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

The measurement of neutron beta decay observables with the Nab spectrometer Stefan Bae β ler 1 Inst. Nucl. Part. Phys.

The neutrino electron correlation coefficient 𝒃 e - p 𝜄 𝑓𝜉 n 𝜉 𝑓 1 + 𝑏 𝑞 𝑓 cos 𝜄 𝑓𝜉 + 𝑐 𝑛 𝑓 𝑒Γ ∝ 𝐹 𝑓 𝐹 𝑓 2

The neutrino electron correlation coefficient 𝒃 e - Novel approach to determine cos 𝜄 𝑓𝜑 : p 𝜄 𝑓𝜉 Kinematics in Infinite Nuclear Mass Approximation: n 𝜉 𝑓 Energy Conservation: 𝐹 𝜑 = 𝐹 𝑓,𝑛𝑏𝑦 − 𝐹 𝑓,𝑙𝑗𝑜 1. 1 + 𝑏 𝑞 𝑓 cos 𝜄 𝑓𝜉 + 𝑐 𝑛 𝑓 2. Momentum Conservation: 𝑒Γ ∝ 𝐹 𝑓 𝐹 𝑓 𝑞 𝑞2 = 𝑞 𝑓2 + 𝑞 𝜑2 + 2𝑞 𝑓 𝑞 𝜑 cos 𝜄 𝑓𝜑 2

The neutrino electron correlation coefficient 𝒃 e - Novel approach to determine cos 𝜄 𝑓𝜑 : p 𝜄 𝑓𝜉 Kinematics in Infinite Nuclear Mass Approximation: n 𝜉 𝑓 Energy Conservation: 𝐹 𝜑 = 𝐹 𝑓,𝑛𝑏𝑦 − 𝐹 𝑓,𝑙𝑗𝑜 1. 1 + 𝑏 𝑞 𝑓 cos 𝜄 𝑓𝜉 + 𝑐 𝑛 𝑓 2. Momentum Conservation: 𝑒Γ ∝ 𝐹 𝑓 𝐹 𝑓 𝑞 𝑞2 = 𝑞 𝑓2 + 𝑞 𝜑2 + 2𝑞 𝑓 𝑞 𝜑 cos 𝜄 𝑓𝜑 1 + 𝑏 𝑞 𝑓 cos 𝜄 𝑓𝜉 𝑞 𝑞2 𝐹 𝑓 2 distribution p p 𝐹 𝑓,𝑙𝑗𝑜 = 450 keV 0.0 0.5 1.0 1.5 2 2 [MeV 2 /c 2 ] p p

The neutrino electron correlation coefficient 𝒃 e - Novel approach to determine cos 𝜄 𝑓𝜑 : p 𝜄 𝑓𝜉 Kinematics in Infinite Nuclear Mass Approximation: n 𝜉 𝑓 Energy Conservation: 𝐹 𝜑 = 𝐹 𝑓,𝑛𝑏𝑦 − 𝐹 𝑓,𝑙𝑗𝑜 1. 1 + 𝑏 𝑞 𝑓 cos 𝜄 𝑓𝜉 + 𝑐 𝑛 𝑓 2. Momentum Conservation: 𝑒Γ ∝ 𝐹 𝑓 𝐹 𝑓 𝑞 𝑞2 = 𝑞 𝑓2 + 𝑞 𝜑2 + 2𝑞 𝑓 𝑞 𝜑 cos 𝜄 𝑓𝜑 1 + 𝑏 𝑞 𝑓 Properties of 𝑞 𝑞2 distribution for fixed 𝐹 𝑓 : cos 𝜄 𝑓𝜉 𝑞 𝑞2 𝐹 𝑓 Edges 𝑞 𝑞2 𝑛𝑗𝑜,𝑛𝑏𝑦 = 𝑞 𝑓 ± 𝑞 𝜑 2 2 distribution 𝑞 𝑓 𝐹 𝑓 cos 𝜄 𝑓𝜉 𝑞 𝑞2 Slope ∝ 1 + 𝑏 cos 𝜄 𝑓𝜉 𝑞 𝑞2 = −1 cos 𝜄 𝑓𝜉 𝑞 𝑞2 = +1 p p 𝐹 𝑓,𝑙𝑗𝑜 = 450 keV J.D. Bowman, Journ. Res. NIST 110, 40 (2005) 0.0 0.5 1.0 1.5 2 2 [MeV 2 /c 2 ] p p

The Fierz Interference Term 𝒄 e - 1 + 𝑏 𝑞 𝑓 cos 𝜄 𝑓𝜉 + 𝑐 𝑛 𝑓 p 𝜄 𝑓𝜉 𝑒Γ ∝ 𝜛 𝐹 𝑓 𝐹 𝑓 𝐹 𝑓 n 𝜉 𝑓 ) s t i n . u b Electron spectrum: r a d ( b = +0.1 l e i SM Y 0 2 0 0 4 0 0 6 0 0 8 0 0 𝐹 𝑓,𝑙𝑗𝑜 (keV) 3

Coupling Constants of the Weak Interaction g A = G F · V ud · λ Coupling Constants in Neutron Decay p = (udu) u e - ν e W ± g V , g A g V = G F · V ud ·1 d n = (ddu) 𝑜 → 𝑞 + 𝑓 − + 𝜉 𝑓 5

Coupling Constants of the Weak Interaction g A = G F · V ud · λ 2 + 3𝑕 𝐵 −1 ∝ 𝑕 𝑊 2 𝜐 𝑜 Coupling Constants in Neutron Decay p = (udu) u e - ν e W ± g V , g A g V = G F · V ud ·1 d n = (ddu) 𝑜 → 𝑞 + 𝑓 − + 𝜉 𝑓 5

Coupling Constants of the Weak Interaction g A = G F · V ud · λ 2 + 3𝑕 𝐵 −1 ∝ 𝑕 𝑊 2 𝜐 𝑜 Coupling Constants in Neutron Decay p = (udu) u e - ν e W ± g V , g A g V = G F · V ud ·1 d n = (ddu) 𝜇 = 𝑕 𝐵 𝑜 → 𝑞 + 𝑓 − + 𝜉 𝑓 𝑕 𝑊 5

Coupling Constants of the Weak Interaction g A = G F · V ud · λ 2 + 3𝑕 𝐵 −1 ∝ 𝑕 𝑊 2 𝜐 𝑜 Coupling Constants in Neutron Decay p = (udu) u e - ν e W ± g V , g A g V = G F · V ud ·1 d n = (ddu) 𝜇 = 𝑕 𝐵 𝑜 → 𝑞 + 𝑓 − + 𝜉 𝑓 𝑕 𝑊 Primordial Nucleosynthesis Solar cycle p e - 2 H + e + W ± ν e W ± n ν e p + p n + ν e ↔ p + e - p + p → 2 H + + e + + ν e Start of Big Bang Nucleosynthesis, Start of Solar Cycle, determines amount of Primordial 4 He abundance Solar Neutrinos 5

Neutron Lifetime Measurements 𝑒𝑂 𝑂 𝑒𝑢 = Beam: Decay rate: 𝜐 𝑜 12 6

Neutron Lifetime Measurements 𝑒𝑂 𝑂 𝑒𝑢 = Beam: Decay rate: 𝜐 𝑜 Bottle: Neutron counts : 𝑂 = 𝑂 0 𝑓 − 𝑢 𝜐 𝑓𝑔𝑔 1 1 1 𝜐 𝑓𝑔𝑔 = 𝜐 𝑜 + with 𝜐 𝑥𝑏𝑚𝑚 UCN Storage bottle(s) UCN Shutter detector UCN from source 13 6

Neutron Lifetime Measurements 𝑒𝑂 𝑂 𝑒𝑢 = Beam: Decay rate: 𝜐 𝑜 Bottle: Neutron counts : 𝑂 = 𝑂 0 𝑓 − 𝑢 𝜐 𝑓𝑔𝑔 1 1 1 𝜐 𝑓𝑔𝑔 = 𝜐 𝑜 + with 𝜐 𝑥𝑏𝑚𝑚 material bottle not used beam UCN 895 Storage bottle(s) Neutron lifetime [s] 890 UCN Shutter detector UCN from source 885 880 875 1985 1990 1995 2000 2005 2010 2015 2020 Experiment publication 14 6

Neutron Lifetime Measurements 𝑒𝑂 𝑂 𝑒𝑢 = Beam: Decay rate: 𝜐 𝑜 Bottle: Neutron counts : 𝑂 = 𝑂 0 𝑓 − 𝑢 𝜐 𝑓𝑔𝑔 1 1 1 𝜐 𝑓𝑔𝑔 = 𝜐 𝑜 + with 𝜐 𝑥𝑏𝑚𝑚 UCNtau material bottle material bottle not used not used magnetic bottle beam beam UCN 895 895 Storage bottle(s) Neutron lifetime [s] Neutron lifetime [s] 890 890 UCN Shutter detector UCN from source 885 885 880 880 875 875 1985 1985 1990 1990 1995 1995 2000 2000 2005 2005 2010 2010 2015 2015 2020 2020 Experiment publication Experiment publication 15 6

Motivation for Nab Determination of ratio 𝜇 = 𝑕 𝐵 𝑕 𝑊 from 𝐵 = −2 Re 𝜇 + 𝜇 2 1 + 3 𝜇 2 or 𝑏 = 1 − 𝜇 2 1 + 3 𝜇 2 : Δ𝜇 𝜇 = 0.03% UCNA (2017) (Nab goal) aCORN (2017) PERKEO II (2013) UCNA (2013) ( ) UCNA (2010) ( ) Byrne (2002) ( ) PERKEO II (2002) My average: Mostovoi (2001) 𝜇 = −1.2756(11) Yerozolimskii (1997) PERKEO II (1997) ( ) Liaud (1997) PERKEO I (1986) Stratowa (1978) −1.30 −1.28 −1.26 −1.24 𝜇 = 𝑕 𝐵 /𝑕 𝑊 7

Motivation for Nab Determination of ratio 𝜇 = 𝑕 𝐵 𝑕 𝑊 from Note: 𝜇 should be fixed by standard model. 𝐵 = −2 Re 𝜇 + 𝜇 2 1 + 3 𝜇 2 or However, precision of its calculation from 𝑏 = 1 − 𝜇 2 1 + 3 𝜇 2 : first principles is insufficiently precise: 𝜇 = 𝑕 𝐵 /𝑕 𝑊 2 + 1 + 1 Δ𝜇 𝜇 = 0.03% 1.00 1.25 1.50 1.75 𝑂 f = UCNA (2017) (Nab goal) PNDME’16 aCORN (2017) PERKEO II (2013) UCNA (2013) ( ) LHPC’12 𝑔 = 2 + 1 UCNA (2010) ( ) LHPC’10 Byrne (2002) RBC/UKQCD’08 ( ) PERKEO II (2002) Lin/Orginos’07 𝑂 My average: Mostovoi (2001) 𝜇 = −1.2756(11) Yerozolimskii (1997) RQCD’14 PERKEO II (1997) ( ) QCDSF/UKQCD’13 𝑔 = 2 Liaud (1997) ETMC’15 PERKEO I (1986) 𝑂 Stratowa (1978) CLS’12 RBC’08 −1.30 −1.28 −1.26 −1.24 𝜇 = 𝑕 𝐵 /𝑕 𝑊 Most recent 2+1+1 flavor Lattice-QCD result from PNDME: T. Bhattacharya et al., PRD 94, 054508 (2016) 7

Motivation for Nab Determination of ratio 𝜇 = 𝑕 𝐵 𝑕 𝑊 from Note: 𝜇 should be fixed by standard model. 𝐵 = −2 Re 𝜇 + 𝜇 2 1 + 3 𝜇 2 or 2. Goal: Test of unitarity of Cabibbo- However, precision of its calculation from 𝑏 = 1 − 𝜇 2 1 + 3 𝜇 2 : Kobayashi-Maskawa (CKM) matrix from first principles is insufficiently precise: 𝑣𝑒 2 𝜐 𝑜 1 + 3𝜇 2 = 4908.7 19 s and 𝑊 𝜇 = 𝑕 𝐵 /𝑕 𝑊 𝑣𝑒 2 + 𝑊 𝑣𝑡 2 + 𝑊 𝑣𝑐 2 = 1 𝑊 2 + 1 + 1 Δ𝜇 𝜇 = 0.03% 1.00 1.25 1.50 1.75 𝑂 f = UCNA (2017) (Nab goal) PNDME’16 0.976 tau aCORN (2017) Kl3 neutron ( λ , →hadrons PERKEO II (2013) (N f =2+1+1 ) τ Storage ) UCNA (2013) ( ) LHPC’12 𝑔 = 2 + 1 0.974 UCNA (2010) ( ) LHPC’10 Kl2 0 + →0 + Byrne (2002) RBC/UKQCD’08 ( ) PERKEO II (2002) mirror V ud Lin/Orginos’07 𝑂 My average: 0.972 Mostovoi (2001) nuclei 𝜇 = −1.2756(11) Yerozolimskii (1997) RQCD’14 PERKEO II (1997) ( ) neutron ( λ , 0.97 QCDSF/UKQCD’13 𝑔 = 2 Liaud (1997) τ Beam ) ETMC’15 PERKEO I (1986) 𝑂 Stratowa (1978) CLS’12 0.968 RBC’08 −1.30 −1.28 −1.26 −1.24 For neutron data to be competitive, want: 𝜇 = 𝑕 𝐵 /𝑕 𝑊 Δ𝜐 𝑜 𝜐 𝑜 ~0.3 s Most recent 2+1+1 flavor Lattice-QCD result from Δ𝜇 𝜇 ~0.03% PNDME: T. Bhattacharya et al., PRD 94, 054508 (2016) 7