A Method to Examine Likelihood of Candidate Theories beyond Parameter Optimization — Application to Specific Heat Data for the Multiband Superconductor Sr2RuO4

When an experimental curve is simple and candidate theories contain many unknown parameters, even unrealistic theories can generate theoretical curves close to the experimental data by adjusting the parameters; hence, it is difficult to derive useful information from the data by parameter fitting. We attempt to overcome this problem for specific heat data of the ruthenate superconductor Sr2RuO4 proposing a simple method to analyze the data: instead of the best-fit curves obtained by parameter optimization, we examine the sizes of parameter areas in which candidate theories accurately reproduce the experimental curve. For a candidate theory, if such an area is small, it is unlikely that the true parameter point falls within the area, i.e., it is unlikely that the theory with the true parameter values accidentally reproduces the experimental curve. Hence, in this case, the data do not support the theory. Conversely, if the area is large, the theory is potentially promising. On this basis, we propose a definition of a score to rate likelihood of candidate theories. In the application to the ruthenate, it is revealed that the data support two d-wave states, a g-wave state, and two interlayer chiral p-wave states as the most likely states. The second-most likely states are two f-wave states and two simple interlayer states, and unlikely states are the s-wave state, chiral p-wave state, d + ig wave state, and the state with the px + ipy and (px + ipy) cos(kz/2) wave gap functions in the γ and α + β bands, respectively. We discuss the validity of this method by comparing the results with other experimental results.