The Neutrino Story

The Neutrino Story What We Think It Tells Us and Why We May Be Wrong C.P. Burgess

Outline • The Most Feebly-Interacting Observed Particles • Why are they observed at all? • Basic Neutrino Properties • How many types are there? • How massive are they? • Do they decay? • Are they distinct from their antiparticles? • Theory • The Standard Model synthesis… • Neutrino Oscillations Neutrinos

You Live in a Neutrino Bath • Around 1010 neutrinos per cm2 per sec pass through the Earth’s surface, coming to us from the Solar core. • By comparison around 1 muon per cm2 per sec arrives at the Earth’s surface, caused by cosmic rays hitting the upper atmosphere. • In 1987 (for about 10 secs) about the same neutrino flux reached the Earth from an exploding star about 150,000 light years away. Neutrinos interact very feebly with matter! Neutrinos

How Do We Know Neutrinos Exist? • In a two-body decay, energy and momentum conservation uniquely fix the energy of the outgoing particles. n → p + e- N E Neutrinos

How Do We Know Neutrinos Exist? • Electrons produced by beta decay do not all have the same energy. • Pauli proposed the existence of an unseen neutral particle to explain the observed electron spectrum. n n → p + e- + n Neutrinos

Neutrinos in the Lab • If neutrinos interact so weakly, how can they be produced for experiments in the lab? • Pions are copiously produced by the strong interactions, but decay into neutrinos close to 100% of the time. • Neutrino beams can be produced from pion beams, or from intensely radioactive sources like nuclear reactors. p n m p+→m++ n Neutrinos

Two Kinds of Reactions • Neutrino beams cause two types of reactions when they hit targets. • ‘Charged current’ interactions always involve an electrically charged ‘lepton’ (ie e, m or t). • ‘Neutral current’ interactions always involve missing energy and momentum, indicating the presence of an unseen neutrino among the final-state particles. X p n m m Charged Current X p n n m Neutral Current Neutrinos

More Than One Neutrino Species • Neutrinos produced with muons always* produce muons in charged-current interactions: n = nm • Neutrinos produced with electrons always* produce electrons in charged-current interactions: n = ne • Neutrinos produced with tau leptons always* produce tau leptons in charged-current interactions: n = nt X p n m m X n n e e Neutrinos

Lepton Number Conservation • The results of charged-current experiments (until recently) were consistent with the existence of three different neutrino species with the separate conservation of Le, Lm and Lt. Neutrinos

How Massive Are They? • Muon neutrino mass is inferred from the final muon energy in the two-body decay of the pion. nm:m < 0.19 MeV (90% cl) • Tau neutrino mass is inferred from the spectrum of pion energies in the decay t→ 5p + n nt:m < 18.2 MeV (95% cl) N mp /2 E Neutrinos

How Massive Are They? • Muon neutrino mass is inferred from the final muon energy in the two-body decay of the pion. nm:m < 0.19 MeV (90% cl) • Tau neutrino mass is inferred from the spectrum of pion energies in the decay t→ 5p + n nt:m < 18.2 MeV (95% cl) N mn  0 mp /2 E Neutrinos

The Electron Neutrino Mass • Electron neutrino masses are inferred from the shape of the electron spectrum in tritium beta decay. Kurie Plot ne:m < 3 eV (95% cl) Neutrinos

Do Neutrinos Decay? • Limits are obtained by observing neutrino induced reactions downstream from a known source. • Laboratory limits: ne: t > 300 sec (m/eV) nm: t > 0.11 sec (m/eV) • Supernova 1987a: ne: t > 3 × 105 sec (m/eV) 150,000 ly SN Us Neutrinos

Kinematics of Massless Neutrinos • Massless particle states may be labelled by their momentum, p, and helicity, h. h = (p . s)/|p| = ± ½ • Observed ns have:h= +½. • CPT symmetry requires the existence of an antiparticle whose helicity is opposite n(p,h) n(p,-h) CPT Neutrinos

Kinematics of Massive Neutrinos • If neutrinos are massive, then the sign of their helicity can be changed by changing the frame of reference. h = (p . s)/|p| • If massive, neutrinos having both signs of helicity must exist. n(p,h) n(p,-h) CPT Boost, if m ≠ 0 Boost, if m ≠ 0 n(p,-h) n(p,h) CPT Neutrinos

Majorana vs Dirac Neutrinos • Since neutrinos are electrically neutral, they could be their own antiparticle (like the photon). • If neutrinos carry a conserved charge (like Lepton number) then this can be used to distinguish particle from antiparticle. • Neutrinos which are their own antiparticles are known as ‘Majorana neutrinos’. n(p,h) n(p,-h) CPT Boost, if m ≠ 0 Boost, if m ≠ 0 n(p,-h) n(p,h) CPT Neutrinos

Double Beta Decay - • Some unstable nuclei cannot decay by single beta emission, but can decay by the much more rare process of double-beta emission. eg for 76Ge: t = (1.5 ± 0.19) × 1021 y n n Neutrinos

Neutrinoless Double Beta Decay - • If neutrinos were Majorana and are massive then two neutrinos having the same helicity could mutually annihilate, leading to neutrinoless double beta decay. n Neutrinos

Neutrinoless Double Beta Decay for 76Ge: t > 1.6 × 1025 y implies < mn > < 0.3 eV (90% c.l.) 0nbb decay 2nbb decay Neutrinos

The Fermi Theory A purely phenomenological description… Neutrinos

The Fermi Theory Neutrinos only appear in Weak Interactions A purely phenomenological description… Neutrinos

The Fermi Theory Charged Current Interactions A purely phenomenological description… Neutrinos

The Fermi Theory Neutral Current Interactions A purely phenomenological description… Neutrinos

The Fermi Theory Destroys a neutrino and creates an electron A purely phenomenological description… Neutrinos

The Fermi Theory Destroys and recreates a neutrino with different momentum A purely phenomenological description… Neutrinos

The Fermi Theory A purely phenomenological description… Neutrinos

Theoretical Features • The Fermi Theory is designed to include the following experimentally-observed features: • All neutrino masses are zero; • All three Lepton numbers are conserved; • Neutrinos appear only in CC and NC interactions; • All couplings are Universal (ie all charged current interactions are described by the single constant, G); • Only left-handed (h = +1) neutrinos appear; • CC and NC interaction strengths have same strength (ie r = 1); • All neutrino interactions break C and P but preserve CP. Neutrinos

Descriptive, Not Explanatory • The Fermi Theory gives no understanding of why neutrinos have these features: • Why are Lepton numbers and CP conserved? • Why are there no right-handed neutrinos? • Why are there only two types of interactions? • Why are the neutrino couplings universal? • Why is r = 1? • Why are neutrinos massless? Neutrinos

Some Interactions NOT Included… Neutrinos

Some Interactions NOT Included… Describes neutron decay into neutrino plus photon, which would violate conservation of lepton number. Neutrinos

Some Interactions NOT Included… Describes L=+1 right-handed neutrinos (or L=-1 left-handed anti-neutrinos). Neutrinos

Some Interactions NOT Included… A Lepton-number conserving ‘Dirac’ mass term. Neutrinos

Some Interactions NOT Included… Lepton-number violating ‘Majorana’ mass terms. Neutrinos

The Standard Model • Weinberg (1967) and Salam (1968) unified the weak and electromagnetic interactions, using a symmetry proposed earlier by Glashow. • Weak interactions are described by the exchange of either a massive, charged W boson (charged current) or a massive, neutral Z boson (neutral current). • The interactions of spin-one particles like the W and Z bosons are strongly constrained by the consistency of special relativity and quantum mechanics. Neutrinos

The Standard Model The Standard Model contains the MOST GENERAL ‘low-energy’ interactions consistent with the known particle content (plus an as-yet-undiscovered particle called the Higgs boson whose existence is required by the existence of masses for the W and Z bosons). Corrections to the Standard Model are O(E/M) for M the mass of any undiscovered, very massive particles. Neutrinos

The Fermi Theory • Amplitude: G Neutrinos

The Fermi Theory Explained • Amplitude: G G/√2 = g2/8MW2 Neutrinos

The Fermi Theory Explained • The Fermi Theory approximates the Standard Model at energies well below the W mass, and in the absence of right-handed neutrinos has the required predictions: • Two types of interactions: charged and neutral current. • Neutrinos must be massless. • Neutrino couplings must be universal. • Coupling strength predicted to be: G/√2 = g2/8MW2, r = 1. • Lepton numbers and CP must be conserved. Explains many of the features of the Fermi Theory! Neutrinos

The Standard Model Tested • Experiments at LEP test the Standard Model predictions to an accuracy of fractions of a percent. Neutrinos

Neutrinos Counted Agreement requires Nn = 3. • All neutrinos which couple to, and are lighter than, the Z boson can be counted by measuring its ‘invisible width’, Z → n n. • Can check by also measuring Z → n n g. Neutrinos

Neutrinos Counted Agreement requires Nn ~ 3. Cuoco et.al., astro-ph/0307213 • Success of Big Bang Nucleosynthesis counts gravitating species when T ~ 1 MeV, and also prefers around 3 species. Neutrinos

Why No Right-Handed Neutrinos? • The Standard Model forbids particles with chiral electroweak couplings from being much heavier than MW. • The Standard Model predicts that right-handed neutrinos are sterile: ie they do not directly participate in the strong, electromagnetic or weak interactions. • Because they are sterile, right-handed neutrinos can and should have masses M»MW. • Even if they should exist, RH neutrinos would naturally be heavy and very weakly coupled, and so escaped detection. • If such heavy RH neutrinos exist, they generically imply masses for LH neutrinos of order mn ~ MW2/M. Neutrinos

Why No Right-Handed Neutrinos? • The Standard Model forbids particles with chiral electroweak couplings from being much heavier than MW. • The Standard Model predicts that right-handed neutrinos are sterile: ie they do not directly participate in the strong, electromagnetic or weak interactions. • Because they are sterile, right-handed neutrinos can and should have masses M»MW. • Even if they should exist, RH neutrinos would naturally be heavy and very weakly coupled, and so escaped detection. • If such heavy RH neutrinos exist, they generically imply masses for LH neutrinos of order mn ~ MW2/M. Naturally light LH neutrinos Neutrinos

The Neutrino Story