1. Antoine Cazes Université Claude Bernard Lyon-I December 16th, 2008
SPL neutrino spectra
Antoine Cazes
Université Claude Bernard Lyon-I
December 16th, 2008
Presentation based on the following paper:
Campagne, Cazes : Eur Phys J C45: ,2006

2. Increasing the proton energy:
Positive aspect
Increase of the pion cross section
Increase of the boost
Negative aspect
Increase of the kaon cross section
Decrease the number of pot (normalization to 4MW)
Optimization is a balance between these arguments
Guide line :
(Dm²  eV²)
CERN-Fréjus = 130km
 En  260 MeV
 pp  600 MeV/c

3. Particle Producion 500 000 protons, Ek < 5GeV at 2.2GeV :
Ep(GeV)
Ep(GeV)
protons, Ek < 5GeV
at 2.2GeV :
0.26 p+/s
K+/s
at 3.5GeV :
0.29 p+/s
K+/s
at 4.5GeV :
0.32 p+/s
K+/s

4. Simulation steps p p p n Target simulation horn simulation
designs
tracking
Decay tunnel
geometry
decay simulation
Fluxes at Fréjus p p n

5. Interaction between proton beam and target.
Simulation done with FLUKA and MARS
Proton beam
Pencil like
Ek=2.2GeV, 3.5GeV, 4.5GeV, 6.5GeV and 8GeV
Target
Liquid mercury
Long : 30cm
 15mm
Normalization: 4MW
106 protons on target have been produced

6. Kinetic energy (GeV) of pions and kaons

7. Horn design p Low energy proton beam (3.5 GeV)
Large transverse momentum for the pions
<qp> = 55°
Target must be inside the horn:
140 cm
220 cm
80 cm

8. Optimisation of the horn design
Set a toroïdal magnetic field
Send a pion from the target, Stop when it is horizontal.
Repeat with different angles
Design your horn ! B2 x
En  300 MeV
pp  800 MeV/c B1
With different proton energy, the horn can be design to produce similar neutrino flux

9. Horn simulation p Drawing from the horn built at CERN
Using Geant 3.2.1
Tracking cuts
µ, hadrons : 100 keV
g, e+, e- : 10 keV
Stepping :
10mrad in the magnetic field
100µm and loose less than 1% of Ek in the conductors

10. Decay Tunnel Parameters
Length
modify purity
L=10m, 20m, 40m and 60m have been tested.
10m40m
nm , nm + 50% to 70%
ne , ne + 50% to 100%
40m60m
nm , nm + 5%
ne , ne + 20%
40m seems better
Radius
modify acceptance
R=1m, 1.5m and 2m have been Tested
1m 2m (L=40)
nm , nm +50%
ne , ne +50% to 70%
2m seems better
This results have been checked on sensitivity to q13 and dCP

11. Flux computation Low energy  Small boost  low focusing
Need a high number of events (~1015 evts!!!)
Use probability
Each time a pion, a muon, or a kaon is decayed by Geant, compute the probability for the neutrino to reach the detector
Use this probability as a weight, and fill an histogram with the neutrino energy
Gives neutrino spectrum.

12. Probability method …. Pions
Pion is tracked by Geant
When it decays, The probability for the neutrino to reach the detector is computed:
p+m+nm : (2-body decay) a q p+ m+ nm d
P = 1 4p A L2
1 – b2
(b cosa -1)2 p
L : distance to detector
A : detector surface
To reach the detector: d = -a

13. Probability method …. Muons
m+e+nmne
But muons have small decay probability.
for each muon
loop on the phase space (q,f,E)
compute decay probability e-x/gct
if it decays, compute probability for the neutrino to reach the detector :
P = 1 4p A L2
1 – bm2
(bmcosr -1)2 2 mm
1 + bmcosqm  *
(f0(x) Pf1(x)cosqm) 
x = 2En/mm
f0(x)
f1(x) nm
2x2(3-2x)
2x2(1-2x) ne
12x2(1-x)
P is the muon polarisation coming from the pion/kaon decay

14. Probability method …. Kaons
Very few kaons :
kaon produced in the target is duplicated many times: ~100.
Decay using Geant
Choose the decay channel
Probability computed depending on the decay channel
2 body decay
3 body decay

15. Neutrino Flux 100km away p+ focusing evts/100m2/y Ek=3.5GeV En ~300MeV
L = 40m,R=2m
p+ focusing
from p and m
from K0
from K
Ekine (GeV)
evts/100m2/y

16. Neutrino flux @ 130km 3.5GeV Kinetic proton beam ~800MeV p focusing
~300MeV neutrinos
40m decay tunnel length
2m decay tunnel radius
Flux available for Ek=2.2GeV, 3.5GeV, 4.5GeV, 6.5GeV and 8GeV and two type of focalization system.

17. Proton beam energy comparizon
En~260MeV
dCP = 0
10-3
sin22q13
Dm223 (eV2)
2.2GeV
3.5GeV
4.5GeV
8GeV
5 year positive focussing
10 years mixte focussing
(8y + and 2y -)
Campagne, Cazes : Eur Phys J C45: ,2006

18. Conclusion Choice of the beam energy is delicate
Tools exist to do another simulation
Proton interaction on target should be better with new version of fluka
Shape of the horns is crucial.
Technical feasability should be taken into account...