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Chapter 12: Q34E (page 557)

Sketch the Feynman diagram if the proposed decay is possible.

μ+→e++ve

Short Answer

Expert verified

The decay is not possible as the lepton number is not conserved.

Step by step solution

01

Given data

The proposed reaction is μ+→e++ve

02

Concept of Feynman diagram

A Feynman diagram is used to show the interaction of particles in quantum field theory. The particles are represented by the lines in the diagram.

03

Step 3:Find whether the charge is conserved

Conservation of charge is shown below:

μ+→e++ve(+e)→(+e)+(0)(+e)→(+e)

Thus, the charge before the decay and after the decay is equal.

Therefore, the charge is conserved.

04

Find conservation of mass

Conservation of mass is given below.

μ+→e++ve106MeV/c2→0.511MeV/c2

The mass after the decay is 0.511MeV/c2 less than that of the initial mass 106MeV/c2.

05

Find conservation of lepton number

Conservation of lepton number:

μ+→e++ve(-1)→(-1)+(-1)(-1)→(-2)

The lepton number is not conserved.

Therefore, the proposed decay is not possible

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Most popular questions from this chapter

Although not truly fundamental, the residual strong force shared by nucleons can also be represented by a feynmandiagram, with pion filling the role of mediating boson.The accompanying diagram represents a force between a neutron and a proton mediated by aπ0 boson.Suggest a diagram in which they exchange a π-particle.

In the following exercises, two protons are smashed together in an attempt to convert kinetic energy into mass and new particles. Indicate whether the proposed reaction is possible. If not, indicate which rules are violated. Consider only those for charge, angular momentum, and baryon number If the reaction is possible, calculate the minimum kinetic energy required of the colliding protons.

p+p→n+n¯+p+p¯

From the experimental evidence that the force between nucleons has a range of about 1 fm. Obtaina rough value (in MeV/c2) for the mass of the particle exchanged to convey this force, the pion.

If a neutrino interacted with a quark every time their separation was within the 10−18 m range generally accepted for the weak force, then the cross-section of a neutron or proton “seen” by a neutrino would be on the order of 10−36 m2. Even at such separation, however the probability of interactions is quite small. The nucleon appears to have an effective cross-section of only about 10−48 m2.

(a) About how many nucleons are there in a column through the earth’s center of 1 m2 cross-sectional area?

(b) what is the probability that a given neutrino passing through space and encountering earth will actually “hit”?

For solutions of Klein-Gordon equation, the quantity,

iψ∗∂∂tψ−iψ∂∂tψ∗is interpreted as charge density. Show that for a positive-energy plane-wavesolution. It is a real constant, and for negative-energy solution.It is a negative of that constant.
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