There is growing interest in explainable recommender systems that provide recommendations along with explanations for the reasoning behind them. When evaluating recommender systems, most studies focus on overall recommendation performance. Only a few assess the quality of the explanations. Explanation quality is often evaluated through user studies that subjectively gather users' opinions on representative explanatory factors that shape end-users' perspective towards the results, not about the explanation contents itself. We aim to fill this gap by developing an objective metric to evaluate Veracity: the information quality of explanations. Specifically, we decompose Veracity into two dimensions: Fidelity and Attunement. Fidelity refers to whether the explanation includes accurate information about the recommended item. Attunement evaluates whether the explanation reflects the target user's preferences. By applying signal detection theory, we first determine decision outcomes for each dimension and then combine them to calculate a sensitivity, which serves as the final Veracity value. To assess the effectiveness of the proposed metric, we set up four cases with varying levels of information quality to validate whether our metric can accurately capture differences in quality. The results provided meaningful insights into the effectiveness of our proposed metric.