Electric Charge vs Mass in Gauge Bosons

The MASSLESSNESS is a consequence of the GAUGE SYMMETRY. In summary, the electromagnetic and strong interactions have massless gauge bosons with no electric charge, while the weak interaction has two massive gauge bosons with electric charge. This is due to the specific way in which electroweak symmetry is broken. The Z0 gauge boson, which is the neutral and massive gauge boson of the weak interaction, fits into the electroweak theory as a combination of the third weak gauge boson and the massless U(1) gauge field. The fact that real fields have no electric charge is related to the global U(1) symmetry and the masslessness is a consequence of the gauge symmetry.
  • #1
Islam Hassan
233
5
Is there any significance to the fact that:
  • The electromagnetic and strong interactions have gauge bosons with no electric charge that are massless; and
  • The weak interaction has two massive gauge bosons which do have electric charge.
If there is a significance to this 'observation' then where does the Z0 gauge boson fit in?IH
 
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  • #3
Islam Hassan said:
Is there any significance to the fact that:
  • The electromagnetic and strong interactions have gauge bosons with no electric charge that are massless; and
  • The weak interaction has two massive gauge bosons which do have electric charge.
If there is a significance to this 'observation' then where does the Z0 gauge boson fit in?

IH

Do you mean why would *weak* gauge bosons have *electric* charge? Sure, there is a good reason; it is because the weak and electromagnetic interaction are unified in electroweak theory.

In pure unbroken gauge theories, all the gauge bosons are only charged under whatever gauge group it is which generates them (except for U(1) gauge bosons), and they are all massless. So gluons have no weak or electric charge because QCD is essentially completely separate to electroweak theory. The same logic doesn't apply to the electroweak sector because of electroweak symmetry breaking, and it is the particular way in which it is broken which leaves you with some neutral and some charged electroweak gauge bosons, and also generates masses for some of them.
 
  • #4
Islam Hassan said:
Is there any significance to the fact that:
The electromagnetic and strong interactions have gauge bosons with no electric charge that are massless; and

It simply means that the [itex]U_{em}(1)[/itex] and [itex]SU_{c}(3)[/itex] gauge fields are REAL fields.

The weak interaction has two massive gauge bosons which do have electric charge. If there is a significance to this 'observation' then where does the Z0 gauge boson fit in?
Weak interaction is the result of gauging the global [itex]SU(2)\times U(1)[/itex] symmetry. The GAUGE group [itex]SU(2)[/itex] has 3 REAL MASSLESS gauge FIELDS [itex]W^{ i }_{ \mu }[/itex], [itex]i = 1, 2 , 3[/itex]. Therefore, they have no em charge. The corresponding MASIVE and CHARGED gauge BOSONS (don't confuse them with gauge fields) of the weak interaction are the following combinations
[tex]W^{\pm}_{ \mu } = \frac{ 1 }{ \sqrt{ 2 } } ( W^{1}_{ \mu } \mp i W^{ 2 }_{ \mu } )[/tex]
These are charged because they are complex fields, i.e. they admit a GLOBAL [itex]U(1)[/itex] symmetry. The 3rd gauge BOSON has no charge because it is given by the follwing REAL combination
[tex]Z^{0}_{ \mu } = W^{ 3 }_{ \mu } \sin \theta - B_{ \mu } \cos \theta ,[/tex]
where [itex]B_{ \mu }[/itex] is a MASSLESS REAL [itex]U(1)[/itex] gauge FIELD.

Sam
 
Last edited:
  • #5
Doug Huffman said:
The weak interaction does have two gauge bosons
No, there are 3 of them. There are, always, as many gague fields as there are generators of the gauge group.
they are the W and the Z, each with two charges W e+/-1 and Z e0/+1
This make them 4?
breaking chiral symmetry.
Which chiral symmetry?
 
  • #6
:s How is reality connected with charge?
Because of the complex conjugation?
 
  • #7
ChrisVer said:
:s How is reality connected with charge?
Because of the complex conjugation?

I don't understand the question...
 
  • #8
kurros said:
I don't understand the question...

Is it a "must" for a real field to be chargeless? For scalars that's obvious...
 
  • #9
ChrisVer said:
Is it a "must" for a real field to be chargeless? For scalars that's obvious...
Yes. The electric charge IS the Noether number associated with the GLOBAL [itex]U(1)[/itex] symmetry. This vanishes for REAL FIELDS.
 

What is the concept of electric charge and mass in gauge bosons?

Electric charge and mass are two fundamental properties of gauge bosons, which are particles that mediate the fundamental forces of nature. Electric charge is a property of particles that determines how they interact with electromagnetic fields, while mass is a measure of the amount of matter in a particle.

How do electric charge and mass differ in gauge bosons?

In gauge bosons, electric charge is determined by the symmetry of the particle's wave function, while mass is determined by the strength of the particle's interaction with the Higgs field. This means that the electric charge of a gauge boson can vary, but its mass remains constant.

Why is the relationship between electric charge and mass important in gauge bosons?

The relationship between electric charge and mass in gauge bosons is important because it helps explain why some particles have mass while others do not. The Higgs mechanism, which is responsible for giving particles mass, relies on the interaction between the Higgs field and the electric charge of particles.

Can gauge bosons have both electric charge and mass?

Yes, gauge bosons can have both electric charge and mass. However, the strength of their interaction with the Higgs field determines their mass, while their electric charge is determined by their symmetry. So, while they can have both properties, they are not directly related to each other.

How does the concept of electric charge and mass in gauge bosons relate to the Standard Model of particle physics?

The Standard Model is a theory that explains the fundamental particles and forces of nature. The concept of electric charge and mass in gauge bosons is a fundamental part of this model, as it helps explain the behavior and interactions of these particles within the framework of the Standard Model.

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