Mass of X (3872) in Bethe—Salpeter Equation for Quarks

Abstract

From Bethe-Salpeter equation, we deduce the equation which describes the two-body system consisting of a scalar meson and a vector meson. This equation is applied to investigate the exotic narrow state X(3872) assumed as a molecule state composed of D 0 D * 0 . The contribution of the resonance D * 0 is the attractive interaction between two heavy mesons in this molecule state. The calculated mass of X is consistent with the experimental data.

Amplitude analysis ofB+→J/ψϕK+decays

“…Therefore, the observation by CDF triggered wide interest. It has been suggested that the Xð4140Þ structure could be a molecular state [3][4][5][6][7][8][9][10][11], a tetraquark state [12][13][14][15][16], a hybrid state [17,18] or a rescattering effect [19,20].…”

Mass of Y(3940) in Bethe–Salpeter equation for quarks

“…Through these further form factors we can obtain the heavy meson interaction with light meson and the potentials between two heavy vector mesons without an extra parameter. Obviously, this approach is closer to QCD than our previous works [4][5][6][7]. Then numerically solving the relativistic Schrödinger-like equation with these potentials, we obtain the wave functions of the pure molecule states D * 0D * , D * + D * − and D * + s D * − s , respectively.…”

“…In our previous works [4][5][6][7] the form factors of heavy vector meson h(k 2 ) describing its internal structure have been calculated, but we did not consider the nonperturbative effects of QCD. In this work, we firstly improve the heavy vector meson BS wave function so that it can include the nonperturbative contribution.…”

Bethe-Salpeter wave functions for the bound states composed of two vector fields of arbitrary spin and their application

“…No matter how high the spin of the bound state is, its BS wave function should satisfy Eq. (12) or (13). However, in order to obtain its BS wave function 13 scalar functions in Eq.…”

“…To construct the kernel between two heavy mesons, we consider that the effective interaction is derived from the usual one light meson ð; ! ; Þ exchange [13]. In the following analysis we consider that the final particle is same to the initial one whose momentum is different from the former's, as shown in Fig.…”