Breit-Wigner Research Articles

Analysis of Overlapping Resonances with Unitary Breit–Wigner and K-Matrix Approaches

We compare two methods for obtaining the parameters of overlapping resonances. The convenience of the Breit–Wigner (BW) approach is based on the fact that it operates with the masses and widths of the states. For several resonances with the same quantum numbers, a sum of BW functions violates the unitarity of the S-matrix. However, unitarity can be maintained by introducing interference phases to a BW implementation of scattering matrix formalism. A background can be added to the BW amplitudes in the standard way by using background phases. The K-matrix method is often used to analyze data related to several resonances with the same quantum numbers. It guarantees the unitarity of the S-matrix, but its parameters can be considered as resonance masses and widths only for well-spaced states. It also does not allow the separation of the resonant and background contributions in scattering amplitudes, which is critically important for determining parameters of wide resonances. To demonstrate the features of these methods, we consider several examples using simulated data.

Direct Measurement of the Branching Fractions B(ψ(3686)→J/ψX) and B(ψ(3770)→J/ψX), and Observation of the State R(3760) in e^{+}e^{-}→J/ψX.

We report a measurement of the observed cross sections of e^{+}e^{-}→J/ψX based on 3.21 fb^{-1} of data accumulated at energies from 3.645 to 3.891GeV with the BESIII detector operated at the BEPCII collider. Inanalysis of the cross sections, we measured the decay branching fractions of B(ψ(3686)→J/ψX)=(64.4±0.6±1.6)% and B(ψ(3770)→J/ψX)=(0.5±0.2±0.1)% for the first time. The energy-dependent line shape of these cross sections cannot be well described by two Breit-Wigner (BW) amplitudes of the expected decays ψ(3686)→J/ψX and ψ(3770)→J/ψX. Instead, it can be better described with one more BW amplitude of the decay R(3760)→J/ψX. Under this assumption, we extracted the R(3760) mass M_{R(3760)}=3766.2±3.8±0.4 MeV/c^{2} , total width Γ_{R(3760)}^{tot}=22.2±5.9±1.4 MeV, and product of leptonic width and decay branching fraction Γ_{R(3760)}^{ee}B[R(3760)→J/ψX]=(79.4±85.5±11.7) eV. Thesignificance of the R(3760) is 5.3σ. The first uncertainties of these measured quantities are from fits to the cross sections and second systematic.

Resonant contributions to three-body B(s)→[D(*),D¯(*)]K+K− decays in the perturbative QCD approach

In this work, we study the $S$, $P$ and $D$ wave resonance contributions to three-body decays $B_{(s)} \to [ D^{(*)}, \bar{D}^{(*)} ] K^+K^-$ by employing the perturbative QCD (PQCD) approach, where the kaon-kaon invariant mass spectra are dominated by the $f_0(980),f_0(1370),$ $\phi(1020),\phi(1680),f_2(1270),f^{\prime}_2(1525),f_2(1750)$ and $f_2(1950)$ resonances. The $KK$ $S$-wave component $f_0(980)$ is modeled with the Flatt\'e formalism, while other resonances are described by the relativistic Breit-Wigner (BW) line shape. The corresponding decay channels are studied by constructing the kaon-kaon distribution amplitude $\Phi_{KK}$, which captures important final state interactions between the kaon pair in the resonant region. We found that the PQCD predictions for the branching ratios for most considered decays agree with currently available data within errors. The associated polarization fractions of those vector-vector and vector-tensor decay modes are also predicted, which are expected to be tested in the near future experiments. The invariant mass spectra for the corresponding resonances in the $B_{(s)} \to [D^{(*)}, \bar{D}^{(*)} ] K^+K^-$ decays are well established, which can be confronted with the precise data from the LHCb and Belle II experiments.

Analysis of Overlapping Resonances Using the K-Matrix and Breit–Wigner Methods

The K-matrix approach is mostly used when analyzing the overlapping resonances. It provides unitarity of the scattering matrix, however, its parameters are not physical quantities; the resonant and background contributions cannot be separated; and the scattering amplitudes have zeros between the positions of resonances. The parameters of the Breit—Wigner (BW) functions are the masses and widths of resonances; however, the sum of such functions violates unitarity. We construct a unitary S-matrix by taking into account the interference of BW functions. In the examples presented in the paper, these two approaches are compared.

Production of Z′-boson resonances with large width at the LHC

Di-lepton searches for Beyond the Standard Model (BSM) Z′ bosons that rely on the analysis of the Breit-Wigner (BW) line shape are appropriate in the case of narrow resonances, but likely not sufficient in scenarios featuring Z′ states with large widths. Conversely, alternative experimental strategies applicable to wide Z′ resonances are much more dependent than the default bump search analyses on the modelling of QCD higher-order corrections to the production processes, for both signal and background. For heavy Z′ boson searches in the di-lepton channel at the CERN Large Hadron Collider (LHC), the transverse momentum qT of the di-lepton system peaks at qT≲10−2Mll, where Mll is the di-lepton invariant mass. We exploit this to treat the QCD corrections by using the logarithmic resummation methods in Mll/qT to all orders in the strong coupling constant αs. We carry out studies of Z′ states with large width at the LHC by employing the program reSolve, which performs QCD transverse momentum resummation up to Next-to-Next-to-Leading Logarithmic (NNLL) accuracy. We consider two benchmark BSM scenarios, based on the Sequential Standard Model (SSM) and dubbed ‘SSM wide’ and ‘SSM enhanced’. We present results for the shape and size of Z′ boson signals at the differential level, mapped in both cross section (σ) and Forward-Backward Asymmetry (AFB), and perform numerical investigations of the experimental sensitivity at the LHC Run 3 and High-Luminosity LHC (HL-LHC).

Gauge-independent approach to resonant dark matter annihilation

In spontaneously broken gauge theories, transition amplitudes describing dark-matter (DM) annihilation processes through a resonance may become highly inaccurate close to a production threshold, if a Breit-Wigner (BW) ansatz with a constant width is used. To partially overcome this problem, the BW propagator needs to be modified by including a momentum dependent decay width. However, such an approach to resonant transition amplitudes generically suffers from gauge artefacts that may also give rise to a bad or ambiguous high-energy behaviour for such amplitudes. We address the two problems of gauge dependence and high-energy unitarity within a gauge-independent framework of resummation implemented by the so-called Pinch Technique. We study DM annihilation via scalar resonances in a gauged U(1)X complex-scalar extension of the Standard Model that features a massive stable gauge field which can play the role of the DM. We find that the predictions for the DM abundance may vary significantly from previous studies based on the naive BW ansatz and propose an alternative simple approximation which leads to the correct DM phenomenology. In particular, our results do not depend on the gauge-fixing parameter and are consistent with considerations from high-energy unitarity.

Poles of Karlsruhe-Helsinki KH80 and KA84 solutions extracted by using the Laurent-Pietarinen method

Poles of partial wave scattering matrices in hadron spectroscopy have recently been established as a sole link between experiment and QCD theories and models. Karlsruhe-Helsinki (KH) partial wave analyses have been ``above the line'' in the Review of Particle Physics (RPP) for over three decades. The RPP compiles Breit-Wigner (BW) parameters from local BW fits, but give only a limited number of pole positions using speed plots (SP). In the KH method only Mandelstam analyticity is used as a theoretical constraint, so these partial wave solutions are as model independent as possible. They are a valuable source of information. It is unsatisfactory that BW parameters given in the RPP have been obtained from the KH80 solution, while pole parameters have been obtained from the KA84 version. To remedy this, we have used a newly developed Laurent + Pietarinen expansion method to obtain pole positions for all partial waves for KH80 and KA84 solutions. We show that differences from pole parameters are, with a few exceptions, negligible for most partial waves. We give a full set of pole parameters for both solutions.

Shear viscosity of hadrons withK-matrix cross sections

Shear viscosity \eta and entropy density s of a hadronic resonance gas are calculated using the Chapman-Enskog and virial expansion methods using the K-matrix parametrization of hadronic cross sections which preserves the unitarity of the T -matrix. In the \pi-K-N-\eta- mixture considered, a total of 57 resonances up to 2 GeV were included. Comparisons are also made to results with other hadronic cross sections such as the Breit-Wigner (BW) and, where available, experimental phase shift parametrizations. Hadronic interactions forming resonances are shown to decrease the shear viscosity and increase the entropy density leading to a substantial reduction of \eta/s as the QCD phase transition temperature is approached.

Meson resonances at large [formula omitted]: Complex poles vs Breit–Wigner masses

The rigorous quantum mechanical definition of a resonance requires determining the pole position in the second Riemann sheet of the analytically continued partial wave scattering amplitude in the complex Mandelstam s variable plane. For meson resonances we investigate the alternative Breit–Wigner (BW) definition within the large NC expansion. By assuming that the pole position is O(NC0) and exploiting unitarity, we show that the BW determination of the resonance mass differs from the pole position by O(NC−2) terms, which can be extracted from ππ scattering data. For the case of the σ (f0(600)) pole, the BW scalar mass is predicted to occur at ∼700 MeV while the true value is located at ∼800 MeV.

Bivariate-tdistribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems

Interacting many-particle systems with a mean-field one-body part plus a chaos generating random two-body interaction having strength lambda exhibit Poisson to Gaussian orthogonal ensemble and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and strength functions with transition points marked by lambda = lambda c and lambda = lambda F, respectively; lambda F >> lambda c. For these systems a theory for the matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with lambda > lambda F, in terms of orbital occupation numbers, level densities, and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using a bivariate-t distribution, the theory extends below from the Gaussian regime to the BW regime up to lambda = lambda c. This is well tested in numerical calculations for 6 spinless fermions in 12 single-particle states.

Strength functions for interacting bosons in a mean-field with random two-body interactions

Strength functions have been studied numerically for dense interacting boson systems (with the example of 10 bosons in 5 single-particle states) using a Hamiltonian H, which is a sum of mean-field one-body H1 and a random two-body interaction H2 with strength λ. The strength functions Fξ(E) (defined with respect to H1 basis) changes gradually form Breit–Wigner (BW) to Gaussian form in the chaotic domain as λ increases. A function interpolating these two forms is shown to describe the intermediate region and to determine λF that marks the transition to Gaussian form. Also given is a complete analytical description of the variance of the strength function. The interpolating form for the strength function is used to study the variation of occupancy of single-particle states with excitation energy E.

Strength functions for interacting bosons in a mean-field with random two-body interactions

Strength functions have been studied numerically for dense interacting boson systems (with the example of 10 bosons in 5 single-particle states) using a Hamiltonian H, which is a sum of mean-field one-body H1 and a random two-body interaction H2 with strength λ. The strength functions Fξ(E) (defined with respect to H1 basis) changes gradually form Breit–Wigner (BW) to Gaussian form in the chaotic domain as λ increases. A function interpolating these two forms is shown to describe the intermediate region and to determine λF that marks the transition to Gaussian form. Also given is a complete analytical description of the variance of the strength function. The interpolating form for the strength function is used to study the variation of occupancy of single-particle states with excitation energy E.

Total Neutron Cross Section of Protactinium-233

Transmission measurements on 233Pa have been taken with the Materials Testing Reactor (MTR) fast chopper. The total cross section has been calculated in the energy range from 0.01 to 10 000 eV. These measurements were made on 700 mg of chemically separated 233Pa in an oxide form. The protactinium was produced by irradiating 280 g of 232Th in the Engineering Test Reactor (ETR). The sample represented approximately 15 000 Ci of activity. The data were taken with a resolution of 0.08 to 2.0 μsec/m. The Breit-Wigner (B-W) resonance parameters have been obtained for the resonances below 18 eV. The average parameters give a value of 0.75 × 10 −4 for the s-wave neutron strength function . Weighting the level spacings inversely as 2J + 1 gives the average observed level spacings per spin state of 1.10 and 1.84 eV. A second-order polynomial least-squares fit to the data between 0.01 and 0.10 eV gives a 2200 m/sec total neutron cross section of 55 ± 3 b, superseding a value of 57 b given previously. The resonance-absorption integral for neutrons with energies above 0.4 eV was calculated to be 901 ± 45 b.