244 research outputs found
Normal origamis of Mumford curves
An origami (also known as square-tiled surface) is a Riemann surface covering
a torus with at most one branch point. Lifting two generators of the
fundamental group of the punctured torus decomposes the surface into finitely
many unit squares. By varying the complex structure of the torus one obtains
easily accessible examples of Teichm\"uller curves in the moduli space of
Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves.
A p-adic origami is defined as a covering of Mumford curves with at most one
branch point, where the bottom curve has genus one. A classification of all
normal non-trivial p-adic origamis is presented and used to calculate some
invariants. These can be used to describe p-adic origamis in terms of glueing
squares.Comment: 21 pages, to appear in manuscripta mathematica (Springer
Degenerating families of dendrograms
Dendrograms used in data analysis are ultrametric spaces, hence objects of
nonarchimedean geometry. It is known that there exist -adic representation
of dendrograms. Completed by a point at infinity, they can be viewed as
subtrees of the Bruhat-Tits tree associated to the -adic projective line.
The implications are that certain moduli spaces known in algebraic geometry are
-adic parameter spaces of (families of) dendrograms, and stochastic
classification can also be handled within this framework. At the end, we
calculate the topology of the hidden part of a dendrogram.Comment: 13 pages, 8 figure
Introduction to Categories and Categorical Logic
The aim of these notes is to provide a succinct, accessible introduction to
some of the basic ideas of category theory and categorical logic. The notes are
based on a lecture course given at Oxford over the past few years. They contain
numerous exercises, and hopefully will prove useful for self-study by those
seeking a first introduction to the subject, with fairly minimal prerequisites.
The coverage is by no means comprehensive, but should provide a good basis for
further study; a guide to further reading is included. The main prerequisite is
a basic familiarity with the elements of discrete mathematics: sets, relations
and functions. An Appendix contains a summary of what we will need, and it may
be useful to review this first. In addition, some prior exposure to abstract
algebra - vector spaces and linear maps, or groups and group homomorphisms -
would be helpful.Comment: 96 page
A series of coverings of the regular n-gon
We define an infinite series of translation coverings of Veech's double-n-gon
for odd n greater or equal to 5 which share the same Veech group. Additionally
we give an infinite series of translation coverings with constant Veech group
of a regular n-gon for even n greater or equal to 8. These families give rise
to explicit examples of infinite translation surfaces with lattice Veech group.Comment: A missing case in step 1 in the proof of Thm. 1 b was added. (To
appear in Geometriae Dedicata.
Non-factorizable contribution in nonleptonic weak interactions of K mesons
Two pion decays of K mesons, K_L-K_S mass difference, two photon and the
Dalitz decays of K_L are studied systematically by assuming that their
amplitude is given by a sum of factorizable and non-factorizable ones. The
former is estimated by using a naive factorization while the latter is assumed
to be dominated by dynamical contributions of various hadron states.Comment: 23 pages,1 figur
Splittings of generalized Baumslag-Solitar groups
We study the structure of generalized Baumslag-Solitar groups from the point
of view of their (usually non-unique) splittings as fundamental groups of
graphs of infinite cyclic groups. We find and characterize certain
decompositions of smallest complexity (`fully reduced' decompositions) and give
a simplified proof of the existence of deformations. We also prove a finiteness
theorem and solve the isomorphism problem for generalized Baumslag-Solitar
groups with no non-trivial integral moduli.Comment: 20 pages; hyperlinked latex. Version 2: minor change
Next-to-Leading Order QCD corrections to -mixing and within the MSSM
We present a calculation of the QCD correction factors and
up to Next-to-Leading Order within the MSSM. We took into account
the region of low for the Higgs- and chargino sector while
neglecting the effect of gluinos and neutralinos.Comment: 38 pages, references added, typos corrected, extended discussion of
gluino-mediated correction
On the Correlations between Flavour Observables in Minimal U(2)^3 Models
The stringent correlations between flavour observables in models with CMFV
are consistent with the present data except for the correlation Delta
M_{s,d}-epsilon_K. Motivated by the recent work of Barbieri et al, we compare
the CMFV correlations with the ones present in a special class of models with
an approximate global U(2)^3 flavour symmetry, constrained by a minimal set of
spurions governing the breakdown of this symmetry and the assumption that only
SM operators are relevant in flavour physics. This analog of CMFV to be called
MU(2)^3 allows to avoid the Delta M_{s,d}-epsilon_K tension in question because
of reduced flavour symmetry and implied non-MFV contributions to Delta M_{s,d}.
While the patterns of flavour violation in K meson system is the same as in
CMFV models, the CP-violation in B_{s,d} meson systems can deviate from the one
in the SM and CMFV models. We point out a stringent triple S_{psi K_S}-S_{psi
phi}-|V_ub| correlation in this class of models that could in the future
provide a transparent distinction between different MU(2)^3 models and in the
context of these models determine |V_ub| by means of precise measurements of
S_{psi K_S} and S_{psi phi} with only small hadronic uncertainties. For fixed
S_{psi K_S} the correlation between B(B^+ -> tau^+nu_tau) and S_{psi phi}
follows. We also find that MU(2)^3 models could in principle accommodate a
negative value of S_{psi phi}, provided |V_ub| is found to be in the ballpark
of exclusive determinations and the particular MU(2)^3 model provides a 25%
enhancement of epsilon_K. A supersymmetric U(2)^3 model worked out in the
Barbieri-School appears to satisfy these requirements. However if B(B^+ ->
tau^+nu_tau)>1.0 10^{-4} will be confirmed by future experiments only positive
S_{psi phi} is allowed in this framework. We summarize briefly the pattern of
flavour violation in rare K and B_{s,d} decays in MU(2)^3 models.Comment: 28 pages, 6 figures; v2: Few references and discussion on CP
violation in B_s-> mu^+ mu^- added; v3: Several clarifying comments added,
conclusions unchanged, version accepted for publication in JHE
An updated analysis of eps'/eps in the standard model with hadronic matrix elements from the chiral quark model
We discuss the theoretical and experimental status of the CP violating ratio
eps'/eps. We revise our 1997 standard-model estimate-based on hadronic matrix
elements computed in the chiral quark model up to O(p^4) in the chiral
expansion-by including an improved statistical analysis of the uncertainties
and updated determination of the Cabibbo-Kobayashi-Maskawa elements and other
short-distance parameters. Using normal distributions for the experimental
input data we find Re eps'/eps = (2.2 \pm 0.8) x 10^{-3}, whereas a flat
scanning gives 0.9 x 10^{-3} < Re eps'/eps < 4.8 x 10^{-3}. Both results are in
agreement with the current experimental data. The key element in our estimate
is, as before, the fit of the Delta I=1/2 rule, which allows us to absorb most
of the theoretical uncertainties in the determination of the model-dependent
parameters in the hadronic matrix elements. Our semi-phenomenological approach
leads to numerical stability against variations of the renormalization scale
and scheme dependence of the short- and long-distance components. The same
dynamical mechanism at work in the selection rule also explains the larger
value obtained for \ratio with respect to other estimates. A coherent picture
of K -> pi pi decays is thus provided.Comment: 15 pages, 11 figures, RevTeX, discussion updated, refs adde
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