S. Ceci, M. Vukšić, B. Zauner
In the course of devising a simple method for extraction of the S-matrix poles from the data, an additional fundamental resonance property emerged. It is a reaction invariant quantity, and since it is directly related to the Breit-Wigner parameters, we call it the Breit-Wigner phase beta. We propose that this beta is added in resonant data tables.
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Chiral symmetry and unitarization are combined into generalized Breit-Wigner expressions describing scalar resonances, which contain free parameters and allow flexible descriptions of masses, widths and pole positions. This theoretical tool is especially designed to be used in analyses of low-energy data.
We show that a slightly modified Breit-Wigner formula can successfully describe the total cross section even for the broad resonances, from light rho(770) to the heavy Z boson. In addition to mass, width, and branching fraction, we include another resonance parameter that turns out to be directly related to the pole residue phase. The new formula has two mathematically equivalent forms: one with the pole, and the other with the Breit-Wigner parameters.
We point out that annihilation of dark matter in the galactic halo can be enhanced relative to that in the early universe due to a Breit-Wigner tail, if the dark matter annihilates through a pole just below the threshold. This provides a new explanation to the "boost factor" which is suggested by the recent data of the PAMELA, ATIC and PPB-BETS cosmic-ray experiments.
Resonances appearing in hadronic scattering processes are described by a two-phase model. In the one phase, scattering products are observed, whereas the other phase describes confinement. A so-called ``Resonance-Spectrum Expansion'' is derived, containing expressions that resemble Breit-Wigner formulae. This method also provides a straightforward explanation for the origin of the light scalar mesons without requiring extra degrees of freedom.
We present an approach to bosonic ($Z^0, W^{\pm}$) as well as fermionic (top-quark) Breit-Wigner propagators which is consistent with gauge invariance arguments. In particular, for the $Z^0$-boson propagator we extend previous analyses and show that the part proportional to $k_μ k_ν/M^2$ must be modified near the resonance. We derive a mass shift which agrees with results obtained elsewhere by different methods. The modified form of a resonant heavy fermion propagator is also given.
Relic Density of Asymmetric Dark Matter with Breit-Wigner Enhancement
该研究将Breit-Wigner增强机制扩展至非对称暗物质领域，探究共振机制的影响并约束相关模型参数，以匹配实验得出的增强因子与天文实验的上限要求。
The nonrelativistic and relativistic Breit-Wigner forms are conventionally used for the resonance fitting. In this note we consider the application of the Breit-Wigner formula with radiative corrections in initial state.
The K-matrix method is often used to describe overlapping resonances. It guarantees the unitarity of the scattering matrix but its parameters are not resonances masses and widths. It is also unclear how to separate resonant and background contributions and to describe background in terms of phase shifts. The Breit-Wigner (BW) approach operates with parameters having direct experimental meaning but a simple sum of the BW functions is not unitary. We show how to construct the unitary S-matrix by taking into account the interference of the BW functions. The method is simple and straightforward, b…
Additivity of Breit-Wigner phases has been proposed to describe interfering resonances in partial waves in $ππ$ scattering. This assumption leads to an expression for partial wave amplitudes that involves products of Breit-Wigner amplitudes. We show that this expression is equivalent to a coherent sum of Breit-Wigner amplitudes with specific complex coefficients which depend on the resonance parameters of all contributing resonances. We use analyticity of $ππ$ partial wave amplitudes to show that they must have the form of a coherent sum of Breit-Wigner amplitudes with complex coefficients and…
Dark matter (DM) annihilation in the galactic halo can be enhanced relative to that in the early Universe due to the Breit-Wigner enhancement, if the DM particles annihilate through a narrow resonance. Although the $s$-wave Breit-Wigner enhancement can provide a consistent explanation for both the observed cosmic-ray (CR) positron excess and the DM thermal relic density, it is severely constrained by the observations of gamma rays from dwarf spheroidal satellite galaxies (dSphs) and the cosmic microwave background (CMB), which have relatively lower allowed DM annihilation cross section and typ…
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 ${\cal O} (N_C^{0})$ and exploiting unitarity, we show that the BW determination of the resonance mass differs from the pole position by ${\cal O} (N_C^{-2})$ terms, which can be extracted from pi-pi scattering data. …
We consider a description of propagators for particle resonances which takes into account the quantum mechanical interference due to the width of two or more nearby states that have common decay channels, by incorporating the effects arising from the imaginary parts of the one-loop self-energies. Depending on the couplings to the common decay channels, the interference effect, not taken into account in the usual Breit-Wigner approximation, can significantly modify the cross section or make the more long-lived resonance narrower. We give few examples of New Physics models for which the effect i…
Rekindling s-Wave Dark Matter Annihilation Below 10GeV with Breit-Wigner Effects
该研究通过布里特-维格纳效应重新激活低于10GeV的s波暗物质湮灭探测，提出迟到冻结机制影响 relic 密度。
The consistent description of resonant transition amplitudes within the framework of perturbative field theories necessitates the definition and resummation of off-shell Green's functions, which must respect several crucial physical requirements. In particular, the generalization of the usual Breit-Wigner formalism in a non-Abelian context constitutes a highly non-trivial problem, related to the fact that the conventionally defined Green's functions are unphysical. We briefly review the main field-theoretical difficulties arising when attempting to use such Green's functions outside the confin…
We discuss the derivation and properties of the general representation of partial wave amplitudes in the context of improving the models currently used in analysis of three particle Dalitz distributions.
Spin Partners of the $B^{(*)}\bar{B}^{(*)}$ resonances with a different approach than the Breit-Wigner parameterization
本文采用能包含阈值效应的Sill分布替代Breit-Wigner参数化，在接触势加单π交换势的分子态图像下研究$Z_b(10610)$和$Z_b(10650)$的重夸克自旋对称伙伴，发现所有伙伴均为束缚态。
We have developed a covariant isobar model to phenomenologically explain the four possible isospin channels of $KΣ$ photoproduction. To obtain a consistent reaction amplitude, which is free from the lower-spin background problem, we used the consistent electromagnetic and hadronic interactions described in our previous report. We used all available experimental data, including the recent MAMI A2 2018 data obtained for the $K^0Σ^+$ and $K^0Σ^0$ isospin channels. By fitting the calculated observables to these data we extract the resonance properties, including their Breit-Wigner and pole paramet…
The relationship between Breit-Wigner distribution as an underlying basis for decaying unstable quantum systems and GSI experiment (anomaly) has not been addressed properly in the literatures. We show that quantum beats can be obtained using a superposition of two Breit-Wigner distributions. This modified distribution can explain the GSI time anomaly with quantum beats resulting from the existence of two energy levels of the decaying ion.
The Breit-Wigner enhancement of the thermally averaged annihilation cross section <σv> is shown to provide a large boost factor when the dark matter annihilation process nears a narrow resonance. We explicitly demonstrate the evolution behavior of the Breit-Wigner enhanced <σv> as the function of universe temperature for both the physical and unphysical pole cases. It is found that both of the cases can lead an enough large boost factor to explain the recent PAMELA, ATIC and PPB-BETS anomalies. We also calculate the coupling of annihilation process, which is useful for an appropriate model bui…
For systems of unstable particles that mix with each other, an approximation of the fully momentum-dependent propagator matrix is presented in terms of a sum of simple Breit-Wigner propagators that are multiplied with finite on-shell wave function normalisation factors. The latter are evaluated at the complex poles of the propagators. The pole structure of general propagator matrices is carefully analysed, and it is demonstrated that in the proposed approximation imaginary parts arising from absorptive parts of loop integrals are properly taken into account. Applying the formalism to the neutr…
In the paper we study the Breit-Wigner enhancement of dark matter (DM) annihilation considering the kinetic decoupling in the evolution of DM freeze-out at the early universe. Since the DM temperature decreases much faster (as $1/R^2$) after kinetic decoupling than that in kinetic equilibrium (as 1/R) we find the Breit-Wigner enhancement of DM annihilation rate after the kinetic decoupling will affect the DM relic density significantly. Focusing on the model parameters that trying to explain the anomalous cosmic positron/electron excesses observed by PAMELA/Fermi/ATIC we find the elastic scatt…
GeV-scale dark matter with $p$-wave Breit-Wigner enhanced annihilation
本文研究GeV尺度标量暗物质通过近质量简并暗光子介导的p波Breit-Wigner共振湮灭，发现动力学退耦会显著降低遗迹密度，并结合CMB畸变、X射线、直接探测和加速器数据对模型参数空间给出强约束。
The broad non-strange meson $f_0$(500) is considered to be a non-Breit-Wigner resonance. It is generally assumed that if a resonance is broad it can hardly be described by a Breit-Wigner form. We show here that is not true neither for the broad Z boson, nor for the much narrower $Δ(1232)$, and explain why the $f_0$(500) fits with them perfectly. Key differences between them boil down to a single parameter: the angle at which we see the resonance pole from the threshold, which explains the background, the residue phase, and the difference between the pole and Breit-Wigner parameters.
Dark Matter Annihilation via Breit-Wigner Enhancement with Heavier Mediator
提出通过 Breit-Wigner 共振增强暗物质早期冻结与黑洞附近湮灭的新场景，利用较重介子避开宇宙微波背景约束，并指出超大质量黑洞可重新激活湮灭产生光子信号，可由 Fermi-LAT 和 COSI 卫星检验。
Whether one starts form the analytic S-matrix definition or the requirement of gauge parameter independence in renormalization theory, a relativistic resonance is given by a pole at a complex value s of energy squared. The complex number s does not define the mass and width separately and this definition does not lead to interfering Breit-Wigner if two or more resonances are involved. To accomplish both we invoke the decaying particle aspect of a resonance and associate to each pole a space of relativistic Gamow kets which transform irreducibly under causal Poincare transformations. A Gamow st…
Critique of Breit-Wigner resonance scattering
本文通过方势阱散射问题，指出Breit-Wigner共振散射方法中相位偏移设定、共振参数符号、能量极点物理意义及衰变态波函数指数增长等问题，并利用反线性PT对称性给出复数共轭能量对解，从而解决这些挑战。
A general expression resembling Breit-Wigner formulae is derived for the description of resonances which appear in meson-meson scattering. Starting point is a unitarised meson model, but reduced to a simpler form and freed from the specific assumption about the confining force. The parameters of the resulting ``Resonance-Spectrum Expansion'' are directly related to the confinement spectrum and the mechanism of $^3P_0$ valence-quark-pair creation for OZI-allowed hadronic decay, and not to the central positions and widths of resonances. The method also provides a straightforward explanation for …
We analyze the quasi-two-body charmed $B$ decays $B^{+,0}_{(s)} \to D_{(s)}^* P_2 \to D_{(s)} P_1 P_2$ with $P_{1,2}$ as a pion or kaon. The intermediate processes $B_{(s)} \to D_{(s)}^* P_2 $ are calculated with the factorization-assisted topological-amplitude approach and the resonant effects are calculated with the Breit-Wigner formalism. Taking all p-wave resonance states $ \bar D_{(s)}^*$ into consideration, we present the related branching fractions, calculate the Breit-Wigner-Tail effects, and investigate the flavor $SU(3)$ breaking effects. Most of our branching fractions are consisten…
We study the property of the $X(3872)$ meson by analyzing the $B\to K D\bar D^*$ and $B\to K J/ψπ^+π^-$ decay processes. The competition between the rescattering mediated through a Breit-Wigner resonance and the rescattering generated from a local $D\bar{D}^* \to D\bar{D}^*$ interaction is carefully studied through an effective lagrangian approach. Three different fits are performed: pure Breit-Wigner case, pure $D\bar{D}^*$ molecule case with only local rescattering vertices (generated by the loop chain), and the mixed case. It is found that data supports the picture where X(3872) is mainly a…
First, we discuss the conditions under which the non-relativistic and relativistic types of the Breit-Wigner energy distributions are obtained. Then, upon insisting on the correct normalization of the energy distribution, we introduce a Flatté-like relativistic distribution -- denominated as Sill distribution -- that (i) contains left-threshold effects, (ii) is properly normalized for any decay width, (iii) can be obtained as an appropriate limit in which the decay width is a constant, (iv) is easily generalized to the multi-channel case (v) as well as to a convoluted form in case of a decay c…
The τ^-\to K^-ην_τdecays have been studied using Chiral Perturbation Theory extended by including resonances as active fields. We have found that the treatment of final state interactions is crucial to provide a good description of the data. The Breit-Wigner approximation does not resum them and neglects the real part of the corresponding chiral loop functions, which violates analyticity and leads to a failure in the confrontation with the data. On the contrary, its resummation by means of an Omnès-like exponentiation of through a dispersive representation provides a successful explanation of …
Verifying the Resonance Schemes of Unstable Particles at Lepton Colliders
本文提出在轻子对撞机上通过Z线形扫描、前后不对称性和WW阈值扫描等方法，区分不稳定粒子的Breit-Wigner、理论和能量依赖共振方案，并利用衰变宽度与质量的缩放关系及费米常数实现方案判别。
Sommerfeld enhancement and Breit-Wigner enhancement of the dark matter annihilation have been proposed to explain the "boost factor" which is suggested by observed cosmic ray excesses. Although these two scenarios can provide almost indistinguishable effects on the cosmic ray fluxes, the cross sections of the self-interaction in those enhancement mechanisms are drastically different. As a result, we show that they can be distinguished by examining the effects of the self-interaction on the halo shapes. In Sommerfeld enhancement models with m_phi<100MeV and m_DM<3TeV, the self-interaction can l…
It is argued in [1] that when the strong coupling to the K Lambda channel is considered, Breit-Wigner mass of the lightest orbital excitation of the nucleon N(1535) shifts to a lower value. The new value turned out to be smaller than the mass of the lightest radial excitation N(1440), which effectively solved the long-standing problem of conventional constituent quark models. In this Comment we show that it is not the Breit-Wigner mass of N(1535) that is decreased, but its bare mass. [1] B. C. Liu and B. S. Zou, Phys. Rev. Lett. 96, 042002 (2006).
We derive relations for baryon photo-decay amplitudes both for the Breit-Wigner and the pole positions. With an updated SAID partial wave analysis, technically similar to the earliest Virginia Tech analysis of photoproduction data, we compare photo-decay amplitudes at both resonance positions for a few selected nucleon resonances. Comparisons are made and a qualitative similarity, seen between the pole and Breit-Wigner values extracted by the Bonn-Gatchina group, is confirmed in the present study.
We analyze $ππ-K\bar{K}$ and $πη-K\bar{K}$ couple channel [1,1] matrix Padé amplitudes of $SU(3)\times SU(3)$ chiral perturbation theory. By fitting phase shift and inelasticity data, we determine pole positions in different channels ($f_0(980)$, $a_0(980)$,$f_0(600)$, $K_0^*(800)$, $K^*(892)$, $ρ(770)$) and trace their $N_c$ trajectories. We stress that a couple channel Breit--Wigner resonance should exhibit two poles on different Riemann sheets and meet each other on the real axis when $N_c=\infty$. Poles are hence classified using this criteria and we conclude that $K^*(892)$ and $ρ(770)$ a…
The multiple-solution problem in determining the three-interfering-resonances' parameters from a fit to an experimentally measured distribution is considered in a mathematical viewpoint. In this paper it is shown that there are four numerical solutions for the fit with three coherent Breit-Wigner functions. Although the explicit analytical formulae can not be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, numerical method is provided to derive the other solutions…
The cross sections of $e^+e^- \rightarrow πZ_c(3900) \rightarrow ππJ/ψ$ and $e^+e^- \rightarrow πZ_c(3900) \rightarrow πD\bar{D}^{*}$ have been measured by BESIII experiment. We try to perform a combined fit to the cross sections with one Breit-Wigner function, the fit results show the structure's mass and width are $M=(4232\pm5)$ MeV/$c^2$, $Γ=(65\pm21)$ MeV. The ratio $\frac{\mathcal{B}(Z_c(3900)\rightarrow D\bar{D}^{*})}{\mathcal{B}(Z_c(3900)\rightarrowπJ/ψ)}$ is determined to be $(16\pm6)$. We also try to fit the cross sections with two Breit-Wigner functions, while we can't come to any de…
Large-Width New Physics at Colliders: A Gauge-Invariant Resummation Approach
针对对撞机上宽共振态易使标准蒙特卡洛方法产生非物理规范赝象的问题，提出结合戴森重求和传播子与重求和顶点的规范自洽框架，证明标准方法在大宽度区间存在估计偏差，需重新审视相关新物理探测限。
We study the dynamics of self-interacting scalar fields with $Z_2$ symmetry governed by a relativistic Israel-Stuart type diffusion equation in the vicinity of a critical point. We calculate spectral functions of the order parameter in mean-field approximation as well as using first-principles classical-statistical lattice simulations in real-time. We observe that the spectral functions are well-described by single Breit-Wigner shapes. Away from criticality, the dispersion matches the expectations from the mean-field approach. At the critical point, the spectral functions largely keep their Br…
Discussion of apparently simple issues related to the resonance close to threshold may lead to misleading results. We clarify some subtle points, in particular the relation between Breit-Wigner and effective range approaches to the f_0-a_0 mesons.
In this work, within the QCD factorization approach, we study the localized integrated $CP$ violation in the $B^-\rightarrow π^-π^+π^-$ decay and the branching fraction of the $B^-\rightarrowσπ^-$ decay. Both the resonance and nonresonance contributions are included when we study the localized $CP$ asymmetry in the $B^-\rightarrow π^-π^+π^-$ decay. The resonance contributions from the scalar $σ(600)$ and vector $ρ^0(770)$ mesons are included. For the $σ(600)$ meson, we apply both the Breit-Wigner and Bugg models to deal with its propagator, and obtain $\mathcal{B}(B^-\rightarrow σ(600)π^-)<1.6…
We propose a phenomenological three component model describing the decay amplitude of the process $D_{s}^{+} \ra 3π$. The first component is a constant background, the second one is a Breit-Wigner amplitude associated to a quasi two-body $f_{0}(980) π^{+}$ state and the third one another Breit-Wigner amplitude corresponding to a possible quasi two-body $ρ(770) π$ state. We show that it is possible to reproduce the observed total rate for $D_{s}^{+} \ra π^{+}π^{+}π^{-}$ as well as the two other measured branching ratios for the non resonant part and the resonant $f_{0}π^{+}$ one. Implication of…
$CP$-violating asymmetries calculated from the Breit-Wigner approximation for unstable particle propagators violate $CPT$. A formalism satisfying $CP$ invariance and unitarity is presented. Applications are given to $t$ decays. For the decay $t\to bν_τ\barτ$ in a class of $CP$-violating models the $CP$-violating asymmetry turns out to be $10^{-4}$ times smaller than the previously reported results.
$q\bar{q}$ scattering phase shift in the $π^0$ channel and $π^0$ meson spectral function under external magnetic field and finite meson momentum
该研究在NJL模型下，分析外磁场与有限介子动量对π⁰道q\bar{q}散射相移及π⁰介子谱函数的影响，揭示了外磁场、手征相变、泡利阻塞等因素对多峰结构与相移跳变的作用。
A model-independent method for the determination of Breit-Wigner resonance parameters is presented. The method is based on eliminating the dependence on the choice of channel basis by analyzing the trace of the K and T matrices in the coupled-channel formalism, rather than individual matrix elements of the multichannel scattering matrix.
Motivated by the possibility of enhancing dark matter (DM) self-interaction cross-section $σ_{\rm self}$, we have revisited the issue of DM annihilation through a Breit-Wigner resonance. In this case thermally averaged annihilation cross-section has strong temperature dependence, whereas elastic scattering of DM on the thermal bath particles is suppressed. This leads to the early kinetic decoupling of DM and an interesting interplay in the evolution of DM density and temperature that can be described by a set of coupled Boltzmann equations. The standard Breit-Wigner parametrization of a resona…
It is shown that the ratio of the production rates of the pairs (B+ B-) and (B0 anti-B0) should experience a substantial and rapid variation with energy within the width of the Upsilon(4S) resonance, crossing the value of one near the center of the resonance. This behavior is due to an interference of the rapidly changing with energy Breit-Wigner phase with the phase introduced in the wave function of charged mesons by their Coulomb interaction.
Role of $Σ^*(1/2^-)$ baryons in $Λ_c\to Λπ^+π^+π^-$ decay
基于Belle数据，研究了$Λ_c\ o Λπ^+π^+π^-$衰变中1435 MeV附近的增强结构，通过Breit-Wigner共振与重散射两种机制描述该现象，并证明$Σ^*(1/2^-)$态对准确拟合不变质量分布至关重要。
A careful reanalysis is made on $e^+e^-\to X(4660)\to (Λ_c\barΛ_c)/(ψ'ππ)$ processes, aiming at resolving the apparent conflicts between Belle and BESIII data above $Λ_c\barΛ_c$ threshold. We use a model containing a Breit-Wigner resonance and $Λ_c\barΛ_c$ four-point contact interactions, with which the enhancement right above the $Λ_c\barΛ_c$ threshold is well explained by a virtual pole generated by $Λ_c\barΛ_c$ attractive final state interaction, located at $M_V=4.566\pm0.007$ GeV. Meanwhile, $X(4660)$ remains to be a typical Breit-Wigner resonance, and is hence of confinement nature. Our a…
High-resolution spectrometer measurements of the reaction H(e,e' K+)X at small Q2 are used to extract the mass and width of the Lambda(1520). We investigate dependence of the resonance parameters on different parametrizations of the background and the resonance peak itself. Our final values for the Breit-Wigner parameters are M=1520.4+-0.6(stat)+-1.5(syst) MeV and Gamma=18.6+-1.9(stat)+-1(syst) MeV. The width appears to be more sensitive to the assumptions than the mass. We also estimate, for the first time, the pole position for this resonance and find that both the pole mass and width seem t…
High-resolution spectrometer measurements of the reaction H(e,e'K+)X at small Q2 are used to extract the mass and width of the Lambda(1520). We investigate the influence of various assumptions used in the extraction. The width appears to be more sensitive to the assumptions than the mass. To reach a width uncertainty about 1 MeV or better, one needs to know the structure of the non-resonant background. Based on the new Jefferson Lab Hall A data, our final values for the Breit-Wigner parameters are M = 1520.4 +- 0.6 (stat) +- 1.5 (syst) MeV, Gamma = 18.6 +- 1.9 (stat) +- 1 (syst) MeV. For the f…
Using a simple parametrization of Breit-Wigner type for the hadronic side of the QCD sum rule for $ρ$ mesons in vacuum as well as in a nuclear medium we explore the range of values for the mass and the width of the $ρ$ meson which are compatible with the operator product expansion.
The decays $τ^-\to K^-ην_τ$ and $K^-η^\primeν_τ$ are studied in the context of Chiral Perturbation Theory supplemented with the explicit inclusion of resonances. For the required vector-form factors we have explored three different possibilities according to the treatment of final-state interactions: Breit-Wigner parametrisation, exponential resummation and dispersive representation. In the first part of the analysis, we predict the invariant mass spectrum and the integrated branching ratio for both decays from a fit to data on $τ^-\to K_Sπ^-ν_τ$ decays. In the second part, we take advantage o…
The Sill distribution for all partial waves
本文将原本局限于s波的西尔分布扩展到任意分波，其p波版本可准确描述Δ(1232)⁺⁺的线形及相关参数，与PDG结果一致。
New kaon photoproduction data on a proton, gamma + p --> K+ + Lambda, are analyzed using a multipole approach. The background terms are given in terms of gauge invariant, crossing symmetric, Born diagrams with hadronic form factors, while the resonances are parameterized using Breit-Wigner forms. Preliminary results suggest a number of new resonances, as predicted by many quark model studies. A comparison between the extracted multipoles and those obtained from KAON-MAID is presented.
We describe the method for extracting the elastic scattering phase shift from a lattice simulation at an introductory level, for non-lattice practitioners. We consider the scattering in a resonant channel, where the resulting phase shift delta(s) allows the lattice determination of the mass and the width of the resonance from a Breit-Wigner type fit. We present the method for the example of P-wave pi-pi scattering in the rho meson channel.
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