0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 M$_{B}$ H GeV L 1.85 1.90 1.95 2.00 2.05 2.10 2.15 R 1 GLYPH<145> R 0 H GeV L 1.2 1.3 1.4 1.5 1.6 1.7 1.8 M$_{B}$ H GeV L 2.20 2.22 2.24 2.26 2.28 2.30 2.32 2.34 R 1 GLYPH<145> R 0 H GeV L first determine a range of τ values for which the sum rule is considered reliable, called the sum rule window. In order to do this it is convenient to define the Borel mass M$_{B}$ = 1 / √ τ . There are multiple ways in which the sum rule window can be defined. All approaches involve fixing lower and upper limits on the Borel mass. Typically contributions from condensates become significant at small values of M$_{B}$ whereas contributions from the continuum become important at large values of M$_{B}$ . Therefore placing restrictions on condensate contributions to the sum rule can be used to place a lower bound on M$_{B}$ , whereas restrictions on continuum contributions can be used to place an upper bound on M$_{B}$ . The resulting range of M$_{B}$ values is where the sum rule is considered to be reliable, or the sum rule window. However, the width of the sum rule window varies with the value of s$_{0}$ . The value of s$_{0}$ can be constrained through the requirement of τ stability [89]: Examples of stable and unstable sum rules are shown in Fig. 1.10. The smallest value of s$_{0}$ in which the mass prediction (1.113) exhibits τ stability within the sum rule window is taken Figure 1.10: Examples of stable (left) and unstable (right) sum rules. The stable sum rule exhibits τ stability within the sum rule window whereas the unstable sum rule does not. In the unstable case there is no region in the sum rule window where the mass prediction given by Eq. (1.113) displays weak dependence on the Borel parameter. Mass predictions made from unstable sum rules are unreliable for this reason. The left and right figures correspond to the scalar and pseudoscalar charm-light diquark sum rules from Chapter 4, respectively. d dτ M ( τ , s$_{0}$ ) = 0 . (1.114) 48