Are there anti virtual particles (mediator bosons)?

Question

I have read these questions:

Can bosons have anti-particles?

Is there a possibility for discovery of anti-graviton, i.e. the graviton antiparticle?

Antiparticle for Higgs boson?

According to the accepted theory, the SM, all elementary particles do have their anti party, so do bosons that mediate.

The EM force is mediated by virtual photons.

Gravity is mediated by theoretical virtual gravitons.

The strong force is mediated by virtual gluons.

The weak force is mediated by virtual W and Z bosons.

All these bosons do have anti version according to the SM, so

1. photons are their own anti particles

2. gravitons too

3. gluons have their anti gluon versions

4. W and Z bosons too have their anti versions

Now since these virtual bosons mediate the fundamental forces, are there anti virtual bosons?

Question:

1. are there anti virtual bosons?

2. do these mediate the anti forces?

Answer 1

are there anti virtual bosons?

As you know, a virtual particle is a mathematical construct and is connected with the real particle of its name by the quantum numbers identifying the particle.

Also, you should know that all particles can be virtual within Feynman diagrams if they are not within the incoming and outgoing legs.

In these Compton scattering diagrams it is the electron that is virtual, or the positron, when the e represents a positron gamma scattering.

So yes, antiparticles can also be mediator virtual particles in an interaction

do these mediate the anti forces?

There are no antiforces, there are attractive or repulsive end results in the interactions studied and modeled with Feynman diagrams in order to calculate the crosssections or decay rates.

The gauge bosons of the four macroscopic forces, identified with the electromagnetic/weak/strong and gravity ( if quantized) are just virtual exchanges in the lowest order diagrams in simple particle-particle interactions. It is only the quantum numbers that they carry, and their mass in the propagator which identify them. The mass is the same for Z+ or Z-, and enters in the propagator, and just the charge characterizes the virtual particle.