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arXiv 1805.03415hep-phnucl-th
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从QCD求和规则计算径向激发光矢量介子的电磁耦合

Electromagnetic couplings of radially excited light vector mesons from QCD sum rules

S. S. Afonin, T. D. Solomko

摘要:

无味矢量介子与$e^+e^-$湮灭的耦合是了解这些共振的性质和结构的重要信息来源,这些共振在强子现象学中起着重要作用。许多径向激发的重矢量介子的耦合被测量,而相应的轻矢量介子的耦合未知。我们提出了一个唯象的方法,允许估计这些未知的耦合。我们的观测表明,$n$波重矢量介子的径向激发的电磁耦合是由$e^+e^-$与$n$以近指数速率的湮灭产生的.很自然地,我们可以假设光矢量介子中也会发生同样的效应,这就可以估计未知的耦合。我们测试了这个假设的帮助下,一个广义版本的borelized QCD谱求和规则饱和的介子状态的线性径向轨迹从唯象。这导致能够预测解耦速率的一致设置。计算出的速率与重矢量介子几乎相同。我们的结果可以解释为介子衰变到$e^+e^-$的非平凡电磁形状因子的一个有效解释,从而超越了大- $N_c$极限.一方面,我们认为,给定的退耦并不一定与以前的大型$N_c$结果Regge类介子谱相矛盾。

英文摘要:

The couplings of unflavored vector mesons to the $e^+e^-$ annihilation are an important source of information on the nature and structure of these resonances which play a prominent role in the hadron phenomenology. The couplings of many radially excited heavy vector mesons are measured, while the corresponding couplings for light vector mesons are not known. We propose a phenomenological method allowing to estimate these unknown couplings. The method is suggested by our observation that the electromagnetic coupling of the $n$-th radial excitation of $S$-wave heavy vector meson decouples from the $e^+e^-$ annihilation with nearly exponential rate with $n$. It becomes natural to assume that the same effect takes place in the light vector mesons and this would allow to estimate the unknown couplings. We tested this assumption with the help of a generalized version of borelized QCD spectral sum rules saturated by a linear radial trajectory of meson states taken from the phenomenology. This leads to a consistent setup which is able to predict the decoupling rate. The calculated rate turned out to be almost the same as in the heavy vector mesons. Our result may be interpreted as an effective account for non-trivial electromagnetic formfactor in meson decays to $e^+e^-$, thus looking beyond the large-$N_c$ limit. On the one hand, we argue that the given decoupling does not necessary contradict to the previous large-$N_c$ results for the Regge like meson spectra.

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