Detecting the polarization in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>χ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:mi>ϕ</mml:mi><mml:mi>ϕ</mml:mi></mml:math> decays to probe hadronic loop effect

نویسندگان

چکیده

In this work, we show that detecting the polarization information of ${\ensuremath{\chi}}_{cJ}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\phi}(J=0,1,2)$ could be a practical way to test hadronic loop effect in these decays. Our results predicted ratios helicity amplitudes are less dependent on parameters involved calculation. The determined $|{F}_{1,1}^{(0)}/{F}_{0,0}^{(0)}|\ensuremath{\approx}0.359$, $|{F}_{1,0}^{(1)}/{F}_{0,1}^{(1)}|=1$, $|{F}_{1,1}^{(1)}/{F}_{0,1}^{(1)}|=0$, $|{F}_{1,0}^{(2)}|/|{F}_{0,0}^{(2)}|=|{F}_{0,1}^{(2)}|/|{F}_{0,0}^{(2)}|\ensuremath{\approx}1.285$, $|{F}_{1,\ensuremath{-}1}^{(2)}|/|{F}_{0,0}^{(2)}|=|{F}_{\ensuremath{-}1,1}^{(2)}|/|{F}_{0,0}^{(2)}|\ensuremath{\approx}5.110$, and $|{F}_{\ensuremath{-}1,\ensuremath{-}1}^{(2)}|/|{F}_{0,0}^{(2)}|=|{F}_{1,1}^{(2)}|/|{F}_{0,0}^{(2)}|\ensuremath{\approx}0.465$. By adopting ratios, use Monte Carlo events moments $⟨{t}_{ij}⟩$ can used as observables reveal transfer decays, their distributions directly related determination amplitudes. We suggest experiments like at BESIII Belle II performing analysis ${\ensuremath{\chi}}_{cJ}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\phi}$ decay future, important understand mechanism underlying ${\ensuremath{\chi}}_{cJ}$

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ژورنال

عنوان ژورنال: Physical review

سال: 2021

ISSN: ['0556-2813', '1538-4497', '1089-490X']

DOI: https://doi.org/10.1103/physrevd.103.096006