# What's the heuristic reasoning for Chiral Symmetry breaking

In Peskin and Schroeder (page 669), and other references, the heuristic reasoning for why one would expect chiral symmetry breaking at low energies is that quark masses are small and hence it's not very energetically costly to create quark-antiquark pairs from the vacuum. These are then generated with zero net linear and angular momentum which forces the pair to have a net chirality and this breaks the chiral symmetry.

Where does the requirement of low energy appear in this line of reasoning?

• Chiral symmetry breaking is an example of spontaneous symmetry breaking, which usually appears at low energy, because the shape of the potential depends on the energy order, see this wiki image Oct 31, 2013 at 10:45
• Thanks, can this be made explicit though? Is there some calculation of the effective action which shows that this is true in the case of pions? Oct 31, 2013 at 17:00
• I only found this interesting evolution of the potential parameters page $16-20$ of this ref. The most interesting diagram is page $18$ top right ($a_1$). If $a_1<0$ (see equation ($18$) page $17$ with the definitions of the parameters of the potential), we have the Mexican hat form of the potential. So, below $530$ Mev, we have chiral symmetry breaking. Oct 31, 2013 at 18:35

$$\langle0|\bar{q}q|0\rangle,$$