On-shell Approximation Research Articles

On-shell approximation for the s -wave scattering theory

We investigate the scattering theory of two particles in a generic $D$-dimensional space. For the $s$-wave problem, by adopting an on-shell approximation for the $T$-matrix equation, we derive analytical formulas which connect the Fourier transform $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}(k)$ of the interaction potential to the $s$-wave phase shift. In this way we obtain explicit expressions of the low-momentum parameters ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}}_{0}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}}_{2}$ of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}(k)={\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}}_{0}+{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}}_{2}{k}^{2}+\ensuremath{\cdots}$ in terms of the $s$-wave scattering length ${a}_{s}$ and the $s$-wave effective range ${r}_{s}$ for $D=3$, $D=2$, and $D=1$. Our results, which are strongly dependent on the spatial dimension $D$, are a useful benchmark for few-body and many-body calculations. As a specific application, we derive the zero-temperature pressure of a two-dimensional uniform interacting Bose gas with a beyond-mean-field correction which includes both scattering length and effective range.

Fermi motion effects in electroproduction of hypernuclei

In a previous analysis of electroproduction of hypernuclei the cross sections were calculated in distorted-wave impulse approximation where the momentum of the initial proton in the nucleus was set to zero (the frozen-proton approximation). In this paper we go beyond this approximation assuming a non zero effective proton momentum due to proton Fermi motion inside of the target nucleus discussing also other kinematical effects. To this end we have derived a more general form of the two-component elementary electroproduction amplitude (Chew-Goldberger-Low-Nambu like) which allows its use in a general reference frame moving with respect to the nucleus-rest frame. The effects of Fermi motion were found to depend on kinematics and elementary amplitudes. The largest effects were observed in the contributions from the longitudinal and interference parts of the cross sections. The extension of the calculations beyond the frozen-proton approximation improved the agreement of predicted theoretical cross sections with experimental data and once we assumed the optimum on-shell approximation, we were able to remove an inconsistency which was previously present in the calculations.

On the nature of X(6900) and other structures in the LHCb di-j/ψ spectrum

The LHCb di-J/ψ spectrum is studied within the framework of effective field theory with four coupled channels {J/ψJ/ψ, J/ψψ(2S), J/ψψ(3770), ψ(2S)ψ(2S)}, in order to unveil possible underlying fully-charmed tetraquark states. The partial-wave analysis is performed properly, and the unitarity of the scattering amplitudes is restored via Bethe-Salpeter equation under on-shell approximation. Four states are found in the energy region [6.2 GeV, 7.6 GeV]. For the partial wave with quantum numbers 0 ++, a bound state X(6200) and a narrow resonance X(7200) can be dynamically generated, while for the 2 ++ partial wave, two different resonant states, one named X(6900) with a narrow width and the other X(6680) with a broad width, can be found. Our results of the mass and width of X(6900) agree well with the experimental ones given by the LHCb collaboration. Furthermore, our findings shed first light on the determination of the J P C quantum numbers of these states

Single-top-quark production in the t-channel at NNLO

We present a calculation of t-channel single-top-quark production and decay in the five-flavor scheme at NNLO. Our results resolve a disagreement between two previous calculations of this process that found a difference in the inclusive cross section at the level of the NNLO coefficient itself. We compare in detail with the previous calculations at the inclusive, differential and fiducial level including b-quark tagging at a fixed scale μ = mt. In addition, we advocate the use of double deep inelastic scattering (DDIS) scales (μ2 = Q2 for the light-quark line and μ2 = Q2 + {m}_t^2 for the heavy-quark line) that maximize perturbative stability and allow for robust scale uncertainties. All NNLO and NLO⊗NLO contributions for production and decay are included in the on-shell and vertex-function approximation. We present fiducial and differential results for a variety of observables used in Standard Model and Beyond Standard Model analyses, and find an important difference between the NLO and NNLO predictions of exclusive t + n-jet cross sections. Overall we find that NNLO corrections are crucial for a precise identification of the t-channel process.

Many-body exchange-correlation effects in MoS2 monolayer: The key role of nonlocal dielectric screening

We calculate the quasiparticle properties of $\rm{MoS_2}$ monolayer at $T=0$ considering the dynamical electron-electron interaction effect within random-phase-approximation (RPA). The calculations are carried out for an electron-doped slab of $\rm{MoS_2}$ monolayer using a minimal massive Dirac Hamiltonian and the quasi-two-dimensional nature of the Coulomb interaction in this system is taken into account considering a modified interaction of Keldysh type. Having calculated the real and imaginary parts of the retarded self-energy, we find the spectral function and discuss the impact of extrinsic variables such as the dielectric medium and the charge carrier density on the appearance and position of the quasiparticle peaks. We also report the results of the renormalization constant and the effective Fermi velocity calculations in a broad range of the coupling constant and carrier density. We show that the effective Fermi velocity obtained solving the self-consistent Dyson equation has an absolutely different behavior from the one found from the on-shell approximation. Our results show that the nonlocal dielectric screening of the monolayer tends to stabilize the Fermi liquid picture in $\rm{MoS_2}$ monolayer and that the interaction strength parameter of this system is a multivariable function of the coupling constant, carrier density, and also the screening length.

Many-body effects due to the electron–electron interaction in silicene under an applied exchange field: The case of valley–spin coupling

We investigate the many-body effects induced by the electron–electron interaction in a valley–spin-polarized silicene under a perpendicularly applied exchange field. We calculate the real and imaginary parts of the self-energy within the leading order dynamical screening approximation where the screened interaction is obtained from the random phase approximation. Our study on the valley- and spin-dependent real and imaginary parts of the self-energy indicates that the different coupled valley–spin subbands may exhibit distinct characteristics. Moreover, we obtain the corresponding spectral functions and find that the plasmaron and quasiparticle peaks have different spectral weights and broadenings in all states. Interestingly, it seems that there are clear dependencies for the position and broadening of the peaks on valley–spin indexes. In addition, we study the effect of the electron–electron interaction on the renormalized velocity in the on-shell approximation and show that the renormalized velocity in gapped states becomes greater, and in gapless states, it becomes smaller as the wave vector grows.

Scalar isovector resonance photoproduction through the final state meson–meson interactions

We construct the amplitudes of [Formula: see text] photoproduction taking into account the effects of the [Formula: see text] interchannel coupling. The idea of our model is to describe the scalar isovectors as dynamically produced in the final state while the initial stage of the reaction being described in terms of meson exchanges. Meson loops which arise this way include not only pseudoscalars but also vector mesons. These amplitudes are used to calculate the [Formula: see text]-wave cross-sections and mass distributions in the [Formula: see text] effective mass region corresponding to the scalar resonances [Formula: see text] and [Formula: see text]. The values we obtained for [Formula: see text] are comparable with predictions of other models while the cross-section for [Formula: see text] is about an order of magnitude larger than prediction based on the quark model. We show that the amplitudes with loops containing vector mesons calculated in the on-shell approximation are not suppressed in contrast to amplitudes containing only pseudoscalar loops. We also estimate the cross-sections for the [Formula: see text]- and [Formula: see text]-waves in the [Formula: see text] channel.

Interference contributions to gluon initiated heavy Higgs production in the two-Higgs-doublet model

We discuss the production of a heavy neutral Higgs boson of a CP-conserving Two-Higgs-Doublet Model in gluon fusion and its decay into a four-fermion final state, $gg (\rightarrow VV) \rightarrow e^+e^-\mu^+\mu^-/e^+e^-\nu_l\bar\nu_l$. We investigate the interference contributions to invariant mass distributions of the four-fermion final state and other relevant kinematical observables. The relative importance of the different contributions is quantified for the process in the on-shell approximation, $gg\rightarrow ZZ$. We show that interferences of the heavy Higgs with the light Higgs boson and background contributions are essential for a correct description of the differential cross section. Even though they contribute below $\mathcal{O}(10\%)$ to those heavy Higgs signal cross sections, to which the experiments at the Large Hadron Collider were sensitive in its first run, we find that they are sizeable in certain regions of the parameter space that are relevant for future heavy Higgs boson searches. In fact, the interference contributions can significantly enhance the experimental sensitivity to the heavy Higgs boson.

Shear viscosities from Kubo formalism in a large-Nc Nambu-Jona-Lasinio model

In this work the shear viscosity of strongly interacting matter is calculated within a two-flavor Nambu--Jona-Lasinio model as a function of temperature and chemical potential. The general Kubo formula is applied, incorporating the full Dirac structure of the thermal quark spectral function and avoiding commonly used on-shell approximations. Mesonic fluctuations contributing via Fock diagrams provide the dominant dissipative processes. The resulting ratio $\eta/s$ (shear viscosity over entropy density) decreases with temperature and chemical potential. Interpolating between our NJL results at low temperatures and hard-thermal-loop results at high temperatures a minimum slightly above the AdS/CFT benchmark $\eta/s=1/4\pi$ is obtained.

Scattering mean free path in continuous complex media: beyond the Helmholtz equation.

We present theoretical calculations of the ensemble-averaged (or effective or coherent) wave field propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that heterogeneity can be accounted for by a random scalar function of the space coordinates, termed the potential. Physically, this amounts to replacing the constant wave speed in Helmholtz' equation by a space-dependent speed. In the case of acoustic waves, we show that this approach leads to incorrect results for the scattering mean free path, no matter how weak the fluctuations. The detailed calculation of the coherent wave field must take into account both a scalar and an operator part in the random potential. When both terms have identical amplitudes, the correct value for the scattering mean free paths is shown to be more than 4 times smaller (13/3, precisely) in the low-frequency limit, whatever the shape of the correlation function. Based on the diagrammatic approach of multiple scattering, theoretical results are obtained for the self-energy and mean free path within Bourret's and on-shell approximations. They are confirmed by numerical experiments.

Disentangling the nature of resonances in coupled-channel models**Supported by National Natural Science Foundation of China (11347146, 11275235, 11175220)

We present several possible hadronic states found in coupled-channel models within the on-shell approximation. The interaction potential is constructed as a sum of the tree-level Feynman diagrams calculated with the effective Lagrangians. Based on the recent empirical data, we illustrate the possible existence of several baryonic and mesonic states with definite quantum numbers in the model. We give their properties for the purpose of further study and discuss the potential of finding them in future experiments.

Off-shell effects on the interaction of Nambu-Goldstone bosons andDmesons

The Bethe-Salpeter equation in unitarized chiral perturbation theory is usually solved with the so-called on-shell approximation. The underlying argument is that the off-shell effects can be absorbed by the corresponding coupling constants and physical masses, which has been corroborated by the success of unitarized chiral perturbation theory in describing a variety of physical phenomena. Such an approximation needs to be scrutinized when applied to study the light-quark mass evolution of physical observables, as routinely performed nowadays. In the present work, we propose to solve the Bethe-Salpeter equation with the full off-shell terms of the chiral potentials and apply this formalism to the description of the latest $n_f=2+1$ lattice QCD (LQCD) data on the scattering lengths of Nambu-Goldstone bosons off $D$ mesons. It is shown that the LQCD data can be better described in this formalism than in the widely used on-shell approximation. On the other hand, no qualitative difference between the on-shell and off-shell approaches is observed for the light-quark mass evolution of the scattering lengths, given the limited LQCD data and their relatively large uncertainties. We also show that the light-quark mass dependence of the $D^*_{s0}(2317)$ remains essentially the same in both approaches.

Quantum transport of atomic matter waves in anisotropic two-dimensional and three-dimensional disorder

The macroscopic transport properties in a disordered potential, namely diffusion and weak/strong localization, closely depend on the microscopic and statistical properties of the disorder itself. This dependence is rich in counter-intuitive consequences. It can be particularly exploited in matter wave experiments, where the disordered potential can be tailored and controlled, and anisotropies are naturally present. In this work, we apply a perturbative microscopic transport theory and the self-consistent theory of Anderson localization to study the transport properties of ultracold atoms in anisotropic two-dimensional (2D) and three-dimensional (3D) speckle potentials. In particular, we discuss the anisotropy of single-scattering, diffusion and localization. We also calculate disorder-induced shift of the energy states and propose a method to include it, which amounts to renormalizing energies in the standard on-shell approximation. We show that the renormalization of energies strongly affects the prediction for the 3D localization threshold (mobility edge). We illustrate the theoretical findings with examples which are relevant for current matter wave experiments, where the disorder is created with laser speckle. This paper provides a guideline for future experiments aiming at the precise location of the 3D mobility edge and study of anisotropic diffusion and localization effects in 2D and 3D.

Velocity renormalization and anomalous quasiparticle dispersion in extrinsic graphene

Using many-body diagrammatic perturbation theory we consider carrier density- and substrate-dependent many-body renormalization of doped or gated graphene induced by Coulombic electron-electron interaction effects. We quantitatively calculate the many-body spectral function, the renormalized quasiparticle energy dispersion, and the renormalized graphene velocity using the leading-order self-energy in the dynamically screened Coulomb interaction within the ring diagram approximation. We predict experimentally detectable many-body signatures, which are enhanced as the carrier density and the substrate dielectric constant are reduced, finding an intriguing instability in the graphene excitation spectrum at low wave vectors where interaction completely destroys all particlelike features of the noninteracting linear dispersion. We also make experimentally relevant quantitative predictions about the carrier density and wave-vector dependence of graphene velocity renormalization induced by electron-electron interaction. We compare on-shell and off-shell self-energy approximations within the ring diagram approximation, finding a substantial quantitative difference between their predicted velocity renormalization corrections in spite of the generally weak-coupling nature of interaction in graphene.

Reconstructing the heavy resonance at hadron colliders

We investigate the method for constructing the invariant mass using the M_T2-assisted on-shell (MAOS) approximation to the invisible particle momenta in the cascade decays of a new particle resonance produced at hadron colliders. We note that the MAOS reconstruction can be defined in several different ways, while keeping the efficiency of approximation at a similar level, and one of them provides a unique solution for each event. It is shown that the invariant mass distribution constructed with the MAOS momenta exhibits a peak at the heavy resonance mass, regardless of the chosen MAOS scheme and the detailed mass spectrum of the particles in the cascade. We stress that the MAOS invariant mass can be used as a clean signal of new particle resonance produced at the LHC, as well as a model-independent method to measure the masses of new particles involved in the event.

Pd Scattering Using a Rigorous Coulomb Treatment

Reliability of the screened Coulomb renormalization method, which was proposed in an elegant way by Alt–Sandhas–Zankel–Ziegelmann (ASZZ), is discussed on the basis of “two-potential theory” for the three-body AGS equations with the Coulomb potential. In order to obtain ASZZ’s formula, we define the on-shell Moller function, and calculate it by using the Haeringen criterion, i.e. “the half-shell Coulomb amplitude is zero”. By these two steps, we can finally obtain the ASZZ formula for a small Coulomb phase shift. Furthermore, the reliability of the Haeringen criterion is thoroughly checked by a numerically rigorous calculation for the Coulomb LS-type equation. We find that the Haeringen criterion can be satisfied only in the higher energy region. We conclude that the ASZZ method can be verified in the case that the on-shell approximation to the Moller function is reasonable, and the Haeringen criterion is reliable.

χ-SU(3) BETHE SALPETER MODEL: EXTENSION TO SU(6) AND SU(8) SPIN-FLAVOR SYMMETRIES

Consistent SU(6) and SU(8) spin-flavor extensions of the SU(3) flavor Weinberg-Tomozawa (WT) meson-baryon chiral Lagrangian are constructed, which incorporate vector meson degrees of freedom. In the charmless sector, the on-shell approximation to the Bethe-Salpeter (BS) approach successfully reproduces previous SU(3) WT results for the lowest-lying s–wave negative parity baryon resonances. It also provides some information on the dynamics of heavier ones and of the lightest d-wave negative parity resonances, as e.g. the Λ(1520). For charmed baryons the scheme is consistent with heavy quark symmetry, and our preliminary results in the strangeness-less charm C = +1 sector describe the main features of the three-star JP = 1/2− Λc(2595) and JP = 3/2− Λc(2625) resonances. We also find a second broad JP = 1/2− state close to the Λc(2595).

Radiative corrections to the semileptonic and hadronic Higgs-boson decays H→WW/ZZ→4 fermions

The radiative corrections of the strong and electroweak interactions are calculated for the Higgs-boson decays H→WW/ZZ→4f with semileptonic or hadronic four-fermion final states in next-to-leading order. This calculation is improved by higher-order corrections originating from heavy-Higgs-boson effects and photonic final-state radiation off charged leptons. The W- and Z-boson resonances are treated within the complex-mass scheme, i.e. without any resonance expansion or on-shell approximation. The calculation essentially follows our previous study of purely leptonic final states. The electroweak corrections are similar for all four-fermion final states; for integrated quantities they amount to some per cent and increase with growing Higgs-boson mass MH, reaching 7–8% at MH ∼ 500 GeV. For distributions, the corrections are somewhat larger and, in general, distort the shapes. Among the QCD corrections, which include corrections to interference contributions of the Born diagrams, only the corrections to the squared Born diagrams turn out to be relevant. These contributions can be attributed to the gauge-boson decays, i.e. they approximately amount to αs/π for semileptonic final states and 2αs/π for hadronic final states. The discussed corrections have been implemented in the Monte Carlo event generator PROPHECY4F.

Precise predictions for the Higgs-boson decayH→WW/ZZ→4leptons

The decay of the standard model Higgs boson into four leptons via a virtual $W$- or $Z$-boson pair is one of the most important decay modes in the Higgs-boson search at the Large Hadron Collider. We present the complete electroweak radiative corrections of $\mathcal{O}(\ensuremath{\alpha})$ to these processes, including improvements beyond $\mathcal{O}(\ensuremath{\alpha})$ originating from heavy-Higgs effects and final-state radiation. The intermediate $W$- and $Z$-boson resonances are described (without any expansion or on-shell approximation) by consistently employing complex mass parameters for the gauge bosons (complex-mass scheme). The corrections to partial decay widths typically amount to some percent and increase with growing Higgs mass ${M}_{H}$, reaching about 8% at ${M}_{H}\ensuremath{\sim}500\text{ }\text{ }\mathrm{GeV}$. For not too large Higgs masses (${M}_{H}\ensuremath{\lesssim}400\text{ }\text{ }\mathrm{GeV}$) the corrections to the partial decay widths can be reproduced within $\ensuremath{\lesssim}2%$ by simple approximations. For angular distributions the corrections are somewhat larger and distort the shapes. For invariant-mass distributions of fermion pairs they can reach several tens of percent depending on the treatment of photon radiation. The discussed corrections have been implemented in a Monte Carlo event generator called Prophecy4f.

On-shell coupled-channel approach to proton-hydrogen collisions without partial-wave expansion

A fully quantal approach to proton collisions with hydrogen based on the atomic-orbital close-coupling method is presented. The method leads to a system of coupled three-dimensional momentum-space integral equations for the scattering amplitudes. These equations are reduced to two-dimensional ones using an on-shell approximation. Furthermore, by considering the symmetry of the problem, we demonstrate that these can be reduced to just one dimension. The resulting equations are solved without partial-wave expansion. Cross sections for electron transfer in proton collisions with the ground state of atomic hydrogen are calculated and shown to agree well with experiment over a wide energy range.