Mass Determination in SUSY-like Events with Missing Energy

We describe a kinematic method which is capable of determining the overall mass scale in SUSY-like events at a hadron collider with two missing (dark matter) particles. We focus on the kinematic topology in which a pair of identical particles is produced with each decaying to two leptons and an invisible particle (schematically, $pp\to YY+jets$ followed by each $Y$ decaying via $Y\to \ell X\to \ell\ell'N$ where $N$ is invisible). This topology arises in many SUSY processes such as squark and gluino production and decay, not to mention t\anti t di-lepton decays. In the example where the final state leptons are all muons, our errors on the masses of the particles $Y$, $X$ and $N$ in the decay chain range from 4 GeV for 2000 events after cuts to 13 GeV for 400 events after cuts. Errors for mass differences are much smaller. Our ability to determine masses comes from considering all the kinematic information in the event, including the missing momentum, in conjunction with the quadratic constraints that arise from the $Y$, $X$ and $N$ mass-shell conditions. Realistic missing momentum and lepton momenta uncertainties are included in the analysis.Comment: 41 pages, 14 figures, various clarifications and expanded discussion included in revised version that conforms to the version to be publishe

Dark matter allowed scenarios for Yukawa-unified SO(10) SUSY GUTs

Simple supersymmetric grand unified models based on the gauge group SO(10) require --in addition to gauge and matter unification-- the unification of t-b-\tau Yukawa couplings. Yukawa unification, however, only occurs for very special values of the soft SUSY breaking parameters. We perform a search using a Markov Chain Monte Carlo (MCMC) technique to investigate model parameters and sparticle mass spectra which occur in Yukawa-unified SUSY models, where we also require the relic density of neutralino dark matter to saturate the WMAP-measured abundance. We find the spectrum is characterizd by three mass scales: first/second generation scalars in the multi-TeV range, third generation scalars in the TeV range, and gauginos in the \sim 100 GeV range. Most solutions give far too high a relic abundance of neutralino dark matter. The dark matter discrepancy can be rectified by 1. allowing for neutralino decay to axino plus photon, 2. imposing gaugino mass non-universality or 3. imposing generational non-universality. In addition, the MCMC approach finds 4. a compromise solution where scalar masses are not too heavy, and where neutralino annihilation occurs via the light Higgs h resonance. By imposing weak scale Higgs soft term boundary conditions, we are also able to generate 5. low \mu, m_A solutions with neutralino annihilation via a light A resonance, though these solutions seem to be excluded by CDF/D0 measurements of the B_s\to \mu^+\mu^- branching fraction. Based on the dual requirements of Yukawa coupling unification and dark matter relic density, we predict new physics signals at the LHC from pair production of 350--450 GeV gluinos. The events are characterized by very high b-jet multiplicity and a dilepton mass edge around mz2-mz1 \sim 50-75 GeV.Comment: 35 pages with 21 eps figure

The Law of Society: Governance Through Contract

This paper focuses on contract law as a central field in contemporary regulatory practice. In recent years, governance by contract has emerged as the central concept in the context of domestic privatization, domestic and transnational commercial relations and law-and-development projects. Meanwhile, as a result of the neo-formalist attack on contract law, governance of contract through contract adjudication, consumer protection law and judicial intervention into private law relations has come under severe pressure. Building on early historical critique of the formalist foundations of an allegedly private law of the market, the paper assesses the current justifications for contractual governance and posits that only an expanded legal realist perspective can adequately explain the complex nature of contractual agreements in contemporary practice. The paper argues for an understanding of contracts as complex societal arrangements that visibilize and negotiate conflicting rationalities and interests. Institutionally, contractual governance has been unfolding in a complex, historically grown and ideologically continually contested regulatory field. Governance through contract, then, denotes a wide field of conflicting concepts, ideas and symbols, that are themselves deeply entrenched in theories of society, market and the state. From this perspective, we are well advised to study contracts in their socio-economic, historical and cultural context. A careful reading of scholars such as Henry Sumner Maine, Morris Cohen, Robert Hale, Karl Llewellyn, Stewart Macaulay and Ian Macneil offers a deeper understanding of the institutional and normative dimensions of contractual governance. Their analysis is particularly helpful in assessing currently ongoing shifts away from a welfare state based regulation (governance) of contractual relations. Such shifts are occurring on two levels. First, they take place against the backdrop of a neo-liberal critique of government interference into allegedly private relations. Secondly, the increasingly influential return to formalism in contract law, which privileges a functionalist, purportedly technical and autonomous design and execution of contractual agreements over the view of regulated contracts, is linked to a particular concept of sovereignty. The ensuing revival of freedom of contract occurs in remarkable neglect of the experiences of welfare state adjudication of private law adjudication and a continuing contestation of the political in private relationships. The paper takes up the Legal Realists\u27 search for the \u27basis of contract\u27, but seeks to redirect the focus from the traditional perspective on state vs. market to a disembedded understanding of contractual governance as delineating multipolar and multirational regulatory regimes. Where Globalization has led to a fragmentation, disembeddedness and transnationalization of contexts and, thus, has been challenging traditional understanding of embeddedness, the task should no longer be to try applying a largely nation-state oriented Legal Realist perspective and critique to the sphere of contemporary contractual governance, but - rather - to translate its aims into a more reflexive set of instruments of legal critique. Even if Globalization has led to a dramatic denationalization of many regulatory fields and functions, it is still not clear, whether and how Globalization replaces, complements or aggravates transformations of societal governance, with and through contract

Collider and Dark Matter Phenomenology of Models with Mirage Unification

We examine supersymmetric models with mixed modulus-anomaly mediated SUSY breaking (MM-AMSB) soft terms which get comparable contributions to SUSY breaking from moduli-mediation and anomaly-mediation. The apparent (mirage) unification of soft SUSY breaking terms at Q=mu_mir not associated with any physical threshold is the hallmark of this scenario. The MM-AMSB structure of soft terms arises in models of string compactification with fluxes, where the addition of an anti-brane leads to an uplifting potential and a de Sitter universe, as first constructed by Kachru {\it et al.}. The phenomenology mainly depends on the relative strength of moduli- and anomaly-mediated SUSY breaking contributions, and on the Higgs and matter field modular weights, which are determined by the location of these fields in the extra dimensions. We delineate the allowed parameter space for a low and high value of tan(beta), for a wide range of modular weight choices. We calculate the neutralino relic density and display the WMAP-allowed regions. We show the reach of the CERN LHC and of the International Linear Collider. We discuss aspects of MM-AMSB models for Tevatron, LHC and ILC searches, muon g-2 and b->s \gamma branching fraction. We also calculate direct and indirect dark matter detection rates, and show that almost all WMAP-allowed models should be accessible to a ton-scale noble gas detector. Finally, we comment on the potential of colliders to measure the mirage unification scale and modular weights in the difficult case where mu_mir>>M_GUT.Comment: 34 pages plus 42 EPS figures; version with high resolution figures is at http://www.hep.fsu.edu/~bae

Mixed Higgsino Dark Matter from a Reduced SU(3) Gaugino Mass: Consequences for Dark Matter and Collider Searches

In gravity-mediated SUSY breaking models with non-universal gaugino masses, lowering the SU(3) gaugino mass |M_3| leads to a reduction in the squark and gluino masses. Lower third generation squark masses, in turn, diminish the effect of a large top quark Yukawa coupling in the running of the higgs mass parameter m_{H_u}^2, leading to a reduction in the magnitude of the superpotential mu parameter (relative to M_1 and M_2). A low | mu | parameter gives rise to mixed higgsino dark matter (MHDM), which can efficiently annihilate in the early universe to give a dark matter relic density in accord with WMAP measurements. We explore the phenomenology of the low |M_3| scenario, and find for the case of MHDM increased rates for direct and indirect detection of neutralino dark matter relative to the mSUGRA model. The sparticle mass spectrum is characterized by relatively light gluinos, frequently with m(gl)<<m(sq). If scalar masses are large, then gluinos can be very light, with gl->Z_i+g loop decays dominating the gluino branching fraction. Top squarks can be much lighter than sbottom and first/second generation squarks. The presence of low mass higgsino-like charginos and neutralinos is expected at the CERN LHC. The small m(Z2)-m(Z1) mass gap should give rise to a visible opposite-sign/same flavor dilepton mass edge. At a TeV scale linear e^+e^- collider, the region of MHDM will mean that the entire spectrum of charginos and neutralinos are amongst the lightest sparticles, and are most likely to be produced at observable rates, allowing for a complete reconstruction of the gaugino-higgsino sector.Comment: 35 pages, including 26 EPS figure

Using kinematic boundary lines for particle mass measurements and disambiguation in SUSY-like events with missing energy

We revisit the method of kinematical endpoints for particle mass determination, applied to the popular SUSY decay chain squark -> neutralino -> slepton -> LSP. 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.Comment: 47 pages, 19 figure