Neutrino factory in stages: Low energy, high energy, off-axis

We discuss neutrino oscillation physics with a neutrino factory in stages, including the possibility of upgrading the muon energy within the same program. We point out that a detector designed for the low energy neutrino factory may be used off-axis in a high energy neutrino factory beam. We include the re-optimization of the experiment depending on the value of theta_13 found. As upgrade options, we consider muon energy, additional baselines, a detector mass upgrade, an off-axis detector, and the platinum (muon to electron neutrino) channels. In addition, we test the impact of Daya Bay data on the optimization. We find that for large theta_13 (theta_13 discovered by the next generation of experiments), a low energy neutrino factory might be the most plausible minimal version to test the unknown parameters. However, if a higher muon energy is needed for new physics searches, a high energy version including an off-axis detector may be an interesting alternative. For small theta_13 (theta_13 not discovered by the next generation), a plausible program could start with a low energy neutrino factory, followed by energy upgrade, and then baseline or detector mass upgrade, depending on the outcome of the earlier phases.Comment: 23 pages, 10 (color) figures. Minor clarifications and changes. Final version to appear in PR

Geometry of canonical self-similar tilings

We give several different geometric characterizations of the situation in which the parallel set $F_\epsilon$ of a self-similar set $F$ can be described by the inner $\epsilon$-parallel set $T_{-\epsilon}$ of the associated canonical tiling $\mathcal T$, in the sense of \cite{SST}. For example, $F_\epsilon=T_{-\epsilon} \cup C_\epsilon$ if and only if the boundary of the convex hull $C$ of $F$ is a subset of $F$, or if the boundary of $E$, the unbounded portion of the complement of $F$, is the boundary of a convex set. In the characterized situation, the tiling allows one to obtain a tube formula for $F$, i.e., an expression for the volume of $F_\epsilon$ as a function of $\epsilon$. On the way, we clarify some geometric properties of canonical tilings. Motivated by the search for tube formulas, we give a generalization of the tiling construction which applies to all self-affine sets $F$ having empty interior and satisfying the open set condition. We also characterize the relation between the parallel sets of $F$ and these tilings.Comment: 20 pages, 6 figure

Minimal Neutrino Beta Beam for Large theta_13

We discuss the minimum requirements for a neutrino beta beam if theta_13 is discovered by an upcoming reactor experiment, such as Double Chooz or Daya Bay. We require that both neutrino mass hierarchy and leptonic CP violation can be measured to competitive precisions with a single-baseline experiment in the entire remaining theta_13 range. We find that for very high isotope production rates, such as they might be possible using a production ring, a (B,Li) beta beam with a gamma as low as 60 could already be sufficient to perform all of these measurements. If only the often used nominal source luminosities can be achieved, for example, a (Ne,He) beta beam from Fermilab to a possibly existing water Cherenkov detector at Homestake with gamma \sim 190-350 (depending on the Double Chooz best-fit) could outperform practically any other beam technology including wide-band beam and neutrino factory.Comment: 11 pages, 2 figures, 1 tabl

Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable

A long-standing conjecture of Lapidus claims that under certain conditions, self-similar fractal sets fail to be Minkowski measurable if and only if they are of lattice type. The theorem was established for fractal subsets of $\mathbb{R}$ by Falconer, Lapidus and v.~Frankenhuijsen, and the forward direction was shown for fractal subsets of $\mathbb{R}^d$, $d \geq 2$, by Gatzouras. Since then, much effort has been made to prove the converse. In this paper, we prove a partial converse by means of renewal theory. Our proof allows us to recover several previous results in this regard, but is much shorter and extends to a more general setting; several technical conditions appearing in previous versions of this result have now been removed.Comment: 20 pages, 6 figure

The crystal structure of Haloferax volcanii proliferating cell nuclear antigen reveals unique surface charge characteristics due to halophilic adaptation

Background: The high intracellular salt concentration re quired to maintain a halophilic lifestyle poses challenges to haloarchaeal proteins that must stay soluble, stable and functional in this extreme environment. Proliferating cell nuclear antigen (PCNA) is a fundamental protein involved in maintaining genome integrity, with roles in both DNA replication and repair. To investigate the halophilic adaptation of such a key protein we have crystallised and solved the structure of Haloferax volcanii PCNA (HvPCNA) to a resolution of 2.0 Å. Results: The overall architecture of HvPCNA is very similar to other known PCNAs, which are highly structurally conserved. Three commonly observed adaptations in halophilic proteins are higher surface acidity, bound ions and increased numbers of intermolecular ion pairs (in oligomeric proteins). HvPCNA possesses the former two adaptations but not the latter, despite functioning as a homotrimer. Strikingly, the positive surface charge considered key to PCNA's role as a sliding clamp is dramatically reduced in the halophilic protein. Instead, bound cations within the solvation shell of HvPCNA may permit sliding along negatively charged DNA by reducing electrostatic repulsion effects. Conclusion: The extent to which individual proteins adapt to halophilic conditions varies, presumably due to their diverse characteristics and roles within the cell. The number of ion pairs observed in the HvPCNA monomer-monomer interface wasunexpectedly low. This may reflect the fact that the trimer is intrinsically stable over a wide range of salt concentrations and therefore additional modifications for trimer maintenance in high salt conditions are not required. Halophilic proteins frequently bind anions and cations and in HvPCNA cation binding may compensate for the remarkable reduction in positive charge in the pore region, to facilitate functional interactions with DNA. In this way, HvPCNA may harness its environment as opposed to simply surviving in extreme halophilic conditions

Heavy Hyperon--Antihyperon Production

Based on the experience from the production of anti-Lambda Lambda and anti-Sigma Sigma pairs at LEAR (experiment PS185) it is suggested to continue the investigations towards the heavier antihyperon--hyperon pairs anti-Xi Xi and anti-Omega Omega in view of: (1) the production dynamics of the heavier antihyperon--hyperon out of the anti-p p annihilation (2) a comparison of the (3s 3anti-s quark system) anti-Omega Omega to the (3 (anti-s s)) 3 phi meson production, where both systems have similar masses (3.345 and 3.057, respectively) and identical valence quark content. A systematic study of the antihyperon--hyperon production with increasing strangeness content is interesting for the following reasons: The anti-Omega Omega production is the creation of two spin 3/2 objects out of the two spin 1/2 anti-p p particles. Results of the PS185 experiments prove a clear dominance of the spin triplet anti-s s dissociation. In the Omega anti-Omega the three s-quarks (three anti-s quarks) are aligned to spin 3/2 each. If the three anti-s s pairs are now all in spin triplet configurations when created out of the gluonic interaction they should have spin parity quantum number as 3^- as long as Omega anti-Omega is created with relative L=0 angular momentum. The comparison of the Omega anti-Omega baryon pair to the phi phi phi three meson production (where the three anti-s s quark pairs might not but can be produced without relative correlation) would provide a unique determination of the intermediate matter state. Measurements of excitation functions and polarization transfers should be used to examine these gluon rich anti-p p --> anti-Omega Omega and anti-p p --> phi phi phi reaction channels. Such experiments should be performed at the PANDA detector at the FAIR facility of the GSI.Comment: 4 pages, 2 figures, Presented at LEAP05: International Conference on Low Energy Antiproton Physics, Bonn - Juelich, Germany, May 16-22, 200

Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators

In a previous paper by the first two authors, a tube formula for fractal sprays was obtained which also applies to a certain class of self-similar fractals. The proof of this formula uses distributional techniques and requires fairly strong conditions on the geometry of the tiling (specifically, the inner tube formula for each generator of the fractal spray is required to be polynomial). Now we extend and strengthen the tube formula by removing the conditions on the geometry of the generators, and also by giving a proof which holds pointwise, rather than distributionally. Hence, our results for fractal sprays extend to higher dimensions the pointwise tube formula for (1-dimensional) fractal strings obtained earlier by Lapidus and van Frankenhuijsen. Our pointwise tube formulas are expressed as a sum of the residues of the "tubular zeta function" of the fractal spray in $\mathbb{R}^d$. This sum ranges over the complex dimensions of the spray, that is, over the poles of the geometric zeta function of the underlying fractal string and the integers $0,1,...,d$. The resulting "fractal tube formulas" are applied to the important special case of self-similar tilings, but are also illustrated in other geometrically natural situations. Our tube formulas may also be seen as fractal analogues of the classical Steiner formula.Comment: 43 pages, 13 figures. To appear: Advances in Mathematic