Particle Physics with Slow Neutrons

Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner

Particle Physics with Slow Neutrons

• I: Neutrons in the Standard Model

• II: Neutrons beyond the Standard ModelRight-handed currentsCP violationBaryon number violation

• Valery Nesvizhevsky: Gravitationally bound quantum states of neutrons: applications and perspectives


I: Neutrons in the SM

• IntroductionThe neutron and its interactionsCold and ultracold neutrons

• Neutron decay in the Standard ModelTheoretical description and

observablesNeutron lifetimeNeutron lifetime and astrophysicsBeta asymmetryUnitarity of the CKM matrix


Passport of the neutron

• Mass mn = 1.001 378 418 70(58) mp

= 939.565360(81) MeV• Charge q = 0.4(1.1)·10-21 e• Spin = ½ ħ• Magnetic moment n = 1.913 042 73(45) N

= 6.030 774 0(14)·10-8 eV/T• Electric dipole moment dn 0.63 ·10-25 e·cm• Life time = 885.7(8) s• Decay modes np e e 100%

np e e 10-3 (to be detected)nH e 4·10-6 (to be detected)

n

eep


Fermi Pseudopotential

• Fermi pseudopotential

coh absib b b 2

0n

2( ) ( )V b

m

r r r n

2

0n

2( ) ( ) ( ) ( )j j

j

V b u x dm

r r r

d~1Å

V10-7eV

Potential of wall

2

12

bn

• Index of refraction

Storage of ultra cold neutrons in material bottlesNeutron guide


Neutrons and Interactions

Strong/nuclear

Weak Gravitational

Kinetic energy: 10-7eV for 4m/s

Electromagnetic

nV μ B

Magnetic moment

magnetic scattering

magnetic potential

10-7eV for 1.7T

3 He( , )n p t( , )Dp n

0 ( )V u x

absorption

scattering

Fermi potential

O(10-7eV)

en p e 6 Li( , )n t

Decay

P asymmetry

nV m gh

Mass

gravitational potential

10-7eV per m


Ultra Cold Neutrons

Magnetic potential

nV μ B

10-7eV for 1.7TO(10-7eV)

Fermi potential• Storage

Let them fall down!

(10-7eV per m)• Detection

100Å, 100neV, 1mK, 5m/s, 10cm-3

Neutrons with less than ~ 10-7 eV

2

n

2( )V b x

m


Cold Neutrons

• Transport

B

0 2 4 6 8 10 12 14 16 18 20-0,950

-0,955

-0,960

-0,965

-0,970

-0,975

-0,980

-0,985

-0,990

-0,995

-1,000

Pol

ariz

atio

n

Neutron wavelength (A)

<P> = (99.72 +/- 0.10)% p0 5.5 Bar p1 4.0 Bar p2 2.1 Bar p3 1.5 Bar p4 1.0 Bar p5 0.67 Bar

Spectrum

(99.7 0.1)%P

3-10Å, 10meV, 30K, 1000m/s, 104cm-3

V10-7eV2

12

bn

10-7eV

FermiVV μB

V

10-7eV

10-7eV

• Polarisation

(same for UCN)


Neutrons at Reactors

From fission to ultra cold neutrons:235U+n2 FF + (2-3) n + 200MeV

Fast n: > 1MeV

Intermediate: 1MeV … 1eV

Slow: < 1eV

epithermal: 1eV … 25meV

thermal: 25meV

cold: 25meV … 50eV

very cold: 50eV … 200neV

ultra cold: <200neV

235U

n 2MeV

ν β

γ

γβ

ν

235Un 0.1eV

235Un

n

10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10010-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

W(E

n)

En [eV]

T30K T293K

UCN Very cold Cold ThermEpitherm

30K

300K


Inside the ILL Reactor

1 m

ILL7H9

H8

H6

IH4

H5IL

L22

H4

H2

IH3

H3

H1

H12

H13

IH1

H10

H11 H

7

VCS

HCS

HSIH

2

thermal

cold

hot

D2OH2O

IH inclined tube


Institute Laue Langevin: A Neutron User Facility


Semileptonic Processes in the SM

eeu

d

W

2W

2 2W

q qM

g

q M

• Propagator for W boson

5e

1

22

ge

• SU(2)L (V-A) structure of weak interaction

51

22

gu d

• Quark mixing: weak and mass eigenstatesmassmassmassweak bVsVdVd ubusud

0%

50%

100%

'down' 'strange' 'bottom'

down strange bottom

2udgV

en p e


Weak coupling constant, Vud

2 2

W5 5 e2 2

W

1 18

ud

q qM

g

q M

g Vu d e

qM W eeu

d

W

2F

2W82

G g

M

F5 5 e1 1

2ud

GV u d e

d

eeu

e55F 112

eG

eeμ

W

eeμ

F5 5 e1 1

2udu eV

Gd


Complication: Neutron ≠ Quarks

F5 5 e1 1

2ud

GH V u d e

n

eep

A

V

g

g 5 e

nF

p5

p

21 1

2ud

GH p n eq

mV

d

eeu

u d

u d

d

eeu 5| 1 |p u d n

2

WM2 2

pV Si i

2V p q q ng q

m

g qg q

2A

2

5 5p

T 2P 5i i

2

g qg qA g qp q q n

m

WM p

P

n

S

A

T

V vector 1

axial vector 1.

winduced scalar 0

induced tensor 0

eak magnetism

induced pseudosca ar

26

l 0

g

gg

g

g

g


Measurement of and Vud

3.3d

d

26.1

a

4.13d

d

26.1

B

6.2d

d

26.1

A

V

A

g

g F

5 5 e1 12

ud

GH p n eV

3 7

R 5 4 2 2 2e F

2 1 1

1 3udf m c GV

Neutron lifetime:

EED

EB

EA

EEaEG

E

W

e

e

e

e

n

n

e

eee

ee

1)(ddd

d ppppσpp

2

2

1

1 3a

2

12

1 3B

2

12

1 3A

J.D. Jackson et al.: Phys. Rev. Lett. 106 (1957) 517

Angular correlation in the decay:


The Neutron Lifetime

Beam

• Detecting decay products along beam section

neutron number

rate of decay particles

N

N

t( ) (0)exp -N t N

e

N

N

Storage

• Detecting surviving neutrons after storage

( )ln

(0)

tN tN

3e n( , ) ( )d

EE r

N

r r

0 100 200 300 400 500 600 700 8000,0

0,2

0,4

0,6

0,8

1,0

1,2

Trig

ger

Effi

cien

cy

Ge(E

e)

Ee [keV]

• Problem: Combination of absolute measurements, solid angle…

storage loss,

1 1 1

i i

n

loss( )

wall collisionE

• Problem: Losses

• Problem: Losses energy dependent, spectrum changes


Neutron Lifetime Beam Experiments

p peff

α 0 n,0

1NL

N v

Penning trap fordecay protons

Neutronmonitor

n

U

0V

800V

L800V 800V

U

0V

800V

L800V 800V

p p

α 0 n,0end

1nl L

N

N v

effL

p

p

α eff

0 n,0

1 rate of decay particles

neutron number

N

N Lv


Neutron Lifetime Beam Experiments

Source Cor Err

Neutron density (6LiF foil area density, 6Li cross section, solid angle, halo, …)

+5.5 3.0

Trap nonlinearity -5.3 0.8

Proton backscatterer calc. 0.4

Proton counting statistics 1.2

Neutron counting statistics 0.1

Total +0.2 3.4M.S. Dewey et al.: Phys. Rev. Lett. 91 (2003) 152302

10ms proton trapping76s proton counting

Background suppression

= (886.8 1.2 3.2) s

(0.4% precision)


Storage in Material Bottles – Losses

Wall collision2 2

2n

i 02

Vt m x

exp ip

x 22

expmV p

x

V

(20nm)

x

Upscattering

H atom•Same mass•Large scattering cross section

Wall, T 100KUCN, T 1mK

Other atoms

Dust

Coherent interaction with wall

Lost

Heated

Heated

Storage Loss

1 1 1

1

v

L 4

VL

S

Losses per collision

Effective collision rate

Variation of v (spectrum) or L (bottle size)

Extrapolation to = 0

abs A abs

510

p N

– Absorption


Example – MAMpe BOttle

0 10 20 30 401.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Sto

r-1 *

100

0 [

s-1]

[s-1]

Storage

11

A. Pichlmaier, PhD Thesis, TU München (1999)


Systematic Effects…

• Faster neutronsmore wall collisionsfaster losses

• Small energy changes

Spectrum changes during storage

Storage time not constant

Storage

1 1

• Surface properties really stable? (especially for liquid surfaces)

• Vacuum equal/constant?

• Temperature of surfaces

• Neutron detection efficiency size-dependent?

• Gravity corrections?

Extrapolation linear?


The Smallest-Stated-Error Neutron Lifetime Measurements

Effect Cor Err

Volume dep. of UCN detect. efficiency -3.10 0.36

Spectral change dep. of UCN detect. effi 0.3

Time dep. of upscattering due to spectrum change

0.2

Volume dep. of thermal neutron detect. effi +0.6 0.3

UCN scattering on residual gas 0.2

Epi-Fomblin neutrons in UCN spectrum 0.2

Temperature gradients in UCN bottle 0.15

A. Serebrov et al.: Phys. Lett. B 605 (2005) 72

= (885.4 0.9 0.4) s

(0.1% precision)

= (878.5 0.7 0.3) s

(0.1% precision)

Effect Cor Err

Statistics 0.7

Calculation of collision rate 0.24

Energy dependence of losses per collision 0.14

UCN spectrum uncertainties 0.10

Trap size uncertainties 0.06

UCN scattering on residual gas 0.4 0.02

Uncertainty in the LTF Fermi potential 0.004

S. Arzumanov et al.: Phys. Lett. B 483 (2000) 15

5.6


History of Neutron Lifetime

World average [PDG]

Last (single)measurement


Magnetic Storage

• No surface interactions• Losses by spin flips,

easier to detect than in material bottles

• Losses still energy dependent

nV μ B

10-7eV for 1.7T

nF μ B

Best magnetic storage experiment

= (877 10 ) sW. Paul et al.: Z. Phys. C 45 (1989) 25

max 00

1R

E Br

2

00

rB B

r

max 0E B


Magnetic Storage – Present Project

First test run (2003):

= (882 16 ) sA.Z. Andreev et al.: ILL Annual Report (2003) 92


Neutron and Astrophysics 1: Big Bang NucleosynthesiskT

[M

eV]

t [s]

d destroyed by (kT < 2.2MeV,

but N / NB 109)

en p e

n

p

1

7

N

N

decay rate

1 200

en e p en p e

2n

p

expN m c

N kT

reaction rate

1

0.1

3

3 4

DD He

He He

n ppn

He

tot p n

n2

4 NM

M N N

4He formation

Freeze-out if Hubble expansion rate greater than

reaction rate

n

p

1

6

N

N

Tf

important for primordial 4He content in Universe

Depends on baryon density NB/N = 101010

Historical: First estimate of number of light neutrino families

(important for cooling down)N = 2.6 ± 0.3


Neutron and Astrophysics 1: Big Bang Nucleosynthesis

• Other primordial elements (D, 3He, 7Li) depend stronger on nuclear reaction rates

• Baryon density NB/N = 101010 can be derived from BBN – consistent?

• Consistent with CMB data?


Neutron and Astrophysics 1: Big Bang Nucleosynthesis

• Other primordial elements (D, 3He, 7Li) depend stronger on nuclear reaction rates

• Baryon density NB/N = 101010 can be derived from BBN – consistent?

• Consistent with CMB data?

Influence of : Shift by 9 (1%) = 885.7(8)s Yp = 0.2479(6) = 878.5(8)s Yp = 0.2463(6)

Observed: large systematic uncertainties,Yp = 0.238(2)(5), Yp = 0.232 … 0.258, …

878.5(8)s

885.7(8)s

G.J. Mathews et al.: Phys. Rev. D 71 (2005) 021302


Neutrons and Astrophysics 2: Solar Cycle, Neutrino Production

e

(Pauli)

Dp p e

Solar luminosity fusion rate T, gA2

Can derive T

3D Hep

2Ag

3 3 4He He He 2 p 85%

3 4 7

7 7e

7 4

He He Be

Be Li

Li 2 He

e

p

0.02%

7 8

8 8 *e

8 * 4

Be B

B Be

Be He

p

e

15%

gA, gV still important for neutrino detection

8B production strongly T dependent, rate gA5

Wrong gA5 responsible for to low 8B-e rate?

No, would require = 800s


Neutrons and Neutrinos: Reaction Cross Sections

e p n e 1

e D n n e 2Ag

e D p p e 2Ag

Charged current

Charged current(SNO, electron detection)

Charged current

NDerive nucleon-neutrino cross section


Vud and the Beta Asymmetry

EED

EB

EA

EEaEG

E

W

e

e

e

e

n

n

e

eee

ee

1)(ddd

d ppppσpp

3 7

R 5 4 2 2 2e F

2 1 1

1 3udf m c GV

2

2

1

1 3a

2

12

1 3B

2

12

1 3A

-1,30 -1,28 -1,26 -1,24 -1,22 -1,200,08

0,09

0,10

0,11

0,12

0,13

0,97

0,98

0,99

1,00

1,01

1,02

|B|

|a|

|a|,

|A|

|A|

|B|

Need to measure beta asymmetry A


Unitarity of Quark Mixing

1 0.0076(28) (2.7 )

1 0.0031(14) From 0+0+ decays: (2.2 )

1!

:222 ubusud VVV

0%

50%

100%

'down' 'strange' 'bottom'

down strange bottom

Uncertainties for neutron may be higher (new lifetime exp.!)New results from Vus could restore agreement

If really new physics:•More quark generations•additional Z boson•right-handed W bosons•coupling to exotic fermions•Supersymmetry Experimental side not settled!

H. Abele et al.: Eur. Phys. J. C 33 (2004) 1

Neutron decay (APerkeo II, n):


Vud

H. Abele et al.: Eur. Phys. J. C 33 (2004) 1

Process Disadvantage Vud

Neutron beta decay gA and gV needed

(or A and )

0.9717(13) Error from A dominates

0+0+ (10C, 14O, 26mAl, 34Cl, 38mK, 42Sc, 46V, 50Mn, 54Co)

Nuclear structure effect corrections

0.9740(5) Error theory-dominated

Pion beta decay Small branching ratio

0.9771(56)

Global fit to angles and phase Assumes CKM unitarity

0.9741 – 0.9756

Theory error: Radiative correctionsEnter in neutron decay and 0+0+

For pion decay theory error factor 2 smaller


Beta Asymmetry A – How to measure

e

e1dE

AWp

P

n e1 A σ p

A = -0.1173(13)

e

e

N NA

N

F

EN

Pp

•Solid angle?•Polarisation / Flipping?•Energy calibration?•Background?

1 2

1 2

N NkA

N N

N NkA

N N

0 200 400 600 8000 -0,14

-0,12

-0,10

-0,08

-0,06

-0,04

-0,02

0,00

A

N2

W d

Ee [a

.u.]

Ee [keV]

N1

A


Beta Asymmetry A - Experimental Situation

e

e

1

2

N NA

N N

F

E

PpSolid angle Polarisation

B

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

[A]

Single Analyzer Crossed Analyzer

(99.7 0.1)%P M. Kreuz et al.: NIM A 547 (2005) 583

e

e

1

2

N N pAFP

EN N

Energy calibration

207Bi

113Sn

137Cs

109Cd

Background• Decay prob.: 10-7

• Scattering : ~10-3 , fast n: ~10-4

• Ee E


Beta Asymmetry A – Perkeo II

Effect Cor % Err % Cor % Err % Polarisation analysis Polarisation efficiency Flipper efficiency

1.1 0.3

0.3 0.1

0.3 0.1

Data set Statistics Background

0.5

0.45 0.25

0.1

0.31 0.1

Detector response function 0.25 0.13 Other corrections 0.18 0.05 0.06 0.13 Sum 2.04 0.66 0.34 0.39

1997 2004 (prelim)


Summary – Neutrons in the Standard Model

• Two parameters of the Standard Model from neutron decay: Vud and

• Observables: Lifetime and correlation coefficients

• Difficult measurements: Low energies, slow decay, … clever ideas for experiments needed

– extrapolation techniques – relative measurements – use of magnetic fields

• Input parameter for solar cycle, BBN

• Test of CKM unitarity

Particle Physics with Slow Neutrons

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