Precise Measurement of the Neutron Beta Decay Parameters a and b - PowerPoint PPT Presentation

Precise Measurement of the Neutron Beta Decay Parameters a and b Dinko Poˇ cani´ c, University of Virginia, for the Nab Collaboration • Basics of the experiment • Measurement technique • Statistical uncertainties • Systematic uncertainties • Summary SNS FnPB PRAC Meeting Oak Ridge, 8 January 2008

2 Nab The Collaboration Arizona State University R. Alarcon, S. Balascuta, A. Klein, W.S. Wilburn, Los Alamos Nat’l. Lab. M.T. Gericke, University of Manitoba J.R. Calarco, F.W. Hersman, Univ. of New Hampshire A. Young, North Carolina State U. J.D. Bowman, T.V. Cianciolo, S.I. Penttil¨ a, Oak Ridge Nat’l. Lab. K.P. Rykaczewski, G.R. Young, V. Gudkov, Univ. of South Carolina G.L. Greene, R.K. Grzywacz, University of Tennessee University of Virginia L.P. Alonzi, S. Baeßler, M.A. Bychkov, E. Frleˇ z, A. Palladino, D. Poˇ cani´ c. Home page – http://nab.phys.virginia.edu

3 Goals of the Experiment ◦ Measure the electron-neutrino parameter a in neutron decay with ∼ 10 − 3 accuracy − 0 . 1054 ± 0 . 0055 Byrne et al ’02 current results: − 0 . 1017 ± 0 . 0051 Stratowa et al ’78 − 0 . 091 ± 0 . 039 Grigorev et al ’68 ◦ Measure the Fierz interference term b in neutron decay with sub-percent accuracy current results: none

4 Neutron Decay Parameters (SM) dw ≃ k e E e ( E 0 − E e ) 2 dE e d Ω e d Ω ν � k e · � � � � � k e × � � � k ν + b m k e k ν k ν � × 1 + a + � � σ n � · A + B + D E e E ν E e E e E ν E e E ν with: A = − 2 | λ | 2 + Re ( λ ) a = 1 − | λ | 2 1 + 3 | λ | 2 1 + 3 | λ | 2 B = 2 | λ | 2 − Re ( λ ) D = 2 Im ( λ ) 1 + 3 | λ | 2 1 + 3 | λ | 2 λ = G A ( D � = 0 ⇔ T invariance violation.) G V

5 Measurement principles: Proton momentum phase space p p2 (MeV 2 /c 2 ) proton phase space 1.4 cos θ e ν = 1 1.2 1 0.8 cos θ e ν = 0 0.6 0.4 0.2 cos θ e ν = -1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 E e (MeV) Note: For a given E e , cos θ eν is a function of p 2 p only.

6 Measurement principles: Proton TOF response functions Yield (arb. units) 1 E e = 0.075 MeV 0.8 E e = 0.236 MeV E e = 0.450 MeV 0.6 E e = 0.700 MeV 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 p p2 (MeV 2 /c 2 ) Slope = β e · a

7 Measurement principles: Spectrometer sketch Neutron Segmented Beam Si�detector TOF�region Decay transition Volume region acceleration region

8 Measurement principles: Spectrometer field profiles P configuration 4 B (T) U (10 4 V) 3 2 1 0 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 z (m)

9 Measurement principles: Detection function (I) Proton time of flight in B field: � p p0 · � t p = f (cos θ p,0 ) cos θ p,0 = � B � where . � p p p p0 B � � decay pt. For an adiabatically expanding field � 1 − B ( z ) sin 2 θ p,0 − e ( U ( z ) − U 0 ) p p z ( z ) = p p B 0 T 0 so that, prior to acceleration, � l � l m p dz m p dz f (cos θ p,0 ) = cos θ p ( z ) = . � B 0 sin 2 θ p,0 1 − B ( z ) z 0 z 0 To this we add effects of magnetic reflections and, later, of electric field acceleration.

10 Measurement principles: Detection function (II) The proton momentum distribution within the phase space bounds is given by P p ( p 2 [ recall: cos θ eν = f ( p 2 p ) = 1 + aβ e cos θ eν , p )] while � 1 � 1 � � � P p ( p 2 , p 2 dp 2 P t = p ) Φ p . p t 2 t 2 p p Detection function Φ relates the proton momentum and time-of-flight distributions! To extract a reliably: • Φ must be as narrow as possible, • Φ must be understood very precisely. Two methods (“A” and “B”) pursued to specify Φ .

11 Measurement principles: Detection function (III) 10 0 2 ) ∝ 1+ a β( E e )cosθ eν 2 ) P p ( p p , p p 2 - p e 2 - p ν 2 2 p e p ν cosθ eν = p p Spectrometer response function Φ( ⋅ 10 -1 2 ) Distribution 10 -2 2 = 0.5 MeV 2 /c 2 p p 2 = 0.9 MeV 2 /c 2 10 -3 P p ( p p p p 2 = 1.3 MeV 2 /c 2 p p 10 -4 10 -5 0.0 0.5 1.0 1.5 0.00 0.02 0.04 0.06 0.08 2 [MeV 2 /c 2 ] 2 [1/µs 2 ] p p 1/ t p E e = 550 keV

12 Measurement principles: Detection function (IV) 10 7 10 6 Simulated count rate Simulated count rate 10 10 5 E e = 300 keV E = 300 keV e E e = 500 keV E = 500 keV e 10 4 E e = 700 keV E = 700 keV e 1 10 3 0.00 0.02 0.04 0.06 0.08 0 0.01 0.02 0.03 0.04 0.05 0.06 2 [1/µs 2 ] µ 2 1/ t p 2 1/t [ s ] p Theoretical calculation Realistic Monte Carlo simulation (method “B”) (1 M decays, GEANT 4) Note: 1. central, straight portion sensitive to physics ( a ), 2. edges sensitive to detection function and calibration.

13 Statistical uncertainties for a E e , min 0 100 keV 100 keV 300 keV t p , max – – 10 µ s 10 µ s √ √ √ √ σ a 2 . 4 / N 2 . 5 / N 2 . 6 / N 3 . 5 / N √ √ σ a † 2 . 5 / N 2 . 6 / N – – † with E cal and l variable. Statistical uncertainties for b E e , min 0 100 keV 200 keV 300 keV √ √ √ √ σ b 7 . 5 / N 10 . 1 / N 15 . 6 / N 26 . 3 / N √ √ √ √ σ b †† 7 . 7 / N 10 . 3 / N 16 . 3 / N 27 . 7 / N †† with E cal variable.

14 Event rates, statistics and running times FnPB neutron decay rate for nominal 1.4 MW SNS operation is r n ≃ 19 . 5 / ( cm 3 s ) . Nab fiducial volume is V f ≃ 2 × 2 . 5 × 2 cm 3 = 20 cm 3 . This gives a rate of about 400 evts./sec . In a typical ∼ 10-day run of 7 × 10 5 s of net beam time we would achieve σ a a ≃ 2 × 10 − 3 σ b ≃ 6 × 10 − 4 and We plan to collect several samples of 10 9 events in several 6-week runs. Consequently, overall accuracy will not be statistics-limited .

15 Systematic uncertainties and checks • Uncertainties due to spectrometer response ◦ Neutron beam profile: 100 µ s shift of beam center induces ∆ a/a ∼ 0 . 2 %; cancels when averaging over detectors; measurement of asymmetry pins it down sufficiently; ◦ Magnetic field map: field expansion ratio r B = B TOF /B 0 ; ∆ a/a ∼ 10 − 3 ⇒ ∆ r B /r B = 10 − 3 , (use calibrated Hall probe); field curvature α , (via proton asymmetry measurement); field bumps ∆ B/B must be kept below 2 × 10 − 3 level; ◦ Flight path length: ∆ l ≤ 30 µ m ⇒ fitting parameter; ( ∃ consistency check); ◦ Homogeneity of the electric field; ◦ Rest gas: requires vacuum of 10 − 9 torr or better; ◦ Doppler effect; ◦ Adiabaticity;

16 Systematic uncertainties and checks (II) • Uncertainties due to the detector ◦ Detector alignment; ◦ Electron energy calibration: requirement 10 − 4 ; we’ll use radioactive sources, other strategies, also as fitting parameter; ◦ Trigger hermiticity: affected by impact angle, backscattering, TOF cutoff (to reduce accid. bgd.); ◦ TOF uncertainties; ◦ Edge effects; • Backgrounds ◦ Neutron beam related background; ◦ Particle trapping; • Uncertainties in b : fewer than for a (no proton detection); dominant are energy calibration and electron backgrounds.

17 SUMMARY The Nab experiment proposes a simultaneous high-statistics measurement of neutron decay parameters a and b with ∆ b ∼ 10 − 3 . ∆ a/a ∼ 10 − 3 and Basic properties of the Nab spectrometer are well understood; fine details of the fields are under study in extensive analytical and Monte Carlo calculations. Nab field profiles do not appear to be incompatible with those of abBA and PANDA in a common spectrometer. Development of abBA/Nab Si detectors is ongoing and remains a technological challenge. DAQ, while not trivial, is amenable to solutions using standard techniques. We propose to perform initial commissioning of the Common Spectrometer and proceed to a Nab production run of 5000 h, accumulating some 5 × 10 9 events.