W. M. SnowPhysics DepartmentIndiana UniversityNPSS, Bar Harbor

Neutron Physics

5 lectures:

1. Physics/Technology of Cold and Ultracold Neutrons2. Electroweak Standard Model Tests [neutron beta decay]3. Nuclear physics/QCD [weak interaction between nucleons]4. Physics Beyond the Standard Model [EDM/T violation]5. Other interesting stuff that neutrons can do [NNN interaction, searches for extra dimensions,…]

SM Tests with Neutron Decay

1. Some facts about the weak interaction2. Connection with Big Bang Theory3. Neutron Decay: description4. Lifetime and T-even correlation coefficients5. Searches for T-odd correlations

Thanks for slides to: K. Bodek (PSI), H. Abele (Heidelberg), Chen-Yu Liu (LANL), Paul Huffman (NC State), Takeyasu Ito (Tennessee/ORNL)

Neutron β-decay

Clean extraction of fundamental parameters at the charged current sector of the electroweak theory.

Combine:

♦ Neutron lifetime + β-asymmetry + µ lifetime ⇒ GF, Vud, gA

♦ Weak decay rate of K,B mesons ⇒ Unitarity of CKM matrix

Why is neutron decay interesting forCosmology?

t~1 sec after Big Bang, neutrons and protons are free (no nuclei). Relative number~Boltzmann factor, kept in equilibrium by weak interactions.

Universe expands and cools. Weak reaction rates fall below expansion rate->neutrons start to decay, proton # goes up

t~few minutes, universe cool enough to bind the deuteron->neutrons are safe again

Nuclear reactions quickly guide almost all neutrons into 4He

BBN Predictionsfor lightElements inEarly Universe(pre-WMAP)

PredictionsFor 4Hewith differentneutino #Width due toneutronlifetime

Lopez/Turner 01

Neutron/Nuclear Beta Decay: What is it Good For?

Now gives the best/comparable constraints on certain forms of:

(1) new T-even V,A charged currents (from L-R symmetric, exotic fermion, leptoquark, R-parity-violating SUSY, and composite models(2) New T-odd V,A charged current interactions (from leptoquark models)

Can soon give the best/comparable constraints on:

new T-odd scalar charged current interactions (from extra Higgs, leptoquark, composite, and some SUSY models)

Can soon give the best measurement of Vud

P. Herczeg, Prog. Part. Nucl. Phys 46 (2001).

The weak interaction: just like EM, except for a few details…

3 “weak photons” [W+, W-, Z0], can change quark type

e- e-

e- e-

γ

one EM photon

e- e-

e-

Z0

e-

u d

u

W+-

d

V(r)=e2/r, mγ=0 ‘V’(r)≈[e2/r]exp(-Mr) , MZ,W≈ 80-90 GeV

“Empty” space (vacuum) is a weak interaction superconductor

|B|

vacuum superconductor

penetration depth

r

weak field

our “vacuum”

1/ MZ,W

r

The weak interaction violates mirror symmetry and changes quark type

u e

ν

W+-

d

Only the weak interaction breaks mirror symmetry: not understood

weakinteraction = eigenstates

[CKM]∗ quark mass eigenstates

Vud in n decayMatrix must be unitary

r->-r in mirror, but s->+s

The Quark Mixing CKM MatrixThe Quark Mixing CKM Matrix

Parametrization: 3 angles, and a phase

A, ρ, η are real

The Quark Mixing CKM Matrix

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

′′′

bsd

Ubsd

CKM

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

=

VVVVVVVVV

tbtstd

cbcscd

ubusud

U CKMd

WVud

eν |Vud|2 + |Vus|2 + |Vub|2 = 1-∆

Vud from

•Nuclear beta decay Vud=0.9740(5), 2.3 sigma•Pi beta decay Vud=0.9717(56)•Neutron beta decay

Vud from

•Nuclear beta decay Vud=0.9740(5), 2.3 sigma•Pi beta decay Vud=0.9717(56)•Neutron beta decay

Vus from

•Hyperon decays•K decays

Vus from

•Hyperon decays•K decays

ud

d

u ud

u u

νν

νµµν

µ γγγγ Ψ−Ψ⋅−

−

⋅Ψ−Ψ⋅= )1()1(8gT 522

2

5

2

fi ew

wduud mk

mkkg

V

Matrix element for d-u transition: µ

µ

νµ

µ γγγγ

lhud

eduud

JJV

V

⋅≡

Ψ−Ψ⋅Ψ−Ψ⋅=

2G

)1()1(2

GT

F

55F

fi

nPp

TAp

nsp

MVp

kkigkm

kgkgiA

kkigkm

kgkgiV

Ψ++Ψ=

Ψ++Ψ=

])(2

)()([

])(2

)()([

52

5

2

52

22

2

γγσγγ

σγ

µν

µνµµ

µν

µνµµvector- and axial vector currents:

V

Aud

F

enp

npp

Vint

ggaAVVG

km

GL

=−+⋅=

Ψ−Ψ⋅Ψ−

++Ψ⋅=

λλ

γγσµµ

λγγ

µµµµ

νµν

µνµ

).)((22

1

)1()2

)1((22

155

v

Lagrange function for neutron decay:

Formalism

CKM Unitarity/Standard Model Tests

Vud from Neutron and Nuclear beta decay

λ=GA/GV

Perkeo result:A0 = -0.1189(7)λ = -1.2739(19)

τn = (885.7 ± 0.7) sworld average

τn = (878.5 ± 0.7st ± 0.3syst) s“Gravitrap” result

♦ Withδc: Coulomb (isospin) correctionδR: nucleus-dependent radiative

correction∆R: nucleus-independent

radiative correction

Superallowed β-transitions

Ft0+→0+=3072.3(9)s Vud=0.9740(5) Towner, Hardy 4 Sept 2002Ft0+→0+=3072.3(9)s Vud=0.9740(5) Towner, Hardy 4 Sept 2002

PDG:Vud=0.9740(10)PDG:Vud=0.9740(10)

)1(2

)1)(1(

2200

00

RudF

Rc

VGkFt

ft

∆+=

≡−−++

++

→

→ δδ

2.5 sigma deviation from unitarity !!2.5 sigma deviation from unitarity !!Nucl-th/0209014Nucl-th/0209014

Pion β-decayπ+ →

µ+ν (1.0)µ+νγ (∼ 2.0 x 10−4)e+ν (∼ 1.2 x 10−4)e+νγ (∼ 1.0 x 10−8)

♦ Br = 1.025(34) .10-8

♦ τπ=2.6033(50) .10-6s

πτδ )1()1(2)νeππ()2ln/(

21

02

RRF

eud fffG

BrKV+∆+

→=

++

Vus=0.9670±0.0160Br ± 0.0009=0.967 ± 0.016Vus=0.9670±0.0160Br ± 0.0009=0.967 ± 0.016

CKM Workshop, HD, September 2002:Br ~ 1.044 ± 0.007syst± 0.009systx 10-8

PIBETA : Vud = 0.9771(51) (Pocanic, Ritt)

CKM Workshop, HD, September 2002:Br ~ 1.044 ± 0.007syst± 0.009systx 10-8

PIBETA : Vud = 0.9771(51) (Pocanic, Ritt)

Vus

♦ Kaon semileptonic decays– K+→π0l+νl

– K0L→π-l+νl s→ul+νl

∆ = (2.12±0.08%), δ = -2.0% for K+ and 0.5% for K0

)1)(1()0(π192

21

253

2

RkusF IfCm

VG∆++=Γ δ

Vus = 0.2196 ± 0.0017exp ± 0.0018th= 0.2196 ± 0.0026 (PDG 2002)

Vus = 0.2196 ± 0.0017exp ± 0.0018th= 0.2196 ± 0.0026 (PDG 2002)

70000 events

Vud from neutron β-decay

)1()31( 221R

Rud fVC ∆+⋅+=− λτ

)8(0240.0),15(71335.1

,101613.1)2/( 14322

=∆=

⋅== −−

RR

eF

f

smGC π

)13(9717.0

)19(2739.1),7(7.885

=

⇒==

udV

λτWilkinson 1982, CKM Workshop September 2002:Marciano et Sirlin

Wilkinson 1982, CKM Workshop September 2002:Marciano et Sirlin

Radiative Correction ∆R

♦ ∆R = α/(2π)[4ln(mz/mp) + ln(mp/mA)

+ 2Cborn] + ...

♦ ∆R = (2.12 - 0.03 + 0.20 + 0.1)%

= 2.40(9)%

Neutron β-decay lifetime

♦ Cold Neutron beam experiments:– Absolute measurements of the neutron number and the decay

particle flux.

♦ Bottled UCN: – Ratio of the neutrons stored for different periods. It is a relative

measurement.– Material bottle -- Mampe (887.6 ± 3 s)

• Wall loss depends strongly on the UCN spectrum.• Systematically limited.

– Magnetic bottle -- hexapole bottle (876.7 ± 10 s), NIST bottle.• Statistically limited.

τ β = N0 /Nd

•

N(T) = N0e−T /τ β ⇒ τ β = T

ln(N0 /N(T))

The best results for neutron lifetime

N beam♦ 889.2±4.8 (Sussex-ILL,

1995)♦ 886.8±1.2±3.2 (NIST,

2004)

♦ Particle data (2003 without PNPI-ILL,2003 & NIST,2004):

♦ τn = (885.7±0.8) s

UCN storage♦ 878.5±0.7± 0.3 (PNPI-

ILL,2004)♦ 885.4±0.9±0.4 (KI-ILL, 1997) ♦ 882.6±2.7 (KI-ILL, 1997) ♦ 888.4±3.1±1.1 (PNPI, 1992) ♦ 887.6±3.0 (ILL, 1989)

`

In-Beam Neutron Lifetime Experiment

In-Beam Lifetime Apparatus

Trapping and detection volume

Acrylic lightguide

Dilution refrigeratormixing chamber

Silver sinteredheat exchangers

77K shieldInner vacum chamber

Superfluiudhelium

heat link

Ioffe type magnet assembly

Liquid helium bath

n

Liquid nitrogen bath

1 meter

Neutron Lifetime Using UCN Magnetic Trap in Superfluid 4He

Goal: 0.1 second precision, 1 order of magnitude improvement

Neutron lifetime τ usingmagnetictrapping

Huffmann et al., Nature

Expression for Neutron Decay Correlation Coefficients

)](1[

)( 20

ee

ee

e

e

ee

en

e

e

e

e

eeeeeee

EpR

EEppD

EpB

EpA

Emb

EEppa

dddEEEEpddWdE

σσ

σν

νν

ν

ν

ννrrrrrr

rrr

×+

×+++++×

ΩΩ−≈ΩΩ

11% -11% 97% SM: 0

βν correlation

βν correlation ν

asymmetryν

asymmetrytriple

correlationtriple

correlationβ asymmetry

β asymmetry

Triplecorrelation

Triplecorrelation

SM: 0

Neutron β decay A Coefficient

♦ Neutron spin – electron momentum angular correlation

♦ Sensitive to GA/GV=λ♦ Important input for determining CKM

element Vud from neutron

Rn

VRF

VRF

Vud

fK

G

GGV

)31()1(1

)1(

22

2

22

λτ +∆+=

∆+=

T-even Angular correlations for Polarized neutrons

Electron

Proton

Neutrino

Neutron SpinA

B

C Observables in neutron decay:

Lifetime τSpinMomenta of decay particles

Observables in neutron decay:

Lifetime τSpinMomenta of decay particles

A Correlation

Coefficient A and lifetime τdetermine Vud and λ

Electron

Neutron SpinA

Electron Neutron SpinA

W(ϑ)=1+v/cPAcos(ϑ)

231)1(

2λ

λλ+

+−=A

⇓⇑

⇓⇑

+−

=NNNNAexp

on flipper spin with spectrum electron

off flipper spin with spectrum electron

:N

:N⇓

⇑

)31(sec44908V 2

2ud λτ +⋅

±=

Principle of A-coefficient Measurement

B fieldDetector 1 Detector 2

Polarized neutron Decay electron

θβ cos)()()()()(

21

21exp AP

ENENENENEA ≈

+−

=

(End point energy = 782 keV)

n

eθ

dW=[1+βPAcosθ]dΓ(E)

Decay Asymmetry Apparatus PERKEO (Abele et al)

UCNA Experiment: Beta asymmetry

Goal: measure A to 0.2% or better with UCN.

R = R0(1+ v /c)PA(E)cosθ

β-asymmetry = A(E) in angular distribution of decaying e-

from polarized neutrons

A = −2λ(λ +1)1+ 3λ2 = −0.1162 ± 0.0013( )

λ = gAgV

= −1.2670 ± 0.0035( )

T. J. Bowles, A. R. Young, et al.

Neutron Polarization Using UCN♦ Can obtain > 99.9% polarization using µ•B potential

wall for wrong spin UCN

♦ A number of methods to measure “depolarization” —only modest accuracy is needed when the polarization is high

♦ Polarization goal: >99.9%

Br

nµr

Experiment DesignNeutron Absorber

Angular correlations in neutron decay with T Violation

Angular distribution with explicit dependence on electron spin contains 4 T-odd observables (lowest order):

D : T-odd P-evenR : T-odd P-oddV : T-odd P-oddL : T-odd P-evenN : T-even P-even

σe

pepν

Pp

Jn

( ) ( ) ( ) ( )⎥⎦

⎤⎢⎣

⎡⋅+

⋅×+

⋅×+

⋅×+

⋅×++

⋅ΩΩ⋅−∝ΩΩ⋅

νν

νν

nepeenepneenνe

eeeeeee

JσPσpJσPJσpJpp N

EEL

EV

ER

EED

dddEEEEpdddEW

eeee

K1

)( 20

T-invariance +neglect of FSE ⇒ D, R, V, L = 0

Angular correlations in neutrondecay with T Violation

D and R are sensitive to distinct aspects of T-violation:

( )

( )

( )

⎟⎠⎞⎜

⎝⎛ ++++⎟

⎠⎞⎜

⎝⎛ +++=ξ

+−−++

+

++

=ξ⋅

+−+−+

=ξ⋅

2'2'2222'2'222

*''**''*

*''*2

'*''*'**

Im21

Im21

1

Im21

ATATGTVSVSF

TVTVASASGTF

AATGT

AVTSAVTSGTF

CCCCMCCCCM

RCCCCCCCCI

IMM

CCCCI

MR

DCCCCCCCCI

IMMD

T

FSI

FSI

D is primarily sensitive to the relative phase between V and Acouplings.

R is sensitive to the linear combination of imaginary parts of scalarand tensor couplings.

The R-correlation for neutron decay

♦ Transverse electron polarization component contained in the plane perpendicular to the parent polarization.

♦ Not measured for the decay of free neutron yet !

⎟⎟⎠

⎞⎜⎜⎝

⎛ +≡⎟⎟

⎠

⎞⎜⎜⎝

⎛ +≡

A

TT

A

SS

CCCT

CCCS

''

Im;Im

TSR ⋅+⋅= 33.028.0

1,,,,26.1Re

,1Re,3,1'''

'

<<−===

=====

TTSSAAA

VVVGTF

CCCCCCC

CCCMM

( )( ) ( )[ ]22

'*'**

3

2Im

AV

SSATTAV

CCCCCCCCCR

+

++++=

One obtains finally:

♦ T-violation in n -decay may arise from:– semileptonic interaction (d→ue-νe)– nonleptonic interactions

♦ SM-contributions for D- and R-correlations:– Mixing phase δCKM gives contribution which is 2nd order in

weak interactions:< 10-10

– θ-term contributes through induced NN PVTV interactions:< 10-9

♦ Candidate models for scalar contributions (at tree-level) are:– Charged Higgs exchange– Slepton exchange (R-parity violating super symmetric

models)– Leptoquark exchange

♦ The only candidate model for tree-level tensor contribution (in renormalizable gauge theories) is:– Spin-zero leptoquark exchange.

Where could it come from?

R-correlation measurements in Nuclei

1st order “Final State Effect”contribution

♦ In the SM:

A = -0.1173(13)

= 0 :

Anticipated accuracy: ∆R (neutron) ≈5×10-3

♦ Needed:– Intense source of highly polarized, free neutrons– Efficient polarimetry for low energy electrons (200-800 keV)

♦ Best combination:– Polarized cold neutron beam: Ndecay ≈ 2 cm-3s-1

– SMott ≈ 0.4 ÷ 0.5

Experiment

Difficulties:o Weak decay source in presence of high background due to neutron

capture.o Depolarization of electrons due to multiple Coulomb scattering in detectors

and Mott target.

Principle of measurement♦ Tracking of electrons in

low-mass, low-ZMWPCs

♦ Identification of Mott-scattering vertex.

♦ R-correlation: asymmetry for events in the plane parallel (ϕ= 0) to the neutron polarization.

♦ Frequent neutron spin flipping.

♦ „Foil-in” and „foil-out”measurements.

Current Situation in Neutron Decay

Lots of experimental activity to measure Vud in n decay, Vus in K decay with higher accuracy to test CKMunitarity

Many correlation coefficients are accessible experimentally,can be used to search for beyond SM physics

New experimental techniques/sources are available