Breit-Wigner Shape Research Articles

Critical dynamics of relativistic diffusion

We study the dynamics of self-interacting scalar fields with Z2 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 Breit-Wigner shape, albeit with non-trivial power-law dispersion relations. We extract the characteristic time-scales as well as the dynamic critical exponent z, verifying the existence of a dynamic scaling regime. In addition, we derive the universal scaling functions implied by the Breit-Wigner shape with critical power-law dispersion and show that they match the data. Considering equations of motion for a system coupled to a heat bath as well as an isolated system, we perform this study for two different dynamic universality classes, both in two and three spatial dimensions.

Subleading contributions to the decay width of the Tcc+ tetraquark

Recently the LHCb collaboration has announced the discovery of the $T_{cc}^+$ tetraquark. Being merely a few hundred ${\rm keV}$ below the $D^{*+} D^0$ threshold, the $T_{cc}^+$ is expected to have a molecular component, for which there is a good separation of scales that can be exploited to make reasonably accurate theoretical predictions about this tetraquark. Independently of its nature, the most important decay channels will be $D^+ D^0 \pi^0$, $D^0 D^0 \pi^+$ and $D^+ D^0 \gamma$. Its closeness to threshold suggests that the mass and particularly the width of the $T_{cc}^+$ tetraquark depend on the resonance profile. While the standard Breit-Wigner parametrization generates a $T_{cc}^+$ that is too broad for current theoretical calculations to reproduce, a three-body unitarized Breit-Wigner shape reveals instead a decay width ($\Gamma_{\rm pole} = 48\pm 2\,{}^{+0}_{-12}\,{\rm keV}$) consistent with theoretical expectations. Here we consider subleading order contributions to the decay amplitude, which though having at most a moderate impact in the width still indicate potentially significant differences with the experimental width that can be exploited to disentangle the nature of the $T_{cc}^+$. Concrete calculations yield $\Gamma^{\rm LO} = 49 \pm 16\,{\rm keV}$ and $\Gamma^{\rm NLO} = 58^{+7}_{-6}\,{\rm keV}$, though we expect further corrections to the ${\rm NLO}$ decay widths from asymptotic normalization effects. We find that a detailed comparison of the ${\rm NLO}$ total and partial decay widths with experiment suggests the existence of a small (but distinguishable from zero) non-molecular component of the $T_{cc}^+$.

Determination of s- and p-wave I = 1/2 Kπ scattering amplitudes in Nf = 2 + 1 lattice QCD

The elastic I=1/2, s- and p-wave kaon-pion scattering amplitudes are calculated using a single ensemble of anisotropic lattice QCD gauge field configurations with Nf=2+1 flavors of dynamical Wilson-clover fermions at mπ=230 MeV. A large spatial extent of L=3.7 fm enables a good energy resolution while partial wave mixing due to the reduced symmetries of the finite volume is treated explicitly. The p-wave amplitude is well described by a Breit–Wigner shape with parameters mK⁎/mπ=3.808(18) and gK⁎KπBW=5.33(20) which are insensitive to the inclusion of d-wave mixing and variation of the s-wave parametrization. An effective range description of the near-threshold s-wave amplitude yields mπa0=−0.353(25).

Anomalies in weak decays of H-like ions

We investigate the emergence of oscillations in the decay law of unstable systems. We discuss in particular the case of the so-called GSI anomaly seen in the electron capture decays of H-like ions and prove that such oscillations cannot be explained by neutrino oscillations. We then discuss how such anomalies could be intimately related to the decay law of unstable systems in the case in which their spectral function deviates from a Breit-Wigner shape.

Asymmetric vector mesons produced in nuclear collisions

It is argued that the experimentally observed phenomenon of asymmetric shapes of vector mesons produced in nuclear media during high energy nucleus-nucleus collisions can be explained as Fano-Feshbach resonances. It has been observed that the mass distributions of lepton pairs created at meson decays decline from the traditional Breit-Wigner shape with some excess in the low-mass wing of the resonance. It is clear that the whole phenomenon is related to some interaction with the nuclear medium. Moreover, it can be further detalized in quantum mechanics as the interference of direct and continuum states in Fano-Feshbach effect. To reveal the nature of the interaction it is proposed to use a phenomenological model of the additional contribution due to Cherenkov gluons. They can be created because of the excess of the refractivity index over 1 just in the low-mass wing as required by the classical Cherenkov treatment. In quantum mechanics, this requirement is related to the positive real part of the interaction amplitude in this wing. The corresponding parameters are found from the comparison with $\rho $-meson data and admit reasonable explanation.

How resonance-continuum interference changes 750 GeV diphoton excess: signal enhancement and peak shift

The new scalar resonance contribution to the 750 GeV diphoton excess observed at the LHC 13 TeV necessarily interferes with the continuum background in the $gg\to \gamma \gamma$. The interference has two considerable effects: (1) enhancing or suppressing diphoton signal rate due to the imaginary-part interference and (2) distorting resonance shape due to the real-part interference. From the best-fit study of two benchmark models (two Higgs doublets with $\sim$50 GeV widths and a singlet scalar with 5 GeV width, both extended with vector-like fermions), we find that the resonance contribution to the 750 GeV excess can be enhanced by a factor of 2(1.6) for 3(6) fb signal rate and the 68%(95%) CL best-fit mass range can shift by 1-4 (any ${\cal O}$(1)) GeV. If the best-fit excess rate decreases with future data, the interference effects will become more significant. The inevitable interferences can also provide a consistency check of a resonance hypothesis, whether or not future precision shape measurements confirm a Breit-Wigner shape or discover interesting deviations.

Local quenches with global effects in interacting quantum systems.

We study one-dimensional lattices of interacting spins-1/2 and show that the effects of quenching the amplitude of a local magnetic field applied to a single site of the lattice can be comparable to the effects of a global perturbation applied instantaneously to the entire system. Both quenches take the system to the chaotic domain, the energy distribution of the initial states approaches a Breit-Wigner shape, the fidelity (Loschmidt echo) decays exponentially, and thermalization becomes viable.

Quantum Wire Hybridized With a Single-Level Impurity

We have studied low-temperature properties of interacting electrons in a one-dimensional quantum wire (Luttinger liquid) side-hybridized with a single-level impurity. The hybridization induces a backscattering of electrons in the wire which strongly affects its low-energy properties. Using a one-loop renormalization group approach valid for a weak electron-electron interaction, we have calculated a transmission coefficient through the wire, T(epsilon), and a local density of states, nu(epsilon) at low energies epsilon. In particular, we have found that the antiresonance in T(epsilon) has a generalized Breit-Wigner shape with the effective width Gamma(epsilon) which diverges at the Fermi level.

Finite-width effects on Delta baryons in QCD sum rules

The quantum chromodynamics (QCD) sum rules for the Delta baryons are analyzed by taking into account the finite-width effects, through explicit utilization of the Breit–Wigner shape. We apply a Monte Carlo based analysis to the ‘traditional’ and the parity-projected sum rules. The first Delta excitation state is also considered as a sub-continuum resonance and the widths are calculated using the mass values as input.

Spectral functions of scalar mesons

In this work we study the spectral functions of scalar mesons in one- and two-channel cases by using nonlocal interaction Lagrangian(s). When the propagators satisfy the K\"allen-Lehman representation, a normalized spectral function is obtained, allowing one to take into account finite-width effects in the evaluation of decay rates. In the one-channel case, suitable to the light $\ensuremath{\sigma}$ and $k$ mesons, the spectral function can deviate consistently from a Breit-Wigner shape. In the two-channel case with one subthreshold channel, the evaluated spectral function is well approximated by a Flatt\'e distribution; when applying the study to the ${a}_{0}(980)$ and ${f}_{0}(980)$ mesons, the tree-level forbidden KK decay is analyzed.

Measurement of thee+e−→π+π−J/ψCross Section Via Initial-State Radiation at Belle

The cross section for e(+)e(-)-->pi(+)pi(-)J/psi between 3.8 and 5.5 GeV/c(2) is measured using a 548 fb(-1) data sample collected on or near the Upsilon(4S) resonance with the Belle detector at KEKB. A peak near 4.25 GeV/c(2), corresponding to the so called Y(4260), is observed. In addition, there is another cluster of events at around 4.05 GeV/c(2). A fit using two interfering Breit-Wigner shapes describes the data better than one that uses only the Y(4260), especially for the lower-mass side of the 4.25 GeV enhancement.

Evidence for In-Medium Modification of theϕMeson at Normal Nuclear Density

Invariant mass spectra of e(+) e(-) pairs have been measured in 12 GeV p + A reactions to detect possible in-medium modification of vector mesons. Copper and carbon targets are used to study the nuclear-size dependence of e(+) e(-) invariant mass distributions. A significant excess on the low-mass side of the phi meson peak is observed in the low betagamma(= beta/square root(1-beta(2))) region of phi mesons (betagamma < 1.25) with copper targets. However, in the high betagamma region (betagamma > 1.25), spectral shapes of phi mesons are well described by the Breit-Wigner shape when experimental effects are considered. Thus, in addition to our earlier publications on rho/omega modification, this study has experimentally verified vector meson mass modification at normal nuclear density.

Propagator of the Δ resonance and determination of the magnetic moment of theΔ+from theγp→γπopreaction

The photon-proton scattering reactions {gamma}p{yields}{pi}{sup o}p,{gamma}p{yields}{gamma}p, and {gamma}p{yields}{gamma}{pi}{sup o}p are investigated in the framework of the three-dimensional time-ordered approach using different models of the on-shell {delta} propagators. These {delta} propagators are taken from the unitary separable models of the {pi}N elastic-scattering amplitude and from the relativistic Breit-Wigner shape representation of the nonunitary {pi}N amplitude in the tree approach. The numerical calculations are performed with the complete set of the one-particle ({pi}-,{omega}-, and {rho}-meson, nucleon, and {delta}) exchange diagrams. It is found that the numerical calculations of the above reactions in the {delta}-resonance region are very sensitive to the model of the {delta} propagator. This sensitivity is explained by the difference between the input {pi}N elastic-scattering observables used for the construction of the {delta} propagator. It is shown, that after additional approximation our calculations reproduce the tree-level model calculations with the Breit-Wigner shape {delta} propagator. This model is in good agreement with the {gamma}p{yields}{pi}{sup o'}p{sup '} reaction and with the preliminary data for the {gamma}p{yields}{gamma}{sup '}{pi}{sup o'}p{sup '} reaction. Conversely, it is demonstrated, that the relativistic Breit-Wigner shape {delta} propagators, obtained from the nonunitary {pi}N amplitudes in the tree approximation, is inconsistent to apply for reproduction of the {gamma}p scattering observablesmore » because they do not describe the {pi}N scattering data in the {delta} resonance region. It is emphasized, that to extract the magnitude of the {delta}{sup +} magnetic moment from the cross sections of the {gamma}p{yields}{gamma}{sup '}{pi}{sup '}N{sup '} reaction it is necessary to fix the form of the {delta} propagator based on the unified description of the two body {pi}p{yields}{pi}N,{gamma}p{yields}{pi}N basic channels together with the essential {gamma}p{yields}{pi}{pi}N and {gamma}p{yields}{gamma}p reactions.« less

Resonances and thermonuclear reaction rates for charged particle collisions

We derive an approximate analytic expression for thermonuclear reaction rate for charged particles for the case that the cross section contains a single narrow or broad resonance described by a Breit-Wigner shape. An asymptotic series is obtained by making a Taylor series expansion which is exact at both the effective energy of the Gamow window and at the resonance energy. The resulting expression is uniformly valid as the effective energy and resonance energy coalesce or separate and as the resonance width is varied from narrow to broad. This is not true of conventional analytic approximations. We compare our uniform approximation with the exact reaction rate numerically and find it to be accurate over a large parameter range. We use our expressions to calculate the reaction rate for $^{12}\mathrm{C}(p,\ensuremath{\gamma})^{13}\mathrm{N}$.

Resonances and the thermonuclear reaction rate

We present an approximate analytic expression for thermonuclear reaction rate of charged particles when the cross section contains a single narrow or wide resonance described by a Breit-Wigner shape. The resulting expression is uniformly valid as the effective energy and resonance energy coalesce. We use our expressions to calculate the reaction rate for 12C(p,γ) 13N.

The spin-boson model with a structured environment: a comparison of approaches

In the spin-boson model, the properties of the oscillator bath are fully characterized by the spectral density of oscillators $J(\omega)$. We study the case when this function is of Breit-Wigner shape and has a sharp peak at a frequency $\Omega$ with width $\Gamma\ll\Omega$. We use a number of approaches such as the weak-coupling Bloch-Redfield equation, the non-interacting blip approximation (NIBA) and the flow-equation renormalization scheme. We show, that if $\Omega$ is much larger than the qubit energy scales, the dynamics corresponds to an Ohmic spin-boson model with a strongly reduced tunnel splitting. We also show that the direction of the scaling of the tunnel splitting changes sign when the bare splitting crosses $\Omega$. We find good agreement between our analytical approximations and numerical results. We illuminate how and why different approaches to the model account for these features and discuss the interpretation of this model in the context of an application to quantum computation and read-out.

The complex phase gradient method applied to leaky Lamb waves.

The classical phase gradient method applied to the characterization of the angular resonances of an immersed elastic plate, i.e., the angular poles of its reflection coefficient R, was proved to be efficient when their real parts are close to the real zeros of R and their imaginary parts are not too large compared to their real parts. This method consists of plotting the partial reflection coefficient phase derivative with respect to the sine of the incidence angle, considered as real, versus incidence angle. In the vicinity of a resonance, this curve exhibits a Breit-Wigner shape, whose minimum is located at the pole real part and whose amplitude is the inverse of its imaginary part. However, when the imaginary part is large, this method is not sufficiently accurate compared to the exact calculation of the complex angular root. An improvement of this method consists of plotting, in 3D, in the complex angle plane and at a given frequency, the angular phase derivative with respect to the real part of the sine of the incidence angle, considered as complex. When the angular pole is reached, the 3D curve shows a clear-cut transition whose position is easily obtained.

The complex phase gradient method: A new tool for the investigation of immersed elastic plate angular resonances

The Phase Gradient Method applied to the complete characterization of the angular resonances of an immersed elastic plate, i.e., the angular poles of the plate reflection coefficient, was proven to be efficient, as far as the pole imaginary parts are not too large when compared to their real parts. This method consists of plotting the reflection coefficient phase partial derivative with respect to the sine of the incidence angle, considered as real, vs incidence angle. At the vicinity of an angular resonance, the plot exhibits a Breit–Wigner shape, whose minimum is located at the pole real part and whose amplitude is the inverse of its imaginary part. However, when the imaginary part is too large, this method does not give its value with a sufficient accuracy, compared to the exact calculation of the root in the complex angle plane. An improvement consists in plotting in 3D, in the complex angle plane, the angular phase derivative with respect to the real part of the sine of the incidence angle, considered as complex. When an angular pole is reached, the 3D curve shows a clear cut transition of very large amplitude, whose position is easily obtained.

Structure of theP11(1440MeV) resonance from α-pand π-Nscattering

To understand the various results on the ${N}^{*}(1440\mathrm{M}\mathrm{e}\mathrm{V})$ resonance in a consistent way, the data on $\ensuremath{\alpha}\ensuremath{-}p$ scattering at ${E}_{\ensuremath{\alpha}}=4.2\mathrm{GeV}$ were reanalyzed assuming projectile and target excitation, and their interference. A quantitative fit of the spectrum is obtained, assuming for the ${N}^{*}$ mass distribution a threshold modified Breit-Wigner shape with momentum-dependent width and resonance parameters $M=1390\ifmmode\pm\else\textpm\fi{}20\mathrm{MeV}$ and $\ensuremath{\Gamma}=190\ifmmode\pm\else\textpm\fi{}30\mathrm{MeV}.$ This, however, is not consistent with the data on \ensuremath{\pi}-N scattering which, in general, require a higher resonance mass and a larger width. Both systems, \ensuremath{\alpha}-p and \ensuremath{\pi}-N, can be described consistently in a T-matrix formalism, assuming two structures in the ${P}_{11}(1440\mathrm{MeV})$ resonance, from which only the first one is observed in \ensuremath{\alpha}-p. For this structure the elastic \ensuremath{\pi}-N width is small and the decay into the $2\ensuremath{\pi}(s)\ensuremath{-}N$ channel is large. This strongly supports the conclusions drawn from \ensuremath{\alpha}-p scattering. The second structure at higher mass has a strong decay into the \ensuremath{\pi}\ensuremath{\Delta} channel and can be well understood as a second-order excitation of the $\ensuremath{\Delta}(1230\mathrm{MeV}).$ The two resonance picture of the ${P}_{11}(1440\mathrm{MeV})$ resonance is supported by \ensuremath{\gamma}-induced reactions; no evidence is found for the first ${N}^{*},$ however, the second resonance is observed (although more or less obscured by nonresonant \ensuremath{\pi}-\ensuremath{\Delta} production). A further crucial test of the existence of two structures in the Roper resonance is provided by exclusive \ensuremath{\alpha}-p experiments; a ${N}^{*}$ decay pattern should be found quite different from \ensuremath{\pi}-N with a very strong 2\ensuremath{\pi} decay.

Field-theoretical description of electromagnetic Δ resonance production and determination of the magnetic moment of the Δ+ (1232) resonance by the ep → e′ N′ π′ γ′ and γp → N′ π′ γ′ reactions

The ep → e′ N′ π′ γ′ and γp → N′ π′ γ′ reactions in the Δ resonance region are investigated in the framework of the relativistic field-theoretical spectral decomposition method for the γ ∗N → γ′π′N′ transition amplitude. This approach allows us to express the amplitude through three-dimensional diagrams with on-mass shell intermediate states. The Δ resonance is constructed as intermediate cluster state | Ψ Δ 〉 with real bare mass M Δ ∼ 1232 MeV and with a complex propagator of Breit-Wigner shape for the P 33 π N amplitude. Thus, the usual off-mass shell ambiguities in spin 3 2 effective Lagrangians do not affect the present description. Using a unified treatment of nucleons, mesons, and Δ's as bound systems of quarks according to the Haag-Nishijima-Zimmermann field-theoretical approach, it is shown that quark-gluon degrees of freedom only change the rule for constructing the form factors in three-dimensional diagrams for obtaining the γ ∗N → γ′π′N′ transition amplitude. However, the structure of these-dimensional diagrams remains the same as in formulations with only meson and nucleon degrees of freedom. A simple redefinition of the γ ∗N → γ′π′N′ amplitude which insures gauge invariance in every order of perturbation theory with an arbitrary choice of phenomenological vertices is considered. We calculate the leading diagram of this amplitude in the Δ resonance region. It is demonstrated that the differential cross section of the ep → e′ N′ π′ γ′ and γp → N′ π′ γ′ reactions is sensitive to the value of the magnetic moment of the Δ + resonance. Thus, the measurement of the differential cross section for ep → e′ N′ π′ γ′ and γp → N′ π′ γ′ reactions can be used for determining the magnetic dipole moment of Δ +.