Simulation of Neutrino Factory beam and quasielastic scattering off

electrons in the near detector

Yordan Karadzhov

University of Sofia “St. Kliment Ohridski”

Initial conditions of simulation : Length of the straight section of muon storage ring –

500 m. Muon decays are evenly distributed along the straight

section. Distance from the end of the straight section to the

detector is 500 m.

Muon beam parameters :

1. polarization : 1, -1 and 0.

2. beam energies : 20, 30, 40 GeV.

3. energy distribution : Gaussian (σ = 80 MeV)

4. angular distribution : Gaussian (σ = 0.5x10-3)

5. Distribution in a plane perpendicular to the beam : Gaussian (σ = 5cm)

Muon decay matrix element

For νμ

For antiνe

where x = 2Eν/mµ , Pµ is the polarization of the muon and θ is the angle between polarization vector and neutrino direction.

22

21cos23 xxθP+x~dxdΩ

Ndμ

ν

22

1cos1 xxθP+x~dxdΩ

Ndμ

ν

Muon decay matrix element (neutrino energies and polar angles in c.m. system)

Distributions of generated events in c.m system.

Neutrino beam Distributions of points where νμ cross a plane situated at

500 m from the end of the straight section and perpendicular to the beam axis for polarization 1 and -1 .

Muon energy 40 GeV

Neutrino beam Distributions of points where antiνe cross a plane situated

at 500 m from the end of the straight section and perpendicular to the beam axis for polarization 1 and -1.

Muon energy 40 GeV.

Neutrino beam Number of neutrinos per cm2 in the same plane for 100000 muon decays

simulated Muon energy 40 GeV.

Distributions of neutrino energies and polar angles in lab. system. Muon energy 40 GeV.

Quasielastic scattering off electrons in the near detector (from “Leptons and quarks” L.B.Okun)

1.

• Cross section is isotropic in c.m. system

μ+e+ e

s

ms

π

G=σ μF

222

Quasielastic scattering off

electrons in the near detector

2.

• Differential cross section in

c.m. system is:

• And total cross section is:

μ+νe+ν μe

2

222 3/12

s

)EE+E(Ems

π

G=σ ν2ν1μeμF

cosθ

m+s

ms+cosθ

m+s

ms+

s

EEms

π

G=

dcosθ

dσ2μ

μ

2e

eμeμF

22

2

222

112

Energy spectrums for νμ (green) and anti νe (blue).

Red line indicates the energy threshold. Muon energy 40 GeV.

Energy spectrum of νμ (green) and anti νe (blue) passing through the

cylinder with radius 1 m and thickness 30 cm, and at 500 m distance from the end of the straight section. Red line indicates the energy threshold .

Muon energy 40 GeV.

Energy spectrums of muons from reaction (green) and (blue) in that cylinder. μ+νe+ν μe

μ+e+ e

Muon energy 40 GeV.

• Energy versus polar angle for muons from reaction

and

μ+e+ e μ+νe+ν μe

Muon energy 20 GeV.

• Distribution of polar angle of muons from reaction

(green) and (blue)

μ+e+ e

μ+νe+ν μe μ+e+ e

Muon energy 20 GeV.

• Total number of muons per year (1021 muon decays per year) produced in a cylindrical detector with radius 1 m, thickness 30 cm and density 1.032 g/cm3(scintillator, total mass ~1 ton), 500 m distant from the end of the straight section.

• The third column shows total number of muons per year produced in the same cylinder from inclusive CC reactions (cross section = k.Eν, k taken from PDG ).

• E = 40GeV , P = 1 6.87x105 5.81x105 1.92x109

• E = 40GeV , P = -1 1.67x106 6.97x104 2.81x109

• E = 30GeV , P = 1 2.02x105 1.97x105 1.32x109

• E = 30GeV , P = -1 5.89x105 1.60x104 1.91x109

• E = 20GeV , P = 1 1.83x104 1.14x104 8.07x108

• E = 20GeV , P = -1 7.83x104 7.76x102 1.14x109

μ+νe+ν μe μ+e+ e

N

N

Total number of muons from pure leptonic reactions as a function of distance between end of the straight section

and detector with 1 m radius and ~ 1 ton mass.

400m long straight section is used for these simultaions.

Muon energy 20 GeV.