arXiv subjects

G. Bohm

Publications and source records attributed to G. Bohm.

15 recordsLinked to original sources

arXiv2013

Statistics of weighted Poisson events and its applications

The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or relevance to a certain type of reaction. The sum is described by the compound Poisson distribution (CPD) which is shortly reviewed. It is shown that the CPD can be approximated by a scaled Poisson distribution (SPD). The SPD is applied to parameter estimation in situations where the data are distorted by resolution effects. It performs considerably better than the normal approximation that is usually used. A special Poisson bootstrap technique is presented which permits to derive confidence limits for observations following the CPD.

physics.data-an↗

arXiv2012

Comments to the article "Parametric fitting of data obtained from detectors with finite resolution and limited acceptance" [arXiv:1011.0662] by Gagunashvili

The publication by Gagunashvili [arXiv:1011.0662] suffers from several caveats: i) The method is based upon the false assumption that the median of chi square distributed random variables is chi square distributed. ii) The information contained in the data is not fully used, iii) It is not clear how the uncertainties associated to the fitted parameters can be evaluated. A correct solution of the problem is presented and results of the cited paper are compared to results obtained using the approach described in the textbook by Bohm and Zech. Finally, we correct false statements in the cited paper about a section in our book.

physics.data-an↗

arXiv2003

What we have learned from direct CP violation studies in kaon decays

A self-consistent analysis of K --> 2pi and K --> 3pi decays within a unique framework of chiral dynamics applied to the QCD-corrected weak nonleptonic quark lagrangian has been performed. The results on K --> 2pi amplitudes at O(p^6), including the value for epsilon'/epsilon, are compared with experiment to fix phenomenological B-factors for mesonic matrix elements of nonpenguin and penguin four-quark operators. The dependence of these B-factors on different theoretical uncertainties and experimental errors of various input parameters is investigated. Finally, we present our estimates at O(p^6) for the CP asymmetry of linear slope parameters in the K+- --> 3pi Dalitz plot.

hep-ph↗

arXiv2003

On perturbative quantum field theory with boundary

Boundary quantum field theory is investigated in the Lagrangian framework. Models are defined perturbatively around the Neumann boundary condition. The analyticity properties of the Green functions are analyzed: Landau equations, Cutkosky rules together with the Coleman-Norton interpretation are derived. Illustrative examples as well as argument for the equivalence with other perturbative expansions are presented.

hep-th↗

arXiv2002

Boundary reduction formula

An asymptotic theory is developed for general non-integrable boundary quantum field theory in 1+1 dimensions based on the Langrangean description. Reflection matrices are defined to connect asymptotic states and are shown to be related to the Green functions via the boundary reduction formula derived. The definition of the $R$-matrix for integrable theories due to Ghoshal and Zamolodchikov and the one used in the perturbative approaches are shown to be related.

hep-th↗

arXiv2000

Direct CP Violation in Nonleptonic Kaon Decays by an Effective Chiral Lagrangian Approach at O(p^6)

A self-consistent analysis of K->2pi and K->3pi decays within a unique framework of chiral dynamics applied to the QCD-corrected weak nonleptonic quark lagrangian has been performed. The results on K->2pi amplitudes at O(p^6), including the value for epsilon'/epsilon, are compared with the experiment to fix phenomenological B-factors for mesonic matrix elements of nonpenguin and penguin four-quark operators. The dependence of B-factors on different theoretical uncertainties and experimental errors of various input parameters is investigated. Finally, we present our estimates at O(p^6) for the CP-asymmetry of linear slope parameters in the K(+-)->3pi Dalitz plot.

hep-ph↗

arXiv1999

Phenomenological analysis of epsilon'/epsilon within an effective chiral lagrangian approach at O(p^6)

We have combined a new systematic calculation of mesonic matrix elements at O(p^6) from an effective chiral lagrangian approach with Wilson coefficients taken from paper by G.Buchalla et al. Rev.Mod.Phys. 68 (1996) 1125, derived in the framework of perturbative QCD, and restricted partly by experimental data. We derive complete expressions for K-->2pi amplitudes and compare the results for epsilon'/epsilon with experiment.

hep-ph↗

arXiv1999

Weak Hopf Algebras I: Integral Theory and C^*-structure

We give an introduction to the theory of weak Hopf algebras proposed recently as a coassociative alternative of weak quasi-Hopf algebras. We follow an axiomatic approach keeping as close as possible to the "classical" theory of Hopf algebras. The emphasis is put on the new structure related to the presence of canonical subalgebras A^L and A^R in any weak Hopf algebra A that play the role of non-commutative numbers in many respects. A theory of integrals is developed in which we show how the algebraic properties of A, such as the Frobenius property, or semisimplicity, or innerness of the square of the antipode, are related to the existence of non-degenerate, normalized, or Haar integrals. In case of C^*-weak Hopf algebras we prove the existence of a unique Haar measure h in A and of a canonical grouplike element g in A implementing the square of the antipode and factorizing into left and right algebra elements. Further discussion of the C^*-case will be presented in Part II.

math.QA↗

arXiv1999

Weak Hopf Algebras II: Representation theory, dimensions and the Markov trace

If A is a weak C^*-Hopf algebra then the category of finite dimensional unitary representations of A is a monoidal C^*-category with monoidal unit being the GNS representation D_eps associated to the counit \eps. This category has isomorphic left dual and right dual objects which leads, as usual, to the notion of dimension function. However, if \eps is not pure the dimension function is matrix valued with rows and columns labelled by the irreducibles contained in D_eps. This happens precisely when the inclusions A^L < A and A^R < A are not connected. Still there exists a trace on A which is the Markov trace for both inclusions. We derive two numerical invariants for each C^*-WHA of trivial hypercenter. These are the common indices I and δ, of the Haar, respectively Markov conditional expectations of either one of the inclusions A^{L/R} < A and Adual^{L/R} < Adual. In generic cases I > δ. In the special case of weak Kac algebras we show that I=δis an integer.

math.QA↗

arXiv1998

Weak C^*-Hopf Algebras and Multiplicative Isometries

We show how the data of a finite dimensional weak C^*-Hopf algebra can be encoded into a pair (H,V) where H is a finite dimensional Hilbert space and V: H øH --> H øH is a partial isometry satisfying, among others, the pentagon equation. In case of V being unitary we recover the Baaj-Skandalis multiplicative unitary of the discrete compact type. Relation to the pseudo- multiplicative unitary approach proposed by J.-M. Vallin and M. Enock is also discussed.

math.QA↗

arXiv1997

Results on K --> 2pi decays at O(p^6) and epsilon'/epsilon from an effective chiral lagrangian approach

We have combined a new systematic calculation of mesonic matrix elements at O(p^6) from an effective chiral lagrangian approach using Wilson coefficients taken from [G.Buchalla, A.J.Buras, M.E.Lautenbacher, Rev.Mod.Phys. 68 (1996) 1125], derived in the framework of perturbative QCD, and restricted partly by experimental data. We derive complete expressions for K --> 2pi amplitudes and give new estimates for epsilon'/epsilon.

hep-ph↗

arXiv1995

A Coassociative C*-Quantum Group with Non-Integral Dimensions

By weakening the counit and antipode axioms of a C*-Hopf algebra and allowing for the coassociative coproduct to be non-unital we obtain a quantum group, that we call a weak C*-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. This amounts to generalizing the Baaj-Skandalis multiplicative unitaries to multipicative partial isometries. Every weak C*-Hopf algebra has a dual which is again a weak C*-Hopf algebra. An explicit example is presented with Lee-Yang fusion rules. We shortly discuss applications to amalgamated crossed products, doubles, and quantum chains.

q-alg↗

arXiv1993

What can we learn from new measurements of Dalitz plot parameters for K $\rightarrow 3 π$ decays ?

We give a simple expression in linear and quadratic Dalitz--plot slopes which does not depend on the charge combination of the $3π$ state $(K^\pm \to π^{\pm}π^{+}π^{-}$ or $π^{\pm}π^{0}π^{0}$ and $K_L^{0} \to π^{+}π^{-}π^{0}$ or $π^{0}π^{0}π^{0})$, if all phases between final states are negligible. After investigating the influence of radiative corrections, it is shown how new measurements, especially of quadratic slopes in the $π^{\pm} π^{0} π^{0}$ channel, could help to test theoretical predictions more stringently. A FORTRAN code for the radiatiative corrections is available on request.

hep-ph↗

arXiv1993

On the $p^4$--corrections to $K \to 3π$ decay amplitudes in nonlinear and linear chiral models

The calculations of isotopic amplitudes and their results for the direct $CP$--violating charge asymmetry in $K^\pm \to 3π$ decays within the nonlinear and linear ($σ$--model) chiral Lagrangian approach are compared with each other. It is shown, that the latter, taking into account intermediate scalar resonances, does not reproduce the $p^4$--corrections of the nonlinear approach introduced by Gasser and Leutwyler, being saturated mainly by vector resonance exchange. The resulting differences concerning the $CP$ violation effect are traced in some detail.

hep-ph↗

arXiv1993

On the Origin of the Enhancementof CP-violating Charge Asymmetries in $K \rightarrow 3π$ Decays Predicted from Chiral Theory

We present an analysis of the enhancement of CP-violating charge asymmetries in $K \rightarrow 3π$ decays. Calculations of decay amplitudes are performed on the basis of bosonized strong and weak Lagrangians derived from QCD-motivated quark Lagrangians. We show that the interplay of fourth-order contributions of chiral Lagrangians for strong interactions and penguin operators in weak interactions significantly enhances the charge asymmetries.

hep-ph↗