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High Energy Physics - Phenomenology

arXiv:hep-ph/0510100 (hep-ph)
[Submitted on 7 Oct 2005 (v1), last revised 18 Jun 2011 (this version, v2)]

Title:Algebraic approach to solve $t\bar{t}$ dilepton equations

Authors:Lars Sonnenschein
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Abstract: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.
Comments: 7 pages, 4 figures, added neutrino and anti-neutrino masses in system of equations. This can be exploited in search for new physics with the same decay topology including invisible massive particles
Subjects: High Energy Physics - Phenomenology (hep-ph)
Cite as: arXiv:hep-ph/0510100
  (or arXiv:hep-ph/0510100v2 for this version)
  https://doi.org/10.48550/arXiv.hep-ph/0510100
Journal reference: Phys.Rev.D72:095020,2005
Related DOI: https://doi.org/10.1103/PhysRevD.72.095020

Submission history

From: Lars Sonnenschein [view email]
[v1] Fri, 7 Oct 2005 18:09:19 UTC (30 KB)
[v2] Sat, 18 Jun 2011 11:51:26 UTC (31 KB)
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