110 Monte Carlo Study Of The AbBA Experiment: Detector .

Volume 110, Number 4, July-August 2005Journal of Research of the National Institute of Standards and Technology[J. Res. Natl. Inst. Stand. Technol. 110, 437-441 (2005)]Monte Carlo Study of the abBA Experiment:Detector Response and Physics AnalysisVolume 110E. Frlez abBA Collaboration,Department of Physics,University of Virginia,Charlottesville, VA 22904-4714USA1.Number 4July-August 2005The abBA collaboration proposes toconduct a comprehensive program ofprecise measurements of neutron β-decaycoefficients a (the correlation between theneutrino momentum and the decayelectron momentum), b (the electronenergy spectral distortion term), A (thecorrelation between the neutron spin andthe decay electron momentum), and B(the correlation between the neutron spinand the decay neutrino momentum) at acold neutron beam facility. We have useda GEANT4-based code to simulate thepropagation of decay electrons and protonsin the electromagnetic spectrometer andstudy the energy and timing response of aIntroduction2.The abBA collaboration is proposing to perform ameasurement of a “complete set” of correlations in theneutron β-decay using the same apparatus, and improvethe precision of the correlation coefficients a, b, A, andB by up to an order of magnitude.GEANT4 is a general-purpose software package forsimulation of the passage of particles through matterthat provides a complete set of tools for all domains ofdetector simulation [1]. In particular, the GEANT4toolkit currently provides particle tracking in nonuniform magnetic and electric fields and handlescombined electromagnetic fields transparently [2]. TheGEANT4 Low Energy Electromagnetic Physics groupvalidates the low energy electromagnetic processes forelectrons down to 250 eV [3].In this report we describe a GEANT4 simulation ofthe abBA spectrometer and outline the algorithm for theextraction of the physics decay parameters.pair of Silicon detectors. We used theseresults to examine systematic effects andfind the uncertainties with which thephysics parameters a, b, A, and B canbe extracted from an over-determinedexperimental data set.Key words: detector Monte Carlosimulation; neutron beta decay; GEANT4.Accepted: August 11, 2004Available online: http://www.nist.gov/jresabBA Detector GeometryIn the tentative design of the abBA spectrometer thedecay particles (electrons and protons) are guided bythe electric and magnetic fields and interact only insensitive detectors thus avoiding the energy losses andscatterings in apertures, grids, or windows [4].The simplified geometry of the detector definestwo sensitive planar Silicon detectors with a 100 mm 100 mm2 area and a 2 mm thickness. The two Si detectors are separated by 4 m. The coordinate system isdefined with the Si detectors at x1,2 2 m (Fig. 1).A passive solenoid magnet is placed around thedecay region, with its axis of symmetry perpendicularto the incident neutron beam, along the x coordinate.The 3 m long magnet with a 0.8 m radius can producea 4 T central magnetic field that decreases to 1 T at thedetector positions, thus guiding charged particles fromthe decay region to the Si detectors. A tubular electrodeheld at 30 kV accelerates the protons so they can bedetected in a silicon detector.437

Volume 110, Number 4, July-August 2005Journal of Research of the National Institute of Standards and TechnologyFig. 1. The schematic drawing of the main elements of the abBA spectrometer.3.Magnetic Fieldwhere φ is the magnetic scalar potential and ρ y 2 z 2is the axial radius coordinate. These fields have beenprogrammed into the GEANT4 user routine.The magnetic field along the x axis of the detectorsolenoid is given by:B( x, ρ 0) 2π NI L xx 2c R 2 ( L x)2R x24. , The electrons from the neutron β-decay are generated from (5 5 5) mm3 central volume with the relativistic differential decay rate given by [5]:where L is the length of the solenoid, R its radius,and x the axial coordinate. Meanwhile, N denotes thenumber of turns per unit length, and I is the electricalcurrent in the closely wound cylindrical coil.Thanks to axial symmetry, the magnetic field offaxis, outside its sources, can be represented in terms ofthe magnetic field strength B(x, 0) along the axis:F ( Ee ) pe Eν(G V ) 2dΓ2 F ud5M ,ˆβdEe dΩ pe dΩ pν(2 π) mn [ Ep Eν Ee ( pν )]where Ee and pe (Eν and pν) are the electron (neutrino)energy and momentum, mn is the neutron mass, GF is theFermi constant, Vud is the Cabbibo-Kobayashi-Maskawamatrix element, β pe/Ee, and F(Ee) is the Fermi function that describes the interaction of the electron and therecoil proton.The transition matrix element squared M 2 is given by2nBx ( x, ρ ) φ( 1) n (2 n ) ρ B ( x) x n 0 (n !) 2 2 2ρ B ( x) B′′( x,0) " ,2andBρ ( x, ρ ) φ( 1) n ρ B(2 n 1) ( x) ρ n 1 (n 1)! n! 2 ρ B ′( x,0) " ,2Event Generator2 n 1M2α R α eV 1 δ α(1) mn mp Ee Eν 1 22ππ α C0 ( Ee )(1 3 g A2 ) 1 1 δ α(2) C1 ( Ee ) β ˆpν 2π438

Volume 110, Number 4, July-August 2005Journal of Research of the National Institute of Standards and Technology m b e Ee α (2) 1 δ α [ C2 ( Ee ) C3 ( Ee ) β ˆpν ] nˆ β 2π [C4 ( Ee ) C5 ( Ee ) β pˆ ν ] n pν },β-decays. We used the values of the correlation coefficients from Ref. [7] (a –0.1039, b 0, A –0.1161,B 0.9878). For each event we recorded the neutronpolarization, generated momenta of the final stateparticles and measured energy depositions and timinghits in the Silicon detectors.The separate GEANT4 run which included systematic effects (energy and timing resolutions of Si detectors,detector calibration uncertainties, detector responsenonlinearities, magnetic field inhomogeneities, neutronpolarization uncertainty, etc.) was used to simulate theexperimental data. (“MC data”). The flow chart of thephysics analysis is summarized in Fig. 2. The correlation coefficients and their fitted uncertainties areextracted using the standard MINUIT code [8].where mp is the proton mass, α is the fine structureconstant, eVR is a low energy constant, δα’s are modelindependent radiative corrections, gA is the axial coupling constant, and the correlation coefficients a, A, Bare incorporated into the recoil corrections Ci(Ee) [6].5.Results and ConclusionsA GEANT4 simulation of abBA detector energyand timing response was performed for 106 neutronFig. 2. A flow diagram of the analysis. Monte Carlo histograms are recalculated in eachstep of MINUIT minimization. The “experiment” depends only on measured quantities(subscript E), while the MC column depends both on generated variables (subscript T) andsimulated detector response (subscript E).439

Volume 110, Number 4, July-August 2005Journal of Research of the National Institute of Standards and TechnologyWe present two example results: (i) the extraction ofthe parameter b with unpolarized neutron beam inFig. 3, and (ii) the asymmetry coefficient A for 80 %polarized neutron beam in Fig. 4. At the current stageof development, a GEANT4 simulation limited to 106neutron decay events and 106 MC data events, runs24 CPU hours on a 1 GHz Linux computer. Given thelimited event statistics, analysis of MC data results inthe coefficient b –0.0025 0.0028 and the coefficientA –0.1170 0.0010, where statistical and systematicuncertainties are combined. The code will be madefaster by using the adiabatic invariants for chargedparticle tracking in the electromagnetic field, whichwill markedly improve the uncertainties of our method.Fig. 3. Monte Carlo energy spectrum of neutron β-decay electron (top) and fractional differences (exp – the)/(exp the) between the simulated and “MC data” spectrum (bottom).440

Volume 110, Number 4, July-August 2005Journal of Research of the National Institute of Standards and TechnologyFig. 4. Monte Carlo histogram of the β asymmetry (top) and fractional differences between thesimulated and “MC data” spectrum as a function of the electron energy (bottom).6.References[5] J. D. Jackson, S. B. Treiman, and H. W. Wyld, Phys. Rev. 106,517-521 (1957).[6] S. Ando, H. W. Fearing, V. Gudkov, K. Kubodera, F. Myhrer,S. Nakamura, and T. Sato, arXiv:nucl-th/0402100 (2004).[7] F. Glück, I. Joó, and J. Last, Nucl. Phys. A 593, 125-150 (1995).[8] F. James, and M. Roos, MINUIT—Function Minimization andError Analysis, CERNLIB D506, CERN, Geneva (1989).[1] GEANT4 Home Page, http://wwwinfo.cern.ch/asd/geant4(May 2004) [Accessed May 31, 2004]. S. Agostinelli et al.,Nucl. Instr. Meth. A 506, 250-303 (2003).[2] D. Wright, Geant4 User’s Guide For Toolkit Developers,CERN, Geneva (2002).[3] P. Nieminen et al., CERN preprint OPEN-99-034, CERN,Geneva (1999).[4] J. D. Bowman et al., The abBA Experiment Proposal: PreciseMeasurement of Neutron Decay Parameters, September 2003.441

[J. Res. Natl. Inst. Stand. Technol. 110, 437-441 (2005)] Monte Carlo Study of the abBA Experiment: Detector Response and Physics Analysis Volume 110 Number 4 July-August 2005 E. Frlez abBA Collaboration, Department of Physics, University of Virginia, Charlottesville, VA 22904-4714 USA The abBA collaboration proposes to conduct a .