Editing Bound state (section)

==Requirements==

A [[boson]] with mass {{math|''m<sub>χ</sub>''}} [[gauge boson|mediating]] a [[Coupling (physics)#Particle physics and quantum field theory|weakly coupled interaction]] produces an [[Yukawa potential|Yukawa-like]] interaction potential,

:<math>V(r) = \pm\frac{\alpha_\chi}{r} e^{- \frac{r}{\lambda\!\!\!\frac{}{\ }_\chi}}</math>,<!--\bar\lambda is an overbar, \sout\lambda is missing-->

where <math>\alpha_\chi=g^2/4\pi</math>, {{math|''g''}} is the gauge coupling constant, and {{math|''ƛ<sub>i</sub>'' {{=}} {{sfrac|ℏ|''m<sub>i</sub>c''}}}} is the [[reduced Compton wavelength]]. A [[scalar boson]] produces a universally attractive potential, whereas a vector attracts particles to antiparticles but repels like pairs. For two particles of mass {{math|''m''<sub>1</sub>}} and {{math|''m''<sub>2</sub>}}, the [[Bohr radius]] of the system becomes

:<math>a_0=\frac{{\lambda\!\!\!^{{}^\underline{\ \ }}}_1 + {\lambda\!\!\!^{{}^\underline{\ \ }}}_2}{\alpha_\chi}</math> <!--<span style="font-size: 1.25em;">{{math|''a''<sub>0</sub> {{=}} ''{{sfrac|ƛ<sub>1</sub> + ƛ<sub>2</sub>|α<sub>χ</sub>}}''}}</span>-->

and yields the dimensionless number

:<math>D=\frac{{\lambda\!\!\!^{{}^\underline{\ \ }}}_\chi}{a_0} = \alpha_\chi\frac{{\lambda\!\!\!^{{}^\underline{\ \ }}}_\chi}{{\lambda\!\!\!^{{}^\underline{\ \ }}}_1 + {\lambda\!\!\!^{{}^\underline{\ \ }}}_2} = \alpha_\chi\frac{m_1+m_2}{m_\chi}</math>.

In order for the first bound state to exist at all, <math>D\gtrsim 0.8</math>.  Because the [[photon]] is massless, {{math|''D''}} is infinite for [[electromagnetism]].  For the [[weak interaction]], the [[Z boson]]'s mass is {{val|91.1876|0.0021|u=GeV/c2}}, which prevents the formation of bound states between most particles, as it is {{val|97.2|u=times}} the [[proton]]'s mass and {{val|178,000|u=times|fmt=commas}} the [[electron]]'s mass.

Note, however, that, if the [[Higgs mechanism|Higgs interaction]] did not break electroweak symmetry at the [[electroweak scale]], then the SU(2) [[weak interaction]] would become [[Confinement (physics)|confining]].<ref>{{cite journal |last1=Claudson |first1=M. |last2=Farhi |first2=E. |last3=Jaffe |first3=R. L. |title=Strongly coupled standard model |journal=Physical Review D |date=1 August 1986 |volume=34 |issue=3 |pages=873–887 |doi=10.1103/PhysRevD.34.873 |pmid=9957220 |bibcode=1986PhRvD..34..873C }}</ref>