Bounded Quantification Is Undecidable

AbstractF≤ is a typed λ-calculus with subtyping and bounded second-order polymorphism. First introduced by Cardelli and Wegner, it has been widely studied as a core calculus for type systems with subtyping. We use a reduction from the halting problem for two-counter Turing machines to show that the subtyping and typing relations of F≤ are undecidable

Regular Expression Subtyping for XML Query and Update Languages

XML database query languages such as XQuery employ regular expression types with structural subtyping. Subtyping systems typically have two presentations, which should be equivalent: a declarative version in which the subsumption rule may be used anywhere, and an algorithmic version in which the use of subsumption is limited in order to make typechecking syntax-directed and decidable. However, the XQuery standard type system circumvents this issue by using imprecise typing rules for iteration constructs and defining only algorithmic typechecking, and another extant proposal provides more precise types for iteration constructs but ignores subtyping. In this paper, we consider a core XQuery-like language with a subsumption rule and prove the completeness of algorithmic typechecking; this is straightforward for XQuery proper but requires some care in the presence of more precise iteration typing disciplines. We extend this result to an XML update language we have introduced in earlier work.Comment: ESOP 2008. Companion technical report with proof

Gaugino and Scalar Masses in the Landscape

In this letter we demonstrate the genericity of suppressed gaugino masses M_a \sim m_{3/2}/ln(M_P/m_{3/2}) in the IIB string landscape, by showing that this relation holds for D7-brane gauginos whenever the associated modulus is stabilised by nonperturbative effects. Although m_{3/2} and M_a take many different values across the landscape, the above small mass hierarchy is maintained. We show that it is valid for models with an arbitrary number of moduli and applies to both the KKLT and exponentially large volume approaches to Kahler moduli stabilisation. In the latter case we explicitly calculate gaugino and moduli masses for compactifications on the two-modulus Calabi-Yau P^4_[1,1,1,6,9]. In the large-volume scenario we also show that soft scalar masses are approximately universal with m_i^2 \sim m_{3/2}^2 (1 + \epsilon_i), with the non-universality parametrised by \epsilon_i \sim 1/ln (M_P/m_{3/2})^2 \sim 1/1000. We briefly discuss possible phenomenological implications of our results.Comment: 15 pages, JHEP style; v2. reference adde

SOFTSUSY: a program for calculating supersymmetric spectra

SOFTSUSY is a program which accurately calculates the spectrum of superparticles in the CP-conserving Minimal Supersymmetric Standard Model (MSSM), with a full flavour mixing structure. The program solves the renormalisation group equations with theoretical constraints on soft supersymmetry breaking terms provided by the user. Weak-scale gauge coupling and fermion mass data (including one-loop finite MSSM corrections) are used as a boundary condition, as well as successful radiative electroweak symmetry breaking. The program can also calculate a measure of fine-tuning. The program structure has been designed to easily generalise to extensions of the MSSM. This article serves as a self-contained guide to prospective users, and indicates the conventions and approximations used.Comment: Updated for SOFTSUSY3.3.3. Can be downloaded from http://projects.hepforge.org/softsusy/ Further updated versions of the manual will be distributed with the cod

Theoretical uncertainties in sparticle mass predictions from computational tools

We estimate the current theoretical uncertainty in sparticle mass predictions by comparing several state-of-the-art computations within the minimal supersymmetric standard model (MSSM). We find that the theoretical uncertainty is comparable to the expected statistical errors from the Large Hadron Collider (LHC), and significantly larger than those expected from a future e+e- Linear Collider (LC). We quantify the theoretical uncertainty on relevant sparticle observables for both LHC and LC, and show that the value of the error is significantly dependent upon the supersymmetry (SUSY) breaking parameters. We also present the theoretical uncertainty induced in fundamental-scale SUSY breaking parameters when they are fitted from LHC measurements. Two regions of the SUSY parameter space where accurate predictions are particularly difficult are examined in detail: the large tan(beta) and focus point regimes.Comment: 22 pages, 6 figures; comment added pointing out that 2-loop QCD corrections to mt are incorrect in some of the programs investigated. We give the correct formul

The Recursive Record Semantics of Objects Revisited

In a call-by-value language, representing objects as recursive records requires using an unsafe fixpoint. We design, for a core language including extensible records, a type system which rules out unsafe recursion and still supports the reconstruction of a principal type. We illustrate the expressive power of this language with respect to object-oriented programming by introducing a sub-language for «mixin-based» programming

Collider and Dark Matter Searches in Models with Mixed Modulus-Anomaly Mediated SUSY Breaking

We investigate the phenomenology of supersymmetric models where moduli fields and the Weyl anomaly make comparable contributions to SUSY breaking effects in the observable sector of fields. This mixed modulus-anomaly mediated supersymmetry breaking (MM-AMSB) scenario is inspired by models of string compactification with fluxes, which have been shown to yield a de Sitter vacuum (as in the recent construction by Kachru {\it et al}). The phenomenology depends on the so-called modular weights which, in turn, depend on the location of various fields in the extra dimensions. We find that the model with zero modular weights gives mass spectra characterized by very light top squarks and/or tau sleptons, or where M_1\sim -M_2 so that the bino and wino are approximately degenerate. The top squark mass can be in the range required by successful electroweak baryogenesis. The measured relic density of cold dark matter can be obtained via top squark co-annihilation at low \tan\beta, tau slepton co-annihilation at large \tan\beta or via bino-wino coannihilation. Then, we typically find low rates for direct and indirect detection of neutralino dark matter. However, essentially all the WMAP-allowed parameter space can be probed by experiments at the CERN LHC, while significant portions may also be explored at an e^+e^- collider with \sqrt{s}=0.5--1 TeV. We also investigate a case with non-zero modular weights. In this case, co-annihilation, A-funnel annihilation and bulk annihilation of neutralinos are all allowed. Results for future colliders are qualitatively similar, but prospects for indirect dark matter searches via gamma rays and anti-particles are somewhat better.Comment: 38 pages including 22 EPS figures; latest version posted to conform with published versio

Reach of the Fermilab Tevatron for minimal supergravity in the region of large scalar masses

The reach of the Fermilab Tevatron for supersymmetric matter has been calculated in the framework of the minimal supergravity model in the clean trilepton channel. Previous analyses of this channel were restricted to scalar masses m_0<= 1 TeV. We extend the analysis to large values of scalar masses m_0\sim 3.5 TeV. This includes the compelling hyperbolic branch/focus point (HB/FP) region, where the superpotential \mu parameter becomes small. In this region, assuming a 5\sigma (3\sigma) signal with 10 (25) fb^{-1} of integrated luminosity, the Tevatron reach in the trilepton channel extends up to m_{1/2}\sim 190 (270) GeV independent of \tan\beta . This corresponds to a reach in terms of the gluino mass of m_{\tg}\sim 575 (750) GeV.Comment: 11 page latex file including 6 EPS figures; several typos corrected and references adde