On the rigidity of back-to-back top quark pairs in e^+e^- annihilation

We consider the effect of gluon radiation on the energy of top/antitop quarks and on the anticollinearity of top-antitop quark pairs produced in $e^+e^-$ annihilation. Our results are presented in terms of the $E_q$-dependence of the $t\bar tg$ cross section and the dependence on the cosine of the opening angle $\theta_{12}$ between top and antitop for a center of mass energy of $\sqrt{q^2}=500 GeV$. We then go on to determine mean values for the top quark's energy as well as its longitudinal and transverse projections, and for the deviation of $\sin\theta_{12}$ and $\cos\theta_{12}$ from the anticollinearity limits $\sin\theta_{12}=0$ and $\cos\theta_{12}=-1$. For a center of mass energy of $500 GeV$ we obtain $=248.22 GeV$, $=247.24 GeV$ and $=4.70 GeV$. Thus, at this energy gluon radiation causes a total average energy loss of 0.71% of the top quark's energy. The average energy loss in the longitudinal direction is 1.06% and the average energy gain in the transverse direction is 1.88%. These percentage figures go up to 3.77%, 5.19% and 6.06%, respectively, at 1000\GeV. For the mean of the acollinearity angle $\bar\theta_{12}=180^0-\theta_{12}$ we obtain $=1.25^0$ at $500 GeV$, the value of which goes up to $4.62^0$ at $1000 GeV$. From an analysis of the transverse momentum of the top we find that the mean transverse momentum of the top stays close to the mean total momentum of the gluon in the energy range from threshold to $1000 GeV$ showing that the gluon momentum has a large mean transverse component in this energy range.Comment: 17 pages, 7 postscript figures, to appear in Nucl. Phys.

What if Supersymmetry Breaking Unifies beyond the GUT Scale?

We study models in which soft supersymmetry-breaking parameters of the MSSM become universal at some unification scale, $M_{in}$, above the GUT scale, \mgut. We assume that the scalar masses and gaugino masses have common values, $m_0$ and $m_{1/2}$ respectively, at $M_{in}$. We use the renormalization-group equations of the minimal supersymmetric SU(5) GUT to evaluate their evolutions down to \mgut, studying their dependences on the unknown parameters of the SU(5) superpotential. After displaying some generic examples of the evolutions of the soft supersymmetry-breaking parameters, we discuss the effects on physical sparticle masses in some specific examples. We note, for example, that near-degeneracy between the lightest neutralino and the lighter stau is progressively disfavoured as $M_{in}$ increases. This has the consequence, as we show in $(m_{1/2}, m_0)$ planes for several different values of $\tan \beta$, that the stau coannihilation region shrinks as $M_{in}$ increases, and we delineate the regions of the $(M_{in}, \tan \beta)$ plane where it is absent altogether. Moreover, as $M_{in}$ increases, the focus-point region recedes to larger values of $m_0$ for any fixed $\tan \beta$ and $m_{1/2}$. We conclude that the regions of the $(m_{1/2}, m_0)$ plane that are commonly favoured in phenomenological analyses tend to disappear at large $M_{in}$.Comment: 24 pages with 11 eps figures; references added, some figures corrected, discussion extended and figure added; version to appear in EPJ

Bayesian approach and Naturalness in MSSM analyses for the LHC

The start of LHC has motivated an effort to determine the relative probability of the different regions of the MSSM parameter space, taking into account the present, theoretical and experimental, wisdom about the model. Since the present experimental data are not powerful enough to select a small region of the MSSM parameter space, the choice of a judicious prior probability for the parameters becomes most relevant. Previous studies have proposed theoretical priors that incorporate some (conventional) measure of the fine-tuning, to penalize unnatural possibilities. However, we show that such penalization arises from the Bayesian analysis itself (with no ad hoc assumptions), upon the marginalization of the mu-parameter. Furthermore the resulting effective prior contains precisely the Barbieri-Giudice measure, which is very satisfactory. On the other hand we carry on a rigorous treatment of the Yukawa couplings, showing in particular that the usual practice of taking the Yukawas "as required", approximately corresponds to taking logarithmically flat priors in the Yukawa couplings. Finally, we use an efficient set of variables to scan the MSSM parameter space, trading in particular B by tan beta, giving the effective prior in the new parameters. Beside the numerical results, we give accurate analytic expressions for the effective priors in all cases. Whatever experimental information one may use in the future, it is to be weighted by the Bayesian factors worked out here.Comment: LaTeX, 19 pages, 3 figure

Higgs Boson Bounds in Three and Four Generation Scenarios

In light of recent experimental results, we present updated bounds on the lightest Higgs boson mass in the Standard Model (SM) and in the Minimal Supersymmetric extension of the Standard Model (MSSM). The vacuum stability lower bound on the pure SM Higgs boson mass when the SM is taken to be valid up to the Planck scale lies above the MSSM lightest Higgs boson mass upper bound for a large amount of SUSY parameter space. If the lightest Higgs boson is detected with a mass M_{H} < 134 GeV (150 GeV) for a top quark mass M_{top} = 172 GeV (179 GeV), it may indicate the existence of a fourth generation of fermions. The region of inconsistency is removed and the MSSM is salvagable for such values of M_{H} if one postulates the existence of a fourth generation of leptons and quarks with isodoublet degenerate masses M_{L} and M_{Q} such that 60 GeV 170 GeV.Comment: 7 pages, 4 figures. To be published in Physical Review

Revisiting the Higgs Mass and Dark Matter in the CMSSM

Taking into account the available accelerator and astrophysical constraints, the mass of the lightest neutral Higgs boson h in the minimal supersymmetric extension of the Standard Model with universal soft supersymmetry-breaking masses (CMSSM) has been estimated to lie between 114 and ~ 130 GeV. Recent data from ATLAS and CMS hint that m_h ~ 125 GeV, though m_h ~ 119 GeV may still be a possibility. Here we study the consequences for the parameters of the CMSSM and direct dark matter detection if the Higgs hint is confirmed, focusing on the strips in the (m_1/2, m_0) planes for different tan beta and A_0 where the relic density of the lightest neutralino chi falls within the range of the cosmological cold dark matter density allowed by WMAP and other experiments. We find that if m_h ~ 125 GeV focus-point strips would be disfavoured, as would the low-tan beta stau-chi and stop -chi coannihilation strips, whereas the stau-chi coannihilation strip at large tan beta and A_0 > 0 would be favoured, together with its extension to a funnel where rapid annihilation via direct-channel H/A poles dominates. On the other hand, if m_h ~ 119 GeV more options would be open. We give parametrizations of WMAP strips with large tan beta and fixed A_0/m_0 > 0 that include portions compatible with m_h = 125 GeV, and present predictions for spin-independent elastic dark matter scattering along these strips. These are generally low for models compatible with m_h = 125 GeV, whereas the XENON100 experiment already excludes some portions of strips where m_h is smaller.Comment: 24 pages, 9 figure

Physics in the Real Universe: Time and Spacetime

The Block Universe idea, representing spacetime as a fixed whole, suggests the flow of time is an illusion: the entire universe just is, with no special meaning attached to the present time. This view is however based on time-reversible microphysical laws and does not represent macro-physical behaviour and the development of emergent complex systems, including life, which do indeed exist in the real universe. When these are taken into account, the unchanging block universe view of spacetime is best replaced by an evolving block universe which extends as time evolves, with the potential of the future continually becoming the certainty of the past. However this time evolution is not related to any preferred surfaces in spacetime; rather it is associated with the evolution of proper time along families of world linesComment: 28 pages, including 9 Figures. Major revision in response to referee comment

Can a wormhole generate electromagnetic field?

We have considered the possibility of a slowly rotating wormhole surrounded by a cloud of charged particles. Due to slow rotation of the wormhole, the charged particles are dragged thereby producing an electromagnetic field. We have determined the strength of this electromagnetic field and the corresponding flux of radiation.Comment: 9 pages, typos fixe

Model Independent Properties and Cosmological Implications of the Dilaton and Moduli Sectors of 4-d Strings

We show that if there is a realistic 4-d string, the dilaton and moduli supermultiplets will generically acquire a small mass O(m_{3/2}), providing the only vacuum-independent evidence of low-energy physics in string theory beyond the supersymmetric standard model. The only assumptions behind this result are (i) softly broken supersymmetry at low energies with zero cosmological constant, (ii) these particles interact with gravitational strength and the scalar components have a flat potential in perturbation theory, which are well-known properties of string theories. (iii) They acquire a $vev$ of the order of the Planck scale (as required for the correct value of the gauge coupling constants and the expected compactification scale) after supersymmetry gets broken. We explore the cosmological implications of these particles. Similar to the gravitino, the fermionic states may overclose the Universe if they are stable or destroy nucleosynthesis if they decay unless their masses belong to a certain range or inflation dilutes them. For the scalar states it is known that the problem cannot be entirely solved by inflation, since oscillations around the minimum of the potential can lead to a huge entropy generation at late times. We discus some possible ways to alleviate this entropy problem, that favour low-temperature baryogenesis, and also comment on the possible role of these particles as dark matter candidates or as sources of the baryon asymmetry through their decay.Comment: 15 pages,CERN-TH.6958/93,NEIP-93-006, IEM-FT-75/93, Late

Constrained Supersymmetric Flipped SU(5) GUT Phenomenology

We explore the phenomenology of the minimal supersymmetric flipped SU(5) GUT model (CFSU(5)), whose soft supersymmetry-breaking (SSB) mass parameters are constrained to be universal at some input scale, $M_{in}$, above the GUT scale, $M_{GUT}$. We analyze the parameter space of CFSU(5) assuming that the lightest supersymmetric particle (LSP) provides the cosmological cold dark matter, paying careful attention to the matching of parameters at the GUT scale. We first display some specific examples of the evolutions of the SSB parameters that exhibit some generic features. Specifically, we note that the relationship between the masses of the lightest neutralino and the lighter stau is sensitive to $M_{in}$, as is the relationship between the neutralino mass and the masses of the heavier Higgs bosons. For these reasons, prominent features in generic $(m_{1/2}, m_0)$ planes such as coannihilation strips and rapid-annihilation funnels are also sensitive to $M_{in}$, as we illustrate for several cases with tan(beta)=10 and 55. However, these features do not necessarily disappear at large $M_{in}$, unlike the case in the minimal conventional SU(5) GUT. Our results are relatively insensitive to neutrino masses.Comment: 23 pages, 8 figures; (v2) added explanations and corrected typos, version to appear in EPJ

Kernel Bounds for Structural Parameterizations of Pathwidth

Assuming the AND-distillation conjecture, the Pathwidth problem of determining whether a given graph G has pathwidth at most k admits no polynomial kernelization with respect to k. The present work studies the existence of polynomial kernels for Pathwidth with respect to other, structural, parameters. Our main result is that, unless NP is in coNP/poly, Pathwidth admits no polynomial kernelization even when parameterized by the vertex deletion distance to a clique, by giving a cross-composition from Cutwidth. The cross-composition works also for Treewidth, improving over previous lower bounds by the present authors. For Pathwidth, our result rules out polynomial kernels with respect to the distance to various classes of polynomial-time solvable inputs, like interval or cluster graphs. This leads to the question whether there are nontrivial structural parameters for which Pathwidth does admit a polynomial kernelization. To answer this, we give a collection of graph reduction rules that are safe for Pathwidth. We analyze the success of these results and obtain polynomial kernelizations with respect to the following parameters: the size of a vertex cover of the graph, the vertex deletion distance to a graph where each connected component is a star, and the vertex deletion distance to a graph where each connected component has at most c vertices.Comment: This paper contains the proofs omitted from the extended abstract published in the proceedings of Algorithm Theory - SWAT 2012 - 13th Scandinavian Symposium and Workshops, Helsinki, Finland, July 4-6, 201