a.ereditato ss 2008 1 elementarteilchenphysik antonio ereditato lhep university of bern lesson...

A.Ereditato SS 2008 1

Elementarteilchenphysik

Antonio Ereditato

LHEP University of Bern

Lesson on: Weak interaction (5)

Exercises: beta decay, V-A structure


Lepton number conservation

Lepton number conservation


Neutron decay

Electron captureInverse beta decay

Examples of charged current weak interaction processes Examples of charged current weak interaction processes


Recall…Recall…

d

e

u

e-

g

g€

1

q2 + MW2

€

G =10−5GeV −2

n p

e-e

€

f (q2) =g2

q2 + M(W ,Z )2

€

G =g2

M(W ,Z )2

≈10−5GeV −2


Lepton universalityLepton universality

The weak coupling is the same for all leptons (e, ) but not for different quarks. Take the example of a leptonic weak process, such as muon decay:

€

G =g2

M(W )2

Dimensionally: G [GeV-2], decay amplitude G, rate G2

€

Γ(μ → e + ν e + ν μ )∝G2mμ5 =

gμ4

M(W )4

mμ5 =

1

τ μ

In a similar way, the weak decay of the , with a branching ratio of 17.8%, gives

€

Γ(τ → e + ν e + ν τ )∝G2mτ5 =

gτ4

M(W )4

mτ5 =

1

τ τ

€

gτ

gμ

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

4

= 0.178mμ

mτ

⎛

⎝ ⎜

⎞

⎠ ⎟

5τ μ

τ τ

⎛

⎝ ⎜

⎞

⎠ ⎟ (inserting the experimental values)

€

gτ

gμ

= 0.999 ± 0.003

Similarly, universality holds for neutral currents (Z0)


Available energy = mnuclei c2

events

e- energy

m > 0

?

Dear Radioactive Ladies and Gentlemen,

As the bearer of these lines, to whom I graciously ask you to listen, will explain to you in more detail, how because of the "wrong" statistics of the N and Li6 nuclei and the continuous beta spectrum, I have hit upon a desperate remedy to save the "exchange theorem" of statistics and the law of conservation of energy. Namely, the possibility that there could exist in the nuclei electrically neutral particles, that I wish to call neutrons, which have spin 1/2 and obey the exclusion principle and which further differ from light quanta in that they do not travel with the velocity of light. The mass of the neutrons should be of the same order of magnitude as the electron mass and in any event not larger than 0.01 proton masses. The continuous beta spectrum would then become understandable by the assumption that in beta decay a neutron is emitted in addition to the electron such that the sum of the energies of the neutron and the electron is constant. I agree that my remedy could seem incredible because one should have seen those neutrons very earlier if they really exist. But only the one who dare can win….

Your humble servantW. Pauli

Pauli's letter of December 4th, 1930Pauli's letter of December 4th, 1930

The -decay problem

Historical link between the understanding of the -decay and the hypothesis of the neutrino

Before 1930: N N’ + e-Before 1930: N N’ + e-

After 1930: N N’ + e-+ After 1930: N N’ + e-+


Solvay congress in Brussels (1933, after the discovery of the neutron):

Fermi invented the name of ‘neutrino’

Soon after, in 1934, Fermi developed a theory of beta decay to include the neutrino, presumed to be massless as well as chargeless

The paper was published in Zeitschrift für Physik, Vol. 88, (1934) 161: Versuch einer Theorie der beta-Strahlen. It had been originally rejected by Nature because: …it contains speculations too remote from reality to be of interest to the reader…

Treating the beta decay as a transition that depended on the strength of coupling between the initial and final states, Fermi developed a relationship which is now referred to as Fermi's Golden Rule

if = | Mif |2 f However, the nature of the interaction which led to beta decay was unknown in Fermi's time (the weak interaction)


Negative beta-decay (e.g. neutron decay)

and an electron capture

-decay-decay

Inside a nucleus (need to supply E) we could have a positive beta-decay:

The results is a different nucleus (same A, different Z):

-

+

e-capture

The beta-decay rate can be calculated according to the Fermi theory by means of Fermi’s Golden rule (see exercise). This brings to the Kurie plot, usually exploited to determine the electron-neutrino mass.

The beta-decay rate can be calculated according to the Fermi theory by means of Fermi’s Golden rule (see exercise). This brings to the Kurie plot, usually exploited to determine the electron-neutrino mass.


Inverse beta decayInverse beta decay

€

e + p → n + e+ This reaction has a kinematical threshold of 1.80 MeV, required to produce the positron “at rest” in the laboratory

The cross section of the process is calculated from:

€

dσ

dΩ(a + b → c + d) =

1

4π 2h4| M if |2

ρ f2

v iv f

One obtains:

€

σ(ν e + p → n + e+) =G2

π| M if |2

p2

v iv f

This gives an incredibly small value:

€

σ(ν e + p → n + e+) =10−38cm2Eν (GeV )

Mean free path for a 1 MeV neutrino: 50 light years of water !!!Mean free path for a 1 MeV neutrino: 50 light years of water !!!

This explains why it took ~25 years from the neutrino hypothesis to the first detection of a neutrino

This is balanced by the huge number of neutrinos around us:

• 330 neutrinos/cm3 of Universe from the Big Bang (very low energy: 10-4 eV)• Solar neutrino flux on Earth: 60 billion neutrinos/cm2 x s• Neutrinos from Supernova explosion, from cosmic-rays, from all the stars• Neutrinos from Earth radioactivity and geo-neutrinos from the Earth core

(30 TW power, equivalent to 30000 nuclear plants)• Neutrinos from mankind (nuclear plants, accelerators)

This is balanced by the huge number of neutrinos around us:

• 330 neutrinos/cm3 of Universe from the Big Bang (very low energy: 10-4 eV)• Solar neutrino flux on Earth: 60 billion neutrinos/cm2 x s• Neutrinos from Supernova explosion, from cosmic-rays, from all the stars• Neutrinos from Earth radioactivity and geo-neutrinos from the Earth core

(30 TW power, equivalent to 30000 nuclear plants)• Neutrinos from mankind (nuclear plants, accelerators)

A.Ereditato SS 2008

Neutrinos and the human body

Electromagnetic radiation interacts with our body depositing its energy. Due to their extremely low cross section neutrinos go through our body without interacting and releasing their energy. Thanks to this life is possible on Earth !

Electromagnetic radiation interacts with our body depositing its energy. Due to their extremely low cross section neutrinos go through our body without interacting and releasing their energy. Thanks to this life is possible on Earth !

Every second a human being is crossed

by: 4 x 1014 neutrinos from the Sun

5 x 1010 neutrinos from Earth rock radioactivity

10-100 x 109 neutrinos from all nuclear plants in the world

Every second a human being is crossed by: 4 x 1014 neutrinos from the Sun

5 x 1010 neutrinos from Earth rock radioactivity

10-100 x 109 neutrinos from all nuclear plants in the world

NOTICE: the human body contains about 20 mg of Potassium 40, which is a -emitter. Therefore, we produce 340 million neutrinos per day, that leave us at the speed of light, transmitting a signal of our presence down to the far corners of the Universe…

NOTICE: the human body contains about 20 mg of Potassium 40, which is a -emitter. Therefore, we produce 340 million neutrinos per day, that leave us at the speed of light, transmitting a signal of our presence down to the far corners of the Universe…


Reines and Cowan (1956)

Experiment at the Savannah River nuclear reactor (~1020 neutrinos/s) :

Neutrino discoveryNeutrino discovery

Cadmium Chloride

e p e+ n Pontecorvo’s idea:


Inverse muon decay: i.e. how to build an accelerator neutrino beamInverse muon decay: i.e. how to build an accelerator neutrino beam

targetfocusing magnetsdecay tunnelabsorbe

rnear

detectors

far detector

Conceptual layout of an accelerator neutrino beam

Conceptual layout of an accelerator neutrino beam


Questions (apparently not related to experimental particle physics….)

1)

Suppose to communicate with an intelligent alien-being in a distant planet e.g. via radio. You can explain to him (her ?) many things about our world asking him to perform experiments and to make ‘observations’ and in the same way you can understand about him and his world.

A problem arise when you want to explain him what is ‘left’ and what is ‘right’

….really ??

2)

Is the world in the mirror identical to our world ?

a.ereditato ss 2008 1 elementarteilchenphysik antonio ereditato lhep university of bern lesson...

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