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Stefan Baeβler
The measurement of neutron beta decay
observables with the Nab spectrometer
1 Inst. Nucl. Part. Phys.
The neutrino electron correlation coefficient 𝒂
2
𝑑Γ ∝ 1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 + 𝑏𝑚𝑒
𝐸𝑒
n
e-
𝜈𝑒
p 𝜃𝑒𝜈
Novel approach to determine cos 𝜃𝑒𝜐:
Kinematics in Infinite Nuclear Mass Approximation:
1. Energy Conservation: 𝐸𝜐 = 𝐸𝑒,𝑚𝑎𝑥 − 𝐸𝑒,𝑘𝑖𝑛
2. Momentum Conservation:
𝑝𝑝2 = 𝑝𝑒
2 + 𝑝𝜐2 + 2𝑝𝑒𝑝𝜐 cos 𝜃𝑒𝜐
The neutrino electron correlation coefficient 𝒂
2
𝑑Γ ∝ 1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 + 𝑏𝑚𝑒
𝐸𝑒
n
e-
𝜈𝑒
p 𝜃𝑒𝜈
𝐸𝑒,𝑘𝑖𝑛 = 450 keV
1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 𝑝𝑝2
pp2 [MeV2/c2]
pp
2 d
istr
ibuti
on
0.0 0.5 1.0 1.5
Novel approach to determine cos 𝜃𝑒𝜐:
Kinematics in Infinite Nuclear Mass Approximation:
1. Energy Conservation: 𝐸𝜐 = 𝐸𝑒,𝑚𝑎𝑥 − 𝐸𝑒,𝑘𝑖𝑛
2. Momentum Conservation:
𝑝𝑝2 = 𝑝𝑒
2 + 𝑝𝜐2 + 2𝑝𝑒𝑝𝜐 cos 𝜃𝑒𝜐
The neutrino electron correlation coefficient 𝒂
2
𝑑Γ ∝ 1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 + 𝑏𝑚𝑒
𝐸𝑒
n
e-
𝜈𝑒
p 𝜃𝑒𝜈
𝐸𝑒,𝑘𝑖𝑛 = 450 keV
1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 𝑝𝑝2
pp2 [MeV2/c2]
pp
2 d
istr
ibuti
on
0.0 0.5 1.0 1.5
Novel approach to determine cos 𝜃𝑒𝜐:
Kinematics in Infinite Nuclear Mass Approximation:
1. Energy Conservation: 𝐸𝜐 = 𝐸𝑒,𝑚𝑎𝑥 − 𝐸𝑒,𝑘𝑖𝑛
2. Momentum Conservation:
𝑝𝑝2 = 𝑝𝑒
2 + 𝑝𝜐2 + 2𝑝𝑒𝑝𝜐 cos 𝜃𝑒𝜐
J.D. Bowman, Journ. Res. NIST 110, 40 (2005)
The neutrino electron correlation coefficient 𝒂
2
𝑑Γ ∝ 1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 + 𝑏𝑚𝑒
𝐸𝑒
n
e-
𝜈𝑒
p 𝜃𝑒𝜈
Properties of 𝑝𝑝2 distribution for fixed 𝐸𝑒:
Edges 𝑝𝑝2
𝑚𝑖𝑛,𝑚𝑎𝑥= 𝑝𝑒 ± 𝑝𝜐
2
Slope ∝ 1 + 𝑎𝑝𝑒
𝐸𝑒cos 𝜃𝑒𝜈 𝑝𝑝
2
cos 𝜃𝑒𝜈 𝑝𝑝2 = +1
cos 𝜃𝑒𝜈 𝑝𝑝2 = −1
Electron spectrum:
0 2 0 0 4 0 0 6 0 0 8 0 0
𝐸𝑒,𝑘𝑖𝑛 (keV)
Y i e
l d (
a r b
. u
n i t
s )
b = +0.1
SM
The Fierz Interference Term 𝒃
3
𝑑Γ ∝ 𝜚 𝐸𝑒 1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 + 𝑏𝑚𝑒
𝐸𝑒
n
e-
𝜈𝑒
p 𝜃𝑒𝜈
d
n = (ddu)
p = (udu)
u
W±
e-
νe gV , gA
Coupling Constants in Neutron Decay
𝑛 → 𝑝 + 𝑒− + 𝜈 𝑒
Coupling Constants of the Weak Interaction
gV = GF·Vud·1
gA = GF·Vud·λ
5
d
n = (ddu)
p = (udu)
u
W±
e-
νe gV , gA
Coupling Constants in Neutron Decay
𝑛 → 𝑝 + 𝑒− + 𝜈 𝑒
Coupling Constants of the Weak Interaction
gV = GF·Vud·1
gA = GF·Vud·λ 𝜏𝑛−1 ∝ 𝑔𝑉
2 + 3𝑔𝐴2
5
d
n = (ddu)
p = (udu)
u
W±
e-
νe gV , gA
Coupling Constants in Neutron Decay
𝑛 → 𝑝 + 𝑒− + 𝜈 𝑒
Coupling Constants of the Weak Interaction
gV = GF·Vud·1
gA = GF·Vud·λ 𝜏𝑛−1 ∝ 𝑔𝑉
2 + 3𝑔𝐴2
𝜆 =𝑔𝐴𝑔𝑉
5
d
n = (ddu)
p = (udu)
u
W±
e-
νe gV , gA
Coupling Constants in Neutron Decay
W±
e-
νe n
p
n + νe ↔ p + e-
Primordial Nucleosynthesis Solar cycle
W±
e+
νe
p + p
2H+
p + p → 2H+ + e+ + νe
𝑛 → 𝑝 + 𝑒− + 𝜈 𝑒
Coupling Constants of the Weak Interaction
Start of Big Bang Nucleosynthesis,
Primordial 4He abundance Start of Solar Cycle, determines amount of
Solar Neutrinos
gV = GF·Vud·1
gA = GF·Vud·λ 𝜏𝑛−1 ∝ 𝑔𝑉
2 + 3𝑔𝐴2
𝜆 =𝑔𝐴𝑔𝑉
5
6
Neutron Lifetime Measurements
Beam: Decay rate: 𝑑𝑁
𝑑𝑡=
𝑁
𝜏𝑛
12
6
Neutron Lifetime Measurements
UCN from source
UCN
Storage
bottle(s)
Shutter UCN
detector
Beam: Decay rate: 𝑑𝑁
𝑑𝑡=
𝑁
𝜏𝑛
Bottle: Neutron counts : 𝑁 = 𝑁0𝑒−
𝑡
𝜏𝑒𝑓𝑓
with 1
𝜏𝑒𝑓𝑓
=1
𝜏𝑛+
1
𝜏𝑤𝑎𝑙𝑙
13
875
880
885
890
895
1985 1990 1995 2000 2005 2010 2015 2020
Neu
tro
n l
ifet
ime
[s]
Experiment publication
material bottle not used beam
6
Neutron Lifetime Measurements
UCN from source
UCN
Storage
bottle(s)
Shutter UCN
detector
Beam: Decay rate: 𝑑𝑁
𝑑𝑡=
𝑁
𝜏𝑛
Bottle: Neutron counts : 𝑁 = 𝑁0𝑒−
𝑡
𝜏𝑒𝑓𝑓
with 1
𝜏𝑒𝑓𝑓
=1
𝜏𝑛+
1
𝜏𝑤𝑎𝑙𝑙
14
875
880
885
890
895
1985 1990 1995 2000 2005 2010 2015 2020
Neu
tro
n l
ifet
ime
[s]
Experiment publication
material bottle not used beam
6
Neutron Lifetime Measurements
UCN from source
UCN
Storage
bottle(s)
Shutter UCN
detector
Beam: Decay rate: 𝑑𝑁
𝑑𝑡=
𝑁
𝜏𝑛
Bottle: Neutron counts : 𝑁 = 𝑁0𝑒−
𝑡
𝜏𝑒𝑓𝑓
with 1
𝜏𝑒𝑓𝑓
=1
𝜏𝑛+
1
𝜏𝑤𝑎𝑙𝑙
15
875
880
885
890
895
1985 1990 1995 2000 2005 2010 2015 2020
Neu
tro
n l
ifet
ime
[s]
Experiment publication
material bottle not used magnetic bottle beamUCNtau
7
Motivation for Nab
Determination of ratio 𝜆 = 𝑔𝐴 𝑔𝑉 from
𝐴 = −2 Re 𝜆 + 𝜆 2 1 + 3 𝜆 2 or
𝑎 = 1 − 𝜆 2 1 + 3 𝜆 2 :
−1.30 −1.28 −1.26 −1.24
UCNA (2010) ( )
PERKEO II (1997) ( )
Stratowa (1978)
PERKEO I (1986)
Liaud (1997)
( ) PERKEO II (2002)
PERKEO II (2013)
UCNA (2013) ( )
Mostovoi (2001)
Yerozolimskii (1997)
Byrne (2002)
My average:
𝜆 = −1.2756(11)
Δ𝜆 𝜆 = 0.03%
(Nab goal)
𝜆 = 𝑔𝐴/𝑔𝑉
aCORN (2017)
UCNA (2017)
7
Motivation for Nab
Most recent 2+1+1 flavor Lattice-QCD result from
PNDME: T. Bhattacharya et al., PRD 94, 054508 (2016)
Note: 𝜆 should be fixed by standard model.
However, precision of its calculation from
first principles is insufficiently precise:
PNDME’16
LHPC’12
LHPC’10
RBC/UKQCD’08
Lin/Orginos’07
RQCD’14
QCDSF/UKQCD’13
ETMC’15
CLS’12
RBC’08
1.00 1.25 1.50 1.75
𝑁𝑓=2
𝑁𝑓=2+1
𝑁f=
2+1+1 𝜆 = 𝑔𝐴/𝑔𝑉
Determination of ratio 𝜆 = 𝑔𝐴 𝑔𝑉 from
𝐴 = −2 Re 𝜆 + 𝜆 2 1 + 3 𝜆 2 or
𝑎 = 1 − 𝜆 2 1 + 3 𝜆 2 :
−1.30 −1.28 −1.26 −1.24
UCNA (2010) ( )
PERKEO II (1997) ( )
Stratowa (1978)
PERKEO I (1986)
Liaud (1997)
( ) PERKEO II (2002)
PERKEO II (2013)
UCNA (2013) ( )
Mostovoi (2001)
Yerozolimskii (1997)
Byrne (2002)
My average:
𝜆 = −1.2756(11)
Δ𝜆 𝜆 = 0.03%
(Nab goal)
𝜆 = 𝑔𝐴/𝑔𝑉
aCORN (2017)
UCNA (2017)
7
Motivation for Nab
Most recent 2+1+1 flavor Lattice-QCD result from
PNDME: T. Bhattacharya et al., PRD 94, 054508 (2016)
Note: 𝜆 should be fixed by standard model.
However, precision of its calculation from
first principles is insufficiently precise:
PNDME’16
LHPC’12
LHPC’10
RBC/UKQCD’08
Lin/Orginos’07
RQCD’14
QCDSF/UKQCD’13
ETMC’15
CLS’12
RBC’08
1.00 1.25 1.50 1.75
𝑁𝑓=2
𝑁𝑓=2+1
𝑁f=
2+1+1 𝜆 = 𝑔𝐴/𝑔𝑉
Determination of ratio 𝜆 = 𝑔𝐴 𝑔𝑉 from
𝐴 = −2 Re 𝜆 + 𝜆 2 1 + 3 𝜆 2 or
𝑎 = 1 − 𝜆 2 1 + 3 𝜆 2 :
−1.30 −1.28 −1.26 −1.24
UCNA (2010) ( )
PERKEO II (1997) ( )
Stratowa (1978)
PERKEO I (1986)
Liaud (1997)
( ) PERKEO II (2002)
PERKEO II (2013)
UCNA (2013) ( )
Mostovoi (2001)
Yerozolimskii (1997)
Byrne (2002)
My average:
𝜆 = −1.2756(11)
Δ𝜆 𝜆 = 0.03%
(Nab goal)
𝜆 = 𝑔𝐴/𝑔𝑉
aCORN (2017)
UCNA (2017)
2. Goal: Test of unitarity of Cabibbo-
Kobayashi-Maskawa (CKM) matrix from
𝑉𝑢𝑑2𝜏𝑛 1 + 3𝜆2 = 4908.7 19 s and
𝑉𝑢𝑑2 + 𝑉𝑢𝑠
2 + 𝑉𝑢𝑏2 = 1
For neutron data to be competitive, want:
Δ𝜏𝑛 𝜏𝑛 ~0.3 s Δ𝜆 𝜆 ~0.03%
0+→0+
neutron (λ, τStorage)
neutron (λ, τBeam)
Kl3 (Nf=2+1+1)
Kl2
tau →hadrons
mirror nuclei
0.968
0.97
0.972
0.974
0.976
Vud
What if the test of CKM unitarity fails?
𝑑′𝑠′𝑏′𝐷′
=
𝑉𝑢𝑑 𝑉𝑢𝑠 𝑉𝑢𝑏 𝑉𝑢𝐷𝑉𝑐𝑑 𝑉𝑐𝑠 𝑉𝑐𝑏 𝑉𝑐𝐷𝑉𝑡𝑑 𝑉𝑡𝑠 𝑉𝑡𝑏 𝑉𝑡𝐷𝑉𝐸𝑑 𝑉𝐸𝑠 𝑉𝐸𝑏 𝑉𝐸𝐷
∙
𝑑𝑠𝑏𝐷
Like all precision measurements, a failure of the unitarity test would not point to a single cause: Various possibilities exist, among those are: 1. Heavy quarks:
2. Exotic muon decays: All determinations of 𝑉𝑢𝑑 use 𝐺𝐹 from muon lifetime. If the muon had additional decay modes (𝜇 → 𝑋 + 𝑌 +⋯), 𝐺𝐹 (and 𝑉𝑢𝑑) would be determined wrong. E.g., 𝜇+ → 𝑒+ + 𝜈 𝑒 +𝜈𝜇 (wrong
neutrinos) would be very relevant for neutrino factories.
3. (Semi-)leptonic decays of nuclei through something other than exchange of 𝑊± bosons:
𝑉𝑢𝐷2 = 1 − 𝑉𝑢𝑏
2 − 𝑉𝑢𝑠2 − 𝑉𝑢𝑑
2
W. Marciano, A. Sirlin, PRL 56, 22 (1986) P. Langacker, D. London, PRD 38, 886 (1988)
K.S. Babu and S. Pakvasa, hep-ph/0204236
Specific models: E.g. W. Marciano, A. Sirlin, PRD 35, 1672 (1987). R. Barbieri et al., PLB 156, 348 (1985) K. Hagiwara et al., PRL 75, 3605 (1995) A. Kurylov, M. Ramsey-Musolf, PRL 88, 071804 (2000) 12
Energy scale of new physics: Λ ≥ 11 TeV V. Cirigliano et al., NPB 830, 95 (2010)
13
Other searches for Beyond Standard Model Physics: S,T interactions (fermions with “wrong”
helicity), e.g. through W’ bosons; weak magnetism; second class currents; …
LHC-Search for 𝑝𝑝 → 𝑒 + 𝜈 + other stuff and 𝑝𝑝 → 𝑒 + 𝑒 + other stuff
Scalar(S) and tensor(T) interactions in beta decay
LHC:
8 TeV, 20 fb-1
Low-energy experiments (mostly 0+ → 0+,
𝜋 → 𝑒𝜈𝛾); 𝑔𝑆,𝑇 from quark model
Low-energy experiments,
𝑔𝑆,𝑇 from Lattice QCD
Low-energy experiments (add 𝑏 < 10−3
in n, 6He); 𝑔𝑆,𝑇 from quark model
Low-energy experiments,
𝑔𝑆,𝑇 from Lattice QCD
LHC:
14 TeV, 10,300 fb-1
14
Nab spectrometer @ FNPB @ SNS
Fundamental Neutron Physics Beamline (FNPB)
@ Spallation Neutron Source (SNS)
Cold Neutron Beam
decay volume
0 kV
0-1 kV
- 30 kV
magnetic filter
region (field
maximum)
Neutron
beam
TOF region
(low field)
4 m flight path skipped
1 m flight path skipped
15
Segmented
Si detector Ø 81 mm
decay volume
0 kV
0-1 kV
- 30 kV
magnetic filter
region (field
maximum)
Neutron
beam
TOF region
(low field)
4 m flight path skipped
1 m flight path skipped
Nab spectrometer operation
15
Segmented
Si detector Ø 81 mm
decay volume
0 kV
0-1 kV
- 30 kV
magnetic filter
region (field
maximum)
Neutron
beam
TOF region
(low field)
4 m flight path skipped
1 m flight path skipped
Original configuration: D. Počanić, S. Baeßler, D. Bowman, V. Cianciolo, G. Greene, S. Penttilä et al., NIM A 611, 211 (2009)
Asymmetric configuration: S. Baeßler, D. Počanić, D. Bowman, S. Penttilä et al., arXiv:1209.4663
Nab spectrometer operation
• Measurement of 𝐸𝑒,𝑘𝑖𝑛 and tp for each event; protons
only in upper detector
→ 1 tp2 gives an estimate for 𝑝𝑝
2, magnetic field
shape gives a narrow detector response function
• Long TOF region improves proton TOF resolution
• Two detector geometry allows to suppress electron
backscattering
Nab spectrometer principle: measurement of Ee and tp
16
decay volume
0 kV
0-1 kV
- 30 kV
magnetic filter
region (field
maximum)
Neutron
beam
TOF region
(low field)
4 m flight path skipped
1 m flight path skipped
• Measurement of 𝐸𝑒,𝑘𝑖𝑛 and tp for each event; protons
only in upper detector
→ 1 tp2 gives an estimate for 𝑝𝑝
2, magnetic field
shape gives a narrow detector response function
• Long TOF region improves proton TOF resolution
• Two detector geometry allows to suppress electron
backscattering
Proton Trajectory
Magnetic Field
Adia
bat
ic
conver
sion
𝑝∥
𝑝⊥
𝑝∥
𝑝⊥
Electron energy measurement with backscattering
suppression
detected Ee [keV]
Yie
ld
1
10 1
10 2
10 3
10 4
10 5
0 50 100 150 200 250 300
detected Ee for e- in lower detector
detected Ee with only lower detector
Detector response for
incoming Ee = 300 keV
• Measurement of 𝐸𝑒,𝑘𝑖𝑛 and tp for each event; protons
only in upper detector
→ 1 tp2 gives an estimate for 𝑝𝑝
2, magnetic field
shape gives a narrow detector response function
• Long TOF region improves proton TOF resolution
• Two detector geometry allows to suppress electron
backscattering
decay volume
0 kV
0-1 kV
- 30 kV
magnetic filter
region (field
maximum)
Neutron
beam
TOF region
(low field)
4 m flight path skipped
1 m flight path skipped
17
18
Nab data analysis
𝐸𝑒,𝑘𝑖𝑛 = 450 keV
cos 𝜃𝑒𝜈 𝑝𝑝2 = +1
1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 𝑝𝑝2
pp2 [MeV2/c2]
pp2 d
istr
ibuti
on
0.0 0.5 1.0 1.5
cos 𝜃𝑒𝜈 𝑝𝑝2 = −1
18
Full GEANT4 spectrometer simulation:
Nab data analysis
𝑡𝑝 =𝑚𝑝 ∙ spectrometer length
𝑝𝑝−component along 𝐵
𝐸𝑒,𝑘𝑖𝑛 = 450 keV
cos 𝜃𝑒𝜈 𝑝𝑝2 = +1
1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 𝑝𝑝2
pp2 [MeV2/c2]
pp2 d
istr
ibuti
on
0.0 0.5 1.0 1.5
cos 𝜃𝑒𝜈 𝑝𝑝2 = −1
0 0.002 0.004 0.006
Yie
ld
Inverse squared proton TOF 1 𝑡𝑝2 [1/μs2]
0
4000
8000
12000
𝐸𝑒,𝑘𝑖𝑛 = 450 keV
𝐸𝑒,𝑘𝑖𝑛 = 300 keV
𝐸𝑒,𝑘𝑖𝑛 = 150 keV
𝐸𝑒,𝑘𝑖𝑛 = 600 keV
𝐸𝑒,𝑘𝑖𝑛 = 750 keV
18
Data analysis: Use edge to determine or verify the spectrometer TOF response function.
Then, use central part to determine slope and
correlation coefficient a.
Full GEANT4 spectrometer simulation:
Nab data analysis
𝑡𝑝 =𝑚𝑝 ∙ spectrometer length
𝑝𝑝−component along 𝐵
𝐸𝑒,𝑘𝑖𝑛 = 450 keV
cos 𝜃𝑒𝜈 𝑝𝑝2 = +1
1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 𝑝𝑝2
pp2 [MeV2/c2]
pp2 d
istr
ibuti
on
0.0 0.5 1.0 1.5
cos 𝜃𝑒𝜈 𝑝𝑝2 = −1
0 0.002 0.004 0.006
Yie
ld
Inverse squared proton TOF 1 𝑡𝑝2 [1/μs2]
0
4000
8000
12000
𝐸𝑒,𝑘𝑖𝑛 = 450 keV
𝐸𝑒,𝑘𝑖𝑛 = 300 keV
𝐸𝑒,𝑘𝑖𝑛 = 150 keV
𝐸𝑒,𝑘𝑖𝑛 = 600 keV
𝐸𝑒,𝑘𝑖𝑛 = 750 keV
19
Statistical uncertainty budget for 𝒂 coefficient
Planned statistical uncertainty budget:
3.6×108 events can be detected in 6 weeks (Decay volume V = 246 cm3, 12.7% of decay
protons go to upper detector, 50% efficiency in use of beam time, 1600 decays/s),
corresponding to Δ𝑎
𝑎 𝑠𝑡𝑎𝑡∼ 2.4 ⋅ 10−3 for this period.
→ 𝚫𝒂
𝒂 𝒔𝒕𝒂𝒕∼ 𝟕 ⋅ 𝟏𝟎−𝟒 can be reached, but it requires 70 weeks of data taking.
lower 𝑬𝐞,𝒌𝒊𝒏 cutoff none 100 keV 100 keV 100 keV
upper 𝒕𝒑 cutoff none none 40 μs 30 μs
𝚫𝐚 (𝑵, 𝒂, 𝒃 variable) 2.4/√N 2.5/√N 2.7/√N 3.0/√N
𝚫𝐚 (𝑵, 𝒂, 𝒃, 𝑬𝒄𝒂𝒍, 𝑳 variable) 2.6/√N 2.7/√N 2.9/√N 3.2/√N
𝚫𝐚 (𝑵, 𝒂, 𝒃, 𝑬𝒄𝒂𝒍, 𝑳 variable, inner 75% of data) 3.4/√N 3.5/√N 3.8/√N 4.3/√N
As above, 10% bg 4.2/√N 4.4/√N 4.6/√N 5.0/√N
Compare to Δ𝑎 𝑎 = 4 % of best existing experimental results (ACORN 2017),
and ∼ 1 % planned for ACORN and aSPECT
20
Experimental parameter Main specification Systematic
uncertainty Δa/a
Magnetic field
... curvature at pinch Δ𝛾/𝛾 = 2% with 𝛾 = 𝑑2 𝐵𝑧(𝑧)/𝑑𝑧2/𝐵𝑧(0) 5.3·10-4
… ratio rB = BTOF/B0 (Δ𝑟𝐵)/𝑟𝐵 = 1% 2.2·10-4
… ratio rB,DV = BDV/B0 (Δ𝑟𝐵,𝐷𝑉)/𝑟𝐵,𝐷𝑉 = 1% 1.8·10-4
Length of the TOF region none
Electrical potential inhomogeneity:
… in decay volume / filter region 𝑈𝐹 − 𝑈𝐷𝑉 < 10 mV 5·10-4
… in TOF region 𝑈𝐹 − 𝑈𝑇𝑂𝐹 < 200 mV 2.2·10-4
Neutron Beam:
… position Δ𝑧𝐷𝑉 < 2 mm 1.7·10-4
… profile (including edge effect) Slope at edges < 10%/cm 2.5·10-4
… Doppler effect small
… Unwanted beam polarization 𝑃𝑛 ≪ 10−4 can be small
Adiabaticity of proton motion 1·10-4
Detector effects:
… Electron energy calibration Δ𝐸𝑒,𝑘𝑖𝑛 < 0.2 keV 2·10-4
… Shape of electron energy response fraction of events in tail to 1% 5.7·10-4
… Proton trigger efficiency 𝜖𝑝 < 100 ppm/keV 3.4·10-4
… TOF shift due to detector/electronics Δ𝑡𝑝 < 0.3 ns 3·10-4
Residual gas 𝑝 < 2 ⋅ 10−9 torr 3.8·10-4
Background / Accidental coincidences small
Sum 1.2·10-3
Systematic uncertainty budget for 𝒂 coefficient
Goal: 𝚫𝐛 ≤ 𝟑 ⋅ 𝟏𝟎−𝟑
Systematic uncertainties:
1. Electron energy determination
2. Most stringent requirement: Non-linearity of 0.01%
3. Background
2% of events in tail
(deadlayer, bremsstrahlung) Y
i e l d
1
10 1
10 2
10 3
10 4
10 5
detected Ee [keV]
0 50 100 150 200 250 300
Detector response to decay
electron with 𝐸𝑒 = 300 keV
decay volume
0 kV
- 30 kV
+1 kV
magnetic filter
region (field
maximum)
Neutron
beam
TOF region
(low field)
4 m flight path skipped
1 m flight path skipped
0 V
-30 kV
Electron spectrum:
0 2 0 0 4 0 0 6 0 0 8 0 0
𝐸𝑒,𝑘𝑖𝑛 (keV)
Y i e
l d (
a r b
. u
n i t
s )
b = +0.1
SM
The measurement of the Fierz Interference Term 𝒃
21
𝑑Γ ∝ 𝜚 𝐸𝑒 1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 + 𝑏𝑚𝑒
𝐸𝑒
n
e-
𝜈𝑒
p 𝜃𝑒𝜈
Goal: 𝚫𝐛 ≤ 𝟑 ⋅ 𝟏𝟎−𝟑
Systematic uncertainties:
1. Electron energy determination
2. Most stringent requirement: Non-linearity of 0.01%
3. Background
2% of events in tail
(deadlayer, bremsstrahlung) Y
i e l d
1
10 1
10 2
10 3
10 4
10 5
detected Ee [keV]
0 50 100 150 200 250 300
Detector response to decay
electron with 𝐸𝑒 = 300 keV
Electron spectrum:
0 2 0 0 4 0 0 6 0 0 8 0 0
𝐸𝑒,𝑘𝑖𝑛 (keV)
Y i e
l d (
a r b
. u
n i t
s )
b = +0.1
SM
The measurement of the Fierz Interference Term 𝒃
21
𝑑Γ ∝ 𝜚 𝐸𝑒 1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 + 𝑏𝑚𝑒
𝐸𝑒
n
e-
𝜈𝑒
p 𝜃𝑒𝜈
22
Status of Nab experiment
Fundamental Neutron Physics Beamline
@ Spallation Neutron Source
22
Status of Nab experiment
Magnet system tested successfully at manufacturer, is
expected to arrive at ORNL this Friday.
Fundamental Neutron Physics Beamline
@ Spallation Neutron Source
22
Status of Nab experiment
Magnet system tested successfully at manufacturer, is
expected to arrive at ORNL this Friday.
Fundamental Neutron Physics Beamline
@ Spallation Neutron Source
𝐵 measured 𝐵 calculated
-200 -100 0 100 300 400 500 600
1
2
3
4
𝑧/cm 200
Nab (and UCNB) detector properties
• DAQ system (A. Sprow, C. Crawford et al.): All
waveforms recorded. Risetime ∼ 40 ns, fall time
∼ 4 µs.
• Energy resolution a few keV, threshold ≤ 10 keV
• Noise low enough to detect protons (average
deposited energy: 18 keV)
• Bad pixels need investigation
Ø 81 mm
Back side
LabVIEW controller C++ coincidence logic
LabVIEW FPGA low-threshold trapezoid trigger on ADC Optical fiber bus, clock & sync 23
Nab (and UCNB) detector properties
• DAQ system (A. Sprow, C. Crawford et al.): All
waveforms recorded. Risetime ∼ 40 ns, fall time
∼ 4 µs.
• Energy resolution a few keV, threshold ≤ 10 keV
• Noise low enough to detect protons (average
deposited energy: 18 keV)
• Bad pixels need investigation
LANL test run with Ce-139 source, Analysis H. Li
Pulse height [ADC reading]
500 1000 1500 2000 2500 3000 3500
Even
ts
0
5
10
15
20
25
30
35
40
45
γ: 33 keV
Ce-139 source
β: 27 keV
β: 127 keV
β: 160 keV
Ø 81 mm
Back side
23
Nab (and UCNB) detector properties
• DAQ system (A. Sprow, C. Crawford et al.): All
waveforms recorded. Risetime ∼ 40 ns, fall time
∼ 4 µs.
• Energy resolution a few keV, threshold ≤ 10 keV
• Noise low enough to detect protons (average
deposited energy: 18 keV)
• Bad pixels need investigation
LANL test run with Ce-139 source, Analysis H. Li
Pulse height [ADC reading]
500 1000 1500 2000 2500 3000 3500
Even
ts
0
5
10
15
20
25
30
35
40
45
γ: 33 keV
Ce-139 source
β: 27 keV
β: 127 keV
β: 160 keV
Ø 81 mm
Back side
Electron, ~ 100 keV, followed by
Proton, ~18 keV, in neighboring pixel
23
Main electrode system: Simulation of the effect of openings
Symmetry axis Electric potential [V]
x
z
Assumption for simulation: Potential of bore tube different by 1 V from electrodes
24
25
Top and bottom part of electrode system, before coating:
Parts are in hand, and are awaiting cleaning and coating.
Main electrode system: Fabrication
Symmetry axis
26
Electrode surface coating: What is the issue?
Most undergraduate textbooks: No electric field in empty hole inside conductor…
26
Electrode surface coating: What is the issue?
...and I have no objection if the conductor is homogenous. However, if not:
- +
E field
Most undergraduate textbooks: No electric field in empty hole inside conductor…
26
_ _ _
+
+ +
Φ1
EF,1
V
Material 1 Material 2
Φ2
EF,2 Φ1 Φ2
EF,1 EF,2
Material 1 Material 2
VC
Electrode surface coating: What is the issue?
...and I have no objection if the conductor is homogenous. However, if not:
- +
E field
Most undergraduate textbooks: No electric field in empty hole inside conductor…
26
_ _ _
+
+ +
Φ1
EF,1
V
Material 1 Material 2
Φ2
EF,2 Φ1 Φ2
EF,1 EF,2
Material 1 Material 2
VC
Electrode surface coating: What is the issue?
...and I have no objection if the conductor is homogenous. However, if not:
- +
E field
Most undergraduate textbooks: No electric field in empty hole inside conductor…
Consequence: Need to establish that electric field is known, or known to be absent, in flight path.
0 50 100 150 200 250 300 350 0
5
10
15
20
25
30
35
40
Angle [°]
Hei
gh
t [m
m]
4900
4950
5000
5050
5100
Work Function [meV]
Work function measurements
In collaboration with Prof. I. Baikie, KP Technologies 27
29
Main electrode system
We previously identified two coating methods that provide good homogeneity of the work function, and are compatible with UHV conditions. A copper/silver spray (which was good always when the coating looked good eye) and a graphite spray (which was mostly good when the coating looked good by eye). We decided to go with copper/silver.
But: Manufacturer changed recipe:
OLD AND GOOD NEW
Present status of testing: • New spray seems to be equally good in terms of work function
uniformity (𝜎 < 10 meV) • Vacuum test so far inconclusive • Cryogenic testing not yet done Next step: Align main electrode substrates, do coating, characterize
WF / meV
0.0 0.5 1.0 1.5 2.0 2.5 0.0
0.5
1.0
1.5
2.0
2.5
X [cm]
Y [cm
]
4600
4640
4680
4720
4760
4800
a Department of Physics, Arizona State University, Tempe, AZ 85287-1504 b Department of Physics, University of Virginia, Charlottesville, VA 22904-
4714 c Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 d Department of Physics and Astronomy, University of Sussex, Brighton
BN19RH, UK e Department of Chemistry and Physics, University of Tennessee at
Chattanooga, Chattanooga, TN 37403 f Department of Physics and Astronomy, University of Kentucky,
Lexington, KY 40506 g Department of Physics, University of Manitoba, Winnipeg, Manitoba, R3T
2N2, Canada
h KIT, Universität Karlsruhe (TH), Kaiserstraße 12, 76131 Karlsruhe,
Germany i Department of Physics and Astronomy, University of Tennessee,
Knoxville, TN 37996 j Department of Physics and Astronomy, University of South Carolina,
Columbia, SC 29208 k Los Alamos National Laboratory, Los Alamos, NM 87545 l Department of Physics, University of Winnipeg, Winnipeg, Manitoba
R3B2E9, Canada m Department of Physics, North Carolina State University, Raleigh, NC
27695-8202 n Universidad Nacional Autónoma de México, México, D.F. 04510, México o University of Michigan, Ann Arbor, MI 48109
The Nab collaboration
R. Alarcona, S.B.b,c (Project Manager), S. Balascutaa, L. Barrón Palosn, K. Bassi, N. Birgei, A. Blosef, D.
Borissenkob, J.D. Bowmanc (Co-Spokesperson), L. Broussardc, A.T. Bryantb, J. Byrned, J.R. Calarcoc,i, T.
Chuppo, T.V. Ciancioloc, J.N. Clementb, C. Crawfordf, W. Fanb, W. Farrarb, N. Fomini, E. Frležb, J. Fryb,
M.T. Gerickeg, M. Gervaisf, F. Glückh, G.L. Greenec,i, R.K. Grzywaczi, V. Gudkovj, J. Hamblene, C.
Hayesm, C. Hendruso, T. Itok, H. Lib, C.C. Lub, M. Makelak, R. Mammeig, J. Martinl, M. Martineza, D.G.
Matthewsf, P. McGaugheyk, C.D. McLaughlinb, P. Muellerc, D. van Pettenb, S.I. Penttiläc (On-site
Manager), D. Počanićc (Co-Spokesperson), G. Randalla, N. Roaneb, C.A. Roysem, K.P. Rykaczewskic, A.
Salas-Baccib, E.M. Scotti, S.K. Sjuek, A. Smithb, E. Smithk, A. Sprowf, E. Stevensb, J. Wexlerm, R.
Whiteheadi, W.S. Wilburnk, A.Youngm, B.Zeckm
30
Main project funding:
Active and recent collaborators:
Goal: 𝚫𝐛 < 𝟑 ⋅ 𝟏𝟎−𝟑
Systematic uncertainties:
1. Electron energy determination
2. Background
2% of events in tail
(deadlayer, bremsstrahlung) Y
i e l d
1
10 1
10 2
10 3
10 4
10 5
detected Ee [keV]
0 50 100 150 200 250 300
Detector response to decay
electron with 𝐸𝑒 = 300 keV
decay volume
0 kV
- 30 kV
+1 kV
magnetic filter
region (field
maximum)
Neutron
beam
TOF region
(low field)
4 m flight path skipped
1 m flight path skipped
0 V
-30 kV
Electron spectrum:
0 2 0 0 4 0 0 6 0 0 8 0 0
E e , k i n ( k e V )
Y i e
l d (
a r b
. u
n i t
s )
b = +0.1
SM
The determination of the Fierz Interference term 𝒃
31
𝑑Γ ∝ 𝜚 𝐸𝑒 1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 + 𝑏𝑚𝑒
𝐸𝑒
n
e-
𝜈𝑒
p 𝜃𝑒𝜈
Goal: 𝚫𝐛 < 𝟑 ⋅ 𝟏𝟎−𝟑
Systematic uncertainties:
1. Electron energy determination
2. Background
2% of events in tail
(deadlayer, bremsstrahlung) Y
i e l d
1
10 1
10 2
10 3
10 4
10 5
detected Ee [keV]
0 50 100 150 200 250 300
Detector response to decay
electron with 𝐸𝑒 = 300 keV
Electron spectrum:
0 2 0 0 4 0 0 6 0 0 8 0 0
E e , k i n ( k e V )
Y i e
l d (
a r b
. u
n i t
s )
b = +0.1
SM
The determination of the Fierz Interference term 𝒃
31
𝑑Γ ∝ 𝜚 𝐸𝑒 1 + 𝑎𝑝𝑒𝐸𝑒
cos 𝜃𝑒𝜈 + 𝑏𝑚𝑒
𝐸𝑒
n
e-
𝜈𝑒
p 𝜃𝑒𝜈
• Main uncertainties in previous best experiment (PERKEO II): statistics, detector, background, polarization
• Superior detector energy resolution, good enough time resolution
• Keep coincidences to improve background
• Statistics @ SNS or NIST is an issue for 𝐴
• Polarization measurement seems manageable (XSM or He-3)
Segmented
Si detector
magnetic filter
region (field
maximum)
TOF region
(field r B · B 0 )
Polarizer:
Supermirror
or Helium-3
AFP
Spin
Flipper
• Beta asymmetry (to extract 𝐴) :
reflect all protons to bottom detector,
use top detector for electrons
• Proton asymmetry (to extract 𝐵):
detect protons at top
Planned continuation (SNS or NIST): Polarized neutrons
32
Polarimetry with
Helium-3
• The Nab collaboration is setting up the Nab spectrometer at the Spallation Neutron Source. Start of commissioning planned in summer 2018. Until tomorrow, the big reason for the delay has been the magnet.
• Goal: Δa/a ≤ 10-3 and Δb ≤ 3·10-3. This is in line with the requirements for standard model tests:
1) Compare renormalization constant 𝜆 = 𝑔𝐴/𝑔𝑉 to direct determination on lattice.
2) Unitarity test of Cabbibo-Kobayashi-Maskawa matrix in first row.
3) Search for new physics at above the TeV scale that manifests itself as S,T interaction.
Summary
33 Thank you for the attention!