What is mass according to the Standard Model?

[Anymodal]

Can someone explain me what is mass according to the Standard Model?
I read that the Higgs boson "gives" mass to particles but I don´t understand what that means.

Here's what I think I got so far :
There is a field called Higgs field in all spacetime. It has a value for empty space which happens to be different than 0. A perturbation in the field is a Higgs boson.
What is mass in all this?


Extra questions
I read that Higgs field is a quantum field: Does that mean that it is a discrete field and that the value of the field for any given position is a multiple of some minimun amount?
And it is a scalar field, a vector field or what?


Thank you

 

[tom.stoer]

There is a field called Higgs field in all spacetime. It has a value for empty space which happens to be different than 0. A perturbation in the field is a Higgs boson.

It has a value different than 0 in vacuum. Here vacuum does not mean 'empty space' but 'state with lowest energy'; so to reduce the Higgs field value to zero would cost (!) energy. The quantum excitation of the Higgs field is the Higgs boson.

I read that Higgs field is a quantum field: Does that mean that it is a discrete field and that the value of the field for any given position is a multiple of some minimun amount?

No, there is no such 'discrete spectrum. Every fundamental particle is described by a 'quantum field' in Quantum Field Theory (QFT); it's a mathematical formalism. The fundamental objects are not classical fields but field operators and they do not have 'a value'; they are not numbers but more complicated mathematical objects

And it is a scalar field, a vector field or what?

It's a spin-0 boson. Otherwise a non-vanishing value in vacuum would destroy symmetries like rotational invariance. Only scalar fields can have non-zero vacuum values w/o breaking such symmetries (and we do not observe such a symmetry breaking in nature).