This question already has an answer here:

In light of the discovery of the Higgs boson. The Higgs Boson is a force particle which interacts with matter particles. My question is what does the Higgs Boson interact with to give itself mass.


marked as duplicate by jinawee, JamalS, Neuneck, Rob Jeffries, ACuriousMind Dec 8 '14 at 14:03

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • 2
    $\begingroup$ To be sure, it is interaction with the Higgs field that 'gives' particles mass, not the Higgs boson. As Lubos writes, the Higgs field has a self-interaction term. $\endgroup$ – Alfred Centauri Dec 8 '14 at 12:48

Yes, it is correct to say that the Higgs boson, just like other elementary particles, get its mass from the interaction with the Higgs boson – which means "with itself" in the case of this particle.

More concretely, the mass may be derived from the Higgs potential (energy density) $$ V(h) = \frac a4 h^4 - \frac b2 h^2 + c$$ where the additive shift $c$ isn't important (in the absence of curved spacetime). The constants $a,b$ determine the shape of the potential or, if you wish, the coefficients of the "quadratic" and "quartic" self-interactions of the Higgs field.

The function $V(h)$ has minima at $$ h_\pm = \pm \sqrt{\frac{b}{a}} $$ and near these minima, the potential may be approximated as $$ V(h_\pm + \Delta h ) = c' + \frac{m^2}{2} (h-h_\pm)^2 $$ and because of this reinterpretation, the parameter $m$ in the coefficient $m^2/2$ above (which is a simple function of $a,b$ again) may be interpreted as the Higgs mass.

This quadratic+quartic self-interaction plays the role of the gauge interaction $h-h-Z$ or $h-h-W$ which gives masses to the Z-bosons or W-bosons; or the $h\bar{\psi}\psi$ Yukawa interactions that give masses to the fermions.

There is one sense in which the "God particle giving mass to itself" is somewhat more vacuous: we had to use the quadratic term, $-bh^2/2$, itself, and quadratic terms are of course nothing else than mass terms in disguise (although the sign of $b$ was the opposite one than for a "direct" Higgs mass). So we could only derive the mass term around the physical vacuum $h_\pm$ because we inserted some (tachyonic) mass term to the initial formula. But that doesn't change the fact that even this mass term of the Higgs boson may be interpreted as a self-interaction of the Higgs with itself.


Not the answer you're looking for? Browse other questions tagged or ask your own question.