Precise reconstruction of sparticle masses without ambiguities

We critically reexamine the standard applications of the method of kinematical endpoints for sparticle mass determination. We consider the typical decay chain in supersymmetry (SUSY) q̃→X̃ ⁰ ₂→ℓ̃ → X̃ ⁰ ₁, which yields a jet j, and two leptons ℓ _n ^± and ℓ _f ^∓. The conventional approaches use the upper kinematical endpoints of the individual distributions m _jℓℓ, m _jℓ(lo) = min m _jℓn,m _jℓf and m _jℓ(hi) = max m _jℓn,m _jℓf, all three of which suffer from parameter space region ambiguities and may lead to multiple solutions for the SUSY mass spectrum. In contrast, we do not use m _jℓℓ, m _jℓ(lo) and m _jℓ(hi), and instead propose a new set of (infinitely many) variables whose upper kinematic endpoints exhibit reduced sensitivity to the parameter space region. We then outline an alternative, much simplified procedure for obtaining the SUSY mass spectrum. In particular, we show that the four endpoints observed in the three distributions m ² _ℓℓ, m ² _jℓn∪m ² _jℓf and m ² _jℓn+m ² _{jℓ f} are sufficient to completely pin down the squark mass _m and the two neutralino masses m _X̃ ⁰ ₂ and m _X̃ ⁰ ₁, leaving only a discrete 2-fold ambiguity for the slepton mass mℓ̃. This remaining ambiguity can be easily resolved in a number of different ways: for example, by a single additional measurement of the kinematic endpoint of any one out of the many remaining 1-dimensional distributions at our disposal, or by exploring the correlations in the 2-dimensional distribution of m ² _jℓn∪m ² _jℓf versus m ² _ℓℓ. We illustrate our method with two examples: the LM1 and LM6 CMS study points. An additional advantage of our method is the expected improvement in the accuracy of the SUSY mass determination, due to the multitude and variety of available measurements.