1. Measurement of the neutrino velocity with the MINOS detectors and NuMI neutrino beam GdR Saclay – 11/04/08 Magali Besnier hep-ex – 0706.0437v3

2. Previous measurements Theory : if M < 3 eV/c² *  |v-c| / c < 10 -9 for a 10 GeV *best limit on neutrino mass (cosmological measurement, 2005) But : some theories allow |v-c| / c ~ 10 -4 |β -β μ |< 4×10 -4 (99% confidence level), with |1-β μ |<10 -5 Previous terrestrial measurement with Fermilab neutrino beam :  comparison between detection of µ and µ emitted in the same time (  + /K + decays) Phys. Rev. Lett. 36, 837 - 840 (1976) |β ( ) -β μ |=|β ( ) -1|<4×10 -5 (95% confidence level) E : 30 - 200 GeV. D ~500m 1) First direct velocity measurement (1976) : 2) Second measurement (1979) : Phys. Rev. Lett. 43, 1361 - 1364 (1979)

3. MINOS detectors @Fermilab =3 GeV (LE) D=732 km MINOS measurements of neutrino velocity Difference with previous measurements : Absolute transit time measurement of an ensemble of neutrinos by comparing arrival times between ND and FD FD ND CCevents @ND

4. Event selection ND selections for  CC-like events: | Tarrival-Texpected | < 7µs At least 1 “good ” reconstructed track  select  or  events Track-Vertex inside the fiducial volume  Remove cosmic background E v reco <30 GeV (E v reco =E µ + P had ) Cut on a likelihood-based variable (PID) to separate NC and CC events ( ) FD selections : | T arrival -T expected | < 50µs 1 “good” track reconstructed with direction within 53° of that of the beam Track-Vertex inside the fiducial volume Neutrino-induced rock muons (track entering from the front face of the detector with direction within 26°) and shower events inside detector volume (mostly NC) also accepted 473 induced events, with 258  CC-events ( ) 1.6 10 6 events

5. Timing measurement ND FD timet FD t ND t0t0 t1=t ND - t 0 - d ND t2=t FD - t 0 - d FD t 0 : time of proton extraction magnet signal t ND and t FD : time of the earliest scintillator hit d ND and d FD : known timing delays (readout time, electronic latency, GPS antenna fiber delays) Deviation from the expected TOF  (massless neutrino)   = (t2- t1) –  Uncorrelated jitter of the GPS clocks   (t ND - t FD )=150 ns. MI Identical GPS receiver underground connected to surface with optical fibers Uncertainty :  |d ND – d FD |) = 64 ns @ 68% CL, mostly due to GPS optical fibers NO ! The neutrino beam pulse is not instantaneous … but 9.7 µs long !

6. Timing measurement ND profile interactions measured @ND P 1 6 (t 1 ) P 1 5 (t 1 ) PDF P 1 n (t 1 ) measured @ ND  (t ND - t FD )=150 ns Expected PDF @ FD : P 2 n (t 2 )=  1/(2  ) exp (- (t 2 -t’)/(2  ²)) P 1 n (t’) dt’ Deviation  from the expected time t 2 -   maximisation of L=  ln(P 2 (t 2 i -  -  )) time of FD events relative to prediction after fitting the TOF  P 2 5 (t 2 -  ) P 2 6 (t 2 -  ) FD  = -126 ± 32(stat.) ± 64(sys.) ns @68% C.L. ( Remember :  |d ND – d FD |) = 64 ns ) NuMI beam pulse is 9.7 µs long with 5 or 6 batches

7. Relativistic mass measurement T m (E )=   ( 1-m c²/E ) Time of flight of a relativistic with a mass m Log-likelihood function : m : free parameter E i reco : reconstructed energy R(E i v, E i reco ) : detector response parametrised through MC E i v : fitted true energy constrained by R and E i reco.  : free parameter constrained by earlier systematic measurement by a gaussian with   =64ns. m =17 +33 -56 (stat.+syst.) MeV/c² @99%C.L. With  =-46 ns E i reco < 10 GeV M =50MeV/c² M =17Mev/c² m =14 +42 -98 (stat.+syst.) MeV/c² @99%C.L. With  =-99  140 (stat) ns

8. Velocity measurement Remember :  = -126 ± 32(stat.) ± 64(sys.) ns @68% C.L. |v-c|/c=|-  /(  )|=5.1 ± 2.9 (stat.+syst.) 10 -5 @68%C.L. For between 1-30 GeV Consistent with the speed of light at less than 1.8 . Most sensitive test of neutrino velocity : Arrival time comparison of photons and neutrinos from SN1987a : |v-c|/c< 2 10 -9, but only for E ~10 MeV L.Stodolsky, Phys. Lett. B201, 353 (1988) Neutrino velocity could be strong function of E. MINOS is the only one measurement constraining v in the 1-30 GeV range. But no improvements wrt previous terrestrial measurements.

9. OPERA is a long baseline neutrino experiment at Gran Sasso laboratories, receiving a  beam ( =17 GeV) from CERN, 730 km away.  It will be able to provide another measurement of v in the 1-30 GeV range Future measurements Possible improvements : Actual OPERA GPS system is equivalent to the one of MINOS. New timing system based on GPS/atomic clock will be installed in the next months both at CERN and LNGS, 10-100 times more precise. Combination with other neutrino experiments at LNGS will improve statistics. Talk from D. Autiero will give more informations on this subject in following GdR meetings

11. Long base=730 km  T= L/c = 2.4 msec L and  T from GPS expected as the best  T < 10 nsec  L < 5 cm ( ? ) Then |  -1|~   ~ 4*10 -6 Remember : FNAL(1976-77) -> 10 -4 CNGS – time of proton bunches OPERA – time of event using RPCs OPERA neutrino velocity measurement Worse case :  GPS > p bunch interspace ( 5ns now)  T ~ p batch length/  12  N (now 2 batchs with 10.5  s length) At present  t ~ 10  s/  12  1000 ~ 100ns   ~ 4*10-5 Is it possible to have 20 p batchs with 1  s length ? Better case :  GPS < p bunch interspace ( 25ns as for LHC)  T ~  GPS ~ 10 ns   ~ 4*10-6 Expected OPERA accuracy