Step: a tool to perform tests of smoothness on differential distributions based on Chebyshev polynomials of the first kind

We motivate and describe a method based on fits with Chebyshev polynomials to test the smoothness of differential distributions. We also provide a header-only tool in C++ called STEP to perform such tests. As a demonstration, we apply the method in the context of the measurement of inclusive jet double-differential cross section in the jet transverse momentum and rapidity at the Tevatron and LHC. This method opens new possibilities to test the quality of differential distributions used for the extraction of physics quantities such as the strong coupling.