Algebraic approach to solve tt dilepton equations
- LPNHE, Universites Paris VI, VII, Place Jussieu 4, Tour 33, RdC, 75252 Paris Cedex 05 (France)
The set of nonlinear equations describing the standard model kinematics of the top quark antiquark production system in the dilepton decay channel has at most a fourfold 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 tt spin correlations. Simple algebraic operations allow one to transform the nonlinear 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 16. 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.
- OSTI ID:
- 20713878
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 72, Issue 9; Other Information: DOI: 10.1103/PhysRevD.72.095020; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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