Charmonium spectroscopy motivated by general features of pNRQCD
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Charmonium spectroscopy motivated by general features of pNRQCD Raghav Chaturvedi1 · A. K. Rai1 Received: 15 June 2020 / Accepted: 25 September 2020 / Published online: 19 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Mass spectrum of charmonium is computed in the framework of potential non-relativistic quantum chromodynamics. O(1/m) and O(1/m2 ) relativistic corrections to the Cornell potential and spin-dependent potential have been added, and is solved numerically. New experimentally observed and modified positive and negative parity states like ψ(4230), ψ(4260), ψ(4360), ψ(4390), ψ(4660), χ c1 (4140) and χ c1 (4274) near open-flavor threshold have also been studied. We explain them as admixtures of S-D wave states and P-wave states. Apart from these states, some other states like X(3915), χ c1 (3872), ψ(3770) and ψ(4160) have been identified as 23 P0 , 23 P1 , 13 D1 and 23 D1 states. Subsequently, the electromagnetic transition widths and γ γ , e+ e− , light hadron and γ γ γ decay widths of several states are calculated at various leading orders. All the calculated results are compared with experimental and results from various theoretical models. Keywords Mass spectrum · pNRQCD · Charmonium
1 Introduction Remarkable experimental progress has been made in recent years in the field of heavy flavour hadrons specially charmonium. All the narrow charmonium states below open ¯ have been observed experimentally and have been successfully studcharm threshold(D D) ied theoretically by many approaches like lattice QCD [1], chiral perturbation theory [2], heavy quark effective field theory [3], QCD sum rules [4], NRQCD [5], dynamical equations based approaches like Schwinger-Dyson and Bethe-Salpeter equations(BSE) [6–9] and some potential models [10–18]. However, there are many questions related to charmonium physics in the region above D D¯ threshold. X and Y states above D D¯ threshold have been reported with unusual properties which are yet to be explained completely. These states Raghav Chaturvedi
[email protected] A. K. Rai [email protected] 1
Department of Applied Physics, Sardar Vallabhbhai National Institute of Technology, Surat 395007, Gujarat, India
International Journal of Theoretical Physics (2020) 59:3508–3532
3509
however could be exotic states, mesonic molecules, multi-quark states or even admixtures of low lying charmonium states, which have been broadly put forward in [19] and references therein. Charmoniumlike states with normal quantum numbers have similar masses when compared to normal charmonium states. In order to study and understand the nature of higher mass states near D D¯ threshold it is necessary to have better understanding of low lying charmonium states. X(3872) (now χ c1 (3872)) was studied for the first time at Belle [20] in 2003 in an exclusive decay of B± which was later reproduced by p+ p− collision [21]. This state was successively studied theoretically, as exotic state by [22, 23], as pure chamonium state by [24–26], as m
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