Improved bounds for the slope and curvature of form factors

We derive a theoretically allwed domain for the slope and curvature of the physical form factor appearing in the decay . Using heavy-quark symmetry, we relate this function to a particular form factor free of ground-state B_c poles below the threshold for BD production, for which almost model-independent constraints are derived from QCD using unitarity and analyticity. Our results are of interest for the extraction of |V_cb| from the recoil spectrum in exclusive semileptonic B decays. Making conservative estimates of the theoretical uncertainties, we find (up to 1/m_Q corrections) and . We also derive the corresponding bounds for the form factor in the decay .     

Unitary bounds on elastic absorptive amplitudes involving total cross section,forward slope and curvature

We obtain rather tight unitarity upper and lower bounds on the absorptive part A(s, t) of elastic amplitudes with given total cross section, slope and curvature at t = 0 and compare them with experiment.     

Volume comparison between spacelike hypersurfaces in a Lorentzian manifold with integral Ricci curvature bounds

We obtain the volume comparison between spacelike hypersurfaces in a Lorentzian manifold with integral Ricci and mean curvature bounds. Also we extend volume comparisons to weighted volume comparisons with integral norms of the generalized Ricci tensor.     

Connections defining representations of zero curvature and the solitons of sine-Gordon and Korteweg-de Vries equations

It is claimed that solutions of travelling-wave type (and, in particular, soliton solutions) of partial differential equations can be created by using connections defining representations of zero curvature. In this paper, we construct solitons of the sine-Gordon and Korteweg-de Vries equations. By previous results of the author, the connections defining representations of zero curvature for a given differential equation generate Bäcklund transformations for this equation. It can be shown that the well-known Lax system (the so-called Lax pair) for the Korteweg-de Vries equation is a special case of a Bäcklund system (i.e., the system of partial differential equations defining a Bäcklund transformation). Note that the creation of solitons by means of the inverse scattering method is in fact a creation of solitons by means of the Lax system (without using connections defining the representations of zero curvature from the very beginning). Moreover, the inverse scattering method is essentially more labor-consuming than the method suggested in the present paper. Further, it is not required to involve any physical notions when using the suggested method. In the final section of the paper, we consider the so-called 2-soliton solutions of sine-Gordon and Korteweg — de Vries equations. Here we systematically use the invariant analytic method developed by G. F. Laptev, which is well-known in differential geometry under the title of Cartan-Laptev method.     

Improved bounds on the radius and curvature of the K$ \pi$ scalar form factor and implications to low-energy theorems

We obtain stringent bounds in the 〈r ² -c plane where these are the scalar radius and the curvature parameters of the scalar K form factor, respectively, using analyticity and dispersion relation constraints, the knowledge of the form factor from the well-known Callan-Treiman point , as well as at , which we call the second Callan-Treiman point. The central values of these parameters from a recent determination are accomodated in the allowed region provided the higher loop corrections to the value of the form factor at the second Callan-Treiman point reduce the one-loop result by about 3% with . Such a variation in magnitude at the second Callan-Treiman point yields 0.12 fm² 〈r ² 0.21 fm²and 0.56 GeV^-4 c 1.47 GeV^-4and a strong correlation between them. A smaller value of shifts both bounds to lower values.     

Remarks on Symplectic Connections

This note contains a short survey on some recent work on symplectic connections: properties and models for symplectic connections whose curvature is determined by the Ricci tensor, and a procedure to build examples of Ricci-flat connections. For a more extensive survey, see Bieliavsky et al. [Int. J. Geom. Methods Mod. Phys. 3, 375–420 2006]. This note also includes a moment map for the action of the group of symplectomorphisms on the space of symplectic connections, an algebraic construction of a large class of Ricci-flat symmetric symplectic spaces, and an example of global reduction in a non-symmetric case.     

Connections on discrete fibre bundles

A new approach to gauge fields on a discrete space-time is proposed, in which the fundamental object is a discrete version of a principal fibre bundle. If the bundle is twisted, the gauge fields are topologically non-trivial automatically.     

Upper bounds on superpartner masses from upper bounds on the Higgs boson mass

The LHC is putting bounds on the Higgs boson mass. In this Letter we use those bounds to constrain the minimal supersymmetric standard model (MSSM) parameter space using the fact that, in supersymmetry, the Higgs mass is a function of the masses of sparticles, and therefore an upper bound on the Higgs mass translates into an upper bound for the masses for superpartners. We show that, although current bounds do not constrain the MSSM parameter space from above, once the Higgs mass bound improves big regions of this parameter space will be excluded, putting upper bounds on supersymmetry (SUSY) masses. On the other hand, for the case of split-SUSY we show that, for moderate or large tanβ, the present bounds on the Higgs mass imply that the common mass for scalars cannot be greater than 10(11) GeV. We show how these bounds will evolve as LHC continues to improve the limits on the Higgs mass.     

Analytic bounds on transmission probabilities

We develop some new analytic bounds on transmission probabilities (and the related reflection probabilities and Bogoliubov coefficients) for generic one-dimensional scattering problems. To do so we rewrite the Schrödinger equation for some complicated potential whose properties we are trying to investigate in terms of some simpler potential whose properties are assumed known, plus a (possibly large) “shift” in the potential. Doing so permits us to extract considerable useful information without having to exactly solve the full scattering problem.     

Strong bounds on weak couplings

Analysis of nonleptonic ΔS = 1 weak decays strongly restricts the possible size of right-handed weak couplings. Limits thus obtained are competitive with those obtained via other means.     

Cosmological bounds on Dirac-Majorana neutrinos

We examine, by way of a detailed numerical calculation, the consequences for primordial nucleosynthesis of a weakly interacting neutrino which possesses both Dirac and Majorana mass terms. In the special limiting case of a pseudo-Dirac neutrino we place bounds on the pseudo-Dirac mass splitting δm_p-D. This bound is relevant to a class of models constructed to incorporate the proposed 17 keV neutrino. We find that in the standard model |δm_p-D|<10⁻¹⁰ eV. In the models with majorons the bound is less restrictive, but still several orders of magnitude more stringent than previous estimates.     

Upper bounds on neutrino masses

Using a recent experimental bound on τ decay into three charged leptons and a weak assumption concerning a general “see-saw” mechanism for neutrino masses, we show that both v_μ and v_τ must be lighter than 65 eV. If the “see-saw” is driven by a right-handed W boson or by a “horizontal” gauge boson, they must be heavier than 50 PeV.     

Connections and Distributions on Quantum Hyperplane

In this paper we introduce basic notions from noncommutative geometry to the quantum hyperplane: linear connections, submanifolds, distributions and we give a Frobenius type theorem for the quantum hyperplane.     

Some bounds on X-ray laser wavelengths

Summary Simple estimates of physical processes in generic X-ray lasers driven by two-body radiative recombination are used to impose approximate bounds on their possible wavelengths of laser action. Other processes are briefly mentioned. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

Cavity bounds on higher-order lorentz-violating coefficients

We determine the sensitivity of a modern Michelson-Morley resonant-cavity experiment to higher-order nonbirefringent and nondispersive coefficients of the Lorentz-violating standard-model extension. Data from a recent year-long run of the experiment are used to place the first experimental bounds on coefficients associated with nonrenormalizable Lorentz-violating operators.     

Quantized Abelian Principal Connections on Lorentzian Manifolds

We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group, namely the group of vertical principal bundle automorphisms. Properties of our functor are investigated in detail and, similar to earlier works, it is found that due to topological obstructions the locality property of locally covariant quantum field theory is violated. Furthermore, we prove that, for Abelian structure groups containing a nontrivial compact factor, the gauge invariant Borchers-Uhlmann algebra of the vector dual of the bundle of connections is not separating on gauge equivalence classes of principal connections. We introduce a topological generalization of the concept of locally covariant quantum fields. As examples, we construct for the category of principal U(1)-bundles two natural transformations from singular homology functors to the quantum field theory functor that can be interpreted as the Chern class and the electric charge. In this case we also prove that the electric charges can be consistently set to zero, which yields another quantum field theory functor that satisfies all axioms of locally covariant quantum field theory.     

Asymptotic bounds on pion form factor

A technique recently developed for inelastic electron proton scattering is applied for inelastic electron pion scattering. It is found that all the derivatives of off-shell form factor of pion nears=m _π ² and for largeQ ² are bounded from above, provided that the dispersion relation for the form factor requires no more than one subtraction. The elastic pion form factor is bounded by [lnQ ²] ^c /Q ², wherec is any positive constant.