论文标题
QCD总规则具有频谱密度在反问题中解决的
QCD sum rules with spectral densities solved in inverse problems
论文作者
论文摘要
我们为非扰动研究构建QCD和规则，而不假设在强子侧低能量的光谱密度具有夸克 - 戴隆偶性。取而代之的是，通过将总规则视为逆问题，通过在夸克侧的操作员产物扩张输入来解决光谱密度的共振和连续贡献。这种新的形式主义不涉及连续阈值，不需要Borel转换和稳定性分析，并且可以扩展以提取激发态的特性。以两电流相关因子为例，我们证明了我们的形式主义中可以出现一系列$ρ$的共振，而衰减构成$ f_ {ρ（770）}（f_ {ρ（1450）}，f_ {ρ（1450）}，f_ {ρ（1700）}，f_ {ρ（1700）}，f_（1900）} ex（1900）} 0.10 0. 1.2.22.22（\ of）。对于质量，$ m_ {ρ（770）}（m_ {ρ（1450）}，m_ {ρ（1700）}，m_ {ρ（1900）}）\ $ 0.78（1.46，1.70，1.90，1.90）GEV。我们还表明，可以通过将Breit-Wigner参数替换为强子侧的$ρ（770）$ pole的衰减宽度$γ_{ρ（770）} \大约0.17 $ GEV。据观察，夸克侧尺寸六的夸克冷凝物对于建立这些$ρ$共振至关重要。以二元性假设为反问题，我们发现文献中广泛采用的多极总和规则并不能合理地描述$ρ$激发。可以通过在夸克一侧包括高阶和高功率校正来系统地改善我们的理论结果的精度。这种形式主义的广泛应用是预计可观察到的大量低能量QCD。
We construct QCD sum rules for nonperturbative studies without assuming the quark-hadron duality for the spectral density at low energy on the hadron side. Instead, both resonance and continuum contributions to the spectral density are solved with the operator-product-expansion input on the quark side by treating sum rules as an inverse problem. This new formalism does not involve the continuum threshold, does not require the Borel transformation and stability analysis, and can be extended to extract properties of excited states. Taking the two-current correlator as an example, we demonstrate that the series of $ρ$ resonances can emerge in our formalism, and the decay constants $f_{ρ(770)} (f_{ρ(1450)},f_{ρ(1700)},f_{ρ(1900)})\approx$ 0.22 (0.19, 0.14, 0.14) GeV for the masses $m_{ρ(770)} (m_{ρ(1450)},m_{ρ(1700)},m_{ρ(1900)})\approx$ 0.78 (1.46, 1.70, 1.90) GeV are determined. We also show that the decay width $Γ_{ρ(770)}\approx 0.17$ GeV can be obtained by substituting a Breit-Wigner parametrization for the $ρ(770)$ pole on the hadron side. It is observed that quark condensates of dimension-six on the quark side are crucial for establishing those $ρ$ resonances. Handling the conventional sum rules with the duality assumption as an inverse problem, we find that the multiple pole sum rules widely adopted in the literature do not describe the $ρ$ excitations reasonably. The precision of our theoretical outcomes can be improved systematically by including higher-order and higher-power corrections on the quark side. Broad applications of this formalism to abundant low energy QCD observables are expected.
