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 C45:643-657,2006

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  2.5 10-3eV²) CERN-Fréjus = 130km  En  260 MeV  pp  600 MeV/c

Particle Producion 500 000 protons, Ek < 5GeV at 2.2GeV : Ep(GeV) Ep(GeV) 500 000 protons, Ek < 5GeV at 2.2GeV : 0.26 p+/s 0.8 10-3 K+/s at 3.5GeV : 0.29 p+/s 2.8 10-3 K+/s at 4.5GeV : 0.32 p+/s 5.2 10-3 K+/s

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

Interaction between proton beam and target. Simulation done with FLUKA 2002.4 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 1.1×1016pot/s@2.2GeV 0.7×1016pot/s@3.5GeV 106 protons on target have been produced

Kinetic energy (GeV) of pions and kaons

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

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

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

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

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.

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

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

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

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

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.

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 C45:643-657,2006

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...