Rise and fall of pentaquarks in the QCD Sum Rules approach

Abstract

We review the existing mass and decay width determinations of pentaquarks with QCD Sum Rules (QCDSR). We give special attention to the intermediate assumptions and choices which we are obliged to do in this approach. As an example, we present the full calculation of the pentaquark mass with Borel sum rules and also with Finite Energy Sum Rules (FESR). We also work out the calculation of the Θ decay width. We take the opportunity to comment our publications on this subject and include new and unpublished material.

Role of unphysical solution in nucleon QCD sum rules

“…This contrasts the earlier statements (cited in [24]) that the QCD sum rules support the existence of the pentaquark. However, the authors of [24] do not make a definite statement on the QCD sum rules predictions about the pentaquark states. In the QCD sum rules analysis of the light tetraquark states [25] it was found that the solution with the domination of the pole can be obtained only for small values of the Borel mass M 2 , where the OPE series does not converge.…”

“…In [28] Eqs. ( 23) and (24) were used for determination of nucleon parameters in framework of the finite energy sum rules. Inclusion of the radiative correction was shown to diminish the value of the nucleon mass, assuming that the threshold value W 2 does not change.…”

“…Note that the problem of the pole dominance emerged in other QCD sum rules studies. In review on the QCD sum rules analysis of the pentaquark states [24] the authors found that it is very difficult to satisfy the requirements of pole domination, OPE series convergence and stability within the Borel window simultaneously. This contrasts the earlier statements (cited in [24]) that the QCD sum rules support the existence of the pentaquark.…”

“…In review on the QCD sum rules analysis of the pentaquark states [24] the authors found that it is very difficult to satisfy the requirements of pole domination, OPE series convergence and stability within the Borel window simultaneously. This contrasts the earlier statements (cited in [24]) that the QCD sum rules support the existence of the pentaquark. However, the authors of [24] do not make a definite statement on the QCD sum rules predictions about the pentaquark states.…”

Revisiting the pentaquark episode for lattice QCD

“…This exposed how much we scientists, despite trying to stress on objectivity, are bound by human limitations of being prejudiced by what is going on around us. I have a long quote below from a sum rules review [19] of this episode only adding a "LQCD"(for lattice QCD) alongside the QCDSR (for QCD sum rules). Apart from saving me the trouble of writing this section myself, this illustrates strikingly how we all went through the same learning curve.…”