# How to understand that Higgs does not imply circular reasoning?

From what I understand about Higgs (boson/field) it gives mass to subatomic particles. When it interacts a lot with the fields it gets a great mass (like a top quark) and when it interacts a little it gets less mass (electron of even a photon). But when I try to figure out why an electron is interacting with less than a top quark with the Higgs field I tend to think that it is because of their mass. That probably isn't correct by making circular reasoning but why are particles interacting differently? What property of a particle makes that difference?

• Irrespective of the technical explanation which I hope you will receive, don't over-think the standard model. All it is, is a bunch of fits to what has been measured (modern epicycles, if you like). Some things have to be in there for symmetry reasons and some mechanism to pick up mass has to be in there because the theory starts with massless fields. The Higgs field, for what it's worth, is one of the most simple of the possible mechanisms of how the massive fields can be constructed from a massless theory. Nature plays ball with the idea... and little has been learned by seeing the Higgs. – CuriousOne Feb 11 '16 at 10:53
• Don't overthink circular reasoning either. To an extent, everything in physics is circular - we use observations to form hypotheses to predict observations in the future which either add or remove credence from the hypotheses in turn. We do not know the fundamental rules of the universe, so we can't work from first principles. The key point is to never count the same evidence twice - that's where the harm of circular reasoning comes from, the magical feedback loop that inflates evidence. As long as you follow this, multiple ways to get the same result add to confidence. – Luaan Feb 11 '16 at 14:18
• If they aren't using circular logic, why are all the particle accelerators giant circles? – corsiKa Feb 11 '16 at 17:24

The mass of a particle depends on the strength of the Yukawa coupling between the Higgs field and the quantum field for that particle. In the Standard Model the Yukawa couplings are free parameters i.e. their values have to be put in by hand to match the observed particle masses.

You ask why the electron interacts with the Higgs less than the top quark, and there isn't an answer for this apart from saying its Yukawa coupling is smaller. At the moment we have no way of explaining why the various Yukawa couplings have the values they do.

• This is a fair and accurate answer, and I appreciate the irony that comes from the answer being basically a restatement of OPs confusion with "mass" replaced by "Yukawa coupling." It subtly highlights that we don't (and probably can't) know "why" the masses of particles have the values they do. – Asher Feb 11 '16 at 20:10

Since in Standard model this problem - why there is the hierarchy between fermions masses - is unsolved (but we may just state that the hierarchy exist, and the reason isn't relevant; this question is like the question about the nature of chiral structure of the Standard model), we may ask ourself: is this hierarchy natural? On the language of quantum field theory, this means following. Suppose we start from the bare electroweak theory parameters, precisely, Yukawa couplings $y_{j}$ of higgs doublet to fermions, defined from the interaction lagrangian, $$L_{\text{Yuk}} = \sum_{j = \text{fermion doublet}}y_{j}\bar{L}_{j}HR_{j} + h.c.,$$ for which there is hierachy; i.e, for example, the coupling $y_{e}$ to electron-electron neutrino doublet $L_{e} \equiv \begin{pmatrix} e \\ \nu_{e}\end{pmatrix}_{L}$ is much smaller than the coupling $y_{t}$ to top-bottom quarks doublet, $L_{t} = \begin{pmatrix} t \\ b\end{pmatrix}_{L}$.

Then these bare parameters $y_{e}, y_{t}$, defined from the experiment, will get quantum corrections because of nontrivial interaction. The question: do these corrections preserve hierarchy, or, more precisely, are corrections for given fermion mass (or, equivalently, for given Yukawa couplings) are of order of this fermion mass? If yes, such theory is called natural theory. If no, theory is unnatural.

For the case of fermions the answer is yes, since there exist symmetry which protects their mass from getting huge corrections. Such symmetry is called chiral global symmetry. If it is unbroken by anomaly, then at high scales, where the mass parameter is much smaller then the given scale, then it possesses the fact that corrections to the bare mass is suppressed by powers of this mass. I.e., this fact directly provides the statement that corrections to fermions masses are proportional to these masses. So hierarchy is naturally preserved in Standard model.

For Higgs doublet there are no such symmetry (the scale symmetry), so at quantum level it may acquire corrections which are larger than the Higgs boson mass. In this sense Higgs mass parameter isn't natural in SM.