Lecture 3/4 The neutrino oscillation industry Solar Neutrinos SuperK : Solar neutrino-gram Light from the solar core takes a million years to reach the surface Fusion processes generate electron neutrinos which take 2s to leave Solar neutrinos are a direct probe of the solar core Roughly 4.0 x 1010 solar e per cm2 per second on earth Solar neutrino generation Solar Neutrino Flux As predicted by Bahcall's Solar model The Solar Neutrino Problem - Homestake SSM Homestake sensitive to 8 B and 7Be electron neutrinos E > 800 keV Observe 1/3 of the expected number of solar neutrinos 1 SNU = 1 interaction per 1036 atoms per second (Super)Kamiokande 1987 – Kamiokande : 1000 phototubes, 5000 tons of water 1997 – SuperKamiokande : 11000 PMT, 50000 tons of water SuperK can only observe the 8B flux (> 5 MeV) Data =0.451±0.017 SSM Confirmation that it wasn't just the radioChemical experiments SuperK only sensitive to e Experimental summary Atmospheric neutrinos High energy cosmic rays interact in the upper atmosphere producing showers of mesons (mostly pions) Neutrinos produced by Expect N ( νμ + νμ ) ≈2 N (ν e + ν e ) At higher energies, the muons can reach the ground before decaying so ratio increases /e Data R= /e MC R ~ 0.6 - 0.7 The Atmospheric Neutrino Anomaly Neutrino Flavour Oscillations Mixing CKM Mechanism u d' , L c s' L d '=d cos c s sin c s '=−d sin c s cos c In the quark sector, the flavour eigenstates (those states which couple to the W/Z) are not identical to the mass eigenstates (those states which are solutions of the Dirac equation) Weak states 0.97 0.23 0.003 d d' s ' = 0.23 0.97 0.04 s 0.008 0.04 0.99 b b' Mass states Mixing CKM Mechanism u d' , L c s' L d '=d cos c s sin c s '=−d sin c s cos c In the quark sector, the flavour eigenstates (those states which couple to the W/Z) are not identical to the mass eigenstates (those states which are solutions of the Dirac equation) Weak states Unitary mixing matrix e 1 =U 2 3 Mass states Neutrino Oscillations * i Amp ∝ ∑i U Prop i U i If we can't resolve the individual mass states then the amplitude involves a coherent superposition of i states Prob = −4 ∑ i j ℜU* i U i U j U* j sin2 m2ij L 4E L 2 ∑ i j ℑU U i U j U sin m 2E * i * j 2 ij If mij2 = 0 then neutrinos don't oscillate Oscillation depends on |m2| - absolute masses, or mass patterns cannot be determined. If there is no mixing (If Ui = 0) neutrinos don't oscillate One can detect flavour change in 2 ways : start with and look for appearance) or start with and see if any disappears (disappearance) Flavour change oscillates with L/E. L and E are chosen by the experimenter to maximise sensitivity to a given m2 Flavour change doesn't alter total neutrino flux – it just redistributes it amongst different flavours (unitarity) Two flavour oscillations =U 1 ⇒U= 2 cos sin −sin cos L P = −4 ∑ i j U i U i U j U j sin m 4E 2 2 ij P() : Appearance Probability P() : Survival Probability L P =−4U 1 U 1 U 2 U 2 sin m 4E 2 2 2 2 L km .=sin 2 sin 1.27 m eV EGeV 2 (changing to useful units) 2 ij Survival Probability L E ≪ m 2 L E L ~ m2 E ≫ m2 L/E 2 2 P 0 x =1−sin 2 sin 1.27 m 2 L /km E /GeV Three Flavour Oscillation The three flavour case is more complicated, but no different e 1 U e1 U e2 U e3 =U 2 ⇔U= U 1 U 2 U 3 3 U 1 U 2 U 3 U is the Pontecorvo-Maskawa-Nakayama-Sakata (PMNS) matrix L Prob = −4 ∑ i j ℜU U i U j U sin m 4E * * 2 L 2 ∑ i j ℑU i U i U j U j sin mij 2E * i * j 2 2 ij Oscillation parameters )( )( U e1 U e2 U e3 c 12 s 12 0 c 13 0 s 13 e i δ 1 0 0 1 0 0 iα U= U μ 1 U μ 2 U μ 3 = −s 12 c12 0 0 c s 0 1 0 0 23 23 0 e U τ1 U τ2 U τ3 0 0 1 −s13 ei δ 0 c13 0 −s 23 c 23 0 0 e iβ ( )( )( ) 2 independent m2 L Prob = −4 ∑ i j ℜU U i U j U sin m 4E * * 2 L 2 ∑ i j ℑU i U i U j U j sin mij 2E * i * j 2 2 ij Oscillation parameters )( )( U e1 U e2 U e3 c 12 s 12 0 c 13 0 s 13 e i δ 1 0 0 1 0 0 iα U= U μ 1 U μ 2 U μ 3 = −s 12 c12 0 0 c s 0 1 0 0 23 23 0 e U τ1 U τ2 U τ3 0 0 1 −s13 ei δ 0 c13 0 −s 23 c 23 0 0 e iβ ( )( )( ) Three angles L Prob = −4 ∑ i j ℜU U i U j U sin m 4E * * 2 L 2 ∑ i j ℑU i U i U j U j sin mij 2E * i * j 2 2 ij Oscillation parameters )( )( U e1 U e2 U e3 c 12 s 12 0 c 13 0 s 13 e U= U μ 1 U μ 2 U μ 3 = −s 12 c12 0 0 1 0 U τ1 U τ2 U τ3 0 0 1 −s13 ei δ 0 c13 ( iδ )( 1 0 0 1 0 0 0 c 23 s 23 0 e i α 0 0 −s 23 c 23 0 0 e iβ )( ) CP violating phase L Prob = −4 ∑ i j ℜU U i U j U sin m 4E * * 2 L 2 ∑ i j ℑU i U i U j U j sin mij 2E * i * j 2 2 ij Oscillation parameters )( )( U e1 U e2 U e3 c 12 s 12 0 c 13 0 s 13 e U= U μ 1 U μ 2 U μ 3 = −s 12 c12 0 0 1 0 U τ1 U τ2 U τ3 0 0 1 −s13 ei δ 0 c13 ( iδ )( 1 0 0 1 0 0 0 c 23 s 23 0 e i α 0 0 −s 23 c 23 0 0 e iβ )( ) Extra Majorana phases The extra Majorana matrix does not affect flavour oscillation processes.....so is usually dropped. However it will affect the interpretation of neutrinoless double beta decay results Explaining the solar data Testing the oscillation hypothesis Solar neutrino problem ne from sun would change to n or n . However these have too little energy to interact via the charged current, and all the detectors are only sensitive to charge current interactions. Non-ne component would effectively disappear, reducing the apparent ne flux. Proof : Neutral current event rate shouldn't change. Sudbury Neutrino Observatory 1000 tonnes of D20 6500 tons of H20 Viewed by 10,000 PMTS In a salt mine 2km underground in Sudbury, Canada SNO e e+ e+0.15*( SNO Results 5.3 appearance of in a e beam Roughly 70% of e oscillates away Naively... First instinct is to assume that neutrinos leave the sun as e and oscillate on their way to the earth. Assuming this 8 2 L∼10 km , E ν< 10 MeV → Δ m ∼3×10 −10 eV 2 Naively... First instinct is to assume that neutrinos leave the sun as e and oscillate on their way to the earth. Assuming this 8 2 −10 -5 L∼10 km , E ν< 10 MeV → Δ m ∼3×10 eV 7 x 10 eV 22 Naively... First instinct is to assume that neutrinos leave the sun as e and oscillate on their way to the earth. Assuming this 8 2 −10 -5 L∼10 km , E ν< 10 MeV → Δ m ∼3×10 7 x 10 eV eV 2 Oscillations come from phase difference between mass states. In a vacuum the phase diff comes from free particle Hamiltonian. In a material there are interaction potentials as well 2 2 2 2 ∂ψ ∂ψ −ℏ ∂ ψ −ℏ ∂ ψ −i ℏ =E ψ= →−i ℏ =( E+ V ) ψ= 2 ∂t 2m ∂ x ∂t 2 m ∂ x2 2 2 E − p =m 2 vac 2 2 → ( E+ V ) − p =m 2 mat → m mat ≈ √ m + 2 E V 2 vac c.f. effective mass of an electron in a semiconductor or light in glass Oscillations in Matter Electrons exist in standard matter – do not. Electron neutrinos travelling in matter can experience an extra charged current interaction that other flavours cannot. V W= 2 GF Ne Interaction Potential V Z=− 2 F e, , e 2 Δ m 2 2 M L P(ν e → ν e )=1−sin (2 θ M )sin ( ) 4E 2 G Oscillation probability modified by matter effects m2M = m2V sin2 2 cos 2− 2 sin2 2 2 sin 2 M = 2 2 sin 2cos 2 − = 2 2 GF N e E m2V Nn Implications 2 sin 2 2 sin 2 M = 2 sin 2cos 2− 2 = 2 2 GF N e E m 2 Vac If m2Vac = 0 or matter is very dense, = ∞ and m = 0 Similarly, if =0, then M = 0 If there is no matter, then = 0 and we have vacuum mixing At a particular electron density, dependent on m2, ζ= 2 √ 2 GF N e E Δ m2 =cos2 θ ⇒ sin2 2 θ M =1 Even if the vacuum mixing angle is tiny, there is a density for which the matter mixing is large Mass heirarchy 2 sin 2 2 sin 2 M = sin2 2cos 2− 2 2 2 GF N e E = m2V If mass of 1 < mass of 2, m2=m12-m22<0 ζ=− 2 √ 2 GF N e E 2 ∣Δ m ∣ 2 sin 2 θ 2 → sin 2 θ M = 2 2 sin 2 θ+ (cos2 θ+ ∣ζ∣) Positive definite – no resonance If mass of 1 > mass of 2, m2=m12-m22>0 ζ= 2 √ 2 GF N e E 2 ∣Δ m ∣ 2 sin 2 θ 2 → sin 2 θ M = 2 2 sin 2 θ+ (cos2θ−∣ζ∣) Mixing matrix )( )( U e1 U e2 U e3 c 12 s 12 0 c 13 0 s13 e U= U μ 1 U μ 2 U μ 3 = −s 12 c 12 0 0 1 0 U τ 1 U τ2 U τ 3 0 0 1 −s 13 e i δ 0 c 13 ( Solar sector o o e =32.5 ±2.4 m212=7.9×10−5 eV 2 iδ )( 1 0 0 0 c 23 s 23 0 −s 23 c 23 ) Explaining the atmospheric data Cosmic Labs cos zenith = 1.0 15km L E ~ 10 km 1000 MeV 13000 km L E ~ 10000 km 1000 MeV 2 ⇒ m 0.00001eV 2 cos zenith = -1.0 2 ⇒ m 0.01eV 2 Atmospheric results Prediction for e rate agrees with data. disappear at large baseline consistent with → Don't detect as Upcoming -below mass threshold -SuperK is awful at detection Downgoing 2 atmos ∣ m ∣≈0.0025 eV sin2 2 atmos ≈1.0 1 2 1− sin 2 2 2 Accelerator Cross-check Δ m 2atmos≈3×10−3 eV 2 → L / E≈400 kmGeV −1 L=250 km→ E ν≈0.6 GeV Beam events tagged using GPS at both near and far detector sites Disappearance Experiments m2 Φ ν (@ FD ) P( ν α → ν α ) → Φ ν (@ ND) : Neutrino Flux Use Near Detector to measure (@ND) T2K verification T2K Disappearance 2 # events observed Δ m L 2 2 =P( νμ → ν μ )=1−sin (2θ )sin ( ) # events expected 4E (best fit) −3 2 eV ∣Δ m223∣=(2.51±0.1)×10 sin2 ( θ23 )=0.514+0.055 −0.056 →θ23 =45.8±3.2 Mixing matrix )( )( U e1 U e2 U e3 c 12 s 12 0 c 13 0 s13 e U= U μ 1 U μ 2 U μ 3 = −s 12 c 12 0 0 1 0 U τ 1 U τ2 U τ 3 0 0 1 −s 13 e i δ 0 c 13 ( o θ eμ=33.7 ±1.1 2 12 −5 Δ m =+(7.54±0.24 )×10 eV )( 1 0 0 0 c 23 s 23 0 −s 23 c 23 Atmospheric sector Solar sector : ν νe o iδ 2 θμ τ =41.4o ±2.0 o 2 −3 2 Δ m23=∣(2.43±0.06)×10 ∣ eV ) So how big is 13? )( )( U e1 U e2 U e3 c 12 s 12 0 c 13 0 s13 e U= U μ 1 U μ 2 U μ 3 = −s 12 c 12 0 0 1 0 iδ U τ 1 U τ2 U τ 3 0 0 1 −s 13 e 0 c 13 ( iδ )( 1 0 0 0 c 23 s 23 0 −s 23 c 23 ) Is it zero ? This would be bad news since the CP violating phase always appears in the PMNS matrix together with 13. Zero 13 would make any CP violation in the light neutrino sector unobservable in principle. Better try to measure it...... How do we measure 13? e oscillations with atmospheric L/E 2 2 2 P e =sin 2 13 sin 23 sin 1.27 m 2 23 L E e appearance in a beam – ideal for accelerator experiments e x disappearance oscillations with atmospheric L/E L p(ν e →ν x ) = P (νe → ν x )=1−sin (2 θ 13)sin (1.27 Δ m ) E C^ P^ 2 e disappearance – ideal for reactor experiments 2 2 23 13 from reactors oscillations due to 13 sin2213 = 0.090 ± 0.008 T2K Results e events observed in SuperK Allowed region for (13) 2 sin (2θ 13)=0.14±0.036 o θ 13≈10.9 3-Neutrino Mixing i c 13 0 s 13 e 1 0 0 U PMNS = 0 c 23 s 23 0 1 0 0 −s 23 c 23 −s 13 ei 0 c13 Atmospheric sector o θ e μ=45.0 ±2.4 −3 o o Δ m =|2.4×10 | eV 2 23 13 Sector e → Solar sector o θ13 =10.6 ±0.3 2 c 12 s12 0 −s 12 c 12 0 0 0 1 e o θ eμ =32.5 ±2.4 o Δ m223=|2.4×10−3| eV 2 Δ m2 =+7.5×10−5 eV 2 12 Summary of Current Knowledge 13 : how much e is in 3 e ( 0.8 0.5 −0.15 U MNSP = −0.4 0.7 0.6 0.4 −0.5 0.7 ) Some elements only known to 10-30% Very very different from the quark CKM matrix A bonfire of anomalies The fly in the ointment The LSND experiment was the first accelerator experiment to report a positive appearance signal + + + e e ↳ e E : 20-55 MeV baseline : 30m L/E 1.0 + e p e n 20-60 MeV n p d 1280 PMTs 167 t liquid scintillator 2.2 MeV LSND Result (1997) 87.9 ± 22.4 ± 6 excess events from → e 3.3 evidence for oscillations m2 = 1.2 eV2 LSND Result (1997) 87.9 ± 22.4 ± 6 excess events from → e Δm Δm 2 solar 2 atmos 3.3 evidence for −5oscillations 2 ∼8×10 eV −3 ∼2.5×10 eV 2 ?? 2 Δ m ∼1eV fourth neutrino ? 2 m2 = 1.2 eV2 MiniBooNE Ran from 2002 to 2014 at Fermilab Average neutrino energy ≈ 1 GeV L/E the same as LSND Same technology as LSND Different energy = different event types = different systematics LSND L/E Region 2013 analysis No excess of e events in signal region (E>450 MeV) Unknown excess of events at low energy (where NC /0 would be) The Gallium Anomaly We've discussed the Homestake experiment which studied the reaction 37 37 ­ e Cl Ar e A couple of experiments (SAGE and GALLEX) also studied 71 71 ν e + Ga→ Ge+ e - In early 2000's the response of the Gallex experiment (remember that?) was being tested using radioactive sources. Sources emitted e which were then observed using the standard Ge signature 2 L/ E≈0.1 m/ 0.1 MeV →Δ m ≈1 eV 2 (or is it our understanding of the inverse beta decay cross section?) Reactor Anomaly Over the years there have been lots of reactor experiments who measured the electron antineutrino flux from reactors and found that observed rates matched expected rates. In 2011, new techniques in modelling nuclear reactions led to a re-evaluation of the expected electron antineutrino flux. The new estimate was about 6% higher than the old. Suddenly all the experiments now observed a general deficit of electron antineutrinos being emitted from reactors Could this be (i) the new flux estimate is just a bit dodgy or (ii) we have short baseline neutrino oscillations to a sterile state? Reactor Anomaly 2 2 Deficit consistent with a sterile state with m 1.5 eV Decaying sterile neutrinos? Lorentz violation? Extra dimensions? CPT Violation? Experimental problems? 3+1 sterile? 3+2 ? 3+n ? No bleedin' idea Wait for more data Summary of sterile hints There are odd hints, each at the level of 2-3 , that they may be at least one other light sterile state floating around with m2 1 eV2. This is not very easy to fit into the standard model. It is very hard to find an oscillation model, including steriles, which is consistent with all of the data Current “best model” is a 3+1 model but it doesn't fit very well and it could all be a conspiracy of systematic uncertainties Many new experiments being proposed to search for signs of steriles in neutrino oscillations Δ m2sterile =1 eV 2 Δm 2 sol 2 Δ m atmos Story is certainly not over.....watch this space To Infinity and Beyond! The next 20 years Measurement 23 13 Method Disapp. T2K, NovA e Appear. T2K, NovA Anti-e Sgn(m232) CP Experiments Why? Is it maximal? Equal to 0? Can't measure CP if it is Reactor When 2009 2012 2012 Disapp. e / anti-e Next Gen Unification, GUT Neutrino Factory Lepton asymmetry 2020 2035? Current Experiments Next generation of experiments DUSEL Underground Neutrino Experiment (DUNE) Hyper-Kamiokande 1300 km MW beams multi-kton far detectors SK (to scale'ish) Dune / HK Comparison DUNE Hyper-K T2K Beam Energy 3 GeV 0.7 GeV 0.7 GeV Baseline (L) 800 km 295 km 295 km Beam Power 1.2 MW 0.75 MW 0.3 MW Type of Beam Wideband Off-axis Off-axis Mass of far detector 70 kton 560 kton 22.5 kton Technology Liquid Ar TPC Running from 2025 Water Cerenkov Water Cerenkov 2025(30) The Future – Mass Heirarchy CP violation and Mass Heirarchy Measuring CP is the ultimate goal of neutrino oscillation experiments. How? CP is a complex phase. L Prob = −4 ∑ i j ℜU U i U j U sin m 4E * * 2 L 2 ∑ i j ℑU i U i U j U j sin mij 2E * i * j 2 2 ij = 0 if CP violation can only take place in appearance experiments Look for P e ≠P e In all it's naked glory P e e = P1P 2P 3P4 2 2 2 P 1=sin 23 sin 2 13 13 2 B +sin L B -+ 2 2 2 2 P 2 =cos 23 sin 2 12 12 2 A sin L A 2 13 23>45 or 23<45 Sign(m232) 23 12 13 B-+ A P 3= J cos cos L sin Lsin L 2 A B-+ 2 2 23 12 13 B-+ A P 4 =±J sin sin L sin Lsin L 2 A B -+ 2 2 m2ij ij = 2E A= 2 G F N e B -+=∣ 13∓A∣ J =cos 13 sin2 12 sin 2 23 sin 2 13 Degeneracies Experiments only measure at most two numbers; but probability has three unknowns and parameters with errors. Need more than one measurement at different L/E to disentangle the parameter space Mass Heirarchy measurements As baseline grows, matter effects increase At distances of around 1000 km we can unambiguously identify the mass heirarchy Once we've done that we need to determine CP phase Heirarchy Measurement m2 m1 Mass hierarchy in 0 decay m3 2 2 2 Γ 0 ν ∝m ν =m1|U e1| + m2|U e 2| + m3|U e3| e In the inverted hierarchy : m3 m1 m2 , m132 m232 and m3 is the lightest mass state, so we can write 2 √ 2 3 2 2 23 √ 2 3 2 23 2 m 2 β =|U e1| m +Δ m +|U e 2| m + Δ m +|U e3| m 2 3 Setting m3 to zero (not a bad approximation) one can show that m2 β > √ Δ m cos θ13 2 23 2 i.e for the inverted hierarchy, the decay rate, 0 would havea lower limit. Mass hierarchy & 0 decay mν [eV ] Current upper limit e IH NH m 3 [eV ] Experimental limit needs to decrease by a factor of 10 Limit scales with mass and run time Experiments need to be 10 times bigger and run 10 times longer These are being built now. Mass Hierarchy Determination A number of different experiments, both accelerator and 0 decay focused, are now trying to determine the mass hierarchy. Timescale : 10-15 years from now (although good indications before hand – mass hierarchy is a binary measurement, after all) A way around the degeneracies e oscillation probability Second maximum First maximum CP = 0 CP = 90 CP = 270 Osc. Prob. @ First Max = f (δCP ) Osc. Prob. @ Second Max E/L Could study CPV using an experiment sensitive to both maxima using only a wide-band neutrino beam. DUNE Sensitivity 5 significance for sin CP 0 over 56% of CP space 20% precision at CP = -90 degrees Hint of CP? Fitting full 3-flavour model to T2K e appearance data suggests CP > 0 disfavoured (mild sensitivity to second oscillation maximum)? What do we really want to do though? We need to do this in the neutrino sector We can't do it only with superbeams Another problem... To do these sort of measurements Measure number of events at Far Detector Compare with expected number of events Number of events=σ Φ T ϵ Cross Section Neutrino Flux Number of Targets Selection Efficiency 15-100% 10-15% 1-2% 10% Effect of Systematics Example of state of the data (pre-2007) The data is impressively imprecise − p p − p n p n Added complication that the final state pions can (i) scatter (ii) be absorbed (iii) charge exchange within the nucleus before being observed (iv) nucleons rescatter producing + 0 n p Getting better CC 0 differential xsec from MINERvA Phys.Lett. B749 (2015) 130-136 CC 0 differential Xsec from T2K arXiv:1602.03652 Lot's of effort going into trying to understand neutrino interaction cross sections But it's hard... 1. We are assuming that the initial target nucleon is just sitting still before interaction. Actually in the nucleus it has some initial momentum distribution. The Fermi momentum modifies the scattering angles and momentum spectra of the outgoing final state 2. The outgoing final state can interact with the target nucleus. This nuclear re-interaction affects the outgoing nucleon momentum direction and charge (through charge exchange interactions) Theoretical uncertainties are large At least 15% If precise knowledge is needed for a particular target (e.g. Water, hydrocarbon) then measurements are needed Last measurements taken in the '70s Quasi-Elastic Scattering + W n p Usually thought of as a single nucleon knock-on process In the past has been used as a “standard candle” to normalise other cross sections Heavily studied in the 1970's and 1980's and considered to be “understood” I. Very important for current oscillation experiments as it contributes the most of the total cross section at a few GeV Quasi-Elastic Scattering + W n p Usually though of as a single nucleon knock-on process In the past has been used as a “standard candle” to normalise other cross sections Heavily studied in the 1970's and 1980's and considered to be “understood” 2 2 2( mN −E B ) E μ −( E B−2 mN E B + mμ ) II. Energy reconstruction is E ν ;rec = unbiased assuming 2 body 2(m N −E B− Eμ +|pμ| cos θ μ) kinematics Extra processes contribute : e.g. W p p + n += n p n p unobserved final state proton Meson Exchange Current (MEC) Effect on energy reconstruction CCQE single nucleon Multinucleon Martini et al, arxiv : 1211.1523 Summary We measure events = flux*cross section We don't generally have a handle on the flux to better than 10% - there is a lot of work trying to deal with this. The other side of the coin, cross-sections, are even more poorly known. We need new, high-statistics, measurements of these cross sections on multiple target materials and at multiple energies. Concluding Remarks We have gone through a lot but I can easily fill another 15 hours of lectures. The neutrino is : light, neutral, left-handed (chiral) and almost left-handed (helicity). It is generated purely in weak interactions (which is why it is chiral). It is generated by many sources : the Big Bang, astrophysical events, supernova, the sun, cosmic rays, radioactive decays, and countless other sources. We can generate them in reactors and accelerators. Their cross sections are tiny and we need big detectors to look at them. They mix and oscillate. They may be the reason that we are here at all. But...what is their mass? Why is it so small? Why are the mixing parameters so odd? What about these hints of a 1 eV sterile state? Still lots of questions remain – watch this space.....