Fast Sorting of Weyl Sequences Using Comparisons

An algorithm is given which makes only $O(\log n)$ comparisons, and which will determine the ordering of the uniformly distributed (pseudo random) Weyl sequences given by $\{ (k\alpha )\bmod 1:1 \leqq k \leqq n\}$, where $\alpha$ is an unspecified irrational number. This result is shown to be best possible in the sense that no algorithm can perform the same task with fewer than $\Omega (\log n)$ comparisons

Precision tests of the MSSM

We present the results of a first global fit to the electroweak observables in the MSSM. The best fit selects either very low or very large values of ~$\tan\beta$ ~and, correspondingly, chargino (higgsino--like) and stop or the ~$CP-$odd Higgs boson are within the reach of LEP 2. Moreover, the best fit gives ~ $\alpha_s(M_Z)=0.118^{+0.005}_{-0.010}$, ~which is lower than the one obtained from the SM fits. The overall fit is excellent ~ ($\chi^2=7.2$ ~for 15 d.o.f. as compared to ~$\chi^2=11$ ~in the SM). Those results follow from the fact that in the MSSM one can increase the value of ~ $R_b\equiv\Gamma_{Z^0\to\bar bb}/\Gamma_{Z^0\to hadrons}$ ~ {\it without} modyfying the SM predictions for other observables.Comment: 10 pages, LaTEX, 7 figures (not included) may be obtained from [email protected] upon request. Modified version of the plenary talk given by S. Pokorski at the ``Beyond the Standard Model IV'', Lake Tahoe, CA, December 199

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

Controls on the distribution of cosmogenic 10Be across shore platforms

Quantifying rates of erosion on cliffed coasts across a range of timescales is vital for understanding the drivers and processes of coastal change and for assessing risks posed by future cliff retreat. Historical records cover at best the last 150 years; Cosmogenic radionuclides, such as 10Be could allow us to look further into past to assess coastal change at millenial timescales. CRNs accumulate in-situ near the Earth surface and have been used extensively to quantify erosion rates, burial dates and surface exposure ages in terrestrial landscapes over the last three decades. More recently, applications in rocky coast settings have quantified the timing of mass wasting events, determined long-term-averaged rates of cliff retreat and revealed the exposure history of shore platforms. In this contribution, we developed and explored a numerical model for the accumulation of 10Be on eroding shore platforms. In a series of numerical experiments, we investigated the influence of topographic and water shielding, dynamic platform erosion processes, the presence and variation in beach cover, and heterogeneous distribution of erosion on the distribution of 10Be across shore platforms. Results demonstrate that, taking into account relative sea level change and tides, the concentration of 10Be is sensitive to rates of cliff retreat. Factors such as topographic shielding and beach cover, act to reduce 10Be concentrations on the platform, and may result in overestimation of cliff retreat rates if not accounted for. The shape of the distribution of 10Be across a shore platform can potentially reveal whether cliff retreat rates are declining or accelerating through time. Measurement of 10Be in shore platforms has great potential to allow us to quantify long-term rates of cliff retreat and platform erosion

Jet Investigations Using the Radial Moment

We define the radial moment, , for jets produced in hadron-hadron collisions. It can be used as a tool for studying, as a function of the jet transverse energy and pseudorapidity, radiation within the jet and the quality of a perturbative description of the jet shape. We also discuss how non-perturbative corrections to the jet transverse energy affect .Comment: 14 pages, LaTeX, 6 figure

Precision Tests of the MSSM

The LEP data and the measurement of $M_W$ confirm the electro weak symmetry breaking by the Higgs mechanism with (2--3)\% accuracy. For the Higgs boson mass, fits to the present data (without the SLD result) give $M_h=121^{+207}_{-118}$ GeV and $M_h<800$ GeV at 95\% C.L. We analyze those fits from the point of view of the impact of different measurements on the final result for $M_h$. All the relevant observables can be grouped into two categories: those which correlate $M_h$ with $m_t$ and those which constrain the range of $m_t$. Using this classification we discuss potential improvements in the limits on $M_h$, anticipating improvements in the precision of the data. Also the sensitivity of the limits on $M_h$ to the value of $\alpha_s(M_Z)$ is discussed in a toy model which reproduces all the results of the SM but the $Z^0\rightarrow\bar bb$ width is increased by hand so that $R_b=0.22$ and, in consequence, the fitted value of $\alpha_s(M_Z)\approx0.11$ (qualitatively similar situation occurs in the Minimal Supersymmetric Standard Model with light chargino and right--handed top squark).Comment: 15 pages, LaTeX; 9 postscript figures in a separate uuencoded Z-compressed file. New SLD result included in the fit. Two figures adde

Supercollider Signatures of Supergravity Models with Yukawa Unification

We study the predictions of the simplest SU(5) grand unified model within the framework of minimal supergravity, including constraints from the radiative breaking of electroweak symmetry. As a consequence of the unification of the $b$-quark and $\tau$-lepton Yukawa couplings, the top quark mass is predicted to be close to its fixed point value. We delineate the regions of the supergravity parameter space allowed by constraints from the non-observation of proton decay and from the requirement that the LSP does not overclose the universe. These constraints lead to a definite pattern of sparticle masses: the feature unique to Yukawa unified models is that some of the third generation squarks are much lighter than those of the first two generations. Despite the fact that all sparticle masses and mixings are determined by just four SUSY parameters at the GUT scale (in addition to $m_t$), we find that the signals for sparticle production can vary substantially over the allowed parameter space. We identify six representative scenarios and study the signals from sparticle production at the LHC. We find that by studying the signal in various channels, these scenarios may be distinguished from one another, and also from usually studied ``minimal models'' where squarks and sleptons are taken to be degenerate. In particular, our studies allow us to infer that some third generation squarks are lighter than other squarks---a feature that could provide the first direct evidence of supergravity grand unification.Comment: 28 pages Revtex files with 5 PS figures available from [email protected], Preprint nos. FSU-HEP-940311, KEK-TH-392, MAD/PH/825, UH-511-785-9

Next to Leading Order Semi-inclusive Spin Asymmetries

We have computed semi-inclusive spin asymmetries for proton and deuteron targets including next to leading order (NLO) QCD corrections and contributions coming from the target fragmentation region. These corrections have been estimated using NLO fragmentation functions, parton distributions and also a model for spin dependent fracture functions which is proposed here. We have found that NLO corrections are small but non-negligible in a scheme where gluons are polarised and that our estimate for target fragmentation effects does not modify significantly charged asymmetries but affects the so called difference asymmetries.Comment: Latex, 14 pages, 6 figures in 4 Postcript file

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

Partons and Jets at the LHC

I review some issues related to short distance QCD and its relation to the experimental program of the Large Hadron Collider (LHC) now under construction in Geneva.Comment: Talk at the conference QCD2002 at IIT Kanpur, India, November 2002. Ten pages with 12 figure