13. Examples of particle interactions described in terms of Feynman vertices

1.       neutron decays to a proton, electron and an anti-electron neutrino

2.       pi-plus decays to mu-plus and a muon neutrino

3.       a positive muon decays to a muon antineutrino, a positron and an electron neutrino

4        K zero decays to a  pi-minus and pi-plus via the weak interaction

5.       lambda zero decays to a proton and a pi-minus via the weak interaction

6        a sigma plus decays to a proton and a pi-zero via the weak interaction

7.       electron positron annihilation to two photons

8        xi-zero decays to a lambda zero and a pi-zero

9        positive kaon decays to three pions

10.     sigma-zero decays to lambda zero and a photon

11.     omega minus decays to xi-zero and a negative pion

12.     positive kaon interacts with a proton to produce a neutral kaon and a delta++

13.     antiproton interacts with a proton to produce a neutron and an antineutron

14.     omega-minus decays to xi-zero, an electron and an electron antineutrino


Example 1

In this case a neutron decays to a proton, an electron and an anti-neutrino via the weak interaction.

The quark analysis shows:

       

        dd

        uu

        du    with the creation of an electron and an anti-neutrino.

 The corresponding Feynman diagram will be:

This is a weak decay of the down quark. It is an allowed vertical change in the same quark generation.

                

The Feynman diagram for the d to u transition is a combination of  quark-W vertex and same generation lepton W vertex.

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Example 2

In this example the up and the antidown quarks in the pi-plus annihilate to produce a W+. The W+ then materialises the lepton-antilepton pair.

The Feynman diagram is a simple combination of a quark weak vertex and a lepton-weak vertex. The quarks come form the same generation. Similarly, the leptons are a first generation pair.

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Example 3

In this example the positive muon emits a W+ and transforms to a muon antineutrino. The W+ then materialises a lepton-antilepton pair from the first generation of the antilepton family.

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Example 4

In this case a  kaon-zero  decays to a  pi-minus and pi-plus via the weak interaction.

The quarks analysis shows:

    with the creation of an antidown - up pair.

 

This is a weak decay of the anti-strange quark. It is an allowed diagonal change between anti-quark generations.

The Feynman diagram shows a combination of an antiquark-weak vertex and a quark-weak vertex.

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Example 5

In this case a lambda zero decays to a proton and a pi-minus via the weak interaction.

The quark analysis shows:

                   

                    u    u       

                    d    d   

                    s      u     with the creation of  a down - antiup pair.

 

The corresponding Feynman diagram will be:

This is a weak decay of the strange quark. It is an allowed diagonal change between quark generations.

       

The Feynman diagram for the s to u transition is a combination of two quark-W vertices. The pion is derived from a same generation quark weak vertex

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Example 6

In this case a Sigma plus decays to a proton and a pi-zero via the weak interaction.

The quark analysis shows:

                 

                     u u       

                     u u   

                     s u     with the creation of  a down - antiup pair.

 

The corresponding Feynman diagram will be:

This is a weak decay of the strange quark. It is an allowed diagonal change between quark generations.

       

The Feynman diagram for the s to u transition is a combination of two quark-W vertices.

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Example 7

This is an annihilation of a positron and an electron.

                  

 

The electron emits a real photon and becomes a virtual electron. This virtual electron then annihilates with the positron with the emission further photon. It is a combination of two electromagnetic-lepton vertices.

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Example 8

X0 L0 + p0

A xi-zero (uss) decays into a lambda zero (uds)  and a pi zero ()

The quark analysis shows:

X0 L0 + p0

s  

u  

s   u with the creation of a down-antiup pair. 

The corresponding Feynman diagram will  be:

 

This is a weak decay of the strange quark. It is an allowed diagonal change between quark generation:

We also can see a quark weak vertex leading to a anti-up and a down quark.

 

This event involves only neutral particles and you may think that it could never be "seen" in a bubble chamber picture. BUT...

The signalled tracks in the picture above shows the xsi zero decay, in the bubble chamber picture of the discovery of omega minus! The two gammas come from pi zero disintegration!

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Example 9

In this case a kaon-plus decays to a pi-minus and two pi-plus via the weak interaction and a gluon.

The quark analysis shows:

u   u

 

This is a weak interaction of the anti-strange quark to an anti-up quark with the creation of a W-plus. The W-plus decays and an anti-down quark and an up quark are created. A gluon is created and materialises a down quark and an anti-down quark.

The anti-strange to anti-up vertex is an allowed diagonal change between antiquark generations.

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Example 10

In this case, one of the quarks in the sigma-zero emits a photon. It is a simple electromagnetic vertex.

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Example 11

W- X0 + p-

A omega minus (sss) decays into a xsi zero (uss) and a pi minus.

The quark analysis shows:

W- X0 + p-

s      s 

s      s 

s      u with the creation of a down-antiup pair. 

The corresponding Feynman diagram will  be:

This is a weak decay of the strange quark. It is an allowed diagonal change between quark generation:

We also can see a quark weak vertex leading to a anti-up and a down quark.

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Example 12

 

In this case there is a collision between a positive kaon (K+) and a proton (p)

In the strong interaction a neutral kaon (K0) and an excited state (D++) are produced.

The D++  then decays to a proton and a positive pion.

 

The suggested Feynman diagram might be:

 

 

This is a strong interaction and involves quark-gluon vertices only.

The quark analysis shows:

            the up quark of the kaon emits a gluon and the gluon materializes into a down quark and an antidown quark

            the down quark of the proton annihilates with the antidown quark emitting a gluon

            the three up quarks recombine as an excited state D++

then....

            an up quark of the excited state emits a gluon and the gluon materializes into a down quark and an antidown quark

            an  up quark and the antidown quark recombine as a positive pion

            two up and the down quark recombine as a proton.

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Example 13

In this case there is a collision between a proton (p) and an antiproton (p).

In the final state a neutron and an antineutron are produced.

The quark analysis shows:

            the antiup quark of the antiproton annihilates with  the up quark of the proton emitting a gluon.

            the antidown quark of the antiproton emits a gluon and the gluon materialize into an antidown and a down quark

 

The corresponding Feynman diagram will be:

           

This is a strong interaction and involves quark gluon vertices only.

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Example 14

In this case an Omega minus decays to a xi- zero, an electron and electron anti-neutrino via the weak interaction.

The quark analysis shows:

             

               s    s       

               s    s   

               s    u     with the creation of  an electron - antineutrino pair.

 

The corresponding Feynman diagram will be:

This is a weak decay of the strange quark. It is an allowed diagonal change between quark generations.

    

The Feynman diagram illustrates that the reaction is a combination of a quark weak vertex and a weak-lepton vertex.

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