Saibal Mitra

The XXZ spin chain at

A number of conjectures have been given recently concerning the connection between the antiferromagnetic XXZ spin chain at Δ=−1/2 and various symmetry classes of alternating sign matrices. Here we use the integrability of the XXZ chain to gain further insight into these developments. In doing so we obtain a number of new results using Baxter’s Q function for the XXZ chain for periodic, twisted and open boundary conditions. These include expressions for the elementary symmetric functions evaluated at the ground state solution of the Bethe roots. In this approach Schur functions play a central role and enable us to derive determinant expressions which appear in certain natural double products over the Bethe roots. When evaluated these give rise to the numbers counting different symmetry classes of alternating sign matrices.

Δ=- 1/2: Bethe roots, symmetric functions and determinants

We consider a model in which dark matter consists of a large self-interacting component (SIDM particles) and a small component with strong interactions with baryons (SIMPs). We show that the DAMA annual modulation signal can be caused by SIDM particles interacting with SIMPs trapped in iodine nuclei in the DAMA/NaI detector.

Has DAMA detected self-interacting dark matter?

Abstract Mirror matter is an entirely new form of matter predicted to exist if mirror symmetry is a fundamental symmetry of nature. Mirror matter has the right broad properties to explain the inferred dark matter of the Universe and might also be responsible for a variety of other puzzles in particle physics, astrophysics, meteoritics and planetary science. It is known that mirror matter can interact with ordinary matter non-gravitationally via photon-mirror photon kinetic mixing. The strength of this possibly fundamental interaction depends on the (theoretically) free parameter ϵ. We consider various proposed manifestations of mirror matter in our solar system examining in particular how the physics changes for different possible values of ϵ. We find new evidence for mirror matter in the solar system coming from the observed sharp reduction in crater rates (for craters less than about 100 m in diameter) on the asteroid 433 Eros. We also re-examine various existing ideas including the mirror matter explanation for the anomalous meteorite events, anomalous slow-down of Pioneer spacecraft etc.

Mirror matter in the solar system: New evidence for mirror matter from Eros

Dark matter annihilations can generate significant amounts of internal heat inside planets if dark matter consists mainly of particles with nuclear cross sections in the microbarn range or larger (SIMPs). By considering a detailed model of Uranuss interior, we calculate upper limits on the S-wave annihilation cross section for these particles as a function of their mass. These upper limits, together with other experimental and theoretical constraints, rule out SIMPs with masses between 150 MeV and 10{sup 4} GeV.

Uranus's anomalously low excess heat constrains strongly interacting dark matter

We present conjectured exact expressions for two kinds of correlations in the dense O (n = 1) loop model on square lattices with periodic boundary conditions. These are the probability that a point is surrounded by m loops and the probability that k consecutive points on a row are on the same or on different loops. The dense O (n = 1) loop model is equivalent to the bond percolation model at the critical point. The former probability can be interpreted in terms of the bond percolation problem as giving the probability that a vertex is on a cluster that is surrounded by clusters and dual clusters. The conjectured expression for this probability involves a binomial determinant that is known to give weighted enumerations of cyclically symmetric plane partitions and also of certain kinds of families of nonintersecting lattice paths. By applying Coulomb gas methods to the dense O (n = 1) loop model, we obtain new conjectures for the asymptotics of this binomial determinant.

Exact conjectured expressions for correlations in the dense O(1) loop model on cylinders

Abstract A new and inexpensive technique for detecting self interacting dark matter in the form of small grains in bulk matter is proposed. Depending on the interactions with ordinary matter, dark matter grains in bulk matter may be isolated by using a centrifuge and using ordinary matter as a filter. The case of mirror matter interacting with ordinary matter via photon–mirror photon kinetic mixing provides a concrete example of this type of dark matter candidate.

Detecting dark matter using centrifuging techniques

Mirror matter type dark matter can exist on the Earths surface, potentially in enhanced concentrations at various anomalous impact sites. Mirror matter fragments can draw in heat from the ordinary matter environment, radiate mirror photons and thereby cool the surrounding ordinary matter. We quantify this effect and suggest that it could be used to help locate mirror matter deposits. This method, together with the centrifuge technique, seems to provide the most promising means to experimentally detect mirror matter type dark matter in the Earth.

Detecting mirror matter on earth via its thermal imprint on ordinary matter

Mirror symmetry is a plausible candidate for a fundamental symmetry of particle interactions which can be exactly conserved if a set of mirror particles exist. The properties of the mirror particles seem to provide an excellent candidate to explain the inferred dark matter of the Universe and might also be responsible for a variety of other puzzles in particle physics, astrophysics, meteoritics and planetary science. One such puzzle\char22{}the orthopositronium lifetime problem\char22{}can be explained if there is a small kinetic mixing of ordinary and mirror photons. We show that this kinetic mixing implies the existence of ordinary atom\char21{}mirror-atom bound states with interesting terrestrial and astrophysical implications. We suggest that sensitive mass spectroscopic studies of ordinary samples containing heavy elements such as lead might reveal the presence of these bound states, as they would appear as anomalously heavy elements. In addition to the effects of single mirror atoms, collective effects from embedded fragments of mirror matter (such as mirror iron microparticles) are also possible. We speculate that such mirror matter fragments might explain a mysterious UV photon burst observed coming from a laser irradiated lead target in a recent experiment.

Ordinary atom mirror atom bound states: A New window on the mirror world

Dark matter in the form of particles from a hidden mirror sector has recently been proposed as an explanation for the DAMA annual modulation signal. Here one assumes that there exists a small mixing between photons and mirror photons. We show that dark matter with this property can also be detected in electromagnetic field penetration experiments. Such experiments can be used to measure the speed and direction of the dark matter halo wind, the local density, the temperature, and the strength of the photon-mirror photon mixing interaction. An additional result would be a significant improvement of the upper limit on the photon mass.

Detecting dark matter in electromagnetic field penetration experiments

A simple technique for expanding the free energy of general six-vertex models about free-fermion points is introduced. This technique is used to verify a Coulomb gas prediction about the behavior of the leading singularity in the free energy of the staggered F-model at zero staggered field.