B1

B0/B1 B0/B1

neutron decay data are useful

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