Nuclear and Particle Physics

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PHY401: Nuclear and Particle Physics

Lecture 4, Monday, August 31, 2020 Dr. Anosh Joseph IISER Mohali Particles and Nuclei A Historical Introduction II

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

Let’s go back to year 1930.

Only 3 elementary particles were known to us at that time.

Protons, neutrons, and electrons.

Study of nuclear beta decay - gave an unusual puzzle.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

Beta decay: a radioactive nucleus A is transformed into a lighter nucleus B, with the emission of electron:

A → B + e−. (1)

Charge conservation requires that B carry one more unit of positive charge than A.

We now know that the underlying process here is the conversion of a neutron, in A, into a proton, in B.

In 1930, the neutron had not yet been discovered.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

Neutron was discovered in 1932.

Examples of beta decay:

40 40 19K −→ 20Ca

64 64 29Cu −→ 30Zn

3 3 1H −→ 2He

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

Upper number is atomic weight (number of neutrons + protons)

Lower number is atomic number (number of protons) of the nucleus.

In two-body decays (A → B + C) outgoing energies are kinematically determined, in the center-of-mass frame.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

If ‘parent’ nucleus (A) is at rest, so that B and e come out back to back with equal and opposite momenta,

...then energy conservation dictates that electron energy is

2 2 2 mA − mB + me 2 Ee = c . (2) 2mA

Ee is ﬁxed once the three masses are speciﬁed.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

When experiments were done, it was found that

...the emitted electrons vary considerably in energy.

Above equation only determines the maximum electron energy for a particular beta decay process.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

3 3 Figure: The beta decay spectrum of tritium ( 1H −→ 2He). Figure taken from Lewis, G. M. (1970) Neutrinos, Wykeham, London, p. 30.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

This was a very disturbing result.

Niels Bohr’s suggestion: abandon the law of conservation of energy.

Pauli took a more sober view.

His suggestion: another particle was emitted along with the electron, a silent partner particle, that carries off the ‘missing’ energy.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

It had to be electrically neutral, to conserve charge.

In 1933, Fermi presented a theory of beta decay that incorporated Pauli’s particle.

From the observed electron energies it follows that the new particle must be extremely light.

Fermi called it the neutrino (‘little neutral one’).

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

We now know that it is in fact the antineutrino.

In modern terminology the fundamental beta decay process is

n → p+ + e− + ν¯. (3)

By 1950, there was compelling theoretical evidence for the existence of neutrinos.

But there was still no direct experimental veriﬁcation.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

Very difﬁcult to detect neutrinos.

Reason: neutrinos interact very weakly with matter.

A neutrino of moderate energy could easily penetrate a thousand light years of lead.

Hundreds of billions of neutrinos per second passes through every square inch of your body, night and day.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

They are coming from the sun.

To have a chance of detecting one you need an extremely intense source.

Neutrinos were detected in the 1950s.

Two physicists, Cowan and Reins, set up a large tank of water near a nuclear reactor

...and watched for the inverse beta decay reaction

ν¯ + p+ → n + e+ (4)

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

At their detector, the antineutrino ﬂux was calculated to be 5 × 1013 particles per square centimeter per second.

Even with this intensity, they could only hope for two or three events every hour.

Their results provided unambiguous conﬁrmation of the neutrino’s existence.

Is the neutrino its own antiparticle?

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

Experiments show that neutrinos and antineutrinos are in fact distinct particles.

What property distinguishes the neutrino from the antineutrino?

One answer is: Lepton number L = +1 for neutrino and L = −1 for antineutrino.

We will see lepton number in detail later.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

The lepton numbers are experimentally determinable.

Second answer is: They differ in helicity.

Neutrinos are left-handed and antineutrinos are right-handed.

We will learn more about helicity later.

In late 1950s and 1960s experiments indicated that there are two kinds of neutrinos: one associated with the electron and the other associated with the muon

The electron neutrino νe and the muon neutrino νµ.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

Neutron beta decay

+ − n → p + e + ν¯e (5)

Pion decay

− − π → µ + ν¯µ (6) + + π → µ + νµ (7)

Muon decay

− − µ → e + ν¯e + νµ (8) + + µ → e + νe + ν¯µ (9)

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

Neutrinos are extremely light.

Until recently it was widely assumed that they were massless.

There was no fundamental reason to assume that the neutrinos were massless.

Now we know that neutrinos have mass.

We still do not know what their masses are.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

Over long distances neutrinos of one type can convert into neutrinos of another type and back again.

This phenomenon is known as neutrino oscillation.

If a neutrino knows how to change into another one it has a ’sense of time.’

That means neutrinos have mass.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Neutrinos (1930 - 1962)

By 1962, the lepton family had grown into eight:

The electron e−, the muon µ−, their respective neutrinos νe and νµ, and the corresponding anti-particles.

Leptons are characterized by the fact that they do not participate in strong interactions.

However, they participate in electromagnetic and weak interactions.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Strange Particles (1947 - 1960)

In 1947, a neutral particle was found in cosmic rays that decayed into two pions.

It was the kaon (or K meson)

K0 → π+ + π−. (10)

In 1949 charged kaons were discovered.

K+ → π+ + π+ + π−. (11)

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Strange Particles (1947 - 1960)

Kaons behave in some respects like heavy pions...

So the meson family was extended to include them.

In due course many more mesons were discovered: η, φ, ω, ρ, and so on.

In 1950 another particle was discovered. It decays into a proton in the following way

Λ → p+ + π−. (12)

Λ belongs with the proton and the neutron in the baryon family.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Strange Particles (1947 - 1960)

Why is a proton stable?

To account for the stability of baryon number we can introduce a law of conservation of baryon number.

Assign all baryons a ‘baryon number’ B = +1, and to the antibaryons B = −1.

Then the total number of baryons is conserved in any physical process.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Strange Particles (1947 - 1960)

Thus neutron beta decay is allowed

+ − n → p + e + ν¯e. (13)

B = +1 before and after.

The reaction in which the antiproton was ﬁrst observed is also allowed.

p + p → p + p + p + p¯. (14)

(B = +2 on both sides.)

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Strange Particles (1947 - 1960)

But the proton - the lightest baryon has nowhere to go.

Conservation of baryon number guarantees its absolute stability.

Grand Uniﬁed Theories (GUTs) allow for a minute violation of baryon number conservation.

No proton decay has been observed.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Strange Particles (1947 - 1960)

Its lifetime is known to exceed 1029 years.

The age of the universe is about 1010 years.

Over the next few years many more heavy baryons were discovered: Σ, ∆, and so on.

These heavy mesons and baryons were called collectively as ‘strange’ particles.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Strange Particles (1947 - 1960)

They seemed ‘strange’:

They are produced copiously (on a time scale of about 10−23 seconds), but decay relatively slowly (typically about 10−10 seconds).

In modern language, the strange particles are produced by the strong force (the same one that holds the nucleus together),

...but they decay by the weak force (the one that accounts for beta decay and all other neutrino processes).

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Strange Particles (1947 - 1960)

Later on, a new property, called ’strangeness’ was assigned to these particles.

Strangeness was conserved in any strong interaction, but not conserved in weak interaction.

One example is pion-proton collision.

π− + p+ → K+ + Σ− → K0 + Σ0 → K0 + Λ. (15)

K’s have S = +1 and Σ’s and Λ’s have S = −1.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Strange Particles (1947 - 1960)

The ‘ordinary’ particles π, p and n have S = 0.

When the strange particles decay, S is not conserved.

Λ → p+ + π− Σ+ → p+ + π0 → n + π+ (16)

These are weak processes.

They do not respect conservation of strangeness.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali Strange Particles (1947 - 1960)

By 1960, the plethora of strongly interacting particles was divided into two families.

The baryons and the mesons.

The members of each family were distinguished by charge, strangeness, and mass.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali The Eightfold Way (1961 - 1964)

In 1961, Murray Gell-Mann introduced the so-called Eightfold Way.

The Eightfold Way arranged the baryons and mesons into weird geometrical patterns, according to their charge and strangeness.

The eight lightest baryons ﬁt into a hexagonal array, with two particles at the center.

This set is known as the baryon octet.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali The Eightfold Way (1961 - 1964)

The eight lightest mesons ﬁll a similar hexagonal pattern,

...forming the (pseudo-scalar) meson octet.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali The Eightfold Way (1961 - 1964)

Hexagons were not the only ﬁgures allowed by the Eightfold Way.

There was also for example, a triangular array,

...incorporating 10 heavier baryons - the baryon decuplet.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali The Eightfold Way (1961 - 1964)

As Gell-Mann was ﬁtting these particles into the decuplet, nine of the particles were known experimentally.

But at that time, the tenth particle (the one at the very bottom) was missing.

Gell-Mann boldly predicted that such a particle would be found.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali The Eightfold Way (1961 - 1964)

He told experimentalists exactly how to produce it.

He also calculated its mass and lifetime.

In 1964, the famous omega-minus particle was discovered,

...precisely as Gell-Mann had predicted.

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali References

I David Grifﬁths, Introduction to Elementary Particles, 2nd edition, Wiley-VCH (2008).

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali End

PHY401: Nuclear and Particle Physics Dr. Anosh Joseph, IISER Mohali