Abstract
We present an alternative method for carrying out a principal-component analysis of Wilson coefficients in standard model effective field theory (SMEFT). The method is based on singular-value decomposition (SVD). The SVD method provides information about the sensitivity of experimental observables to physics beyond the standard model that is not accessible in the Fisher-information method. In principle, the SVD method can also have computational advantages over diagonalization of the Fisher information matrix. We demonstrate the SVD method by applying it to the dimension-6 coefficients for the process of top-quark decay to a $b$ quark and a $W$ boson and use this example to illustrate some pitfalls in widely used fitting procedures. We also outline an iterative procedure for applying the SVD method to dimension-8 SMEFT coefficients.
Highlights
In recent years, standard model effective theory (SMEFT) [1,2,3,4] has been a focus of activity in both the theoretical and experimental particle-physics communities
We present an alternative method for carrying out the principal-component analysis (PCA) of the standard model effective field theory (SMEFT) coefficients that is based on singular-value decomposition (SVD)
In using experimental data to constrain the Wilson coefficients in standard model effective field theory (SMEFT), a difficulty that often arises is that observables may be insensitive to certain linear combinations of SMEFT coefficients
Summary
Standard model effective theory (SMEFT) [1,2,3,4] has been a focus of activity in both the theoretical and experimental particle-physics communities. If the number of SMEFT coeffients is much larger than the number of observables, the matrix that is analyzed in the SVD approach is much smaller than the Fisher matrix, and so the computation time may be smaller in the SVD approach It remains to be seen whether these advantages will be significant in extensive and/or iterated global fits of SVD coefficients. We demonstrate the SVD method by applying it to a restricted class of observables that appear in decay of the top quark to a b quark and a W boson.1 This example allows us to show how the SVD method can be used to deal with correlated theoretical and experimental errors and with the difficulties of flat directions.
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