778 research outputs found
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 and the \MS parameter
It happens that and 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 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 , is not
independent of the previous one since a good physical reason exists for
s_\Eff^2 and 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 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
- …