The stransverse mass, MT2, in special cases

This document describes some special cases in which the stransverse mass, MT2, may be calculated by non-iterative algorithms. The most notable special case is that in which the visible particles and the hypothesised invisible particles are massless -- a situation relevant to its current usage in the Large Hadron Collider as a discovery variable, and a situation for which no analytic answer was previously known. We also derive an expression for MT2 in another set of new (though arguably less interesting) special cases in which the missing transverse momentum must point parallel or anti parallel to the visible momentum sum. In addition, we find new derivations for already known MT2 solutions in a manner that maintains manifest contralinear boost invariance throughout, providing new insights into old results. Along the way, we stumble across some unexpected results and make conjectures relating to geometric forms of M_eff and H_T and their relationship to MT2.Comment: 11 pages, no figures. v2 corrects minor typos. v3 corrects an incorrect statement in footnote 8 and inserts a missing term in eq (3.9). v4 and v5 correct minor typos spotted by reader

The swan song: the disappearance of the nucleus of NGC 4051 and the echo of its past glory

BeppoSAX observed the low-luminous Seyfert 1 Galaxy NGC4051 in a ultra-dim X-ray state. The 2-10 keV flux (1.26 x 10^{-12} erg/cm^2/s) was about 20 times fainter than its historical average value, and remained steady along the whole observation (~2.3 days). The observed flat spectrum (\Gamma ~ 0.8) and intense iron line (EW ~600 eV) are best explained assuming that the active nucleus has switched off, leaving only a residual reflection component visible.Comment: 5 pages, Latex, 3 Postscript figures, accepted for publication in MNRA

The Fundamental Plane in RX J0142.0+2131: a galaxy cluster merger at z=0.28

We present the Fundamental Plane (FP) in the z = 0.28 cluster of galaxies RX J0142.0+2131. There is no evidence for a difference in the slope of the FP when compared with the Coma cluster, although the internal scatter is larger. On average, stellar populations in RX J0142.0+2131 have rest-frame V-band mass-to-light ratios (M/L_V) 0.29+-0.03 dex lower than in Coma. This is significantly lower than expected for a passively-evolving cluster formed at z_f=2. Lenticular galaxies have lower average M/L_V and a distribution of M/L_V with larger scatter than ellipticals. Lower mass-to-light ratios are not due to recent star formation: our previous spectroscopic observations of RX J0142.0+2131 E/S0 galaxies showed no evidence for significant star-formation within the past ~4 Gyr. However, cluster members have enhanced alpha-element abundance ratios, which may act to decrease M/L_V. The increased scatter in the RX J0142.0+2131 FP reflects a large scatter in M/L_V implying that galaxies have undergone bursts of star formation over a range of epochs. The seven easternmost cluster galaxies, including the second brightest member, have M/L_V consistent with passive evolution and z_f = 2. We speculate that RX J0142.0+2131 is a cluster-cluster merger where the galaxies to the east are yet to fall into the main cluster body or have not experienced star formation as a result of the merger.Comment: 4 pages, 2 figures, accepted for publication in ApJ Letter

Sqrt{shat}_{min} resurrected

We discuss the use of the variable sqrt{shat}_{min}, which has been proposed in order to measure the hard scale of a multi parton final state event using inclusive quantities only, on a SUSY data sample for a 14 TeV LHC. In its original version, where this variable was proposed on calorimeter level, the direct correlation to the hard scattering scale does not survive when effects from soft physics are taken into account. We here show that when using reconstructed objects instead of calorimeter energy and momenta as input, we manage to actually recover this correlation for the parameter point considered here. We furthermore discuss the effect of including W + jets and t tbar+jets background in our analysis and the use of sqrt{shat}_{min} for the suppression of SM induced background in new physics searches.Comment: 23 pages, 9 figures; v2: 1 figure, several subsections and references as well as new author affiliation added. Corresponds to published versio

Absolutely stable proton and lowering the gauge unification scale

A unified model is constructed, based on flipped SU(5) in which the proton is absolutely stable. The model requires the existence of new leptons with masses of order the weak scale. The possibility that the unification scale could be extremely low is discussed

Geometric CP Violation with Extra Dimensions

We discuss how CP symmetry can be broken geometrically through orbifold projections in hidden extra dimensions in the context of D-brane models for particle unifications. We present a few toy models to illustrate the idea and suggest ways to incorporate this technique in the context of realistic models.Comment: 6 pages, one figure; references updated and a new model adde

Effects of the K+→π+ννˉK^+\to\pi^+\nu\bar{\nu} and of other processes on the mixing hierarchies in the four-generation model

We analyze in the four-generation model the first measurement of the branching ratio of rare kaon decay $K^+\to\pi^+\nu\bar{nu}$, along with the other processes of $K_L-K_S$ mass difference $\Delta m_K$, CP-violating parameter $\epsilon_K, B_d-\bar{B_d}$ mixing, $B_s-\bar{B_s}$ mixing, $B(K_L\to\mu\bar{\mu})$, and the upper bound values of $D^0-\bar{D^0}$ mixing and $B(K_L\to\pi^0\nu\bar{\nu})$, and try to search for mixing of the fourth generation in the hierarchical mixing scheme of the Wolfenstein parametrization. Using the results for the mixing of the fourth generation, we discuss predictions of the $D^0-\bar{D^0}$ mixing ($\Delta m_D$) and the branching ratio of directly CP-violating decay process $K_L\to\pi^0\nu\bar{\nu}$, and the effects on the CP asymmetry in neutral B meson decays and the unitarity triangle.Comment: 29 pages written in LaTex. 6 figures(drawn on LaTeX). Revised from "$K^+\to\pi^+\nu\bar{\nu}$ in the four-generation model" of the same Authors(TOKUSHIMA 99-1, January 1999). A minor chang

Momentum asymmetries as CP violating observables

Three body decays can exhibit CP violation that arises from interfering diagrams with different orderings of the final state particles. We construct several momentum asymmetry observables that are accessible in a hadron collider environment where some of the final state particles are not reconstructed and not all the kinematic information can be extracted. We discuss the complications that arise from the different possible production mechanisms of the decaying particle. Examples involving heavy neutralino decays in supersymmetric theories and heavy Majorana neutrino decays in Type-I seesaw models are examined.Comment: 20 pages, 9 figures. Clarifying comments and one reference added, matches published versio

Cohomological descent theory for a morphism of stacks and for equivariant derived categories

In the paper we answer the following question: for a morphism of varieties (or, more generally, stacks), when the derived category of the base can be recovered from the derived category of the covering variety by means of descent theory? As a corollary, we show that for an action of a reductive group on a scheme, the derived category of equivariant sheaves is equivalent to the category of objects, equipped with an action of the group, in the ordinary derived category.Comment: 28 page

Paying to play - the pricing policies of casinos

Wherever gambling activity is permitted it becomes a major competitor for the household budget.*(3) The growth in gambling in the US has become an important social and political issue and the subject of a National Commission, the National Gambling Impact Study Commission (NGISC 1999).*(4) The Commission indicates that more than 86 per cent of all Americans have gambled at least once and that over $50 bn. was spent (amount wagered minus prizes received) on gambling activities in the US in 1998. Lotteries accounted for 52 per cent of this in 1998, casinos 29 per cent and horse racing 7 per cent (NGICS Overview (1999): 72-75). In 1996 the gross revenues of all the organisations providing gambling or gaming opportunities in the US were estimated at$46.07 bn. or just under about 0.09 per cent of all private consumption expenditures for that year