Signal Modelling with Overdetermined Morphing Technique

TL;DR

The paper tackles the nonuniform statistical power of conventional Monte Carlo morphing, which relies on a fixed, invertible morphing basis to predict observables that depend polynomially on multiple couplings. It introduces overdetermined morphing, leveraging QR factorization to solve a least-squares problem when more base samples than independent monomials are available, thereby improving numerical stability and extending the region of parameter space where predictions are reliable. The authors demonstrate consistent gains in uniformity of statistical power and effective sample size across Higgs production and decay processes, supported by Monte Carlo studies and angular distributions, and provide an accessible Mathematica implementation. This approach offers a robust, scalable enhancement to MC-based morphing, with practical impact for precision predictions in high-energy physics analyses.

Abstract

Precise modelling of a signal in processes with multiple observables, exhibiting a complex dependency on the underlying parameters, is often a difficult and challenging task. Predicting the results of experimental measurements in high-energy physics reactions serves a good example. The reaction rates and distributions of momenta of the final state particles, depend on the parameters of the underlying physics model in a non-trivial way. The conventional way to predict the experimental of observables is to use the Monte Carlo morphing technique on a finite discrete set of simulated samples. In this article we extend this technique by using the overdetermined morphing basis. We show that our approach yields a better result than the traditional technique in terms of the statistical power and uniformity of the resulting prediction, and delivers better precision. We further demonstrate that the overdetermined morphing is better suited for description of extended regions of phase space than the conventional morphing. We use the modelling of kinematic distributions of the final state particles produced in decays of non-Standard Model Higgs bosons as an example.

Figures (7)

• Figure 1: An example of distribution of the effective sample ratio $\mathfrak{N}_2$ as a function of two parameters $g_1$ and $g_2$ for a morphing basis of $15$ input samples. White circles indicate the position of the base samples in $(g_1,g_2)$ space.
• Figure 2: The effective weights ratio $\mathfrak{N}_1$ (left) and the effective sample ratio $\mathfrak{N}_2$ (right) as a function of the $kHZZ$ parameter value. The magenta curve corresponds to the standard morphing based on the minimal number of base samples with $kHZZ = (-8, -6, -4, -3, -2)$. The blue curve represents overdetermined morphing using $kHZZ = (-14, -12, -10, -8, -6, -4, -3, -2, 0, 1, 2, 4, 6, 8, 10)$.
• Figure 3: Cross section of the VBF process as a function of the $kHZZ$ parameter value. The magenta curve corresponds to the standard morphing for base samples $kHZZ = (-8, -6, -4, -3, -2)$. The blue curve gives the cross section obtained by the overdetermined morphing with $kHZZ = (-14, -12, -10, -8, -6, -4, -3, -2, 0, 1, 2, 4, 6, 8, 10)$. Red dots represent simulated cross sections.
• Figure 4: Density plot for the effeciive weights ratio $\mathfrak{N}_1$ vs parameters $k_{HZZ}$ and $k_{AZZ}$. White dots correspond to base samples.
• Figure 5: Density plot for effective sample ratio $\mathfrak{N}_2$ as a function of parameters $k_{HZZ}$ and $k_{AZZ}$. White dots correspond to base samples.