Velocity and mass and particles

If mass increases as velocity increases how can I associate this with the fact that some particles such as neutrinos which barely have no mass, go faster when they have less mass or less interaction with the Higgs field. Or does it mean that a neutrino, if I try to accelerate it will increase in mass which could mean that if the neutrino increase in mass it's velocity increase too...? So if a photon which has no mass increase its mass it's velocity will increase( obviously no It is just for the purpose of explanation). So if the photon's velocity is higher than the neutrino's does it mean it has more mass...which is the opposite of what the interaction with the Higgs field tell us. So the question remains: how can I associate the 2 facts together.

Answer

Elementary particles are quantum mechanical entities and are governed by the postulates of quantum mechanics and the theories developed withing it,and by the mechanics of special relativity.

You are using classical mechanics intuition for a framework, elementary particles, where it does not work. Classical mechanics emergence from the underlying frameworks of the microworld can be demonstrated mathematically in a complex manner.

Let us try to see the misunderstanding:

If mass increases as velocity increases

The mass that is increasing as velocity increases, is the inertial mass, i.e. the mass that is need to balance classical mechanics postulates, F=ma, which is only useful in trying to describe the kinematics of spaceships traveling close to the velocity of light. It is called the relativistic mass.

Relativistic mass is not used, in particle physics, where the mass describing the particles is the length of the special relativity four vector for each particle. That is invariant to Lorentz transformations and characterizes uniquely particles and complex systems.

how can I associate this with the fact that some particles such as neutrinos which barely have no mass, go faster when they have less mass

This is wrong. The mass of the neutrinos, the rest mass,does not change with motion. At rest, it is the same as the relativistic mass. Their relativistic mass is irrelevant for the particle interactions that just need the four vectors to balance energy and momentum.

or less interaction with the Higgs field

This is also a misconception coming from popularization of particle physics.

The Higgs mechanism is not an interaction, it gives a unique mass to elementary particles at electroweak symmetry breaking time in the creation of matter in our universe, once. It is part of the model of particle physics on how particles acquire their unique mass.

One has to study physics at graduate level to be able to understand the mathematical models used. The popularization tries to give an equivalence in a classical model on how particles move in a space where a Higgs field exists, but it is not what is happening in the microworld of particles and the interactions controlling their motion.

Hope this helps.