The strength of the amplitudes for the coupling between the bottomonium $Υ(nS)$ states, the bottomonium-like isovector resonances $Z_b$ and a pion, $Υ(nS) Z_b π$, is considered. These amplitudes describe the decays $Z_b \to Υ(nS) π$ for $n=1,\,2,\,3$, and the processes $Υ(nS) \to Z_b π$ for $n=5,\,6, \ldots$ with either $Z_b(10610)$ or $Z_b(10650)$. It is pointed out that analyticity and unitarity impose a sum rule for these couplings to each of the $Z_b$ resonances. With the currently available data it appears to be difficult or impossible to simultaneously satisfy the sum rules for the $Z_b(10610)$ and $Z_b(10650)$ resonances. This difficulty can be resolved if there is a considerable dissimilarity in the yield of the states $Z_b(10610) π$ and $Z_b(10650) π$ in the $e^+e^-$ annihilation at energies above the $Υ(5S)$ resonance.
In this work, we study the resonance contributions to the decay $B^-\to K^+K^-π^-$, which is dominated by the scalar $f_0(980), K_0^*(1430)$, vector $ρ(1450), ϕ(1020), K^*(892)$ and tensor $f_2(1270)$ resonances. The three-body decay is reduced to various quasi two-body decays, where the $B$ meson firstly decays into a resonance and a pion or a kaon, subsequently the resonance decays into the other two final-state mesons. The quasi two-body decays are calculated within the light-cone sum rule approach utilizing the leading twist $B$ meson light-cone distribution amplitudes. Finally, the decay …
Gaussian Sum-Rules and Prediction of Resonance Properties
使用高斯QCD求和规则预测强子共振特性的技术开发的单共振和双共振唯象模型，并制定标准，以确定这些模型是需要分析一个特定的强子通道。耦合到$ρ$介子的矢量流求和规则与单共振模型一致，高斯求和规则分析得到了精确的$ρ$质量预测，其结果与唯象模型的理论预测非常吻合.一个双共振模型被证明是必要的高斯求和规则的非奇异夸克标量（$\bar n n$）电流。用双共振高斯求和规则分析了标量介子的等势和等矢量（$I=0,1$）$\bar n n$，结果表明理论预测与唯象模型符合得很好.在这个双共振模型中对$I=0,1$ $\bar n n$标量介子共振性质的预测为解释包括X（1775）在内的标量介子提供了有价值的信息。
One Sum To Rule Them All: A Second Order Master Rate Sum Rule for Charm Decays
Walter Burke Institute for Theoretical Physics, California Institute of Technology（加州理工学院沃尔特·伯克理论物理研究所）；Department of Physics, LEPP, Cornell University（康奈尔大学物理系、LEPP）；Institute for Particle Physics Phenomenology, Department of Physics, Durham University（杜伦大学物理系粒子物理现象学研究所）
We perform a systematic study of $SU(2)$ flavor amplitude sum rules with particular emphasis on $U$-spin. This study reveals a rich mathematical structure underlying the sum rules that allows us to formulate an algorithm for deriving all $U$-spin amplitude sum rules to any order of the symmetry breaking. This novel approach to deriving the sum rules does not require one to explicitly compute the Clebsch-Gordan tables, and allows for simple diagrammatic interpretation. Several examples that demonstrate the application of our novel method to systems that can be probed experimentally are provided…
We explore the idea of higher-order flavor sum rules, i.e. sum rules that hold to higher orders in the flavor symmetry-breaking parameters. In particular, we consider isospin sum rules based on $B \to nπ$ decays, and U-spin sum rules based on $B_d$ and $B_s$ decays to $n$ charged pions and/or kaons. We also demonstrate that sum rules exist to arbitrary orders by considering decay modes with increasing number of final state mesons $n$. Finally, we identify various theoretical and practical issues that need to be addressed in utilizing these sum rules.
pySecDec is a program that numerically calculates dimensionally regularized integrals. We use pySecDec to compute QCD Laplace sum-rules for pseudoscalar (i.e., $J^{PC}=0^{-+}$) charmonium hybrids, and compare the results to sum-rules computed using analytic results for dimensionally regularized integrals. We find that the errors due to the use of numerical integration methods is negligible compared to the uncertainties in the sum-rules stemming from the uncertainties in the parameters of QCD, e.g., the coupling constant, quark masses, and condensate values. Also, we demonstrate that numerical …
