Editing Pion (section)

== Theoretical overview ==
In the standard understanding of the [[strong force]] interaction as defined by [[quantum chromodynamics]], pions are loosely portrayed as [[Goldstone boson]]s of spontaneously [[Chiral symmetry breaking|broken chiral symmetry]]. That explains why the masses of the three kinds of pions are considerably less than that of the other mesons, such as the scalar or vector mesons. If their current [[quark]]s were massless particles, it could make the chiral symmetry exact and thus the Goldstone theorem would dictate that all pions have a zero mass.

In fact, it was shown by Gell-Mann, Oakes and Renner (GMOR)<ref name="GMOR">{{cite journal |last1=Gell-Mann |first1=M. |last2=Renner |first2=B. |title=Behavior of current divergences under SU{{sub|3}}×SU{{sub|3}} |journal=Physical Review |volume=175 |issue=5 |pages=2195–2199 |year=1968 |bibcode=1968PhRv..175.2195G |doi=10.1103/PhysRev.175.2195 |url=https://authors.library.caltech.edu/3634/1/GELpr68.pdf}}</ref> that the square of the pion mass is proportional to the sum of the quark masses times the [[Vacuum expectation value|quark condensate]]: 
<math display=block>M^2_\pi = (m_u+m_d)B+\mathcal{O}(m^2),</math> 
with {{mvar|B}} the quark condensate: 
<math display=block>B = \left\vert \frac{\rm \langle 0 \vert \bar{u}u \vert 0 \rangle}{f^2_\pi} \right\vert_{m_q \to 0}</math> 
This is often known as the '''GMOR relation''' and it explicitly shows that <math>M_\pi=0</math> in the massless quark limit. The same result also follows from [[Light-front quantization applications#Light-front holography|light-front holography]].<ref name="Light-Front Holographic QCD and Emerging Confinement">{{cite journal |first1=S.J. |last1=Brodsky |first2=G. F. |last2=de Teramond |first3=H.G. |last3=Dosch |first4=J. |last4=Erlich |year=2015 |title=Light-front holographic QCD and emerging confinement |journal=Physics Reports |volume=584 |pages=1–105  |url=https://arxiv.org/abs/1407.8131}}</ref>

Empirically, since the light quarks actually have minuscule nonzero masses, the pions also have nonzero [[rest mass]]es. However, those masses are ''almost an order of magnitude smaller'' than that of the nucleons, roughly<ref name=GMOR/> <math>\ m_\pi \approx \tfrac{ \sqrt{ v\ m_q\ } }{\ f_\pi } \approx \sqrt{ m_q\ }\ </math> 45&nbsp;MeV, where {{mvar|m{{sub|q}}}} are the relevant current quark masses, around {{val|5|-|10|u=MeV/c2}}.

The pion is one of the particles that mediate the residual strong interaction between a pair of [[nucleons]]. This interaction is attractive: it pulls the nucleons together. Written in a non-relativistic form, it is called the [[Yukawa potential]]. The pion, being spinless, has [[kinematics]] described by the [[Klein–Gordon equation]]. In the terms of [[quantum field theory]], the [[effective field theory]] [[Lagrangian (field theory)|Lagrangian]] describing the pion-nucleon interaction is called the [[Yukawa interaction]].

The nearly identical masses of {{math|{{SubatomicParticle|Pion+-}}}} and {{math|{{SubatomicParticle|Pion0}}}} indicate that there must be a symmetry at play: this symmetry is called the [[SU(2)]] [[flavour symmetry]] or [[isospin]]. The reason that there are three pions, {{math|{{SubatomicParticle|Pion+}}}}, {{math|{{SubatomicParticle|Pion-}}}} and {{math|{{SubatomicParticle|Pion0}}}}, is that these are understood to belong to the triplet representation or the [[Adjoint representation of a Lie group|adjoint representation]] '''3''' of SU(2). By contrast, the up and down quarks transform according to the [[fundamental representation]] '''2''' of SU(2), whereas the anti-quarks transform according to the conjugate representation '''2*'''.

With the addition of the [[strange quark]], the pions participate in a larger, SU(3), flavour symmetry,  in the adjoint representation, '''8''', of SU(3). The other members of this [[Eightfold way (physics)#Meson octet|octet]] are the four [[kaon]]s and the [[eta meson]].

Pions are [[pseudoscalar (physics)|pseudoscalar]]s under a [[parity (physics)|parity]] transformation. Pion currents thus couple to the axial vector current and  so  participate in the [[chiral anomaly]].