The Neutrino of the OPERA:

The Neutrino of the OPERA: constraints on neutrino velocity. Giacomo Cacciapaglia KC London & IPN Lyon meeting @ King s College London 23 November 2011

Experimental situation OPERA announced a time of flight (TOF) anomaly in the neutrinos propagating from CERN to Gran Sasso Laboratories: E ν = 28.1 GeV E beam = 17 GeV δt = 57.8 ± 7.8 (stat) +8.3 5.9 v c ( = 2.4 ± 0.32 (stat) +0.34 ) c 0.23 (sys) 10 5 (sys) nsec In 2007, MINOS released a similar measurements, hinting to superluminality with low significance: E ν = 3 GeV v c c δt = 126 ± 32(stat) ± 64(sys) nsec = (5.1 ± 2.9) 10 5 Previous measurements: Fermilab 1979 L 500 m E ν 20 200 GeV v ν v µ c < 4 10 5 Bound from Supernova SN1987a L 50000 pc E 10 MeV v c c < 10 9

The Supernova challenge The supernova SN1987a emitted a burst of neutrinos and photons that reached Earth in 1987, from a distance of 51 kpc A handful of electron neutrino events were detected in various experiments that day

The Supernova challenge The supernova SN1987a emitted a burst of neutrinos and photons that reached Earth in 1987, 51 kpc away A handful of electron neutrino events were detected in various experiments that day

The Supernova challenge The supernova SN1987a emitted a burst of neutrinos and photons that reached Earth in 1987, 51 kpc away A handful of electron neutrino events were detected in various experiments that day Important data: The neutrino energies range from 7 to 40 MeV The duration of the neutrino burst is 10 seconds: even without relying on a model of neutrino emission, this poses a serious bound! Light has been observed the same day (with OPERA speed, the neutrinos should have arrived 4 years earlier!)

Flavour violation: ruled out! i.e. Giudice, Sibiryakov, Strumia 1109:5682 Can the speed of electron and muon neutrino be different? Oscillations can be described by this effective Hamiltonian: H eff = E(1 + δv νi )+ m2 i 2E Therefore, the phase of the oscillation in MINOS would be: δv ν EL + m2 L 2E δv ν m2 2E 2 2.4 10 3 ev 2 2(3 10 9 ev) 2 10 22 The effect must be flavour independent! Oscillations may pose a serious constraint on any model of LV that attempts to explain the OPERA anomaly.

Energy dependence of the effect: there is more in the data than a TOF shift! Cacciapaglia, Deandrea, Panizzi 1109:4980 Both MINOS and OPERA neutrino bunches have a time-structure that is reproduced by the neutrino data. An energy dependent velocity MUST also modify the shape of the bunch, because the neutrino beams have an energy spectrum. MINOS data

Energy dependence of the effect: there is more in the data than a TOF shift! Cacciapaglia, Deandrea, Panizzi 1109:4980 Both MINOS and OPERA neutrino bunches have a time-structure that is reproduced by the neutrino data. An energy dependent velocity MUST also modify the shape of the bunch, because the neutrino beams have an energy spectrum. OPERA

Fit of MINOS data We define a power law dependence of the velocity correction: v ν 1= Eα ν 2M α Our simulation of near detector (black) and far detector (blue) data: α=0.7 α=2.1 MINOS data show a shift but NOT a smear -> α must be small! NOTE: non integer α and effect only for neutrinos can be explained in models of conformal neutrinos or models in warped extra dimensions. For the purpose of this talk, this is just an illustrative toy model!

SN1987a data We simulated 10 000 data sets, with energy distribution according to errors. We evolve them back to obtain a distribution of initial time spreads. 800 Distribution of initial time intervals 600 Μ 28.7355 sec Σ L 4.74091 sec Σ R 5.38805 sec counts 400 200 0 20 25 30 35 40 45 50 seconds

SN1987a data We simulated 10 000 data sets, with energy distribution according to errors. We evolve them back to obtain a distribution of initial time spreads. We generate a set of neutrinos emitted by the SN1987a, with energy spectrum given by SN models, and time duration according to our previous results. ν counts 4000 3000 2000 Energy spectrum at supernova Μ 10.9992 MeV Σ L 4.45896 MeV Σ R 6.61341 MeV 1000 0 0 10 20 30 40 50 MeV

SN1987a data We simulated 10 000 data sets, with energy distribution according to errors. We evolve them back to obtain a distribution of initial time spreads. We generate a set of neutrinos emitted by the SN1987a, with energy spectrum given by SN models, and time duration according to our previous results. We evolve the simulated neutrinos forward to Earth, and compare the arrival times with the measured spread of 10 seconds 800 Distribution of shifts We fiddled with the parameters of the simulation, and the results are stable! counts 600 400 Μ 26.7653 sec Σ L 2.59678 sec Σ R 2.60789 sec Only (mild) model dependence from the spectrum of the SN! 200 0 20 25 30 35 seconds

Combined plot Α.. 2.0... 1.5.. 1.0 1.64Σ Supernova Bound Statistic + Systematic Only Statistic 0.5 1Σ 0.0 5 10 15 20 Log M

Combined plot 2.0 1.5 Supernova Bound For Alpha > 2.5, advance compatible with SN. Statistic + Systematic Alpha > 1.5 likely to be excluded by shape Only Statistic analysis! The OPERA data should be analysed in the same way! Α 1.0 1.64Σ 0.5 1Σ 0.0 5 10 15 20 Log M

Alternative energy dependence: exponential v ν 1=δ (1 e E/µ ) 10 Allowed t ν < 10 sec SN1987a t νγ < 10 hours SN1987a Log Μ GeV 5 0 v ν 1 < 4 10 5 FERMILAB79 MINOS 1σ region MINOS 3σ bound 5 OPERA 3σ region 12 10 8 6 4 2 0 Log

Alternative energy dependence: threshold v ν 1=δ ( 1 + tanh ( E m µ )) 1.0 0.8 m' 1 GeV t ν < 10 sec SN1987a Μ GeV 0.6 0.4 t νγ < 10 hours SN1987a v ν 1 < 4 10 5 FERMILAB79 MINOS 1σ region 0.2 0.0 Allowed 10 8 6 4 2 0 Log MINOS 3σ bound OPERA 3σ region

Glashow+Cohen, Gonzales-Mestres, Bi et al: energy loss due to Cherenkov-like emission Assuming a modified dispersion relation: p = g(e) v ν = E p = 1 g (E) Cohen, Glashow, 1109.6562 Gonzales-Mestres, 1109.6630 Bi, Yin, Yu, Yuan, 1109.6667... For the process ν ν + e + + e, energy and momentum conservation yield Eν 2 g(e ν ) 2 = 2 2 E f p f > (2m e ) 2 f If the speed of neutrinos is constant, then the process is kinematically allowed for neutrino energies above f g(e ν )= E ν v ν E ν min. = 2m ev ν v 2 ν 1 15 MeV Super-luminal OPERA neutrinos may lose all their energy before reaching Gran Sasso!

Glashow+Cohen, Gonzales-Mestres, Bi et al: energy loss due to Cherenkov-like emission Assuming a modified dispersion relation: Assumption 1: p = g(e) v ν = E p = 1 g (E) Cohen, Glashow, 1109.6562 Gonzales-Mestres, 1109.6630 Bi, Yin, Yu, Yuan, 1109.6667... For the process ν ν + e + + e, energy and momentum conservation yield Eν 2 g(e ν ) 2 = 2 2 Assumption 2: E f p f > (2m e ) 2 f If the speed of neutrinos is constant, then the process is kinematically allowed for neutrino energies above f g(e ν )= E ν v ν E ν min. = 2m ev ν v 2 ν 1 150 MeV Super-luminal OPERA neutrinos may lose all their energy before reaching Gran Sasso!

Glashow+Cohen, Gonzales-Mestres, Bi et al: energy loss due to Cherenkov-like emission Cohen, Glashow, 1109.6562 Gonzales-Mestres, 1109.6630 Bi, Yin, Yu, Yuan, 1109.6667... Calculation of the decay width (mean free path) from the standard expression of amplitudes and standard phase space integral! Assumption 3: Γ(ν νe + e )= 1 14 G F 192π 3 E5 ν(v 2 ν 1) 3 1 700 km ( Eν 20 GeV ) 5 This decay rate should be calculated in detail in any model that aims at explaining the OPERA result! Other processes: ν νµe E ν min. 15 GeV ν νµµ E ν min. 31 GeV ν πµ E ν min. 36 GeV

Glashow+Cohen, Gonzales-Mestres, Bi et al: energy loss due to Cherenkov-like emission Argument based on this threshold equation: Eν 2 g(e ν ) 2 = 2 effective mass! E f f f p f 2 > (2m e ) 2 Cohen, Glashow, 1109.6562 Gonzales-Mestres, 1109.6630 Bi, Yin, Yu, Yuan, 1109.6667... Simple way-out: tachyon-like behaviour! p = g(e ν ) >E ν for instance: g(e ν )= E 2 ν + m 2 tach However: v ν = 1+ m2 tach E 2 ν 1+ m2 tach 2E 2 ν...

Gonzales-Mestres and Bi et al: energy from pion decay The effective mass of the neutrino is such that the pion decay is kinematically forbidden for large neutrino energies! Neutrino energies bounded below 5 GeV! Gonzales-Mestres, 1109.6630 Bi, Yin, Yu, Yuan, 1109.6667... 50 tachyon Maximum neutrino energy EΝ 40 30 Special Relativity 20 10 0 0 10 20 30 40 50 60 constant velocity EΠ

Giudice, Sibiryakov, Strumia: LV propagates to charged leptons at loop level Giudice, Sibiryakov, Strumia 1109:5682 Assuming the integral dominated by energies around OPERA energy: A detailed model is required to reliably calculate the loop! Many bounds on electron speed based on Glashow argument: revision needed! Synchrotron from LEP Cosmic rays: e eγ Cosmic rays: γγ e + e Cosmic rays: γ e + e Synchrotron from CRAB δv e < 5 10 15 δv e < 10 13 δv e < 10 15 δv e < 2 10 16 δv e < 5 10 15

Giudice, Sibiryakov, Strumia: LV propagates to charged leptons at loop level Giudice, Sibiryakov, Strumia 1109:5682 Assuming the integral dominated by energies around OPERA energy: If the LV were generated by a mass term : A detailed pmodel 2 mis 2 LV required (E) v ν Synchrotron 1+O(m 2 fromlv LEP ) to reliably calculate the ( Cosmic rays: e eγ loop! δ p 2 (m e + δ loop m LV ) 2 2 v e 1+O loop δv ν Cosmic rays: γγ δ e + e loop m e δv ν Many bounds on electron speed based on Glashow argument: revision needed! Cosmic rays: γ e + e Synchrotron from CRAB δv e < 5 10 15 δv e < 10 13 δv e < 10 15 ) δv e < 2 10 16 δv e < 5 10 15

Conclusions (so far): if the OPERA anomaly were due to super-luminal propagation in vacuo The speed of neutrinos must be flavour universal to a very good accuracy! Strong energy dependence in the few GeV - 30 GeV range disfavoured by the absence of shape distortion. There must a kink or threshold dependence on energy! (SN1987a) Cherenkov emission and pion decay prefer a tachyonic behaviour (model dependent) Kinematic bounds (Glashow and pion decay) and loop corrections are (highly) model-dependent!