Download - The Neutrino Story

The Neutrino Story

What We Think It Tells Us

and

Why We May Be Wrong

C.P. Burgess

04/19/23 Neutrinos

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

04/19/23 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!

04/19/23 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-

0

ep

nep

pp

MEE

E

N

04/19/23 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 → p + e- +

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Outline





04/19/23 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.

→ +

04/19/23 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, or ).

• ‘Neutral current’ interactions always involve missing energy and momentum, indicating the presence of an unseen neutrino among the final-state particles.

X

X

Charged Current

Neutral Current

04/19/23 Neutrinos

More Than One Neutrino Species

• Neutrinos produced with muons always* produce muons in charged-current interactions: =

• Neutrinos produced with electrons always* produce electrons in charged-current interactions: = e

• Neutrinos produced with tau leptons always* produce tau leptons in charged-current interactions: =

X

e

n X

e

04/19/23 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, L and L.

0,...,;1,;1, eeeee LeLeL

LLLL e

0,...,;1,;1, eeLLL

04/19/23 Neutrinos

How Massive Are They?

• Muon neutrino mass is inferred from the final muon energy in the two-body decay of the pion.

m < 0.19 MeV (90% cl)

• Tau neutrino mass is inferred from the spectrum of pion energies in the decay

→ 5 + m < 18.2 MeV (95% cl)

m

mmE

2

22

E

N

m/2

04/19/23 Neutrinos

How Massive Are They?

• Muon neutrino mass is inferred from the final muon energy in the two-body decay of the pion.

m < 0.19 MeV (90% cl)

• Tau neutrino mass is inferred from the spectrum of pion energies in the decay

→ 5 + m < 18.2 MeV (95% cl)

m

mmE

2

22

E

N

m/2

m

04/19/23 Neutrinos

The Electron Neutrino Mass

• Electron neutrino masses are inferred from the shape of the electron spectrum in tritium beta decay.

eeHeH 33

2/1

EFpE

NK e

EFmQEQEpENe

2/122

em < 3 eV (95% cl)

Kurie Plot

04/19/23 Neutrinos

Do Neutrinos Decay?

• Limits are obtained by observing neutrino induced reactions downstream from a known source.

• Laboratory limits:e > 300 sec (m/eV)

> 0.11 sec (m/eV)

• Supernova 1987a:e: > 3 × 105 sec (m/eV)

SN Us

150,000 ly

04/19/23 Neutrinos

Kinematics of Massless Neutrinos

• Massless particle states may be labelled by their momentum, p, and helicity, h.

h = (p . s)/|p| = ± ½

• Observed s have: h= +½. • CPT symmetry requires

the existence of an antiparticle whose helicity is opposite

(p,h) (p,-h)CPT

04/19/23 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.

(p,h) (p,-h)CPT

(p,h)(p,-h)CPT

Boost, if m ≠ 0

Boost, if m ≠ 0

04/19/23 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’.

(p,h) (p,-h)CPT

(p,h)(p,-h)CPT

Boost, if m ≠ 0

Boost, if m ≠ 0

04/19/23 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: = (1.5 ± 0.19) × 1021 y

-

04/19/23 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.

04/19/23 Neutrinos

Neutrinoless Double Beta Decay

for 76Ge: > 1.6 × 1025 y implies < m < 0.3 eV (90% c.l.)

2 decay

0 decay

04/19/23 Neutrinos

Outline





04/19/23 Neutrinos

The Fermi Theory

weakEMstrongint HHHH

A purely phenomenological description…

**weak ncnccccc JJGJJGH

...*** ecc eJ

...**** eenc eeJ

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The Fermi Theory




...*** ecc eJ

...**** eenc eeJ

Neutrinosonly appearin Weak Interactions

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The Fermi Theory




...*** ecc eJ

...**** eenc eeJ

ChargedCurrent Interactions

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The Fermi Theory




...*** ecc eJ

...**** eenc eeJ

NeutralCurrent Interactions

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The Fermi Theory




...*** ecc eJ

...**** eenc eeJ

Destroys a neutrino and creates an electron

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The Fermi Theory




...*** ecc eJ

...**** eenc eeJ

Destroys andrecreates a neutrino withdifferent momentum

04/19/23 Neutrinos

The Fermi Theory




...*** ecc eJ

...**** eenc eeJ

qq’

e

04/19/23 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 = 1);• All neutrino interactions break C and P but preserve CP.

04/19/23 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 = 1?• Why are neutrinos massless?

04/19/23 Neutrinos

Some Interactions NOT Included…

mni

imn

i FngH *Lepton

j

j

i ijij

ijij

t

NM

m

NH

i

i

*

*

mass

04/19/23 Neutrinos


mni

imn

i FngH *Lepton

j

j

i ijij

ijij

t

NM

m

NH

i

i

*

*

mass

Describes neutron decay into neutrino plus photon, which would violate conservation of lepton number.

04/19/23 Neutrinos


j

j

i ijij

ijij

t

NM

m

NH

i

i

*

*

mass

Describes L=+1 right-handed neutrinos (or L=-1 left-handed anti-neutrinos).

mni

imn

i FngH *Lepton

04/19/23 Neutrinos


j

j

i ijij

ijij

t

NM

m

NH

i

i

*

*

mass

A Lepton-number conserving ‘Dirac’ mass term.

mni

imn

i FngH *Lepton

04/19/23 Neutrinos


j

j

i ijij

ijij

t

NM

m

NH

i

i

*

*

mass

Lepton-number violating ‘Majorana’ mass terms.

mni

imn

i FngH *Lepton

04/19/23 Neutrinos

The Standard Model

ncccSM JZgccJWgH .

• 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.

04/19/23 Neutrinos

ncccSM JZgccJWgH .

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.

W

e

04/19/23 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.

04/19/23 Neutrinos

The Fermi Theory

qq’

e

• Amplitude: G

04/19/23 Neutrinos

The Fermi Theory Explained

qq’

e

W

qq’

e • Amplitude: G

G/√2 = g2/8MW2

04/19/23 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 = g2/8MW

2, = 1.• Lepton numbers and CP must be conserved.

ExplainsExplains many of the features of the Fermi Theory!

04/19/23 Neutrinos

The Standard Model Tested

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

04/19/23 Neutrinos

Neutrinos Counted

• All neutrinos which couple to, and are lighter than, the Z boson can be counted by measuring its ‘invisible width’, Z → .• Can check by also measuring Z →

Agreement requires N = 3.

04/19/23 Neutrinos

Neutrinos Counted

• Success of Big Bang Nucleosynthesis counts gravitating species when T ~ 1 MeV, and also prefers around 3 species.

Agreement requires N ~ 3.

Cuoco et.al., astro-ph/0307213

04/19/23 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 m ~ MW

2/M.

04/19/23 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 m ~ MW

2/M.

Naturally light LH neutrinos

04/19/23 Neutrinos

Outline





04/19/23 Neutrinos

Neutrino Masses and Universality

• If neutrinos are massive then charged-current interactions need no longer be universal.

• Transition amplitudes are predicted to be unitary:

j U*ji Ujk = ik

• If there are no light RH neutrinos then overall Lepton number is broken so neutrinos are majorana particles.

1,,

e,,

W

ijji UeA

04/19/23 Neutrinos

Neutrino Oscillations

• Time-dependent interference between neutrino species occurs if their masses differ because Ei-Ej ≈ (mi

2-mj2)/2E

tiEjkkji

j

ijeUUeeA *

ei

X

ek

j

Uij Ujk

04/19/23 Neutrinos

Two-Flavour Oscillations

Probabilities parameterized by and m2.

cossin

sincos

21

21

UU

UU ee

tiEtiE eet 21 sincos 21

E

LmLEPe 4

sin2sin,2

22

04/19/23 Neutrinos

Solar Neutrinos

• The sun bathes us in neutrinos, which are observed in terrestrial neutrino detectors.

SNO

• The observed neutrino flux is only consistent with predictions if the neutrinos oscillate while en route from the solar core.

GONG

04/19/23 Neutrinos

Solar Neutrinos

• Different experiments can detect neutrinos having different energies.

• Theory accurately predicts the neutrino spectrum.

J. Bahcall

04/19/23 Neutrinos

Solar Neutrino Deficit

• For decades the disagreement between observations of the solar neutrino flux and solar model predictions has prevented using neutrinos to infer the properties of the deep solar interior.

J. Bahcall

04/19/23 Neutrinos

Neutrino Oscillations

• This deficit is now understood as a consequence of neutrinos oscillating while en route from the solar core.

SNO

04/19/23 Neutrinos

Terrestrial Evidence

• The evidence for neutrino oscillations is also now supported by direct terrestrial experiments, which measure a disappearance of e’s while en route to a detector from various nuclear reactors.

KamLands

04/19/23 Neutrinos

Atmospheric Neutrinos

Cosmic Ray

Cosmic rays (which are mostly protons) produce pions when they hit atoms in the upper atmosphere.

04/19/23 Neutrinos


Cosmic Ray

→

The pions decay, producing muons…

04/19/23 Neutrinos


e

Cosmic Ray

e

→

→ e e

The muons decay into electrons…

04/19/23 Neutrinos


e

Cosmic Ray

e

→

→ e e

45.0)(

)(

theory

N

N e

04/19/23 Neutrinos

Oscillations Observed?

• The Super-K detector in Japan instead finds an observed ratio which is closer to one.• They find the expected number

of electron neutrinos, but fewer muon neutrinos.

• How certain are the theoretical errors?

E

LmP

4sin2sin

222

04/19/23 Neutrinos

Oscillations Observed?

• The Super-K detector in Japan instead finds an observed ratio which is closer to one.• They find the expected number

of electron neutrinos, but fewer muon neutrinos.

• How certain are the theoretical errors?

• Super-K also sees an up/down asymmetry: • Up/Down = 0.54 ± 0.04• Insensitive to theory, and as

expected from - oscillations since neutrinos travel for different distances, L.

E

LmP

4sin2sin

222

04/19/23 Neutrinos

Atmospheric Oscillations

• Atmospheric neutrino observations are consistent with oscillations between neutrinos which are dominantly muon and tau type.

• The terrestrial K2K experiment also measures disappearance for neutrinos sent from an accelerator.

04/19/23 Neutrinos

The Three-Neutrino Picture

• Two mass differences also fix the third but cannot fix the overall neutrino mass scale.• Heaviest neutrino is at least

0.05 eV in mass.• Could instead have small mass

splittings for the heavier pair of neutrinos.

m2 in eV2;

L in km; E in GeV.

04/19/23 Neutrinos

The Three-Neutrino Picture

Global fit to neutrino data gives:

100

0

0

0

010

0

0

0

001

1212

1212

1313

1313

2323

2323 cs

sc

cs

sc

cs

scU

In absence of CP violating phases

252sol

221 eV109.6 mm

232atm

232

231 eV106.2 mmm

3.0sin 122 5.0sin 23

2 .).%90(029.0sin 132 lc

04/19/23 Neutrinos

A Fly in the Ointment?

The ‘Los Alamos’ Neutrino:• Expect no e’s, so look for e + p → e+ + n.

• Search for Cerenkov light from the e+ and ray from the n capture.• Find 22 events for an expected background of about 5.

• Almost inconsistent with the KARMEN experiment.

beam

+ decay at rest

e

e

Mineral oil

04/19/23 Neutrinos

Conclusions and Outlook

• For the very first time there is compelling evidence that the Standard Model is beginning to fail, due to experimental indications for neutrino oscillations. • Evidence for Atmospheric and Solar neutrino oscillations

are both supported by terrestrial oscillation experiments.

• Would like to have a terrestrial appearance measurement.

• We are entering a period of precision measurements for neutrino masses and mixings.• New phenomena? CP violation? Majorana mass?

Our first inklings of very high-energy physics!