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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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)
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
Institute Laue Langevin: A Neutron User Facility
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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:
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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)
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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)
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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?
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
History of Neutron Lifetime
World average [PDG]
Last (single)measurement
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
Magnetic Storage – Present Project
First test run (2003):
= (882 16 ) sA.Z. Andreev et al.: ILL Annual Report (2003) 92
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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?
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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):
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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)
Particle Physics with Slow Neutrons I LNGS Summer Institute, September 2005 Torsten Soldner
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