Presheaf models for constructive set theories

This chapter introduces new kinds of models for constructive set theories based on categories of presheaves. It concentrates on categories of classes rather than sets, following the lines of algebraic set theory. It defines a general notion of what is a categorical model for CST, and shows that categories of presheaves provide examples of such models. To do so, it considers presheaves as functors with values in a category of classes. The models introduced are a counterpart of the presheaf models for intuitionistic set theories defined by Dana Scott in the 1980s. In this work, the author has to overcome the challenges intrinsic to dealing with generalized predicative formal systems rather than impredicative ones. An application to an independence result is discussed

B -> D* at zero recoil revisited

We examine the B -> D* form factor at zero recoil using a continuum QCD approach rooted in the heavy quark sum rules framework. A refined evaluation of the radiative corrections as well as the most recent estimates of higher order power terms together with more careful continuum calculation are included. An upper bound on the form factor of F(1)< 0.93 is derived, based on just the positivity of inelastic contributions. A model-independent estimate of the inelastic contributions shows they are quite significant, lowering the form factor by about 6% or more. This results in an unbiased estimate F(1) \approx 0.86 with about three percent uncertainty in the central value.Comment: 9 pages, 3 figures

Perturbative corrections to semileptonic b decay distributions

We compute O(alpha_s) and O(alpha_s^n beta_0^{n-1}) (BLM) corrections to the five structure functions relevant for b->q l nu decays and apply the results to the moments of a few distributions of phenomenological importance. We present compact analytic one-loop formulae for the structure functions, with proper subtraction of the soft divergence.Comment: 23 pages, LaTex. A number of textual changes are added for clarity, a missing definition is provide

Homotopy limits for 2-categories

We study homotopy limits for 2-categories using the theory of Quillen model categories. In order to do so, we establish the existence of projective and injective model structures on diagram 2-categories. Using these results, we describe the homotopical behaviour not only of conical limits but also of weighted limits. Finally, pseudo-limits are related to homotopy limits

On the numerical closeness of the effective phenomenological electroweak mixing angle θ\theta and the \MS parameter θ^\hat\theta

It happens that $s^2$ and $\hat s^2$ are equal with 0.1% accuracy, though they are split by radiative corrections and a natural estimate for their difference is 1%. This degeneracy occurs only for $m_t$ value close to 170\GeV, so no deep physical reason can be attributed to it. However, another puzzle of the Standard Model, the degeneracy of s_\Eff^2 and $s^2$, is not independent of the previous one since a good physical reason exists for s_\Eff^2 and $\hat s^2$ degeneracy. We present explicit formulas which relate these three angles.Comment: 10 pages, latex, 3 figures included; published on MPLA. A few numerical estimates are improved; journal-ref is adde

Wellfounded Trees and Dependent Polynomial Functors

We set out to study the consequences of the assumption of types of wellfounded trees in dependent type theories. We do so by in- vestigating the categorical notion of wellfounded tree introduced in [16]. Our main result shows that wellfounded trees allow us to define initial algebras for a wide class of endofunctors on locally cartesian closed cat- egories

QCD corrections to the Wilson coefficients C9 and C10 in two-Higgs doublet models

In this letter we present the analytic results for the two-loop corrections to the Wilson coefficients C_9(mu_W) and C_10(mu_W) in type-I and type-II two-Higgs-doublet models at the matching scale mu_W. These corrections are important ingredients for next-to-next-to-leading logarithmic predictions of various observables related to the decays B -> X_s l^+ l^- in these models. In scenarios with moderate values of tan(beta) neutral Higgs boson contributions can be safely neglected for e,mu. Therefore we concentrate on the contributions mediated by charged Higgs bosons.Comment: 12 pages, 3 figure

Double adjunctions and free monads

We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg--Moore objects in double categories. We improve upon our earlier result in "Monads in Double Categories", JPAA 215:6, pages 1174-1197, 2011, to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category. We also prove that a double category admits Eilenberg--Moore objects if and only if a certain parameterized presheaf is representable. Along the way, we develop parameterized presheaves on double categories and prove a double-categorical Yoneda Lemma

Renormalization of the Cabibbo-Kobayashi-Maskawa Quark Mixing Matrix

We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix. When considering the prescription which is formulated with reference to the case of zero mixing we find it doesn't satisfy the unitary condition of the bare CKM matrix. After added a delicate patch this problem can be solved at one-loop level. In this paper We generalize this prescription to all loop levels and keep the unitarity of the bare CKM matrix, simultaneously make the amplitude of an arbitrary physical process involving quark mixing convergent and gauge independent. We also find that in order to keep the CKM counterterms gauge independent the unitarity of the bare CKM matrix must be preserved.Comment: has been revised, 8 pages, 1 figur

Higher Order Power Corrections in Inclusive B Decays

We discuss order 1/m_b^4 and 1/m_b^5 corrections in inclusive semileptonic decay of a $B$ meson. We identify relevant hadronic matrix elements of dimension seven and eight and estimate them using the ground-state saturation approximation. Within this approach the effects on the integrated rate and on kinematic moments are estimated. The overall relative shift in V_{cb} turns out about +0.4% as applied to the existing fits. Similar estimates are presented for B -> X_s+\gamma decays.Comment: 30 pages, 16 figure