8 - 11 October 2018, CINVESTAV, Mexico SYMMETRIES AND THEIR BREAKING IN THE FUNDAMENTAL LAWS OF PHYSICS

José Bernabéu IFIC - Valencia SYMMETRY OF OBJECTS

Characteristic feature of geometric forms,

of material objects,

Symmetry Group of sphere

ATLAS experiment of LHC of biological bodies, related to their invariance under definite transformations. Vitrubio, Leonardo da Vinci (1487) One object is symmetric if, after a transformation is applied, the result remains the same: it remains “invariant”. SYMMETRY BREAKING This three-span arch, painted bright blue and orange, appears perfectly symmetric when viewed directly from below, but has a carefully calculated asymmetry from its other views. The former Fermilab Director R.R. Wilson freely adopted the style of the sculptor A.Calder for giving an example of Symmetry and Symmetry Breaking, which are so important in the field of elementary particle physics.

SYMMETRIES IN THE LAWS OF PHYSICS WORDING

FLAVOUR FAMILIES COLOUR CHARGES, CONFINEMENT PARTONS, JETS, HADRONISATION

ASYMPTOTIC FREEDOM QUANTUM ANOMALIES CHIRALITY SYMMETRY VIOLATION OSCILLATIONS SPONTANEOUS BREAKING I.- STRONG INTERACTION

Symmetries as Guiding Principle of Particles and Interactions

Flavour SU(3): Are Quarks real? Flavour and Colour of Quarks QCD: From Scale Invariance to Dimensional Transmutation SYMMETRY AS GUIDING PRINCIPLE FOR PARTICLES AND INTERACTIONS -Symmetry implemented by Unitary Transformation of states and observables

Invariant Dynamics under the transformation

- Under infinitesimal transformation with Ĝ the Generator

Ĝ is Hermitian, it corresponds to an Observable

Symmetry conservation law

For LOCAL Gauge Symmetries, Ĝ is a "charge" and the requirement of Invariance leads to a Covariant Derivative with a Mediator Field responsible of Interactions.

Yang-Mills Theory -> SYMMETRY DICTATES INTERACTION Proliferation of Hadrons -> FLAVOUR SU(3) - The fundamental representations 3, 3 are the elementary building blocks for arbitrary higher-dimensional representations.

- Baryons  Combination of three u, d, s states in Strangeness, Charge and Isospin axes

Ω-

- Gell Mann-Nishijima  Charge Q = I3+Y/2 , Hypercharge Y=B+S ARE QUARKS REAL?

Mesons 3 x ퟑ = 1 + 8, Baryons 3 x 3 x 3 = 1 + 8s + 8a + 10

Deep Inelastic Scattering "Jet" of hadrons: probing the insides of hadrons narrow cone of hadrons produced by the hadronization of a quark

Leptons (electrons, muons, neutrinos)

find PARTONS in the proton Quarks exist!, but they cannot propagate asymptotically with high momentum transfer events Quarks are CONFINED Quark EXCHANGE SYMMETRY: COLOUR

++ ↑ ↑ ↑ 3 3  The Δ puzzle: u u u ; S = 2 , + 2  Symmetric under exchange of space (L=0), spin (↑) and flavour (u) !?

 A new degree of freedom is necessary for Quarks, its "colour“ (r, g, b), with ANTISYMMETRY for its exchange in Baryons.

 The singlet colour wave function is antisymmetric

i.e., qqq bound states exist, but hadrons are colourless!

 Colour is confined

 Experimental evidence that Nc = 3 comes from

휎 푒+푒−→퐻푎푑푟표푛 + − + − = 푁퐶표푙표푢푟 푞2 + − 휎 푒 푒 →휇 휇 푓 푖푛 푒 푒 → 푓푓 reactions 푓 QUANTUM CHROMODYNAMICS (QCD)  Colour Charge as generator of SU(3) Local Gauge Symmetry  Colour Interaction of Quarks mediated by Gluons

 "q" are quark flavours, "a" is q-colour index and C runs from 1 to 8 

Only mq break flavour independence, external to QCD!

 Quarks are in the fundamental, Gluons in the Adjoint Representation - The field tensor is covariant (A=1, ...,8) leading to gluon self-interaction

- Gluon Jet Discovery Gluon self-interaction

e+e− → qqg: 1979 at PETRA (DESY) experiments FROM SCALE INVARIANCE TO DIMENSIONAL TRANSMUTATION 2 푔푆  훼푆 = 4휋 dimensionless  classical QCD field theory in the chiral limit is SCALE INVARIANT  Conformal Symmetry  In the perturbative quantum QCD, predictions for observables in terms of the renormalised 2 coupling 훼푆 휇푅 , function of the renormalisation scale. Taking it close to the momentum 2 2 transfer Q , 훼푆 푄 indicates the effective strength of the interaction.

 RUNNING COUPLING  The coupling satisfies the RGE

with the 1 loop beta-function coefficient b0 = (33-2nf)/(12 π)

 ASYMPTOTIC FREDOM ↔ The minus sign in the running.

 Approximate analytic solution, distinct to QED

with Λ a constant of integration  the non-perturbative scale of QCD

Λ~250 MeV ↔ Conformal Anomaly, ORIGIN OF NUCLEON MASS and MASS OF UNIVERSE II.- ELECTROWEAK INTERACTION AND DISCRETE SYMMETRIES

 Chiral Gauge ElectroWeak Theory  Flavour Physics  Discrete Symmetries: CP, T, CPT  Gauge Anomalies: Quark-Lepton Symmetry PARITY VIOLATION  CHIRAL GAUGE ELECTROWEAK THEORY  P, C, T are DISCRETE SYMMETRIES:   -Parity rPr

-Charge Conjugation qCq

-Time Reversal  t   T    t , Motion Reversal

 CHIRALITY  A chiral phenomenon is not identical to its mirror image. The spin of a particle may be used to define a handedness, or helicity, which, in the case of a massless particle, is the same as chirality.  Invariance under parity by a Dirac fermion ψ is called chiral symmetry 1 1 Using Projectors, 1 − 훾 휓 → 1 + 훾 휓 2 5 2 5  The UNIFIED ELECTROWEAK THEORY SU(2)L x U(1)Y distinguishes L- and R-projections  L transform as Doublets under 푆푈(2)퐿 R transform as Singlets under 푆푈(2)퐿

CHIRAL GAUGE THEORY WEAK NEUTRAL CURRENTS

 SU(2)L× U(1)Y gauge group.  gGauge bosons are: - The three W bosons of weak isospin from SU(2)L (W1, W2, and W3) - The B boson of weak hypercharge Y from U(1)Y

 Gauge symmetry is BROKEN by Mass  Physical Fields with definite mass: W±, γ, Z 훾 푐표푠휃푤 푠푖푛푤 퐵 푀푊 0 = , 푀푧 = 푍 −푠푖푛휃푤푐표푠푤 푊3 푐표푠휃푤 with θW the weak mixing angle

 DISCOVERIES: Neutral Current Interaction

휈휇 푒 ⟶ 휈휇 푒 Massive W, Z Bosons

+ + 휈휇 휌 ⟶ 휈휇 푋 푢 푑 ⟶ 푊 ⟶ 푙 휈푙

+ − 푢 푢 , 푑푑 ⟶ 푍 ⟶ 푙 푙 S푝 푝푆 푈퐴1, 푈퐴2 퐶퐸푅푁 1983 Gargamelle Bubble Chamber CERN 1973

Triumph of STANDARD MODEL GIM Mechanism -> Need of CHARM  With u, d, s quarks ONLY  Cabibbo d-s Mixing in Charged Weak Current leads by + - SU(2)L to Strangeness-Changing-Neutral Currents KL μ μ AGAINST experiment.

푢 푐  GIM 1970  With an additional fourth quark flavour , 푑 푠 cos 휃 −sin 휃 Cabibbo Mixing reinterpreted, with the two doublets, 푈 = sin 휃 cos 휃 as a Unitary Matrix for Charged Currents between Flavour and Mass eigenstates

 Neutral Currents U+ U = 1 are Diagonal and Universal  Flavour-Conserving-Neutral-Current

 At higher orders, F-Changing-N-C can be induced, BUT highly suppressed by GIM ퟐ ퟐ 풎풄 −풎풖 with an additional factor ퟐ 푴푾

- Discovery of 푐 푐 J/ψ meson in 1974 at SLAC and BNL  The "November Revolution"  Charmed c푑 , 푐푠 , 푐푢푑... Hadrons discovered later CP VIOLATION -> MATTER-ANTIMATTER ASYMMETRY  CP-symmetry  Laws of Physics should be the same if a particle is interchanged with its antiparticle (C symmetry) while its spatial coordinates are inverted ("mirror" or P symmetry).

 퐾0 퐾 0 Mixing (ΔS=2) by weak interactions  Physical KL, KS should be CP eigenstates  KL  π π should be FORBIDDEN, but OBSERVED!

 Can CPV be inserted in the SM? K-M 1973 discovered this possibility by particle content  Enlarging to 3 Families, at lest, of Fermions U(CKM) has a physical relative phase such that for antifermions  U*(CKM)  NEED OF 3 FAMILES ACTIVE! α - b푏 Υ meson discovered in 1977 at Fermilab - CPV by U(CKM) in agreement with 푢 푐 푡 γ β

experiments in K, B and D physics!!! 푑 푠 푏 Unitarity triangle

Not enough to explain MATTER-ANTIMATTER ASYMMETRY IN THE UNIVERSE

TOP QUARK  Top Quark The most massive of all observed elementary particles. Mass of 172.44 GeV/c2, like an atom of tungsten!

 "Weak" Decay t  b W, with lifetime 5×10−25 s., which is 1/20 of the timescale for Hadronisation  "bare" quark studies!

 First "seen" in indirect non-decoupling virtual quantum effects

푩ퟎ 푩ퟎ Mixing Z boson self energy 풁 풃 풃 vertex

UA1 & ARGUS 1987 Veltman LEP 1990's J.B.,Pich,Santamaria

 Direct detection 푝푝 TeVatron 1995

- A collision event involving top quarks

- Top Quark Factory at LHC p p Collider Strong g g  푡푡 + Weak u 푑  t 푏 WHAT IS “TIME REVERSAL”?  A symmetry transformation, T, that changes one physical system into another with an inverted sense of time evolution is called Time Reversal.

The operator UT must be ANTI-UNITARY: Antilinear + Unitary ANTIUNITARITY introduces many intriguing subtleties:

S T  S i f UT f UT i

T - Violation means Asymmetry under in out sates

vi  0 - vi  0

v T - v

v f - v f WHAT IS T-TRANSFORMATION EXPERIMENTALLY ? The problem is in the preparation and filtering of the appropriate initial and final meson states for a T-test: ENTANGLEMEND & DECAY Entangled state Entangled state projects projects B0 B Υ(4S) Υ(4S)  t1 t1 J/ψ l T

KL t1 t1  

J/ψ  0 t2 t2 l B Tagging B Tagging It is NOT Ks the exchange t t projects 1 2 projects 0 0 B  0   B B B B B  BABAR observes (PRL 2012) 14σ Genuine True TRV effect using this concept MESON TRANSITION PROBABILITY DOUBLE DECAY RATE INTENSITY  In a B factory operating at the Υ(4S) peak, our initial two-meson state is Einstein- Podolsky-Rosen entangled,

which maintains its antisymmetric entangled character in the H eigenstate basis. This implies the antisymmetric character of the two meson state at all times and ퟎ ퟎ for any two independent linear combinations of Entangled 푩풅 풂풏풅 푩풅. The corresponding evolution before the first decay is therefore trivial for perfect Entanglement.

 Given a decay "f", the Partner Meson is tagged by

and the "filtered state" is its orthogonal

 The FILTERING IDENTITY establishes the connection between the Meson Transition Probability and the experimental "reduced" Intensity 2 푔 푇 퐵↛푓 푡 ⊥ 2 퐼 푓, 푔; 푡 = 2 2 = 퐵↛푔 퐵↛푓 푡

퐴푔 + 퐴푔  There are NO FAKE TERMS for a proof of Symmetry Breaking if the ratio of

decay amplitudes 퐴/퐴 is a pure phase: 퐵− ↔ 퐽/ψ KS , 퐵+ ↔ 퐽/ψ KL . Controlled in the same experiment. SEPARATE T, CP, CPT ASYMMETRIES t i t ~ e  Ci cosmt Si sinmt C'i cosht S'i sinht 

CPT CPT

CP CP T T

 The Processes (f, g) and (g,f) exchanging the Time Ordering of the Decays are NOT CONNECTED BY A SYMMETRY OPERATION! T-RAW ASYMMETRIES & SIGNFICANCE

0 B  B

0 B  B

0 B  B

2 SNoT  226 14 GENUINE T, CP, CPT ASYMMETRIES

J.B., F. Botella, M. Nebot, JHEP 1606 (2016) 100

 3 different Observables ΔCh, ΔCc, ΔSc for each symmetry 9 Asymmetry parameters with different information content Using BABAR data PRL 2012, we obtain 푇 퐶푃 ∆푆푐 = −0.687 ± 0.020 ; ∆푆푐 = −0.680 ± 0.021 Impressive separate evidence of TRV, CPV  “Intriguing” 2σ - effect for CPTV 퐶푃푇 퐶푃푇 −2 ∆퐶푐 = −∆퐶ℎ = 2.7 ± 1.5 ∙ 10 interpreted in the evolution Hamiltonian 퐶푃 −2 it should be seen in ∆퐶푐 = 5.0 ± 1.5 ∙ 10 at LHCb: Unorthodox CPV term!  Analysis assuming perfect ENTANGLEMENT The two Time-Ordered Decays f, g satisfy

Ch (f,g) = Ch (g,f) ; Cc (f,g) = Cc (g,f) ; Sc (f,g) = -Sc (g,f) GAUGE ANOMALIES -> QUARK-LEPTON SYMMETRY  Gauge Anomaly: feature of quantum mechanics, a one-loop diagram, invalidating the gauge symmetry of a quantum field theory.

 All gauge anomalies must cancel out. Anomalies in gauge symmetries would destroy the required cancellation of unphysical degrees of freedom (such as a photon polarized in time direction).

 Are they cancelled in the Standard Model? Anomalies appear in even D spacetime dimensions with CHIRAL fermions running in the loop with n =1+D/2 vertices. For D=4, n=3, it is VVA! Condition  The symmetrized trace over the ?! generators of the gauge group vanishes: tr({τi,τj}τk) = 0

푢 푐 푡 휐푒 휐휇 휐휏 ↔ Symmetry between 푑 푠 푏 푒 휇 휏 3 Families of Quarks and Leptons Quarks and Leptons III.- NEUTRINOS

 Beta Decay Puzzles: "Dear Radioactive Ladies and Gentlemen"  Neutrino Flavours: How many?  Neutrino Oscillations: Pending Questions  Neutrino Masses: Dirac-Majorana "confusion" BETA DECAY PUZZLES Carbon-14 into Nitrogen-14 with a half-life of about 5,730 years:

14 14 6C → 7N + e− ENERGY and ANGULAR MOMENTUM NOT CONSERVED

 Lise Meitner and Otto Hahn in 1911 & Jean Danysz in 1912  first hint that beta particles have a continuous spectrum.

 James Chadwick in 1914  the spectrum was continuous.

 Molecular band spectra  the nuclear spin of Nitrogen-14 is 1 (explained later by the proton-neutron model of the nucleus)

 In 1920–1927, Charles Drummond Ellis  the spectrum is continuous!

 Niels Bohr  conservation of energy true in a statistical sense.

DEAR RADIOACTIVE LADIES AND GENTLEMEN

 In 1930, Pauli  letter of 4 December to Lise Meitner et al.: he proposed the existence of a hitherto unobserved neutral particle with a small mass, no greater than 1% the mass of a proton. . desperate remedy to save the "exchange theorem“ of statistics and the law of conservation of energy. . “I cannot appear in Tubingen personally since I am indispensable here in Zurich because of a ball on the night of 6/7 December”.

 In 1934, Enrico Fermi incorporated the particle, which he called a neutrino, into his theory of beta decay.

 In 1956, Cowan–Reines experiment: antineutrinos created in a nuclear reactor by + beta decay detected by 휈 e + p → n + e THE FAMILY PROBLEM • μ-e Universality  A decade before the (V-A) theory of (charged current) weak interactions (WI), B. Pontecorvo, PR (1947) discussed the “universality” of WI for processes of nuclear β-decay together with those with muon and neutrino!

 He introduced μ – capture   (A,Z)   (A,Z 1) and compared with probability for e-capture. (e)  The idea of μ-e universality was also followed by G. Puppi, NC(1948) with the famous “Puppi triangle” ( pn) () μ- capture Question: The same  in the two vertices? LEPTON FLAVOUR

 The idea of different neutrinos  e ,   appeared published in the paper μ+ B. Pontecorvo, J Phys. (1959) + and, more important, in the proposal made π by Pontecorvo for generating a  beam ! B. Pontecorvo, Sov. Phys. JETP (1960) ν e  The Brookhaven  experiment was the first with high ? energy  ' s from π decay. μ It was a great event in physics and TWO LEPTON FAMILIES COMPLETED

(e ,e) &( ,)

G. Danby et al., PRL (1962)

 An earlier indication  e ≠   The search for the decay  → e

•G. Feinberg, PR (1958) estimated the BR in the V-A theory with the W-boson if -4 -8  e =    Rth ~10 , Rexp < 10 when Brookhaven experiment HOW MANY NEUTRINO SPECIES?  Method 1  Helium abundance in universe  Method 2  LEP e+ e- Collider Legacy

 Invisible Width Γ = 푁 Γ 𝑖푛푣 휐 휐 The photon is detected and nothing else. not measurable directly Cross section normalized to μ μ  the visible cross section depends on 푁휐 휇 , 휈

, 휈

푁휐=3 NEUTRINO OSCILLATIONS  Neutrino oscillation  quantum mechanical phenomenon whereby a neutrino created with a specific lepton flavour (electron, muon, or tau) can later be measured to have a different flavour.  Experimental discovery by Super-Kamiokande (1998) with atmospheric neutrinos and Sudbury (2002) for solar neutrinos. Later with reactor and accelerator neutrinos. It demonstrates that NEUTRINOS HAVE MASS AND FLAVOUR MIXING i 1 0 0  c 0 s e  c s 0  13 13  12 12 U (PMMS)  0 c23 s23 0 1 0  s12 c12 0  i  0  s c   s e 0 c  0 0 1  23 23 13 13  

Two mass differences-frequencies-and Three Mixings-probabilities-already measured - (2,3) Mixing above or below 45 degrees? - CP-Violating Flavour Phase and (?) Two CPV Majorana Phases in U(PMNS) - Neutrino Mass Spectrum Hierarchy  normal, inverted - Absolute Neutrino Mass Scale

ARE NEUTRINOS DIRAC OR MAJORANA PARTICLES ?

UP’S & DOWN’S NEUTRINO MASS

 PV in processes involving  ' s  Advent of Two-component  theory

If are exactly massless  Goldhaber experiment, M. Goldhaber et al., PR(1958)

proved that  -helicity is -1  L !

 But … Universal V-A theory of WI tells that L-handed Chiral Fields enter for ALL Fermions  No rationale why are special and massless.

 Still, contrary to other fermions, have no electric charge. Do they have a Lepton Charge? OPEN Question in 2018! : GLOBAL LEPTON NUMBER ?

 Pontecorvo proposal (1946)! : •  ' s produced in β- decay in Reactors, Can them produce e’s ? • Davis (1959), BAPS (1959)

DIRAC or MAJORANA NEUTRINOS ?

Most important Open Question:

DIRAC MAJORANA

푐 휈 푅 푚퐷 휈퐿 휈퐿 푚푀 휈퐿

Needs sterile 휈푅, ΔL = 0 Global LNV, ΔL = 2

Origin by Standard Higgs BSM Origin GLOBAL LEPTON NUMBER VIOLATION /Δ L=2/ Neutrinoless Double Beta Decay Resonant Atom Mixing: Doble e-capture • ΔL = 2 mixing, only if Majorana ν, followed by 2 X-ray emission

• Signature: Tϒϒ = Q • No intrinsic background on the resonance

[S. Pascoli, CERN Courier, July-August 2016]

• ΔL=2 process, only if Majorana ν

• Signature: Tee = Q

• Background by 2v mode with Tee < Q IV.- ELECTROWEAK SYMMETRY BREAKING

 Standard Model  Spontaneous Breaking of the Gauge Symmetry  The Higgs Boson at CERN  Beyond-Standard-Model Physics STANDARD MODEL OF PARTICLE PHYSICS

 The Gauge Symmetries in SU(3)xSU(2)LxU(1)Y are generated by the "charges": Colour, Weak Isospin, Weak Hypercharge.The last two

combined to Electric Charge of U(1)e.m.

 The Interactions are EXCHANGE FORCES with the Mediators Gluon (m=0, confined), Photon (m=0), Massive W+-, Z.

 SM not only predicted New Particles and New Interactions, but AGREEMENT with precision experimental results of detailed OBSERVABLES is impressive in the last decades.

 However, these are EXACT SYMMETRIES in the massless limit only! One should have in Nature a very subtle Mechanism for Origin of Mass without affecting the Interactions, in the

SU(2)L x U(1)Y  U(1)e.m. Gauge Symmetry Breaking BROUT-ENGLERT-HIGGS MECHANISM - ORIGIN OF MASS from SPONTANEOUS ELECTROWEAK SYMMETRY BREAKING (SEWSB):

A symmetric Law of Physics can lead to asymmetric solutions Jean Buridan (1300-1358)  To define a Quantum Field Theory, one has to specify not only the physical law, but also the QUANTUM VACUUM, the lowest energy state from which particles are created and annihilated.

 SEWSB means the physical law is symmetric . the vacuum is asymmetric. How?  Space-time is filled with a "medium", a field with the interaction like a "mexican hat". Instead of a unique symmetric lowest energy state, there are many possible vacua. One choice breaks the symmetry.

 The particle created from the new vacuum is the HIGGS BOSON, a remnant of the Brout-Englert-Higgs Mechanism, hence its importance.

 The signature of the Higgs: its coupling to all particles is given by their mass. The ORIGIN OF MASS comes from the asymmetry of the new vacuum. HIGGS BOSON DISCOVERY -> THE DATA

CERN 2012 CMS

Higgs Couplings ESTABLISHED HIGGS PROPERTIES HIGGS LAGRANGIAN

Higgs Production

Higgs Decays H b푏 . H b푏 has the largest branching fraction (58%) for

MH= 125 GeV . Unique final state to measure coupling with down-type quarks . Drives the uncertainty of the total Higgs boson width - Limits the sensitivity to BSM contributions

. QCD background  Solution: VH(bb) V= W± , Z VH(bb) observed

. ATLAS and CMS have 5,4σ and 5,6σ separate observations of the Hbb Decay, with signal strengths μ(ATLAS) = 1.01 ± 0.20 and μ(CMS) = 1.04 ± 0.20

. Standard Model result on Yukawa coupling to b’s confirmed within the present uncertainty HIGGS POTENTIAL

- SM Higgs is a doublet under SU(2) Complex Fields

- Besides gauge and Yukawa couplings, the HIGGS POTENTIAL invariant under local gauge transformations.

- For has a minimum at in the Mexican hat.

- Let us choose the direction ,

we look for the equations satisfied by the Higgs H(x).

Choosing a direction  three broken global symmetries  three massless Goldstone Bosons  the longitudinal W±, Z  local gauge symmetry appears broken WHEN TRANSFORMING FIELDS OF DEFINITE MASS  SSB!

- After symmetry breaking, the SM Higgs Potential becomes 2 2 2 푚퐻 2 푆푀 3 푆푀 4 푆푀 푚퐻 푆푀 푚퐻 V 퐻 = − 퐻 − 휆3 푣퐻 − 휆4 퐻 , 휆3 = , 휆4 = 2 2푣2 8푣2 where the Higgs vacuum expectation value (VEV) v = 246 GeV is related to the Fermi constant GF measured in muon decay. - The self-couplings of the Higgs are the keystone of the Higgs potential in the SM, never probed.

BEYOND-STANDARD-MODEL (BSM- Physics)  Quantization of electric charge  Magnetic Monopoles? “Threeality” in fundamental physics Naturalness problem for scalars  SuperSymmetry, Grand Unification  p-decay? Baryon-Asymmetry of the Universe Neutrino Mass, Mixing, CPV↔ Majorana? Charged-Lepton-Flavour Violation? Dark Matter Dark Energy CPTV? ↔ QFT? OUTLOOK  Symmetry as Guiding Principle for Particles and Interactions

 Breaking by:

- Mass (“by hand”)  Gauge, Chirality

Vector  Conformal - Quantum Anomalies Chiral  Gauge

- Particle Content  Discrete CP and T

Gauge - Spontaneous (Hidden) Origin of Mass for elementary particles - Quantum Gravity Space-Time  CPT ? Thank you very much for your attention P 풱퐿 풱푅 풱퐿 C

퐶 퐶 퐶 풱푅 풱퐿 풱퐿 μ+ Π+

ν e ? μ NEUTRINO OSCILLATIONS  Neutrino oscillation  quantum mechanical phenomenon whereby a neutrino created with a specific lepton flavour (electron, muon, or tau) can later be measured to have a different flavour.  Experimental discovery by Super-Kamiokande (1998) with atmospheric neutrinos and Sudbury (2002) for solar neutrinos. Later with reactor and accelerator neutrinos. It demonstrates that NEUTRINOS HAVE MASS AND FLAVOUR MIXING Two mass differences-frequencies-and Three Mixings-probabilities-already measured  Most important Open Questions:

ARE NEUTRINOS DIRAC OR MAJORANA PARTICLES ? 푐 휈 푅 푚퐷 휈퐿 휈퐿 푚푀 휈퐿 Needs sterile 휈푅 Breaks Global Lepton Number Origin by Standard Higgs Doublet Beyond Standard Origin

- CP-Violating Flavour Phase and (?) Two CPV Majorana Phases in U(PMNS) - Absolute Neutrino Mass Scale - Neutrino Mass Spectrum Hierarchy  normal, inverted - (2,3) Mixing above or below 45 degrees?