The measurement of neutron beta decay observables with the Nab - - PowerPoint PPT Presentation

Stefan Baeβler The measurement of neutron beta decay

• bservables with the Nab spectrometer

1

• Inst. Nucl. Part. Phys.

The neutrino electron correlation coefficient 𝒃

2

𝑒Γ ∝ 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 + 𝑐 𝑛𝑓 𝐹𝑓 n e- 𝜉𝑓 p 𝜄𝑓𝜉

Novel approach to determine cos 𝜄𝑓𝜑: Kinematics in Infinite Nuclear Mass Approximation: 1. Energy Conservation: 𝐹𝜑 = 𝐹𝑓,𝑛𝑏𝑦 − 𝐹𝑓,𝑙𝑗𝑜 2. Momentum Conservation: 𝑞𝑞2 = 𝑞𝑓2 + 𝑞𝜑2 + 2𝑞𝑓𝑞𝜑 cos 𝜄𝑓𝜑

The neutrino electron correlation coefficient 𝒃

2

𝑒Γ ∝ 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 + 𝑐 𝑛𝑓 𝐹𝑓 n e- 𝜉𝑓 p 𝜄𝑓𝜉

𝐹𝑓,𝑙𝑗𝑜 = 450 keV

1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 𝑞𝑞2

pp

2 [MeV2/c2]

pp

2 distribution

0.0 0.5 1.0 1.5

Novel approach to determine cos 𝜄𝑓𝜑: Kinematics in Infinite Nuclear Mass Approximation: 1. Energy Conservation: 𝐹𝜑 = 𝐹𝑓,𝑛𝑏𝑦 − 𝐹𝑓,𝑙𝑗𝑜 2. Momentum Conservation: 𝑞𝑞2 = 𝑞𝑓2 + 𝑞𝜑2 + 2𝑞𝑓𝑞𝜑 cos 𝜄𝑓𝜑

The neutrino electron correlation coefficient 𝒃

2

𝑒Γ ∝ 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 + 𝑐 𝑛𝑓 𝐹𝑓 n e- 𝜉𝑓 p 𝜄𝑓𝜉

𝐹𝑓,𝑙𝑗𝑜 = 450 keV

1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 𝑞𝑞2

pp

2 [MeV2/c2]

pp

2 distribution

0.0 0.5 1.0 1.5

Novel approach to determine cos 𝜄𝑓𝜑: Kinematics in Infinite Nuclear Mass Approximation: 1. Energy Conservation: 𝐹𝜑 = 𝐹𝑓,𝑛𝑏𝑦 − 𝐹𝑓,𝑙𝑗𝑜 2. Momentum Conservation: 𝑞𝑞2 = 𝑞𝑓2 + 𝑞𝜑2 + 2𝑞𝑓𝑞𝜑 cos 𝜄𝑓𝜑

J.D. Bowman, Journ. Res. NIST 110, 40 (2005)

The neutrino electron correlation coefficient 𝒃

2

𝑒Γ ∝ 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 + 𝑐 𝑛𝑓 𝐹𝑓 n e- 𝜉𝑓 p 𝜄𝑓𝜉

Properties of 𝑞𝑞2 distribution for fixed 𝐹𝑓: Edges 𝑞𝑞2

𝑛𝑗𝑜,𝑛𝑏𝑦 = 𝑞𝑓 ± 𝑞𝜑 2

Slope ∝ 1 + 𝑏

𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 𝑞𝑞2

cos 𝜄𝑓𝜉 𝑞𝑞2 = +1 cos 𝜄𝑓𝜉 𝑞𝑞2 = −1

Electron spectrum:

2 4 6 8

𝐹𝑓,𝑙𝑗𝑜 (keV) Y i e l d ( a r b . u n i t s )

b = +0.1 SM

The Fierz Interference Term 𝒄

3

𝑒Γ ∝ 𝜛 𝐹𝑓 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 + 𝑐 𝑛𝑓 𝐹𝑓 n e- 𝜉𝑓 p 𝜄𝑓𝜉

d n = (ddu) p = (udu) u W± e- νe gV , gA

Coupling Constants in Neutron Decay

𝑜 → 𝑞 + 𝑓− + 𝜉 𝑓

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

𝑜 → 𝑞 + 𝑓− + 𝜉 𝑓

Coupling Constants of the Weak Interaction

gV = GF·Vud·1 gA = GF·Vud·λ

𝜐𝑜

−1 ∝ 𝑕𝑊 2 + 3𝑕𝐵 2

5

d n = (ddu) p = (udu) u W± e- νe gV , gA

Coupling Constants in Neutron Decay

𝑜 → 𝑞 + 𝑓− + 𝜉 𝑓

Coupling Constants of the Weak Interaction

gV = GF·Vud·1 gA = GF·Vud·λ

𝜐𝑜

−1 ∝ 𝑕𝑊 2 + 3𝑕𝐵 2

𝜇 = 𝑕𝐵 𝑕𝑊

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 𝑜 → 𝑞 + 𝑓− + 𝜉 𝑓

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

𝜐𝑜

−1 ∝ 𝑕𝑊 2 + 3𝑕𝐵 2

𝜇 = 𝑕𝐵 𝑕𝑊

5

6

Neutron Lifetime Measurements

Beam: Decay rate:

𝑒𝑂 𝑒𝑢 = 𝑂 𝜐𝑜

12

6

Neutron Lifetime Measurements

UCN from source UCN Storage bottle(s) Shutter UCN detector

Beam: Decay rate:

𝑒𝑂 𝑒𝑢 = 𝑂 𝜐𝑜

Bottle: Neutron counts : 𝑂 = 𝑂0𝑓− 𝑢

𝜐𝑓𝑔𝑔

with

1 𝜐𝑓𝑔𝑔 = 1 𝜐𝑜 + 1 𝜐𝑥𝑏𝑚𝑚

13

875 880 885 890 895 1985 1990 1995 2000 2005 2010 2015 2020

Neutron lifetime [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:

𝑒𝑂 𝑒𝑢 = 𝑂 𝜐𝑜

Bottle: Neutron counts : 𝑂 = 𝑂0𝑓− 𝑢

𝜐𝑓𝑔𝑔

with

1 𝜐𝑓𝑔𝑔 = 1 𝜐𝑜 + 1 𝜐𝑥𝑏𝑚𝑚

14

875 880 885 890 895 1985 1990 1995 2000 2005 2010 2015 2020

Neutron lifetime [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:

𝑒𝑂 𝑒𝑢 = 𝑂 𝜐𝑜

Bottle: Neutron counts : 𝑂 = 𝑂0𝑓− 𝑢

𝜐𝑓𝑔𝑔

with

1 𝜐𝑓𝑔𝑔 = 1 𝜐𝑜 + 1 𝜐𝑥𝑏𝑚𝑚

15

875 880 885 890 895 1985 1990 1995 2000 2005 2010 2015 2020

Neutron lifetime [s] Experiment publication material bottle not used magnetic bottle beam

UCNtau

7

Motivation for Nab

Determination of ratio 𝜇 = 𝑕𝐵 𝑕𝑊 from 𝐵 = −2 Re 𝜇 + 𝜇 2 1 + 3 𝜇 2

• r

𝑏 = 1 − 𝜇 2 1 + 3 𝜇 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: 𝜇 = −1.2756(11)

Δ𝜇 𝜇 = 0.03% (Nab goal) 𝜇 = 𝑕𝐵/𝑕𝑊

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: 𝜇 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

𝑂

𝑔 = 2

𝑂

𝑔 = 2 + 1

𝑂f = 2 + 1 + 1 𝜇 = 𝑕𝐵/𝑕𝑊

Determination of ratio 𝜇 = 𝑕𝐵 𝑕𝑊 from 𝐵 = −2 Re 𝜇 + 𝜇 2 1 + 3 𝜇 2

• r

𝑏 = 1 − 𝜇 2 1 + 3 𝜇 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: 𝜇 = −1.2756(11)

Δ𝜇 𝜇 = 0.03% (Nab goal) 𝜇 = 𝑕𝐵/𝑕𝑊

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: 𝜇 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

𝑂

𝑔 = 2

𝑂

𝑔 = 2 + 1

𝑂f = 2 + 1 + 1 𝜇 = 𝑕𝐵/𝑕𝑊

Determination of ratio 𝜇 = 𝑕𝐵 𝑕𝑊 from 𝐵 = −2 Re 𝜇 + 𝜇 2 1 + 3 𝜇 2

• r

𝑏 = 1 − 𝜇 2 1 + 3 𝜇 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: 𝜇 = −1.2756(11)

Δ𝜇 𝜇 = 0.03% (Nab goal) 𝜇 = 𝑕𝐵/𝑕𝑊

aCORN (2017) UCNA (2017)

• 2. Goal: Test of unitarity of Cabibbo-

Kobayashi-Maskawa (CKM) matrix from 𝑊

𝑣𝑒 2𝜐𝑜 1 + 3𝜇2 = 4908.7 19 s and

𝑊

𝑣𝑒 2 + 𝑊 𝑣𝑡 2 + 𝑊 𝑣𝑐 2 = 1

For neutron data to be competitive, want: Δ𝜐𝑜 𝜐𝑜 ~0.3 s Δ𝜇 𝜇 ~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?

𝑒′ 𝑡′ 𝑐′ 𝐸′ = 𝑊

𝑣𝑒

𝑊

𝑣𝑡

𝑊

𝑣𝑐

𝑊

𝑣𝐸

𝑊

𝑑𝑒

𝑊

𝑑𝑡

𝑊

𝑑𝑐

𝑊

𝑑𝐸

𝑊

𝑢𝑒

𝑊

𝑢𝑡

𝑊

𝑢𝑐

𝑊

𝑢𝐸

𝑊

𝐹𝑒

𝑊

𝐹𝑡

𝑊

𝐹𝑐

𝑊

𝐹𝐸

∙ 𝑒 𝑡 𝑐 𝐸 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 𝑊

𝑣𝑒 use 𝐻𝐺 from muon lifetime. If the muon had additional decay modes

(𝜈 → 𝑌 + 𝑍 + ⋯), 𝐻𝐺 (and 𝑊

𝑣𝑒) would be determined wrong. E.g., 𝜈+ → 𝑓+ + 𝜉 𝑓 +𝜉𝜈 (wrong

neutrinos) would be very relevant for neutrino factories. 3. (Semi-)leptonic decays of nuclei through something other than exchange of 𝑋± bosons:

𝑊

𝑣𝐸 2 = 1 − 𝑊 𝑣𝑐 2 − 𝑊 𝑣𝑡 2 − 𝑊 𝑣𝑒 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 𝑞𝑞 → 𝑓 + 𝜉 + other stuff and 𝑞𝑞 → 𝑓 + 𝑓 + other stuff

Scalar(S) and tensor(T) interactions in beta decay

LHC: 8 TeV, 20 fb-1 Low-energy experiments (mostly 0+ → 0+, 𝜌 → 𝑓𝜉𝛿); 𝑕𝑇,𝑈 from quark model Low-energy experiments, 𝑕𝑇,𝑈 from Lattice QCD Low-energy experiments (add 𝑐 < 10−3 in n, 6He); 𝑕𝑇,𝑈 from quark model Low-energy experiments, 𝑕𝑇,𝑈 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 𝐹𝑓,𝑙𝑗𝑜 and tp for each event; protons
• nly in upper detector

→ 1 tp

2

gives an estimate for 𝑞𝑞2, 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 𝐹𝑓,𝑙𝑗𝑜 and tp for each event; protons
• nly in upper detector

→ 1 tp

2

gives an estimate for 𝑞𝑞2, 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

Adiabatic conversion

𝑞∥ 𝑞⊥ 𝑞∥ 𝑞⊥

Electron energy measurement with backscattering suppression

detected Ee [keV] Yield

1 10

1

10

2

10

3

10

4

10

5

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 𝐹𝑓,𝑙𝑗𝑜 and tp for each event; protons
• nly in upper detector

→ 1 tp

2

gives an estimate for 𝑞𝑞2, 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

𝐹𝑓,𝑙𝑗𝑜 = 450 keV

cos 𝜄𝑓𝜉 𝑞𝑞2 = +1 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 𝑞𝑞2

pp

2 [MeV2/c2]

pp

2 distribution

0.0 0.5 1.0 1.5

cos 𝜄𝑓𝜉 𝑞𝑞2 = −1

18

Full GEANT4 spectrometer simulation:

Nab data analysis

𝑢𝑞 = 𝑛𝑞 ∙ spectrometer length 𝑞𝑞−component along 𝐶

𝐹𝑓,𝑙𝑗𝑜 = 450 keV

cos 𝜄𝑓𝜉 𝑞𝑞2 = +1 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 𝑞𝑞2

pp

2 [MeV2/c2]

pp

2 distribution

0.0 0.5 1.0 1.5

cos 𝜄𝑓𝜉 𝑞𝑞2 = −1

0.002 0.004 0.006

Yield Inverse squared proton TOF 1 𝑢𝑞

2

[1/μs2]

4000 8000 12000

𝐹𝑓,𝑙𝑗𝑜 = 450 keV 𝐹𝑓,𝑙𝑗𝑜 = 300 keV 𝐹𝑓,𝑙𝑗𝑜 = 150 keV 𝐹𝑓,𝑙𝑗𝑜 = 600 keV 𝐹𝑓,𝑙𝑗𝑜 = 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

𝑢𝑞 = 𝑛𝑞 ∙ spectrometer length 𝑞𝑞−component along 𝐶

𝐹𝑓,𝑙𝑗𝑜 = 450 keV

cos 𝜄𝑓𝜉 𝑞𝑞2 = +1 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 𝑞𝑞2

pp

2 [MeV2/c2]

pp

2 distribution

0.0 0.5 1.0 1.5

cos 𝜄𝑓𝜉 𝑞𝑞2 = −1

0.002 0.004 0.006

Yield Inverse squared proton TOF 1 𝑢𝑞

2

[1/μs2]

4000 8000 12000

𝐹𝑓,𝑙𝑗𝑜 = 450 keV 𝐹𝑓,𝑙𝑗𝑜 = 300 keV 𝐹𝑓,𝑙𝑗𝑜 = 150 keV 𝐹𝑓,𝑙𝑗𝑜 = 600 keV 𝐹𝑓,𝑙𝑗𝑜 = 750 keV

19

Statistical uncertainty budget for 𝒃 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

Δ𝑏 𝑏 𝑡𝑢𝑏𝑢 ∼ 2.4 ⋅ 10−3 for this period.

→

𝚬𝒃 𝒃 𝒕𝒖𝒃𝒖 ∼ 𝟖 ⋅ 𝟐𝟏−𝟓 can be reached, but it requires 70 weeks of data taking.

lower 𝑭𝐟,𝒍𝒋𝒐 cutoff none 100 keV 100 keV 100 keV upper 𝒖𝒒 cutoff none none 40 μs 30 μs 𝚬𝐛 (𝑶, 𝒃, 𝒄 variable) 2.4/√N 2.5/√N 2.7/√N 3.0/√N 𝚬𝐛 (𝑶, 𝒃, 𝒄, 𝑭𝒅𝒃𝒎, 𝑴 variable) 2.6/√N 2.7/√N 2.9/√N 3.2/√N 𝚬𝐛 (𝑶, 𝒃, 𝒄, 𝑭𝒅𝒃𝒎, 𝑴 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 Δ𝑏 𝑏 = 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 Δ𝛿/𝛿 = 2% with 𝛿 = 𝑒2 𝐶𝑨(𝑨)/𝑒𝑨2/𝐶𝑨(0) 5.3·10-4 … ratio rB = BTOF/B0 (Δ𝑠

𝐶)/𝑠𝐶 = 1%

2.2·10-4 … ratio rB,DV = BDV/B0 (Δ𝑠

𝐶,𝐸𝑊)/𝑠𝐶,𝐸𝑊 = 1%

1.8·10-4 Length of the TOF region none Electrical potential inhomogeneity: … in decay volume / filter region 𝑉𝐺 − 𝑉𝐸𝑊 < 10 mV 5·10-4 … in TOF region 𝑉𝐺 − 𝑉𝑈𝑃𝐺 < 200 mV 2.2·10-4 Neutron Beam: … position Δ𝑨𝐸𝑊 < 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 𝑄

𝑜 ≪ 10−4

can be small Adiabaticity of proton motion 1·10-4 Detector effects: … Electron energy calibration Δ𝐹𝑓,𝑙𝑗𝑜 < 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 𝜗𝑞 < 100 ppm/keV 3.4·10-4 … TOF shift due to detector/electronics Δ𝑢𝑞 < 0.3 ns 3·10-4 Residual gas 𝑞 < 2 ⋅ 10−9 torr 3.8·10-4 Background / Accidental coincidences small Sum 1.2·10-3

Systematic uncertainty budget for 𝒃 coefficient

Goal: 𝚬𝐜 ≤ 𝟒 ⋅ 𝟐𝟏−𝟒 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]

50 100 150 200 250 300

Detector response to decay electron with 𝐹𝑓 = 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:

2 4 6 8

𝐹𝑓,𝑙𝑗𝑜 (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 𝒄

21

𝑒Γ ∝ 𝜛 𝐹𝑓 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 + 𝑐 𝑛𝑓 𝐹𝑓 n e- 𝜉𝑓 p 𝜄𝑓𝜉

Goal: 𝚬𝐜 ≤ 𝟒 ⋅ 𝟐𝟏−𝟒 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]

50 100 150 200 250 300

Detector response to decay electron with 𝐹𝑓 = 300 keV

Electron spectrum:

2 4 6 8

𝐹𝑓,𝑙𝑗𝑜 (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 𝒄

21

𝑒Γ ∝ 𝜛 𝐹𝑓 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 + 𝑐 𝑛𝑓 𝐹𝑓 n e- 𝜉𝑓 p 𝜄𝑓𝜉

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 𝐶 measured 𝐶 calculated

• 200
• 100

100 300 400 500 600 1 2 3 4

𝑨/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

Events

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

Events

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

• bjection 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

• bjection 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

• bjection 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.

50 100 150 200 250 300 350 5 10 15 20 25 30 35 40 Angle [°] Height [mm] 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 (𝜏 < 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

• 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: 𝚬𝐜 < 𝟒 ⋅ 𝟐𝟏−𝟒 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]

50 100 150 200 250 300

Detector response to decay electron with 𝐹𝑓 = 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:

2 4 6 8

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 𝒄

31

𝑒Γ ∝ 𝜛 𝐹𝑓 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 + 𝑐 𝑛𝑓 𝐹𝑓 n e- 𝜉𝑓 p 𝜄𝑓𝜉

Goal: 𝚬𝐜 < 𝟒 ⋅ 𝟐𝟏−𝟒 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]

50 100 150 200 250 300

Detector response to decay electron with 𝐹𝑓 = 300 keV

Electron spectrum:

2 4 6 8

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 𝒄

31

𝑒Γ ∝ 𝜛 𝐹𝑓 1 + 𝑏 𝑞𝑓 𝐹𝑓 cos 𝜄𝑓𝜉 + 𝑐 𝑛𝑓 𝐹𝑓 n e- 𝜉𝑓 p 𝜄𝑓𝜉

• 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 𝐵
• Polarization measurement seems manageable (XSM or He-3)

Segmented Si detector magnetic filter region (field maximum) TOF region (field r

B

· B )

Polarizer: Supermirror

• r Helium-3

AFP Spin Flipper

• Beta asymmetry (to extract 𝐵) :

reflect all protons to bottom detector, use top detector for electrons

• Proton asymmetry (to extract 𝐶):

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 𝜇 = 𝑕𝐵/𝑕𝑊 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!