Lattice QCD study of four-quark components of the isosinglet scalar mesons: Significance of disconnected diagrams

Abstract

We study the possible significance of four-quark states in the iso-singlet scalar mesons (J P C = 0 ++ , I = 0) by performing two-flavor full lattice QCD simulations on an 8 3 × 16 lattice using the improved gauge action and the clover-improved Wilson quark action. In particular, we evaluate the propagators of molecular and tetra-quark operators together with singly disconnected diagrams.In the computation of the singly disconnected diagrams we employ the Z 2 -noise method with the truncated eigenmode approach. We show that the quark loops given by the disconnected diagrams play an essential role in propagators of tetraquark and molecular operators.

From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance

“…Thus, although the lattice calculation is still far from describing the physical f 0 (500) the results are nevertheless very encouraging. Finally, it is worth remarking that in a very recent work by the same group [165], the significance of four-quark components in isoscalar mesons has also been studied, by calculating the propagators of "molecular" and tetraquark states as well as singly connected diagrams. Once again it is shown that within this framework, disconnected diagrams are essential for four-quark states to exist.…”

“…The possibility for tetraquarks to bound into scalar mesons was shown in [161], although for large quark masses. There are several works that find a σ meson [162,163,164,165] with a large tetraquark/molecular component. Of course, these are still calculations at high pion masses so that the σ cannot decay and have a width, but the results are very encouraging.…”

Investigating efficient methods for computing four-quark correlation functions

“…While in specific cases this might be justified, it is certainly not a general rule that these diagrams are negligible compared to their 4× connected counterparts. A recent study [29] has stressed this and we moreover have found that the contribution of 2× connected diagrams is in many cases sizable. For illustration we show a few cases in Figure 18, where the ratio |C 2×con jk |/(|C 4×con jk | + |C 2×con jk |) is plotted, i.e.…”

Computation of correlation matrices for tetraquark candidates with $J^P = 0^+$ and flavor structure $q_1 \bar{q_2} q_3 \bar{q}_3$

“…Several lattice QCD studies of the light scalar mesons have been published in the last couple of years [4,5,6,7,8,9,10]. In this work we continue our investigation of the a 0 (980) meson [11,12,13,14,15,16,17] and briefly discuss the applicability of our methods and codes to other systems, the D * s0 meson and some of the charged cc X states.…”