5911478
Phase transition with the Berezinskii-Kosterlitz-Thouless singularity in the Ising model on a growing network.
We consider the ferromagnetic Ising model on a highly inhomogeneous network created by a growth process. We find that the phase transition in this system is characterized by the Berezinskii-Kosterlitz-Thouless singularity, although critical fluctuations are absent and the mean-field description is exact. Below this infinite order transition, the magnetization behaves as exp((-const/square root of(Tc-T)). We show that the critical point separates the phase with the power-law distribution of the linear response to a local field and the phase where this distribution rapidly decreases. We suggest that this phase transition occurs in a wide range of cooperative models with a strong infinite-range inhomogeneity.
115160247
Another derivation of the geometrical KPZ relations
We give a physicist's derivation of the geometrical (in the spirit of Duplantier–Sheffield) KPZ relations, via heat kernel methods. It gives a covariant way to define neighborhoods of fractals in 2D quantum gravity, and shows that these relations are in the realm of conformal field theory.
59058647
COVARIANT DIFFERENTIAL EQUATIONS AND SINGULAR VECTORS IN VIRASORO REPRESENTATIONS
Abstract We give explicit expressions for the singular vectors in highest weight representations of the Virasoro algebra using a precise definition of fusion.
173517385
A Short Introduction to Critical Interfaces in 2D
These notes are meant as a gentle introduction to the concepts of Loewner chains, local growth, Stochastic Loewner Evolutions (SLE) and their relationships to Conformal Field Theories (CFT). These concepts have played an important role in physics and mathematics during the recent years. The first section describes two discrete examples, the exploration process and loop-erased random walks. It can be read almost without any prerequisites. The aim is to show that even for curves defined purely in geometrical terms, it is useful to have a statistical mechanics viewpoint where the measure on curves is derived from a measure on local degrees of freedom of some model. A third model, diffusion-limited aggregation (DLA) is also introduced. The second section introduces Loewner chains and their relevance for the description of growth processes. A prerequisite is a minimal knowledge of complex analysis. The third section contains the derivation of the relevance of SLE in the description of interfaces when two properties, conformal invariance and the domain Markov property, are assumed/proved. The prerequisites are some knowledge of complex analysis and probability theory. The last section outlines the relation with Conformal Field Theory. This relation is via martingales and singular vectors. Again, the reader is assumed to have some basic knowledge of complex analysis and probability theory, and some familiarity with CFT. The discussion is informal. There is little or no claim at originality. We try to give some intuition based on explicit examples.
121411195
Singular vectors of the Virasoro algebra
Abstract We present an explicit construction of the singular (or null) vectors in highest weight Verma modules.
119268338
Light dark matter, naturalness, and the radiative origin of the electroweak scale
A bstractWe study classically scale invariant models in which the Standard Model Higgs mass term is replaced in the Lagrangian by a Higgs portal coupling to a complex scalar field of a dark sector. We focus on models that are weakly coupled with the quartic scalar couplings nearly vanishing at the Planck scale. The dark sector contains fermions and scalars charged under dark SU(2) × U(1) gauge interactions. Radiative breaking of the dark gauge group triggers electroweak symmetry breaking through the Higgs portal coupling. Requiring both a Higgs boson mass of 125.5 GeV and stability of the Higgs potential up to the Planck scale implies that the radiative breaking of the dark gauge group occurs at the TeV scale. We present a particular model which features a long-range abelian dark force. The dominant dark matter component is neutral dark fermions, with the correct thermal relic abundance, and in reach of future direct detection experiments. The model also has lighter stable dark fermions charged under the dark force, with observable effects on galactic-scale structure. Collider signatures include a dark sector scalar boson with mass ≲ 250 GeV that decays through mixing with the Higgs boson, and can be detected at the LHC. The Higgs boson, as well as the new scalar, may have significant invisible decays into dark sector particles.
118498826
Soft collinear effective theory for heavy WIMP annihilation
A bstractIn a large class of models for Weakly Interacting Massive Particles (WIMPs), the WIMP mass M lies far above the weak scale mW . This work identifies universal Sudakov-type logarithms ∼ α log2(2 M/mW ) that spoil the naive convergence of perturbation theory for annihilation processes. An effective field theory (EFT) framework is presented, allowing the systematic resummation of these logarithms. Another impact of the large separation of scales is that a long-distance wavefunction distortion from electroweak boson exchange leads to observable modifications of the cross section. Careful accounting of momentum regions in the EFT allows the rigorous disentanglement of this so-called Sommerfeld enhancement from the short-distance hard annihilation process. The WIMP is described as a heavy-particle field, while the electroweak gauge bosons are treated as soft and collinear fields. Hard matching coefficients are computed at renormalization scale μ ∼ 2 M , then evolved down to μ ∼ mW , where electroweak symmetry breaking is incorporated and the matching onto the relevant quantum mechanical Hamiltonian is performed. The example of an SU(2)W triplet scalar dark matter candidate annihilating to line photons is used for concreteness, allowing the numerical exploration of the impact of next-to-leading order corrections and log resummation. For M ≃ 3 TeV, the resummed Sommerfeld enhanced cross section is reduced by a factor of ∼ 3 with respect to the treelevel fixed order result.
122254340
SIMULATIONS OF MUON-INDUCED NEUTRON BACKGROUND WITH GEANT4
18560327
Commissioning run of the CRESST-II dark matter search
Abstract The CRESST cryogenic direct dark matter search at Gran Sasso, searching for WIMPs via nuclear recoil, has been upgraded to CRESST-II by several changes and improvements. The upgrade includes a new detector support structure capable of accommodating 33 modules, the associated multichannel readout with 66 SQUID channels, a neutron shield, a calibration source lift, and the installation of a muon veto. We present the results of a commissioning run carried out in 2007. The basic element of CRESST-II is a detector module consisting of a large ( ∼ 300 g ) CaWO 4 crystal and a very sensitive smaller ( ∼ 2 g ) light detector to detect the scintillation light from the CaWO 4 . The large crystal gives an accurate total energy measurement. The light detector permits a determination of the light yield for an event, allowing an effective separation of nuclear recoils from electron–photon backgrounds. Furthermore, information from light-quenching factor studies allows the definition of a region of the energy-light yield plane which corresponds to tungsten recoils. A neutron test is reported which supports the principle of using the light yield to identify the recoiling nucleus. Data obtained with two detector modules for a total exposure of 48 kg-days are presented. Judging by the rate of events in the “all nuclear recoils” acceptance region the apparatus shows a factor ∼10 improvement with respect to previous results, which we attribute principally to the presence of the neutron shield. In the “tungsten recoils” acceptance region three events are found, corresponding to a rate of 0.063 per kg-day. Standard assumptions on the dark matter flux, coherent or spin independent interactions, then yield a limit for WIMP-nucleon scattering of 4.8 × 10 - 7 pb , at M WIMP ∼ 50 GeV .
122884706
Latest results from the CRESST-II Dark Matter Search
The CRESST-II experiment is searching for Dark Matter particles in the form of WIMPs via their elastic scattering off nuclei in a target material. The CRESST target consists of scintillating CaWO4 crystals which are operated as cryogenic calorimeters at millikelvin temperatures and read out by transition edge sensors. Each interaction in CaWO4 produces a phonon signal in the target crystal and also a light signal that is measured by a secondary cryogenic calorimeter, allowing a very efficient discrimination between electron recoils from radioactive e/γ background and nuclear recoils. Moreover, to some extent, the different types of recoiling nuclei (O, Ca, W) can be distinguished. In the paper we present the latest results of the experiment, obtained from a net exposure of 730kg days acquired with 8 detectors between July 2009 and March 2011. The data has shown a considerable number of events in our signal region. Since this large number of events is not consistent with the known sources of background in our experiment, we discuss the compatibility of this excess of events with a possible WIMP-signal.