What can(not) be measured with ton-scale dark matter direct detection experiments

Direct searches for dark matter have prompted in recent years a great deal of excitement within the astroparticle physics community, but the compatibility between signal claims and null results of different experiments is far from being a settled issue. In this context, we study here the prospects for constraining the dark matter parameter space with the next generation of ton-scale detectors. Using realistic experimental capabilities for a wide range of targets (including fluorine, sodium, argon, germanium, iodine and xenon), the role of target complementarity is analysed in detail while including the impact of astrophysical uncertainties in a self-consistent manner. We show explicitly that a multi-target signal in future direct detection facilities can determine the sign of the ratio of scalar couplings $f_n/f_p$, but not its scale. This implies that the scalar-proton cross-section is left essentially unconstrained if the assumption $f_p\sim f_n$ is relaxed. Instead, we find that both the axial-proton cross-section and the ratio of axial couplings $a_n/a_p$ can be measured with fair accuracy if multi-ton instruments using sodium and iodine will eventually come online. Moreover, it turns out that future direct detection data can easily discriminate between elastic and inelastic scatterings. Finally, we argue that, with weak assumptions regarding the WIMP couplings and the astrophysics, only the dark matter mass and the inelastic parameter (i.e. mass splitting) may be inferred from the recoil spectra -- specifically, we anticipate an accuracy of tens of GeV (tens of keV) in the measurement of the dark matter mass (inelastic parameter).Comment: 31 pages, 7 figures, 7 table

The Spectral Action Principle in Noncommutative Geometry and the Superstring

A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma model and derive an expression for the generalized loop space Dirac operator, in presence of a general background, using canonical quantization. The spectral action principle is then used to determine a spectral action valid for the fluctuations of the string modes.Comment: Latex file, 13 pages. Correction to equation 47, which should read Tr| |^2 and not |Tr |^2. Final form to appear in Physics Letters

Conditions for Successful Extended Inflation

We investigate, in a model-independent way, the conditions required to obtain a satisfactory model of extended inflation in which inflation is brought to an end by a first-order phase transition. The constraints are that the correct present strength of the gravitational coupling is obtained, that the present theory of gravity is satisfactorily close to general relativity, that the perturbation spectra from inflation are compatible with large scale structure observations and that the bubble spectrum produced at the phase transition doesn't conflict with the observed level of microwave background anisotropies. We demonstrate that these constraints can be summarized in terms of the behaviour in the conformally related Einstein frame, and can be compactly illustrated graphically. We confirm the failure of existing models including the original extended inflation model, and construct models, albeit rather contrived ones, which satisfy all existing constraints.Comment: 8 pages RevTeX file with one figure incorporated (uses RevTeX and epsf). Also available by e-mailing ARL, or by WWW at http://star-www.maps.susx.ac.uk/papers/infcos_papers.html; Revised to include extra references, results unchanged, to appear Phys Rev

Models of Dynamical Supersymmetry Breaking with Gauged U(1)RU(1)_R Symmetry

We present simple models of dynamical supersymmetry breaking with gauged U(1)_R symmetry. The minimal supersymmetric standard model and supersymmetric SU(5) GUT are considered as the visible sector. The anomaly cancellation conditions for U(1)_R are investigated in detail and simple solutions of the R-charge assignments are found. We show that this scenario of dynamical supersymmetry breaking is phenomenologically viable with the gravitino mass of order 1 TeV or 10 TeV.Comment: 15 pages, uses REVTEX macro, No figure

Pure type I supergravity and DE(10)

We establish a dynamical equivalence between the bosonic part of pure type I supergravity in D=10 and a D=1 non-linear sigma-model on the Kac-Moody coset space DE(10)/K(DE(10)) if both theories are suitably truncated. To this end we make use of a decomposition of DE(10) under its regular SO(9,9) subgroup. Our analysis also deals partly with the fermionic fields of the supergravity theory and we define corresponding representations of the generalized spatial Lorentz group K(DE(10)).Comment: 28 page

Anomaly-Free Gauged R-Symmetry in Local Supersymmetry

We discuss local \R-symmetry as a potentially powerful new model building tool. We first review and clarify that a $U(1)$ \R-symmetry can only be gauged in local and not in global supersymmetry. We determine the anomaly-cancellation conditions for the gauged \R-symmetry. For the standard superpotential these equations have {\it no} solution, independently of how many Standard Model singlets are added to the model. There is also no solution when we increase the number of families and the number of pairs of Higgs doublets. When the Green-Schwarz mechanism is employed to cancel the anomalies, solutions only exist for a large number of singlets. We find many anomaly-free family-independent models with an extra $SU(3)_c$ octet chiral superfield. We consider in detail the conditions for an anomaly-free {\it family dependent} $U(1)_R$ and find solutions with one, two, three and four extra singlets. Only with three and four extra singlets do we naturally obtain sfermion masses of order the weak-scale. For these solutions we consider the spontaneous breaking of supersymmetry and the $R$-symmetry in the context of local supersymmetry. In general the $U(1)_R$ gauge group is broken at or close to the Planck scale. We consider the effects of the \R-symmetry on baryon- and lepton-number violation in supersymmetry. There is no logical connection between a conserved \R-symmetry and conserved \R-parity. For conserved \R-symmetry we have models for all possibilities of conserved or broken \R-parity. Most models predict dominant effects which could be observed at HERA.Comment: 29 pages, latex, including 3 tables. Final version accepted for publication in NPB. Slight revision of supersymmetry breaking and dropped sub-section on mu problem, which will appear expaned elsewher

Combinatorial Markov chains on linear extensions

We consider generalizations of Schuetzenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other has a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence L=S_n is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is R-trivial and then using Steinberg's extension of Brown's theory for Markov chains on left regular bands to R-trivial monoids.Comment: 35 pages, more examples of promotion, rephrased the main theorems in terms of discrete time Markov chain

Some polynomial solutions for the non-axisymmetric Boussinesq problem

Solutions to the Boussinesq problem for the circular punch without axial symmetry can be obtained from corresponding axisymmetric solutions by parametric differentiation. The method is applied to the problem of the tilted flat punch, originally solved by Green, and to the indentation of a cylindrical surface by a flat circular punch.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42671/1/10659_2004_Article_BF00041668.pd

Bianchi type I space and the stability of inflationary Friedmann-Robertson-Walker space

Stability analysis of the Bianchi type I universe in pure gravity theory is studied in details. We first derive the non-redundant field equation of the system by introducing the generalized Bianchi type I metric. This non-redundant equation reduces to the Friedmann equation in the isotropic limit. It is shown further that any unstable mode of the isotropic perturbation with respect to a de Sitter background is also unstable with respect to anisotropic perturbations. Implications to the choice of physical theories are discussed in details in this paper.Comment: 5 pages, some comment adde

Friedmann Equation and Stability of Inflationary Higher Derivative Gravity

Stability analysis on the De Sitter universe in pure gravity theory is known to be useful in many aspects. We first show how to complete the proof of an earlier argument based on a redundant field equation. It is shown further that the stability condition applies to $k \ne 0$ Friedmann-Robertson-Walker spaces based on the non-redundant Friedmann equation derived from a simple effective Lagrangian. We show how to derive this expression for the Friedmann equation of pure gravity theory. This expression is also generalized to include scalar field interactions.Comment: Revtex, 6 pages, Add two more references, some typos correcte