# Were fermions ever massless?

In a discussion of the Standard model and Higgs mechanism it was claimed that accordingly:

"During an early phase of the cosmos all fermions were massless."

I wonder whether this claim can be challenged. Therefore the following more detailed questions:

1. Is it fair to say that, according to the standard model, the mass of any fermion is an "effective mass", that it may vary depending on the Higgs field strength, and that it must necessarily vanish only if the Higgs field strength is exactly zero?

2. Is it fair to say that under conditions "during an early phase of the cosmos" (or: at sufficiently large temperature, density, ...), and while fermions are present, the Higgs field strength is not necessarily exactly zero?

• The Higgs field and the mechanism of symmetry breaking are a quantum mechanical effect. It is not a continuous field distortion . As energy is increased a value is arrived where symmetry is unbroken and what is the higgs field below breaking energy is zero mass goldstone bosons above the breaking energy physics.indiana.edu/~dermisek/QFT_09/qft-II-6-4p.pdf . – anna v Oct 14 '13 at 10:29
• @anna v: "As energy is increased a value is arrived where symmetry is unbroken" -- Is there some expression for this "breaking energy" value, perhaps in terms of parameter $\lambda$, or others? $\, \, \, \,$ "what is the higgs field below breaking energy is zero mass goldstone bosons above the breaking energy" -- Fine; but does that have any consequence for the possibility of the Lagrange function containing "fermion mass terms"? (If the nice lecture notes that you linked address these questions, I'd appreciate some more specific clues ...) – user12262 Oct 14 '13 at 17:57
• Unfortunately I am an experimentalist, not a theorist, and retired fro the last ten years . I can get the gist of a theoretical argument when scanning equations but I cannot presume to point at the exact parametrization. If you are really that much interested you should invest in learning the mathematics and spend the time in deciphering the details of the change in the Lagrangian. As an experimentalist I trust the interpretation theorists give, enough to spend a working life in experiments. People who want to change interpretations have to devote time to learning the stuff first. – anna v Oct 15 '13 at 4:16
• If you go to the link I gave you and search for "fermion" you will see the second item is the mass for the fermions, which depends on values of the broken lagrangian. Trust means that one trusts that the theorist making these mathematical claims is better than me in maths and correct. It has worked well up to now. – anna v Oct 15 '13 at 4:21
• This talk might help: hep.uchicago.edu/~pilcher/p463/Old/Lecture08%20Higgs.bw.pdf . It is the vacuum expectation value of the Higgs field that at very high energies goes to 0 and the coupling to the particles which gives their masses depends on this v. – anna v Oct 15 '13 at 4:37