Speaker
Bing An Li
(University of Kentucky)
Description
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\begin{document}
\title{New dynamical gauges of the SM of EW interactions }
\author{Bing An Li\\Department of Physics, Univ. of Kentucky, Lexington, USA}
\maketitle
In this talk it shows that new gauge fixings of the SM of EW interactions are $\bf{dynamically}$ generated from the
theory itself, which can be tested by LHC experiments. A new mechanism of chiral symmetry breaking, inspired
by Weinberg's second sum rule, \(m^2_a=2m^2_\rho\), is proposed.
This new mechanism is found from a chiral field theory of pseudoscalar, vector, and axial-vector mesons,
in which mesons are coupled to quarks. Quarks have dynamical quark mass.
The vacuum polarization of the $a_1$ field which is coupled to axial-vector current of massive quark is expressed as
\[\Pi_{\mu\nu}^{ij}(q^2)=\delta_{ij}\{F_1(q^2)(q_\mu q_\nu-q^2 g_{\mu\nu})+F_2(q^2)q_\mu q_\nu+{1\over2}\Delta m^2 g_{\mu\nu}\}.\]
Therefore, both the gauge fixing term($F_2$) and the mass term of $a_1$ field are dynamically generated from
dynamical quark mass. These two terms lead to
\[(1-{1\over 2\pi^2 g^2})m^2_a=2m^2_\rho,\]
where g is a universal constant of the theory. This formula fits data better.
The two new terms are treated $\bf{nonperturbatively}$.
Comparing with QCD and QED, theory of EW interactions have both axial-vector currents and charged
vector currents of massive fermions. The vacuum polarizations of Z-filed and W-field have both gauge fixing and mass terms.
They are dynamically generated from fermion masses and they should be treated nonperturbatively.
In this talk only the gauge fixing terms dynamically generated from fermion masses are discussed.
The propergators of Z- and W- fields are derived as
\[\Delta_{\mu\nu}^Z=
\frac{1}{q^2-m^2_Z}\{-g_{\mu\nu}+(1+\frac{1}{2\xi_Z})\frac{q_\mu q_\nu}{
q^2-m^2_{\phi^0}}\}\]
where \(m_{\phi^0}=m_t e^{\frac{m^2_z}{m^2_t}{16\pi^2\over3\bar{g}^2}+1}
=3.78\times10^{14}GeV,\;\;\;
\xi_Z=-\frac{m^2_Z}{2m^2_{\phi^0}}=-1.18\times10^{-25}\).
\[\Delta^W_{\mu\nu}=
\frac{1}{q^2-m^2_W}\{-g_{\mu\nu}+(1+\frac{1}{2\xi_W})\frac{q_\mu q_\nu}{
q^2-m^2_{\phi_W}}\}\]
where \(m_{\phi_W}=m_t e^{{16\pi^2\over3g^2}{m^2_W\over m^2_t}}
=9.31\times10^{13}GeV,\;\;\;
\xi_W=-{m^2_W\over2m^2_{\phi_W}}=-3.73\times10^{-25}\).
Top quark plays dominant role in the determination of these propagators.
These results are independent of spontaneously chiral symmetry breaking. The effects of these propergators
can be found in loop diagrams and can be tested by LHC experiments.
\end{document}
Author
Bing An Li
(University of Kentucky)
