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The well-known model of the triangle diagrams with D*D¯D* and D¯*DD¯* mesons in the loops is compared with the modern data on the amplitude of the X(3872)→π0χc1(1P) decay. Considering the X(3872) object as a χc1(2P) charmonium state, we introduce a parameter ξ characterizing the scale of the isotopic symmetry violation in this decay and find a lower limit of ξ≃0.0916. The model incorporates the only fitted parameter associated with the form factor. We analyze in detail the influence of the form factor on the amplitude X(3872)→π0χc1(1P) and on the parameter ξ. As the suppression of the amplitude by the form factor increases, ξ increases. Because the X(3872) resonance is located practically at the threshold of the D0D¯*0 channel, the amplitude of X(3872)→π0χc1(1P) turns out to be proportional to md−mu. Using the estimating values for the coupling constants gXDD¯*, gχc1DD¯*, and gD*0D*0π0, we show that the model of the triangle loop diagrams is in reasonable agreement with the available data. Apart from the difference in the masses of neutral and charged charmed mesons, any additional exotic sources of isospin violation in X(3872)→π0χc1(1P) (such as a significant difference between the coupling constants gXD0D¯*0 and gXD+D*−) are not required to interpret the data. This indirectly confirms the isotopic neutrality of the X(3872), which is naturally realized for the cc¯ state χc1(2P). Published by the American Physical Society 2024
Achasov et al. (Mon,) studied this question.