8-13 August 2011
Rhode Island Convention Center
US/Eastern timezone

Theory of EW interactions with dynamically generated scalars, gauge fixings, and masses of Z and W bosons

Aug 9, 2011, 12:35 PM
Rhode Island Convention Center

Rhode Island Convention Center

One Sabin Street Providence, RI 02903
Poster Poster Session Poster Session


Bing An Li (University of Kentucky)


A new theory of the EW interactions without spontaneous symmetry breaking, Higgs, and Fadeev-Popov procedure is presented in this talk. It consists of three parts: $SU(2)_L\times U(1)$ gauge fields, massive fermion fields, and their interactions. New mechanism of $SU(2)_L\times U(1)$ symmetry breaking caused by the fermion masses are found. Nonperturbative solutions are found. The vacuum polarization of the Z field is expressed as \[\Pi_{\mu\nu}(q^2)=\{F_1(q^2)(q_\mu q_\nu-q^2 g_{\mu\nu})+F_2(q^2)q_\mu q_\nu+{1\over2}\Delta m^2_Z g_{\mu\nu}\}.\] Therefore, both the gauge fixing term($F_2$) and the mass term of the field are dynamically generated from the fermion masses. Top quark mass plays a dominant role. No zero $\partial_\mu Z^\mu$ leads to a scalar field and a gauge fixing term for the Z field. The mass of the scalar field is determined to be \[m_{\phi^0}=m_t e^{\frac{m^2_Z}{m^2_t}\frac{16\pi^2}{3\bar{g}^2}+1}=3.78\times10^{14}GeV.\] The gauge fixing is determined to be \[\xi_z=-1.18\times10^{-25}.\] After renormalization it is determined \[m_z={1\over2}\bar{g}^2 m^2_t\] it agrees well with the data. Similarly, the vacuum polarization of W boson is found. A charge scalar field is dynamically generated \[m_{\phi^{\pm}}=m_t e^{\frac{m^2_W}{m^2_t}\frac{16\pi^2}{3g^2}}=9.31\times10^{13}GeV.\] \[\xi_W=-3.73\times10^{-25}.\] After renormalization the mass of the W boson is determined as \[m^2_W={1\over2}g^2 m^2_t.\] It agrees well with the data. It also obtain \[\frac{m^2_W}{m^2_Z}=\frac{g^2}{\bar{g}^2}=cos^2\theta_W.\] \[G_F=\frac{1}{2\sqrt{2}m^2_t}.\] The Fermi coupling constant in good agreement with data. The propergators of Z- and W- fields are derived as \[\Delta_{\mu\nu}^Z= \frac{1}{q^2-m^2_Z}\{-g_{\mu\nu}+(1+\frac{1}{2\xi_Z})\frac{q_\mu q_\nu}{ q^2-m^2_{\phi^0}}\}\] \[\Delta^W_{\mu\nu}= \frac{1}{q^2-m^2_W}\{-g_{\mu\nu}+(1+\frac{1}{2\xi_W})\frac{q_\mu q_\nu}{ q^2-m^2_{\phi_W}}\}\] This theory can be tested by LHC experiments.

Primary author

Bing An Li (University of Kentucky)

Presentation materials