Narrow resonances in systems with short-range interactions are discussed in an effective field theory (EFT) framework. An effective Lagrangian is formulated in the form of a combined expansion in powers of a momentum Q << Lambda--a short-distance scale--and an energy difference delta epsilon = |E-epsilon_0| << epsilon_0--a resonance peak energy. At leading order in the combined expansion, a two-body scattering amplitude is the sum of a smooth background term of order Q^0 and a Breit-Wigner term of order Q^2 (delta epsilon)^{-1} which becomes dominant for delta epsilon <~ Q^3. Such an EFT is applicable to systems in which short-distance dynamics generates a low-lying quasistationary state. The EFT is generalized to describe a narrow low-lying resonance in a system of charged particles. It is shown that in the case of Coulomb repulsion, a two-body scattering amplitude at leading order in a combined expansion is the sum of a Coulomb-modified background term and a Breit-Wigner amplitude with parameters renormalized by Coulomb interactions.
Possibility of narrow resonances in nucleon-nucleon channels
复合态表现为束缚态、共振态或基元态,它们的性质由它们与连续统的相互作用决定。如果相互作用经历扰动,复合态可以改变其表现形式。核子-核子散射的相位分析表明在3S 1,1 S 0和3 P0通道中存在基元。电磁相互作用可以将基元从单一切割中转移,将它们转变为窄共振。我们评估这种影响的1 S 0质子-质子散射通道的Simonov-Dyson模型的框架内。我们表明,电磁相互作用把一个质量为2000 MeV的素子变成一个大约相同的质量和宽度为260 keV的重子共振。类似性质的窄共振可能发生在其他核子-核子通道中。窄共振存在的实验证实将对核子-核子相互作用理论具有重要意义。
Photoproduction of eta-mesons on the deuteron above S11(1535) in the presence of a narrow P11(1670) resonance
本文研究了氘核上η介子的非相干光生。主要的注意力是支付给上述的区域的S11(1535)共振,而狭窄的共振结构中提取的总截面的γ n -> η n已被报道。从唯象的观点分析了相应的实验结果,模型中包含一个质量约为1670 MeV,宽度小于30 MeV的重子P11。在最近的一些工作中,这种共振被认为是J^P=1/2^+的五夸克反十重态的非奇异成员。计算了$η$介子的极化和非极化角分布。此外,我们给出了我们对中性K介子和双π光生的截面的预测,其中假设相同的窄P11(1670)共振通过衰变到K^0 λ和π δ组态。
We discuss some general features of the effective range expansion, the content of its parameters with respect to the nature of the pertinent near-threshold states and the necessary modifications in the presence of coupled channels, isospin violations and unstable constituents. As illustrative examples, we analyse the properties of the $χ_{c1}(3872)$ and $T_{cc}^+$ states supporting the claim that these exotic states have a predominantly molecular nature.