arXiv subjects
Publications and source records attributed to Bing An Li.
In the framework of an effective chiral theory of mesons, pi K scattering is stydied. The scattering lengths, phase shifts, and cross sections are calculated. Theoretical results agree well with data. There is no new parameter in this study.
A new dynamical symmetry breaking of $SU(2)_{L}\times U(1)$ caused by the combination of the axial-vector component and the fermion mass is found in electroweak theory. We obtain (m^{2}_{W}={1/2}g^{2}m^{2}_{t}) and (m^{2}_{Z}=ρm^{2}_{W}/cos^{2}θ_{W}) with (ρ\simeq 1), (G_{F}={1/2 \sqrt{2}m^{2}_{t}})}}). Two fixed gauge fixing terms for W and Z boson fields are dynamically generated. Massive neutrinos are required.
A Lagrangian of electroweak interactions without Higgs is used to study the contributions of quarks and leptons to the masses of the W and the Z bosons. It is shown that the $SU(2)\times U(1)$ symmetry is broken by both fermion masses and axial-vector components of the intermediate bosons. The masses of the W and the Z bosons are obtained to be (m^{2}_{W}={1\over2}g^{2}m^{2}_{t}) and (m^{2}_{Z}=ρm^{2}_{W}/cos^{2}θ_{W}) with (ρ\simeq 1). Two fixed gauge fixing terms for W and Z boson fields are derived respectively. A coupling between photon and Z boson is predicted. Massive neutrinos are required.
To one-loop order and $O(α_{em})$, the electromagnetic mass splittings of $π$, $a_1$, $K$, $K_1(1400)$, and $K^*(892)$ are calculated in the framework of $U(3)_L\times U(3)_R$ chiral field theory. The logarithmic divergences emerging in the Feynman integrations of the mesonic loops are factorized by using an intrinsic parameter $g$ of this theory. No other additional parameters or counterterms are introduced to absorb the mesonic loop divergences. When $f_π$,$m_ρ$ and $m_a$ are taken as inputs, the parameter $g$ will be determined and all the physical results are finite and fixed. Dashen's theorem is satisfied in the chiral SU(3) limit of this theory, and a rather large violation of the theorem is revealed at the order of $m_s$ or $m_K^2$. Mass ratios of light quarks have been determined. A relation for electromagnetic corrections to masses of axial-vector mesons is obtained. It could be regarded as a generalization of Dashen's theorem. Comparing with data, it is found that the non-electromagnetic mass difference of $K^*$ is in agreement with the estimation of Schechter, Subbaraman, Weigel.
The effects of the anomalous contact terms are taken into account in tau to eta(eta')2pi nu decay. tau to 3pi nu is computed. Theoretical result agrees with data. It is the first time the anomalous vertex eta aa is tested. An a_{1} resonance is predicted in the final state. The decay rate of tau to eta'3pi nu is predicted.
A theory of tau mesonic decays is proposed. The general formula of the axial-vector currents of mesons is presented. The meson vertices are obtained from an effective chiral theory of mesons. The vertices depend on momentum. Many decay modes are studied. Theoretical results agree reasonably well with the data. There are predictions.
A general expression of the axial-vector current is presented, in which both the effects of the chiral symmetry breaking and the spontaneous chiral symmetry breaking are included. A new resonance formula of the axial-vector meson is derived and in the limit of $q^{2}\rightarrow 0$ this formula doesn't go back to the ``chiral limit``. The studies show that the dominance of the axial-vector meson is associated with the satisfaction of PCAC. The dominance of pion exchange is companied by the strong anomaly of PCAC.
Strong anomaly of the PCAC is found in $τ\rightarrowωππν$ and $ωρν$ in the chiral limit. It originates in WZW anomaly. Theoretical result of $τ\rightarrowωππν$ agrees with data well and the measurement of $τ\rightarrowωρν$ will confirm the strong anomaly of PCAC. The strong anomaly of PCAC is studied.
The meson fields are simulated by quark operators and an effective chiral theory of mesons is presented. There are spontaneous chiral symmetry breaking and dynamical chiral symmetry breaking. Theoretical results agree with data well.
In terms of an effective chiral theory of mesons it is shown quantitatively that in the limit of $m_{q}=0$, the masses of $ρ$, $ω$, $K^{*}(892)$, $m_ϕ$, $a_{1}$, $f_{1}(1286)$, $K_{1}(1400)$, and $f_{1}(1510)$ mesons originate from dynamical chiral symmetry breaking.
A mass relation of rho and a_[1} mesons has been obtained from Weinberg's first sum rule and KSFR sum rule.
The chiral theory of mesons of two flavors have been extended to mesons containing strange flavor. Two new mass relations between vector and axial-vector mesons have been obtained. In chiral limit, the physical processes of normal parity and abnormal parity have been studied. Due to the universality of the coupling of this theory many interesting results have been obtained. In chiral limit theoretical results are in reasonable agreement with data.
By applying the Ward identity found by Weinberg two new relations of the amplitude of $a_{1}\rightarrowρπ$ with other physical quantities have been found.
A $U(2)_{L}\times U(2)_{R}$ chiral theory of pseudoscalar, vector, and axial-vector mesons has been proposed. VMD has been revealed from this theory. The physical processes of normal parity and abnormal parity have been studied by using the same lagrangian and the universality of coupling has been revealed. Two new mass relations between vector and axial-vector mesons have been found. Weinberg's first sum rule and new relations about the amplitude of $a_{1}$ decay are satisfied. KSFR sum rule is satisfied pretty well. The $ρ$ pole in pion form factor has been achieved. The theoretical results of $ρ\rightarrowππ$, $ω\rightarrow ππ$, $a_{1}\rightarrowρπ$ and $πγ$, $τ\rightarrow ρν$, $τ\rightarrow a_{1}ν$, $π^{0}\rightarrow γγ$, $ω\rightarrowπγ$, $ρ\rightarrowπγ$, $f_{1} \rightarrowρππ$, $f_{1}\rightarrowηππ$, $ρ\rightarrowηγ$, $ω\rightarrowηγ$ are in good agreement with data. Weinberg's $ππ$ scattering lengths and slopes and $a^{0}_{2}$, $a^{2}_{2}$, and $b^{1}_{1}$ have been obtained. Especially, the $ρ$ resonance in the amplitude $T^{1}_{1}$ of $ππ$ scattering has been revealed from this theory. Two coefficients of chiral perturbation theory have been determined and they are close to the values used by chiral perturbation theory.