Related papers: Sum rules for total hadronic widths of mesons
The ambiguity in the definition for the mass and width of relativistic resonances is discussed, in particular for the case of the Z-boson. This ambiguity can be removed by requiring that a resonance's width $\Gamma$ (defined by a…
Gaussian sum-rules, which are related to a two-parameter Gaussian-weighted integral of a hadronic spectral function, are able to examine the possibility that more than one resonance makes a significant contribution to the spectral function.…
In this paper, we present several explicit formulas of the sums and hyper-sums of the powers of the first (n+1)-terms of a general arithmetic sequence in terms of Stirling numbers and generalized Bernoulli polynomials.
We compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. In particular, we show that chaotic random…
We analyze the behavior of Urysohn width of manifolds under a connected sum operation, specifically, bounding widths of summands in terms of widths of the sum and vice versa. Our methods also apply to the universal covers of these spaces,…
We first introduce the Hamming distance between two strings. Then, we apply this concept to the representations of whole numbers in base n for all positive integers n > 2. We claim that a simple formula exists for the sum of all Hamming…
A method used previously to calculate the masses of the vector mesons is extended to the calculation of the nucleon resonances. The method is based on the choice of integration kernels which eliminate the unknown parts of the spectrum. We…
We construct new dispersive sum rules for the effective field theory of the standard model at mass dimension six. These spinning sum rules encode information about the spin of UV states: the sign of the IR Wilson coefficients carries a…
We derive explicit expressions for the sum rules of the eigenvalues of inhomogeneous strings with arbitrary density and with different boundary conditions. We show that the sum rule of order $N$ may be obtained in terms of a diagrammatic…
The half width rule provides a way to consider 1/Nc corrections to hadronic models containing resonances. Consequences of such ideas for hadron form factors and Regge trajectories are explored, with special emphasis on the possibility to…
It is shown that the well known sum rules for oscillator strengths for Hydrogen atom can be generalised to a whole class of sum rules. The sum rules have contributions from the discrete and the continuum parts of the spectrum neither of…
An introduction to the method of QCD sum rules is given for those who want to learn how to use this method. Furthermore, we discuss various applications of sum rules, from the determination of quark masses to the calculation of hadronic…
1. QCD Sum Rules: 20 Years After; 2. QCD Vacuum and Basics of the SVZ Method: 2.1 General ideas; 2.2. Getting started/Playing with toy models; 3. Vacuum Condensates; 4. Rho Meson in QCD; 5. Basic Theoretical Instrument -- Wilson's OPE; 6.…
The fully charmed hadronic scalar molecules $\mathcal{M}_1=\eta_c \eta_c$ and $\mathcal{M}_2=\chi_{c0}\chi_{c0}$ are studied in the context of the QCD sum rule method. The masses $m$, $\widetilde{m}$ and current couplings $f$, $…
Mass and full width of the heavy scalar molecule $\mathcal{M}$ composed of the mesons $B_{c}^{+}$ and $B_{c}^{-}$ are calculated in the QCD sum rule framework. To find its mass and current coupling, we apply the two-point sum rule method.…
The masses of octet baryons are calculated by the method of QCD sum rules. Using generalized interpolating fields, three independent sets of QCD sum rules are derived which allow the extraction of low-lying N* states with spin-parity 1/2+,…
Based on the analysis of both Borel and Finite-Energy QCD sum rules, the inclusion of finite mesonic widths leads to a dramatic effect on the predictions for the momentum dependence of the rho-omega mixing matrix element. It is shown that…
Sum rules are derived relating Dirac mean square radii and anomalous magnetic moments of various couples of the ground state $1/2^+$ octet baryons with the convergent integral of the difference of hadron photoproduction cross-sections on…
We study the accuracy of the bound-state parameters obtained with the method of dispersive sum rules, one of the most popular theoretical approaches in nonperturbative QCD and hadron physics. We make use of a quantum-mechanical potential…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…