Cafe Scientifique Neutrinos Thomas Gajdosik

Neutrinos and their Oscillations

· Historical Context Thomas Gajdosik · Todays Understanding Faculty of Physics · Meaning of Oscillations Department of Theoretical Physics Cafe Scientifique Neutrinos Thomas Gajdosik

Historical Context

discoveries in particle physics Cafe Scientifique Neutrinos Thomas Gajdosik

Radioactivity

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u While working on phosphorescent mate- u

u rials Antoine-Henri Becquerel discovers u

Radioactivity. He finds traces on photo- u graphic plates that were not exposed to u u light. u

u u

u u

u u

u Becquerel u

u u

Henri Becquerel: Photographic plate showing effects of radioactivity. ↑ u u 1896 u {w I Cafe Scientifique Neutrinos Thomas Gajdosik . u e− the electron . u u

u u

u u

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J.J. Thomson u u

u u

u u

u u

u u

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u u 1897 u {{w I Cafe Scientifique Neutrinos Thomas Gajdosik

Transmutation of Chemical Elements . u e− . . u u γ u. u

u u

u u

u u Soddy Rutherford u u

u 1901 Frederick Soddy and Ernest Rutherford discovered u

that radioactive thorium was converting itself into radium. u u At the moment of realization, Soddy later recalled, he shouted out: "Rutherford, this u is transmutation!" Rutherford snapped back, "For Christ’s sake, Soddy, don’t call it u transmutation. They’ll have our heads off as alchemists." u u 1896 1901 u {{ {w I Cafe Scientifique Neutrinos Thomas Gajdosik

Continuous electron spectrum . u in radioactive -decay − β e . . u u γ u. u

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u u

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1911 Otto Hahn and Lise Meitner u u observe a continuous spectrum of u electrons coming from radioactive u Meitner Hahn u β-decay. u 1896 1911 u {{ { {w I Cafe Scientifique Neutrinos Thomas Gajdosik

Radioactive displacement law . u of Fajans and Soddy − e . . u u γ u. u

u u

u u

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u Fajans Soddy u

u u

u 1913 Frederick Soddy and Kazimierz Fajans u

formulate independently the radioactive u u displacement law. u u 1896 1913 u {{ { { {w I Cafe Scientifique Neutrinos Thomas Gajdosik . u p the proton – the atomic nucleus . . u u e− . . u u γ THOMSON fluorescentscreen u. u

gold foil u u

alpha particle beam u u

radiation source (radium) u Rutherford u

RUTHERFORD u u

u u

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u Geiger Marsden u u u 1896 1914 u {{ { { {{w I Cafe Scientifique Neutrinos Thomas Gajdosik

Stern-Gerlach experiment → Spin . u e− . . u u . γ u. p u . u u

u u Gerlach Stern u u

u u

u u

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u Uhlenbeck Goudsmit u u u 1897 1922 1925 u {{ { { {{ {w {w I Cafe Scientifique Neutrinos Thomas Gajdosik . u the neutrino – theory prediction ν . . u u e− . . u u . γ u. u p . . u u . n . Pauli: u u ”neutron” Fermi: ”neutrino” µ− . . u u . π . + u e u . u u

u u

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u u 1897 1930 1956 u {{{ { { {{ { { {wI ws Cafe Scientifique Neutrinos Thomas Gajdosik

Fermi Theory

• 1933 Enrico Fermi explained the radioactive beta decay – by coupling charged currents

• the same coupling constant . . −5 1.16637×10 e− G = describes . F GeV2 – radioactive beta-decay . .. + . ν¯e µ – muon decay . . µ− . . + . π – charged pion decay . νµ . . . νµ – neutrino interactions . .

F but it cannot work for energies bigger than ∼100 GeV 1897 1933

{{{ { { {{ { { { {w I Cafe Scientifique Neutrinos Thomas Gajdosik . u the neutron n . . u u e− . . u u . γ u. p u . u u

u u

u Chadwick u

u . . u

u

. u

u u

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u u 1897 1932 u {{{{ {{{ {{ {{{w I Cafe Scientifique Neutrinos Thomas Gajdosik . u − the muon µ . . u u Raby: ”Who ordered that one?” e− . . u u . γ u. u Cosmic p . Rays . u (10km) u n u. Hess Anderson u u u

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u Spark Chamber u u u 1897 1936 u {{{{ {{{ {{ {{{{w I Cafe Scientifique Neutrinos Thomas Gajdosik

Nuclear fusion cycle in the sun . u e− . . u u pp-chain . γ u. u 1 1 1 1 p . H H H H . CNO-cycle u u n ν ν . 4 u He 1 H u 1H 2H 1H 1H 2H Weizsäcker u 12C u 15 N 13N γ γ u u 3He 3He

15 O 13C u 14 u N

u 1H 1H 1H u 1H

Proton Proton Gamma Ray u γ Gamma Ray 4 Neutron Neutron Neutrino u ν Neutrino He Positron Positron Bethe u u 1897 1937-1939 u {{{ { { {{ { { { {{ {{{{w w w I Cafe Scientifique Neutrinos Thomas Gajdosik . u antineutrino ν¯ . . u u Cowan–Reines neutrino experiment e− . . u Savannah River Site u . γ u. u p . . u u . n . + u u e . . u u . ν ν¯e from u. reactor p¯ u . u u

used the antineutrino flux from the u nuclear reactors of the Savannah u River Site (South Carolina). u u

u u ...1956 u {w I Cafe Scientifique Neutrinos Thomas Gajdosik . u ν muon neutrino µ . . the Alternating Gradient Synchrotron (AGS) u u e− . 1962 . u u γ Leon Lederman . u. u Melvin Schwartz p . . u u Jack Steinberger . n . + u u use the pions and kaons of the e . . u u AGS. These dacays produce also . ν . ν¯(anti)neutrinos;e from with a similar setup u reactor p¯ u like the Cowan–Reines experiment they . u u detect muons, but no electrons u ⇒ the neutrinos coming from pions and u u kaons have to differ from the neutrinos u

coming from the reactors. u u . . . 1956 1962 u {{w I Cafe Scientifique Neutrinos Thomas Gajdosik

Solar neutrino flux . the standard solar model (SSM) u e− . . u u . γ Around 1964 John Bahcall starts u. p u to calculate the flux of neutrinos . . u u from the nuclear fusion processes in . n . + u the sun, searching for all physical u e . processes that have an impact on . u u the possibility to measure their flux . ν u. in an experiment on earth. p¯ u . u ⇒ the standard solar model (SSM) u u u

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u u . . . 1956 1964+ u {{{w I Cafe Scientifique Neutrinos Thomas Gajdosik

partons / parton model . u Richard Feynman 1969 e− . . u u . ν u. u p . . u u . n . + u u e . . u u . ν¯ u. u a hadron is composed of point- p¯ . . u like constituents, called ”par- u γ tons”. The number of partons de- u. pends on the probing energy u u ⇒ parton distribution functions u

u u . . . 1965 1969 u {{{{w I Cafe Scientifique Neutrinos Thomas Gajdosik

Homestake experiment . solar neutrino deficit u γ . . u From 1970 to 1994 u ν u. Raymond Davis, Jr., u . measures the flux of u u τ− solar neutrinos using u. u the radio-chemical re- . u action u u . 37 37 − u ν + Cl → Ar + e u . u but he only finds 1/3 of the flux u d predicted by John Bahcall ! u. u ⇒ solar neutrino deficit u u

u u . . . 1956 1970 till 1994 u { { { {{w {w I Cafe Scientifique Neutrinos Thomas Gajdosik

u lepton τ . u u γ . . u u ν u. Martin Perl u . (SLAC-LBL) u u − 1975 τ u. u • using Mark I . (SLAC-LBL Magnetic Detector) u u u . – first 4π-detector u u . • comparing signal u u to background d u. u

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u u . . . 1956 1975 u { { { {{w {{ I Cafe Scientifique Neutrinos Thomas Gajdosik

u u hints for W ±- and Z-boson Zp . u u u γ p p . . u p u ν u. u W . p u pu p e− u. p u . u u . u Weak charged currents were known from u. u neutrino detection. g . . u CERN announced the experimental obser- u d vation of weak neutral currents, shortly u. u after they were predicted by the electro- u weak theory of Abdus Salam, Sheldon u

Glashow and Steven Weinberg. u u . . . 1956 1973 u { { { {{u {{{ I Cafe Scientifique Neutrinos Thomas Gajdosik

neutrino oscillations . 1957 predicted by B. Pontecorvo u γ . . u Super Kamiokande (SK) u ν . announces first experimental u u evidence for atmospheric W . p u neutrino oscillations in pu p e− 1998 u. p u Z . Sudbury Neutrino Ob- p u u servatory (SNO) pro- p. p u u. vides clear evidence of p u g . neutrino flavor change in . u solar neutrinos in 2001 u d u. only then the solar neu- u trino puzzle was solved u u

Nobel Price 2015 u u . . . 1957 1998 2001 2015 u {w { { {{ {{{{ {{{w w w I Cafe Scientifique Neutrinos Thomas Gajdosik

u tau neutrino . Discovery by the DONUT collaboration (E872 Fermilab) u u γ . . u u ντ u. u W . p u pu p τ− u. p u Z . p u u p. p t u. p u g . . u u b u. u

u u

u u . . . 1956 2000 u { { { {{ {{{{ {w {{ { I Cafe Scientifique Neutrinos Thomas Gajdosik

”Todays” Understanding

in the context of particle physics Cafe Scientifique Neutrinos Thomas Gajdosik

How do we distinguish particles? • according to Special Relativity with mass and spin – particles with the same mass and the same spin are the same particles

• by spin: a boson is different from a fermion – 4He behaves differently than 3He

• by mass: a muon has a differnt mass than an electron – proton and neutron have nearly the same mass ∗ π+ and π− have exactly the same mass • by charge: – proton has a positive charge, the neutron is neutral ∗ π+ and π− have opposite charge

F for neutrinos this is all (approximately) the same ! Cafe Scientifique Neutrinos Thomas Gajdosik

Ordering principle: discreet symmetries

• Parity P . . u u − − eL eR – left-handed or right-handed . . u u

• Charge Conjugation . . C u + u e− e – particle or antiparticle . . u u

2 -1 • Charge Q or Flavour 0 -1 3 3 . . . – possible values: ν u u u u d u . . . u u u u

• Generation . . u u u µ− τ− – first– second– third . . u u u Cafe Scientifique Neutrinos Thomas Gajdosik

Weak Interactions: modern explanation . . . • weak interactions couple a pair µ− νµ of fermions with another pair . . . – via vector bosons ν¯e • the Fermi coupling constant . √ Wp . 2 g2 − GF = p p e 8 2 . . mW p . is independent of energy . . + only if the energy is (much) uL µ F . . . . smaller than the mass ¯ Wp of the W -boson (80 GeV) dR νµ .. p p . p Cafe Scientifique Neutrinos Thomas Gajdosik

Additional ordering principle: according to the charged weak interactions

• particles of the same spin but of 0 -1 different mass and different charge . .

ν u e− u are grouped together into doublets . . u u

these are the objects that F 2 1 3 -3 ∗ make the charged current . . u u d u ± . . ∗ couple to the W -bosons u u

. . . ”flavours” for neutrinos: u u u I νe νµ ντ . . . u u u Cafe Scientifique Neutrinos Thomas Gajdosik

Observed fermions of the Standard Model: Fermions left right

...... ν − − e eL uL dL eR uR dR ...... − − νµ µL cL sL µR cR sR ......

particles ν − − τ τL tL bL τR tR bR ......

...... + ¯ ν¯ + ¯ eL u¯L dL e eR u¯R dR ...... + + µL c¯L s¯L ν¯µ µR c¯R s¯R ...... + ¯ ¯ ν¯ + ¯ ¯ τL tL bL τ τR tR bR ...... antiparticles Cafe Scientifique Neutrinos Thomas Gajdosik

Meaning of Oscillations

in the context of quantum mechanics Cafe Scientifique Neutrinos Thomas Gajdosik

From quarks we know

• the charged current (i.e. W ±) mixes the generations – parametrized by the quark mixing or CKM matrix

• quarks are not observed as free particles – the mixing is also seen in boundstates: K− → π− + π0

∗ without mixing this decay u¯p u¯♣ d¯♣ p ♣ ♣ p p I ♣ ♣ + ♣ ♣ would not happen psp p ♣d ♣ ♣d ♣ p ♣ ♣ pp p ♣♣ ♣ ♣♣ ♣ p ♣ ♣ • mesons (i.e. boundstates of quarks) exhibit oscillations ¯0 0 – the probability to find Bs instead of Bs changes with time – they form mass-eigenstates B0 and B0 ¯0 0 sH sL Bs ↔ Bs

∗ which have slightly different masses: s¯♣ ¯b♣ ♣ ♣ ♣♣ ♣ ♣ J I ♣♣ ♣ ♣ ∆mB0 = mB0 − mB0 ≈ 0.0734 eV b s s sH sL ♣♣ ♣♣ ♣♣ ♣ ♣♣ ♣ ♣ for comparison 0 ≈ 5 367 GeV ♣ ∗ mBs . Cafe Scientifique Neutrinos Thomas Gajdosik

What about neutrinos?

• like for the quarks: ν the charged current can mix the generations ♣1 ♣ ♣ ν♣ – generation means now the mass eigenstate ♣2 ♣ ♣ ∗ a mass eigenstate is what we usually just call a particle ν♣ ♣3 ♣ ♣ • as long as neutrinos have the same mass ♣ – ∗ if they are massless (like in the SM) they have the same mass...

– we see no effect . νe I . ∗ the state produced . νµ I in the interaction . . stays the same ντ I . Cafe Scientifique Neutrinos Thomas Gajdosik

When neutrinos have different masses

• again like for the quarks: we describe the interactions with a mixing matrix

 .       

νe ν1  .  Ue1 Ue2 Ue3  ♣     .             ♣ ♣     νµ  = U U U ·  ν♣2  = U ·    .   µ1 µ2 µ3   ♣  PMNS    .     ♣ ♣     ν      τ Uτ 1 Uτ 2 Uτ 3 ν♣3 . ♣ ♣ ♣ ♣ F propagation of the state produced in the interaction           I          †  = U · I · U =  PMNS   PMNS            I   VOLUME 81, NUMBER 8 PHYSICAL REVIEW LETTERS 24AUGUST 1998

cally, final state leptons with p ϳ 100 MeV͞c carry 65% of the incoming neutrino energy increasing to ϳ85% at p ෇ 1 GeV͞c. The neutrino flight distance L is esti- mated following Ref. [18] using the estimated neutrino energy and the reconstructed lepton direction and flavor. Figure 4 shows the ratio of FC data to Monte Carlo for e-like and m-like events with p . 400 MeV as a func- tion of L͞En, compared to the expectation for nm $ nt oscillations with our best-fit parameters. The e-like data show no significant variation in L͞En, while the m-like events show a significant deficit at large L͞En. At large L E n Cafe Scientifique ͞ n, the m have presumablyThomas undergone Gajdosik numerous os- Neutrinos cillations and have averaged out to roughly half the initial rate. The asymmetry A of the e-like events in the present data is consistent with expectations without neutrino oscilla- tions and two-flavor ne $ nm oscillations are not favored. What we see from the atmosphereThis is in agreement with recent results from the CHOOZ FIG. 2. The 68%, 90%, and 99% confidence intervals are experiment [22]. The LSND experiment has reported the 2 2 shown for sin 2u and Dm for nm $ nt two-neutrino oscil- appearance of ne in a beam of nm produced by stopped lations based on 33.0 kton yr of Super-Kamiokande data. The pions [23]. The LSND results do not contradict the • a pion, produced90% by confidence a cosmic interval obtained ray by the in Kamiokande the experi- upperpresent atmosphere, results if they are observing small mixing angles. ment is also shown. With the best-fit parameters for nm $ nt oscillations, we decays into muon and muon-neutrino expect a total of only 15–20 events from nt charged- case overlapped at 1 3 1023 ,Dm2 ,431023 eV2 current interactions in the data sample. Using the current 2 – the muon decaysfor into sin 2u electron,෇ 1. electron-neutrino, andsample, muon-neutrino oscillations between nm and nt are indistinguish- As a cross-check of the above analyses, we have re- able from oscillations between nm and a noninteracting L E we get twice asconstructed many the bestν estimateµ than of the ratioνe ͞producedn for each sterile neutrino. I event. The neutrino♣ energy is estimated♣ by applying a Figure 2 shows the Super-Kamiokande results overlaid ♣ ♣ ♣ ♣ correction to the final♣ state lepton momentum.♣ Typi- with the allowed region obtained by the Kamiokande • Super-Kamiokande sees fewer s than expected – depending on the traveldistance

FIG. 3. Zenith angle distributions of m-like and e-like events for sub-GeV and multi-GeV data sets. Upward-going particles have cos Q,0and downward-going particles have cos Q.0. Sub-GeV data are shown separately for p , 400 MeV͞c and p . 400 MeV͞c. Multi-GeV e-like distributions are shown for p , 2.5 and p . 2.5 GeV͞c and the multi-GeV m-like are shown separately for FC and PC events. The hatched region shows the Monte Carlo expectation for no oscillations normalized to the data live time with statistical errors. The bold line is the best-fit expectation for nm $ nt oscillations with the overall flux normalization fitted as a free parameter.

1566 Cafe Scientifique Neutrinos Thomas Gajdosik

What we see from the sun

• the sun produces only low energetic ν s e♣ ♣ ♣ – highest energy ≤ 18 MeV ♣

I in a detector they can only produce electrons

• the Homestake experiment measured only ∼1/3 of the flux predicted by the standard solar model

• SNO confirmed the result from the Homestake experiment – but measured also the neutral current (= all νs) ∗ consistent with the standard solar model I confirmed the explanation: oscillations are responsible Cafe Scientifique Neutrinos Thomas Gajdosik

Oscillations in vacuum

i(Et−px) • combining mixing UPMNS with propagation e

– we get the approximate amplitude A = P ∗ −i(Ekt−px) να→νβ k UαkUβke 2 – and the approximate probability Pνα→νβ = |Aνα→νβ | • taking ultra-relativistic neutrinos with average energy E  m – we get t ≡ L and m2 − m2 ∆m2 E − E ≈ ` k = `k ` k 2E 2E with αβ ∗ ∗ I Jk` ≡ UαkUβkUα`Uβ` 2 ! X h αβi 2 ∆mk`L Pν →ν = δ − 4 Re J sin α β αβ k` 4E k>` 2 ! X h i ∆m L +2 Im Jαβ sin k` k` 2E k>` Cafe Scientifique Neutrinos Thomas Gajdosik

Oscillations in vacuum

• are parametrized by – the distance L between production and detection – the mass differences 2 between the neutrinos ∆mk` – the ”oscillation angles” ( ) in αβ ∗ ∗ θk` Jk` ≡ UαkUβkUα`Uβ` • trying to fit all data from neutrino measurements 2 −5 2 2 −3 2 ∆m21 ≈ 7.6 · 10 eV ”  ” ∆m31 ≈ 2.5 · 10 eV

I this hierarchy allows the separation into 2 ∗ atmospheric paramters: ∆m31 and θ23 2 ∗ solar paramters: ∆m21 and θ12

∗ reactor angle: θ13 Cafe Scientifique Neutrinos Thomas Gajdosik

Oscillations in matter

• only ν has a charged current interaction with normal matter e♣ ♣ ♣ – this♣ interaction changes the dispersion relation ∗ like when light travels though matter – this changes the propagation picture: ∗ each mass eigenstate feels a ”drag” proportional to its component

I the mass is changed to an effective mass

∗ one gets different effective mass differences and effective mixing angles

F MSW-effect: Wolfenstein (1978), and Mikheyev and Smirnov (1986)

• the MSW-effect is needed to explain the solar neutrino deficit

– that only 1/3 of the higher energetic neutrinos from the sun are seen as electron-type neutrinos

– it does not affect the atmospheric oscillations Cafe Scientifique Neutrinos Thomas Gajdosik

Consequences for the theoretical description

F we have to add additional singlet fermions the the SM: left right

...... ν − ν − e eL uL dL eR eR uR dR ...... − − νµ µL cL sL νµR µR cR sR ......

particles ν − ν − τ τL tL bL τR τR tR bR ......

...... ν¯ + ¯ ν¯ + ¯ eL eL u¯L dL e eR u¯R dR ...... + + ν¯µL µL c¯L s¯L ν¯µ µR c¯R s¯R ...... ν¯ + ¯ ¯ ν¯ + ¯ ¯ τL τL tL bL τ τR tR bR ...... antiparticles Cafe Scientifique Neutrinos Thomas Gajdosik

.

What are these νeR ? .

• they do not interact with any other particle of the SM – except the Higgs and the corresponding ν e♣ ♣ ♣ I they are really invisible! ♣

• the effective coupling between Higgs, and is < 10−11 – why so small, but not zero ? ∗ a possible explanation is the seesaw mechanism

• adding a very large Majorana

mass term Mme for 2 – gives the mass me for mν = M

I becomes Majorana, too ! i.e.: its own antiparticle Cafe Scientifique Neutrinos Thomas Gajdosik

Our approach

. . . we did not invent it, but we work on it

. . .

• instead of adding νeR νµR ντR . . . – and the corresponding coupling matrix to the Higgs

we set = = =: ν • ♣R ♣ ♣ – so we need onlya coupling vector♣ to the Higgs

– and only a single Majorana mass term MR ∗ this implements the seesaw mechanism

but we have to add a second Higgs doublet – this predicts additional Higgs bosons

• LHC searches for these additional Higgs bosons

– we can constrain the Higgs parameter space with our model . . . Cafe Scientifique Neutrinos Thomas Gajdosik

Questions ?

Discussion !