Blondel, A

Donega, M

Gilardoni, S S

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CERN - EUROPEAN ORGANISATION FOR NUCLEAR RESEARCHNuFact Note 2000-53November 23, 2000Neutrino fluxes from a conventional neutrinobeam using CERN SPLA. Blondela, M. Donegab1, S. Gilardoni a2a Departement de Physique, Universite de Geneve, Switzerlandb Dipartimento di sica, Universita degli studi di MilanoAbstractThis note describes a possible low energy neutrino beam from ahorn-focused pion beam generated by 2.2 GeV protons.1Erasmus student at the Universite´ de Gene`ve and CERN2Supported by the CERN Doctoral Student Program.open-2000-34323/11/20001 IntroductionIt has been suggested that a conventional low energy neutrino beam frompion decay could be used to study neutrino oscillations [1], [2]. Based on thehorn study for pion collection for the neutrino factory [3],[4], the fluxes ofneutrinos are calculated here for a decay tunnel of 1 meter radius and 5 to30 meter length. The SPL proton energy of 2.2 GeV (kinetic energy) wasassumed.The advantage of the low energy proton beam is that strange particle pro-duction is negligible.2 System configurationPions are produced from a proton beam of 2.2 GeV (kinetic energy) imping-ing on a Hg target and focused with a magnetic horn (see Figure 1).ZR10 cm0 30 cm 100 cm1.6 cmInner conductorPion trajectoryFigure 1: Focusing system1The magnetic horn focuses only pi+, while pi− are defocused (and vice-versa reversing the current in the horn). Pions and muons decay in a cylin-drical decay tunnel of 1 meter radius and 5 to 30 meters length. The fluxesare calculated considering a detector of area A=10 m x 10 m = 100 m2 ata distance L= 50 km. This solid angle is so small that the flux for dierent(long) distances can be assumed to scale as A/L2.Pions are generated and tracked by MARS [5].Instead of a Monte Carlo simulation, an analytical expression of the decayprobabilities has been calculated for both pion and subsequent muon decayand for the probability of neutrinos to reach the detector. Muon polarisationhas been neglected for this rst evaluation.3 Neutrinos from PionsEach pion is rst propagated through the horn (pion decays in the focusingsystem are not accounted for). The probability to decay in the decay tunnelis then calculated. Finally the probability that the neutrino coming fromthat pion reaches the detector is evaluated.As soon as the particle reaches the walls of the decay tunnel, it is assumed tobe absorbed, and no further decay is considered. Since pion decay is a twobody process only one set of centre of mass decay angle produces a neutrinothat reaches the far detector. The analytical formula for the probability thata pion with a certain angle and energy produces a neutrino that reaches thedetector is given below. It is assumed that the proton beam and the decaytunnel are in line with the detector and the target. The tunnel radius andlength are considered small with respect to the target-detector distance.P (α, β) = 14pi(AL2)1−β2(βcosα−1)2α = angle between pion trajectory and decay tunnel-detector axisβ = speed of the pion (in speed of light units)A = detector areaL = distance between decay tunnel and detector24 Neutrinos from MuonsMuon decay is a three body process and there is a family of neutrinos ofdierent energies that can reach the detector. The muons produced in piondecay produce neutrinos from the process µ+ ! e+νeνµ. The calculation ofthe flux requires integration over the following variables:- pion decay angles θ and ϕ- pion decay length- neutrino energy in the muon rest frame.This integration is performed by uniform sampling. Once these are deter-mined, there is only one set of neutrino angles in the muon rest frame forwhich the neutrino reaches the detector, and the probability that the muonsdecay before reaching the walls of the decay tunnel can be readily calculated.The analytical formula for the probability density that a muon with a cer-tain angle and energy produces a νe or a νµ that reaches the detector is asfollows. It is still assumed that the proton beam and the decay tunnel arein line with the detector and the target. The tunnel radius and length areconsidered small with respect to the target-detector distance.For µ+ ! νe (νµe+)dPdEνL2dcosθ∗dϕ =62piAL2x2 (1− x)(2Eµ11+βµcosθ∗ν)(1−β2µ(βµcosδ−1)2)For µ+ ! νµ (νee+)dPdEνL2dcosθ∗dϕ =12piAL2x2 (3− 2x)(2Eµ11+βµcosθ∗ν)(1−β2µ(βµcosδ−1)2)withx = 2EνEµ11+βµcosθ∗νδ = angle between muon trajectory and decay tunnel-detector axisβµ = speed of the muon (in speed of light units)A = detector areaL = distance between decay tunnel and detectorθν = angle of the emitted neutrino in the centre of mass of the muon decayEµ, Eν= muon and neutrino energies in the laboratory frame35 Results5.1 Fluxes for a 30 meter long decay tunnelFigures 2,3,4,5,6,7, are the fluxes of neutrinos reaching a 100 m2 detectorsituated at 50 km from the target for a decay tunnel of 30 m length, and aproton beam of 2.2 GeV kinetic energy impinging on a Hg target. The fluxesof neutrinos per 20 MeV bin are given for 1023 protons (i.e. the number ofprotons given by the SPL for one year).5.2 Fluxes for a 5 meter long decay tunnelFigure 8,9,10,11,12,13, are the fluxes of neutrinos reaching a 100 m2 detectorsituated at 50 km from the target for a decay tunnel of 5m length, and aproton beam of 2.2 GeV kinetic energy impinging on a Hg target. The fluxesof neutrinos per 20 MeV bin are given for 1023 protons (i.e. the number ofprotons given by the SPL for one year).5.3 Event numberIn order to illustrate the sensitivity of such a beam for a search of νµ ! νeoscillations we give in Table 5.3 the number of events making the (unphysical)assumptions that:- all νµ oscillates to νe- νe do not oscillateThe cross section used is 0.710−38 (cm2 /GeV) Eν (GeV) which is a reasonableapproximation of the νen ! e−p cross section in the relevant energy range.Events number are calculated for neutrinos reaching a 1 kT detector situatedat 50 km from the target, considering 1023 protons.length of decay tunnel 30 m 20 m 10 m 5 mνµ ! νe from pi+ decay 259 219 145 84νe from µ+ decay 1.2 0.7 0.3 0.08Ratio 4.5 10−3 3.3 10−3 1.8 10−3 0.9 10−3Table 1: Number of events for dierent decay tunnel lengths.It can be seen that the contamination of the νe from the beam can becontrolled and reduced below 10−3 by reducing the length of the decay tunnel.4Figure 2: νµ from pion decay (pi+ ! µ+νµ). Flux of neutrinos reaching a100 m2 detector situated at 50 km from the target for a decay tunnel of 30m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.5Figure 3: νe from muon decay (µ+ ! e+νeνµ). Flux of neutrinos reaching a100 m2 detector situated at 50 km from the target for a decay tunnel of 30m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.6Figure 4: νµ from muon decay (µ+ ! e+νeνµ). Flux of neutrinos reaching a100 m2 detector situated at 50 km from the target for a decay tunnel of 30m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.7Figure 5: νµ from pion decay (pi− ! µ−νµ). Flux of neutrinos reaching a100 m2 detector situated at 50 km from the target for a decay tunnel of 30m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.8Figure 6: νe from muon decay (µ− ! e−νeνµ). Flux of neutrinos reaching a100 m2 detector situated at 50 km from the target for a decay tunnel of 30m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.9Figure 7: νµ from muon decay (µ− ! e−νeνµ). Flux of neutrinos reaching a100 m2 detector situated at 50 km from the target for a decay tunnel of 30m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.10Figure 8: νµ from pion decay (pi+ ! µ+νµ). Flux of neutrinos reaching a100 m2 detector situated at 50 km from the target for a decay tunnel of 5m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.11Figure 9: νe from muon decay (µ+ ! e+νeνµ). Flux of neutrinos reachinga 100 m2 detector situated at 50 km from the target for a decay tunnel of 5m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.12Figure 10: νµ from muon decay (µ+ ! e+νeνµ). Flux of neutrinos reachinga 100 m2 detector situated at 50 km from the target for a decay tunnel of 5m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.13Figure 11: νµ from pion decay (pi− ! µ−νµ). Flux of neutrinos reaching a100 m2 detector situated at 50 km from the target for a decay tunnel of 5m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.14Figure 12: νe from muon decay (µ− ! e−νeνµ). Flux of neutrinos reachinga 100 m2 detector situated at 50 km from the target for a decay tunnel of 5m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.15Figure 13: νµ from muon decay (µ− ! e−νeνµ). Flux of neutrinos reachinga 100 m2 detector situated at 50 km from the target for a decay tunnel of 5m length, and a proton beam of 2.2 GeV kinetic energy impinging on a Hgtarget. The flux of neutrinos per 20 MeV bin is given for 1023 protons.16References[1] K. Hu¨bner in \Mandate for the Neutrino Factory Working Group forAccelerator Aspects", May 1999, requested in \options to be exam-ined":\direct neutrino production from pi"[2] B. Richter, \Conventional Beams or Neutrino Factories: The Next Gen-eration of Accelerator-Based Neutrino Experiments", SLAC-PUB-8587[3] A. Ball et al., \Preliminary Magnetic Horn Studies in the CollectionScheme for a Neutrino Factory", proceedings of the NuFact’99 , NIM A451 (2000) 359-361[4] A. Ball et al., \Updated results of the horn study for the Nufact", NufactNote 42[5] N.V. Mokhov, \The MARS Code System User’s Guide", Fermilab-FN-628(1995)N.V. Mokhov, \MARS Code Development, Benchmarking and Applica-tions" Fermilab-Conf-00-066(2000)O.E. Krivosheev and N.V. Mokhov, \A New MARS and its Applications",Fermilab-Conf-98/43 (1998)N.V. Mokhov, S.I. Striganov, A. Van Ginneken, S.G. Mashnik, A.J. Sierkand J. Ranft, \MARS Code Developments", Fermilab-Conf-98/379 (1998)17

Neutrino Fluxes from a Conventional Neutrino Beam Using CERN SPL

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