Neutron Physics - Brookhaven National Laboratory decay rate of K,B mesons ⇒Unitarity of CKM matrix...
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Transcript of Neutron Physics - Brookhaven National Laboratory decay rate of K,B mesons ⇒Unitarity of CKM matrix...
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
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
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)
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)
`
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
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)
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
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?
♦ 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