The Equivalence Theorem in Effective Theories

The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of generating functional for Green functions. This allows one to trace (directly in terms of graphs) the mutual cancelation of different groups of contributions.Comment: 21 pages, 7 figures; v2: Section 4 is modified, plus minor corrections in other sections, version accepted for publication in PR

Weak quenched disorder and criticality: resummation of asymptotic(?) series

In these lectures, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range-correlated random-site disorder, and (iii) random anisotropy. Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of these lectures is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models.Comment: Lectures given at the Second International Pamporovo Workshop on Cooperative Phenomena in Condensed Matter (28th July - 7th August 2001, Pamporovo, Bulgaria). 51 pages, 12 figures, 1 style files include

Early transitions and tertiary enrolment: The cumulative impact of primary and secondary effects on entering university in Germany

Our aim is to assess how the number of working class students entering German universities can effectively be increased. Therefore, we estimate the proportion of students from the working class that would successfully enter university if certain policy interventions were in place to eliminate primary effects (performance differentials between social classes) and/or secondary effects (choice differentials net of performance) at different transition points. We extend previous research by analysing the sequence of transitions between elementary school enrolment and university enrolment and by accounting for the impact that manipulations at earlier transitions have on the performance distribution and size of the student ‘risk-set’ at subsequent transitions. To this end, we develop a novel simulation procedure which also seeks to find viable solutions to the shortcomings in the German data landscape. Our findings show that interventions are most effective if they take place early in the educational career. Neutralizing secondary effects at the transition to upper secondary school proves to be the single most effective means to increase participation rates in tertiary education among working class students. However, this comes at the expense of lower average performance levels. (DIPF/author

Novel Sets of Coupling Expansion Parameters for low-energy pQCD

In quantum theory, physical amplitudes are usually presented in the form of Feynman perturbation series in powers of coupling constant \al . However, it is known that these amplitudes are not regular functions at $\alpha=0 .$ For QCD, we propose new sets of expansion parameters {\bf w}_k(\as) that reflect singularity at \as=0 and should be used instead of powers \as^k. Their explicit form is motivated by the so called Analytic Perturbation Theory. These parameters reveal saturation in a strong coupling case at the level \as^{eff}(\as\gg1)={\bf w}_1(\as\gg 1) \sim 0.5 . They can be used for quanitative analysis of divers low-energy amplitudes. We argue that this new picture with non-power sets of perturbation expansion parameters, as well as the saturation feature, is of a rather general nature.Comment: 8 pages, 1 figure, submitted to Part. Nucl. Phys. Let

An apparatus to search for mirror dark matter via the invisible decay of orthopositronium in vacuum

Mirror matter is a possible dark matter candidate. It is predicted to exist if parity is an unbroken symmetry of the vacuum. The existence of the mirror matter, which in addition to gravity is coupled to our world through photon-mirror photon mixing, would result in orthopositronium (o-Ps) to mirror orthopositronium (o-Ps') oscillations. The experimental signature of this effect is the invisible decay of o-Ps in vacuum. This paper describes the design of the new experiment for a search for the o-Ps -> invisible decay in vacuum with a sensitivity in the branching ratio of Br(o-Ps -> invisible)\simeq 10^{-7}, which is an order of magnitude better than the present limit on this decay mode from the Big Bang Nucleosynthesis. The experiment is based on a high-efficiency pulsed slow positron beam, which is also applicable for other experiments with o-Ps, and (with some modifications) for applied studies. Details of the experimental design and of a new pulsing method, as well as preliminary results on requirements for the pulsed beam components are presented. The effects of o-Ps collisions with the cavity walls as well as the influence of external fields on the o-Ps to o-Ps' oscillation probability are also discussed.Comment: 28 pages, 8 figure

Annihilation Emission from the Galactic Black Hole

Both diffuse high energy gamma-rays and an extended electron-positron annihilation line emission have been observed in the Galactic Center (GC) region. Although X-ray observations indicate that the galactic black hole Sgr A$^*$ is inactive now, we suggest that Sgr A$^*$ can become active when a captured star is tidally disrupted and matter is accreted into the black hole. As a consequence the galactic black hole could be a powerful source of relativistic protons. We are able to explain the current observed diffuse gamma-rays and the very detailed 511 keV annihilation line of secondary positrons by $p-p$ collisions of such protons, with appropriate injection times and energy. Relativistic protons could have been injected into the ambient material if the black hole captured a 50M$_\odot$ star at several tens million years ago. An alternative possibility is that the black hole continues to capture stars with $\sim$1M$_\odot$ every hundred thousand years. Secondary positrons produced by $p-p$ collisions at energies \ga 30 MeV are cooled down to thermal energies by Coulomb collisions, and annihilate in the warm neutral and ionized phases of the interstellar medium with temperatures about several eV, because the annihilation cross-section reaches its maximum at these temperatures. It takes about ten million years for the positrons to cool down to thermal temperatures so they can diffuse into a very large extended region around the Galactic center. A much more recent star capture may be also able to account for recent TeV observations within 10 pc of the galactic center as well as for the unidentified GeV gamma-ray sources found by EGRET at GC. The spectral difference between the GeV flux and the TeV flux could be explained naturally in this model as well.Comment: Accepted by ApJ on March 24, 200

The AGASA/SUGAR Anisotropies and TeV Gamma Rays from the Galactic Center: A Possible Signature of Extremely High-energy Neutrons

Recent analysis of data sets from two extensive air shower cosmic ray detectors shows tantalizing evidence of an anisotropic overabundance of cosmic rays towards the Galactic Center (GC) that ``turns on'' around $10^{18}$ eV. We demonstrate that the anisotropy could be due to neutrons created at the Galactic Center through charge-exchange in proton-proton collisions, where the incident, high energy protons obey an $\sim E^{-2}$ power law associated with acceleration at a strong shock. We show that the normalization supplied by the gamma-ray signal from EGRET GC source 3EG J1746-2851 -- ascribed to pp induced neutral pion decay at GeV energies -- together with a very reasonable spectral index of 2.2, predicts a neutron flux at $\sim 10^{18}$ eV fully consistent with the extremely high energy cosmic ray data. Likewise, the normalization supplied by the very recent GC data from the HESS air-Cerenkov telescope at \~TeV energies is almost equally-well compatible with the $\sim 10^{18}$ eV cosmic ray data. Interestingly, however, the EGRET and HESS data appear to be themselves incompatible. We consider the implications of this discrepancy. We discuss why the Galactic Center environment can allow diffusive shock acceleration at strong shocks up to energies approaching the ankle in the cosmic ray spectrum. Finally, we argue that the shock acceleration may be occuring in the shell of Sagittarius A East, an unusual supernova remnant located very close to the Galactic Center. If this connection between the anisotropy and Sagittarius A East could be firmly established it would be the first direct evidence for a particular Galactic source of cosmic rays up to energies near the ankle.Comment: 57 pages, 2 figure

Summability of the perturbative expansion for a zero-dimensional disordered spin model

We show analytically that the perturbative expansion for the free energy of the zero dimensional (quenched) disordered Ising model is Borel-summable in a certain range of parameters, provided that the summation is carried out in two steps: first, in the strength of the original coupling of the Ising model and subsequently in the variance of the quenched disorder. This result is illustrated by some high-precision calculations of the free energy obtained by a straightforward numerical implementation of our sequential summation method.Comment: LaTeX, 12 pages and 4 figure

Divergent Perturbation Series

Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by the saddle-point configurations (instantons) of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series. Summing it, one can solve (in a certain approximation) various strong-coupling problems. This approach is demonstrated by determining the Gell-Mann - Low functions in \phi^4 theory, QED, and QCD for arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic forms are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical schemes for summation of perturbation series are described for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. High-order corrections to the Lipatov asymptotics are discussed.Comment: Review article, 45 pages, PD

Magnetic behaviour of Eu_2CuSi_3: Large negative magnetoresistance above Curie temperature

We report here the results of magnetic susceptibility, electrical-resistivity, magnetoresistance (MR), heat-capacity and ^{151}Eu Mossbauer effect measurements on the compound, Eu_2CuSi_3, crystallizing in an AlB_2-derived hexagonal structure. The results establish that Eu ions are divalent, undergoing long-range ferromagnetic-ordering below (T_C=) 37 K. An interesting observation is that the sign of MR is negative even at temperatures close to 3T_C, with increasing magnitude with decreasing temperature exhibiting a peak at T_C. This observation, being made for a Cu containing magnetic rare-earth compound for the first time, is of relevance to the field of collosal magnetoresistance.Comment: To appear in PRB, RevTex, 4 pages text + 6 psFigs. Related to our earlier work on Gd systems (see cond-mat/9811382, cond-mat/9811387, cond-mat/9812069, cond-mat/9812365