# DPF 2011

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

9 Aug 2011, 12:35
1m
Rhode Island Convention Center

#### Rhode Island Convention Center

One Sabin Street Providence, RI 02903
Poster Poster Session

### Speaker

Bing An Li (University of Kentucky)

### Description

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)

 Slides