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The analysis of the LHCb data on $X(6900)$ found in the di-$jpsi$ system is performed using a momentum-dependent Flatt{e}-like parameterization. The use of the pole counting rule and spectral density function sum rule give consistent conclusions that both confining states and molecular states are possible, or it is unable to distinguish the nature of $X(6900)$, if only the di-$jpsi$ experimental data with current statistics are available. Nevertheless, we found that the lowest state in the di-$J/psi$ system has very likely the same quantum numbers as $X(6900)$, and $X(6900)$ is probably not interpreted as a $J/psi-psi(2S)$ molecular state.
Two criteria for planarity of a Feynman diagram upon its propagators (momentum flows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can pla
Recently, a new hadronic structure at around $6.9$ GeV was observed in an LHCb experiment. From its limited yet known decay mode, one could still determine that it contains at least four charm quarks and hence belongs to the category of exotic state.
We exhibit a particular free subarrangement of a certain restriction of the Weyl arrangement of type $E_7$ and use it to give an affirmative answer to a recent conjecture by T.~Abe on the nature of additionally free and stair-free arrangements.
The twin group $T_n$ is a right angled Coxeter group generated by $n- 1$ involutions and having only far commutativity relations. These groups can be thought of as planar analogues of Artin braid groups. In this note, we study some properties of twin
We study in this paper three aspects of Mean Field Games. The first one is the case when the dynamics of each player depend on the strategies of the other players. The second one concerns the modeling of noise in discrete space models and the formu