Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2005-10-07
Phys.Rev.D72:095020,2005
Physics
High Energy Physics
High Energy Physics - Phenomenology
7 pages, 4 figures, added neutrino and anti-neutrino masses in system of equations. This can be exploited in search for new ph
Scientific paper
10.1103/PhysRevD.72.095020
The set of non-linear equations describing the Standard Model kinematics of the top quark antiqark production system in the dilepton decay channel has at most a four-fold ambiguity due to two not fully reconstructed neutrinos. Its most precise solution is of major importance for measurements of top quark properties like the top quark mass and $t\bar{t}$ spin correlations. Simple algebraic operations allow to transform the non-linear equations into a system of two polynomial equations with two unknowns. These two polynomials of multidegree eight can in turn be analytically reduced to one polynomial with one unknown by means of resultants. The obtained univariate polynomial is of degree sixteen. The number of its real solutions is determined analytically by means of Sturm's theorem, which is as well used to isolate each real solution into a unique pairwise disjoint interval. The solutions are polished by seeking the sign change of the polynomial in a given interval through binary bracketing.
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