Gravitons and Pions

可重整化无 pion 有效场论在次领头阶下的带电粒子散射：$pd$、$dd$ 和 $p^3\mathrm{He}$ 情形

Charged Particle Scattering in Renormalizable Pionless Effective Field Theory at Next-to-Leading Order: The $pd$, $dd$, and $p^3\mathrm{He}$ Case

本文在次领头阶构建了含非微扰库仑修正的可重整化无 pion 有效场论，利用随机变分法计算了 $pd$、$dd$ 和 $p^3\mathrm{He}$ 散射长度与有效力程，结果与实验及势模型计算吻合良好。

Gravitational form factors of light mesons

We calculate the gravitational form factors of the pion, sigma meson, and rho meson in the Nambu-Jona-Lasinio (NJL) model of quantum chromodynamics. The canonical energy-momentum tensor (EMT) is used in their derivation, allowing the possibility of an antisymmetric contribution when the hadron has intrinsic spin. We show that the asymmetric graviton vertex arising from the canonical EMT satisfies a simpler Ward-Takahashi identity (WTI) than the symmetric graviton vertex of the Belinfante EMT. The necessity of fully dressing the graviton vertex through the relevant Bethe-Salpeter equation is de…

Taking dibaryon fields seriously

We propose a low energy effective field theory of QCD at the scale of pion mass for the $N_B=2$ sector, $N_B$ being the baryon number, which contains two dibaryon fields in addition to the nucleons and pions. It has a well defined counting, is renormalizable and the nucleon-nucleon scattering amplitudes are manifestly unitary at leading order. We work out a lower energy effective theory for nucleons with energy much lower than the pion mass and three momentum comparable to it, which also has a well defined counting and is renormalizable. The dibaryon fields must also be kept as explicit degree…

A renormalizable extension of the NJL-model

The Nambu-Jona-Lasinio model is supplemented by the quark interaction generated by the one-gluon exchange. The employed gluon propagator exhibits the correct large momentum behavior of QCD, whereas the Landau-pole at low energies is screened. The emerging constituent quark model is one-loop renormalizable and interpolates between the phenomenologically successful Nambu-Jona-Lasinio model at low energies and perturbative QCD at high momenta. Consequently, the momentum dependence of the quark self-energy at high energy coincides with the prediction from perturbative QCD. The chiral phase transit…

Weinberg's approach to nucleon-nucleon scattering revisited

We propose a new, renormalizable approach to nucleon-nucleon scattering in chiral effective field theory based on the manifestly Lorentz invariant form of the effective Lagrangian without employing the heavy-baryon expansion. For the pion-less case and for the formulation based on perturbative pions, the new approach reproduces the known results obtained by Kaplan, Savage and Wise. Contrary to the standard formulation utilizing the heavy-baryon expansion, the nonperturbatively resummed one-pion exchange potential can be renormalized by absorbing all ultraviolet divergences into the leading S-w…

Ghost poles in the nucleon propagator in the linear-sigma model approach and its role in pion-nucleon low-energy theorems

Complex mass poles, or ghost poles, are present in the Hartree-Fock solution of the Schwinger-Dyson equation for the nucleon propagator in renormalizable models with Yukawa-type meson-nucleon couplings, as shown many years ago by Brown, Puff, and Wilets (BPW). These ghosts violate basic theorems of quantum field theory and their origin is related to the ultraviolet behavior of the model interactions. Recently, Krein et.al, proved that the ghosts disappear when vertex corrections are included in a self-consistent way, softening the interaction sufficiently in the ultraviolet region. In previous…