We propose to use the M T 2 concept to measure the masses of all particles in SUSY-like events with two unobservable, identical particles. To this end we generalize the usual notion of M T 2 and define a new M (n,p,c) T 2 variable, which can be applied to various subsystem topologies, as well as the full event topology. We derive analytic formulas for its endpoint M (n,p,c) T 2,max as a function of the unknown test massM c of the final particle in the subchain and the transverse momentum p T due to radiation from the initial state. We show that the endpoint functions M (n,p,c) T 2,max (M c , p T ) may exhibit three different types of kinks and discuss the origin of each type. We prove that the subsystem M (n,p,c) T 2 variables by themselves already yield a sufficient number of measurements for a complete determination of the mass spectrum (including the overall mass scale). As an illustration, we consider the simple case of a decay chain with up to three heavy particles, X 2 → X 1 → X 0 , which is rather problematic for all other mass measurement methods. We propose three different M T 2 -based methods, each of which allows a complete determination of the masses of particles X 0 , X 1 and X 2 . The first method only uses M (n,p,c) T 2 endpoint measurements at a single fixed value of the test massM c . In the second method the unknown mass spectrum is fitted to one or more endpoint functions M (n,p,c) T 2,max (M c , p T ) exhibiting a kink. The third method is hybrid, combining M T 2 endpoints with measurements of kinematic edges in invariant mass distributions. As a practical application of our methods, we show that the dilepton W + W − and tt samples at the Tevatron can be used for an independent determination of the masses of the top quark, the W boson and the neutrino, without any prior assumptions. 42 -2 - [18,19,27,38,39].• III. M T 2 methods. These methods explore the transverse invariant mass variable M T 2 originally proposed in [13] and later used and developed in [17,24,26,28,37,40,41,45].Recently it was shown that under certain circumstances, the endpoint of the M T 2 distribution, when considered as a function of the unknown test massM 0 of the lightest new particle X 0 , exhibits a kink and the true mass M 0 of X 0 , i.e. atM 0 = M 0 [29-32,36].One could also combine two or more of these techniques into a hybrid method, e.g. a mixed polynomial and endpoint method [34], a mixed M T 2 and endpoint method [33,43], or a mixed M T 2 and polynomial method [47,48]. In Section 2 we shall describe in detail each of these three basic approaches I -III. We shall then contrast them to each other and discuss their pros and cons. In particular, we shall concentrate on their applicability as a function of the length of the decay chain, i.e. the number n of intermediate resonances in Fig. 1. We shall find that for sufficiently long decay chains, namely n ≥ 3, each method I -III by itself is able to completely determine the unknown particle spectrum, at least as a matter of principle. Therefore, if Nature is so ki...

We revisit the method of kinematical endpoints for particle mass determination, applied to the popular SUSY decay chainq →χ 0 2 →l →χ 0 1 . We analyze the uniqueness of the solutions for the mass spectrum in terms of the measured endpoints in the observable invariant mass distributions. We provide simple analytical inversion formulas for the masses in terms of the measured endpoints. We show that in a sizable portion of the SUSY mass parameter space the solutions always suffer from a two-fold ambiguity, due to the fact that the original relations between the masses and the endpoints are piecewise-defined functions. The ambiguity persists even in the ideal case of a perfect detector and infinite statistics. We delineate the corresponding dangerous regions of parameter space and identify the sets of "twin" mass spectra. In order to resolve the ambiguity, we propose a generalization of the endpoint method, from single-variable distributions to two-variable distributions. In particular, we study analytically the boundaries of the {m jℓ(lo) , m jℓ(hi) } and {m ℓℓ , m jℓℓ } distributions and prove that their shapes are in principle sufficient to resolve the ambiguity in the mass determination. We identify several additional independent measurements which can be obtained from the boundary lines of these bivariate distributions. The purely kinematical nature of our method makes it generally applicable to any model that exhibits a SUSY-like cascade decay.

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Ankylosaurian systematics can be assessed using morphological, textural, and histological characters of osteoderms. Archosaur osteoderms have cortices surrounding cancellous cores. Ankylosaurs are united by an external cortex distinguishable from the core and by the presence of mineralized structural fibers. Nodosaurid osteoderms lack a well-developed basal cortex and have dense external cortical fibers. Ankylosaurid osteoderms are thinner than those of other ankylosaurs. Polacanthine osteoderms have a cancellous core, but share this feature with other derived and primitive taxa. Cortical thickness overlaps among groups, so a thick cortex is not diagnostic for polacanthines. Specialized elements diverge histologically from the primitive condition to suit their specific functions. Some shapes and external textures are diagnostic for specific taxa, such as Ankylosaurus and Glyptodontopelta. Parsimony analyses suggest osteodermal support for a monophyletic Polacanthinae (excluding Mymoorapelta) and Shamosaurinae.

We outline a general strategy for measuring spins, couplings and mixing angles in the case of a heavy partner decay chain terminating in an invisible particle. We consider the common example of a heavy scalar or fermion D decaying sequentially to other heavy particles C, B and A by emitting a quark jet j and two leptons ℓ ± n and ℓ ∓ f . We derive analytic formulas for the dilepton ({ℓ + ℓ − }) and the two jet-lepton ({jℓ n } and {jℓ f }) invariant mass distributions for the case of most general couplings and mixing angles of the heavy partners. We then consider various spin assignments for the heavy particles A, B, C and D, and for each case, derive the relevant functional basis for the invariant mass distributions which contains the intrinsic spin information and does not depend on the couplings and mixing angles. We propose a new method for determining the spins of the heavy partners, using the three experimentally observable distributions {ℓ + ℓ − }, {jℓ + } + {jℓ − } and {jℓ + } − {jℓ − }. We show that the former two only depend on a single model-dependent parameter α, while the latter may depend on two other parameters β and γ. By fitting these distributions to our set of basis functions, we are able to do a pure measurement of the spins per se. Our method is also applicable at a pp collider such as the Tevatron, for which the previously proposed lepton charge asymmetry is identically zero and does not contain any spin information. In the process of determining the spins, we also end up with an independent measurement of the parameters α, β and γ, which represent certain combinations of the couplings and the mixing angles of the heavy partners A, B, C and D.