Independent Amplitudes Research Articles

Topological diagram analysis of [formula omitted] decays in the SU(3)F limit and beyond

Charm baryon decay plays an important role in studying non-perturbative baryonic transitions. Compared to other hadron multiplets, the flavor symmetry of baryon decuplet is more simple and attractive. In this work, we study the topological amplitudes of charmed baryon decays into decuplet baryon in the flavor symmetry and the linear SU(3)F breaking. It is found most of topological diagrams are suppressed by the Körner-Pati-Woo theorem in the SU(3)F limit. Only two independent amplitudes contributing to the Bc3‾→B10M decays, with one dominating the branching fractions. The Lee-Yang parameters of all Bc3‾→B10M modes are the same in the SU(3)F limit, and there are only four possible values for the CP asymmetries. After including the first-order SU(3)F breaking effects, the Ξc+→Σ⁎+K‾0 and Ξc+→Ξ⁎0π+ decays have non-zero branching fractions. The number of free parameter contributing to the Bc3‾→B10M decays in the linear SU(3)F breaking is smaller than the available data. The SU(3)F breaking part of the quark loop diagram can be extracted by global fitting of branching fractions, which could help us understand the CP violation in charm sector. Additionally, some new isospin equations are proposed to test the Körner-Pati-Woo theorem.

Block-Correlated Coupled Cluster Theory with up to Four-Pair Correlation for Accurate Static Correlation of Strongly Correlated Systems.

A block-correlated coupled cluster method with up to four-pair correlation based on the generalized valence bond wave function (GVB-BCCC4) is first implemented, which offers an alternative method for electronic structure calculations of strongly correlated systems. We developed some techniques to derive a set of compact and cost-effective equations for GVB-BCCC4, which include the definition of n-block (n = 1-4) Hamiltonian matrices, the combination of excitation operators, and the definition of independent amplitudes. We then applied the GVB-BCCC4 method to investigate several potential energy surfaces of strongly correlated systems with singlet ground states. Our calculations demonstrate that the GVB-BCCC4 method can provide nearly exact static correlation energies as the density matrix renormalization group method (on the basis of the same GVB orbitals). This work highlights the significance of four-pair correlation in quantitative descriptions of static correlation energy for strongly correlated systems.

Planar three-loop QCD helicity amplitudes for V+jet production at hadron colliders

We compute the planar three-loop Quantum Chromodynamics (QCD) corrections to the helicity amplitudes involving a vector boson V=Z,W±,γ⁎, two quarks and a gluon. These amplitudes are relevant to vector-boson-plus-jet production at hadron colliders and other precision QCD observables. The planar corrections encompass the leading colour factors N3, N2Nf, NNf2 and Nf3. We provide the finite remainders of the independent helicity amplitudes in terms of multiple polylogarithms, continued to all kinematic regions and in a form which is compact and lends itself to efficient numerical evaluation. The presented amplitude respects the conjectured symbol-adjacency constraints for amplitudes with three massless and one massive leg.

Switching field distribution of ultradense arrays of single-crystalline magnetic nanowires

Ultradense arrays of magnetic nanoelements present considerable interest for extending areal densities in magnetic recording media, provided that they display high switching fields and corresponding low standard deviations. Here, we report the switching field distribution of bottom–up synthesized single-crystalline vertical Co nanowires self-organized in 2D hexagonal superlattices. The combined shape and Co hexagonal compact magnetocrystalline anisotropies in individual nanowires of diameter as small as 6 nm define a robust perpendicular magnetic anisotropy despite important interactions in superlattices of 10 × 1012 NWs/in2. Using quantitative analysis of temperature-dependent first-order reversal curves, we capture the switching field distribution in this dipolar-coupled perpendicularly magnetized nanomagnets. First, the interwire dipolar interactions are treated separately and show a dominant mean field character with temperature independent amplitudes that scale with the nanowire packing fraction. Then, the intrinsic switching field distribution, namely, independent of interwire interactions, is determined as a function of temperature in the 5–300 K range. The mean value and deviation are both found to be driven by the intrawire dipolar interaction and the temperature-dependent uniaxial magnetocrystalline anisotropy, but of smaller amplitudes than those expected from bulk behavior. With coercive fields ranging between 0.3 and 0.8 T, the switching field deviations relative to coercivity reach 20%, which is a moderate value regarding pitch arrays as small as 8 nm.

Analytical 1D transfer functions for layered soils

Transfer functions are constantly used in both Seismology and Geotechnical Earthquake Engineering to relate seismic ground motion at different depths within strata. In the context of diffusive theory, they also appear in the expression of the imaginary part of 1D Green’s functions. In spite of their remarkable importance, their mathematical structure is not fully understood yet, except in the simplest cases of two or three layers at most. This incomplete understanding, in particular as to the effect of increasing number of layers, hinders progress in some areas, as researchers have to resort to expensive and less conclusive numerical parametric studies. This text presents the general form of transfer functions for any number of layers, overcoming the above issues. The mathematical structure of these transfer functions comes defined as a superposition of independent harmonics, whose number, amplitudes and periods we fully characterize in terms of the properties of the layers in closed-form. Owing to the formal connection between seismic wave propagation and other phenomena that, in essence, represent different instances of wave propagation in a linear-elastic medium, we have extended the results derived elsewhere, in the context of longitudinal wave propagation in modular rods, to seismic response of stratified sites. The ability to express the reciprocal of transfer functions as a superposition of independent harmonics enables new analytical approaches to assess the effect of each layer over the overall response. The knowledge of the general closed-form expression of the transfer functions allows to analytically characterize the long-wavelength asymptotics of the horizontal-to-vertical spectral ratio for any number of layers.

Investigating the color-suppressed decays Λb→Λψ in the perturbative QCD approach

The nonleptonic two-body ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\ensuremath{\psi}$ decays with $\ensuremath{\psi}=J/\ensuremath{\psi}$ or $\ensuremath{\psi}(2S)$ are investigated based on the perturbative QCD approach. These are color-suppressed processes in which the nonfactorizable contributions are confirmed to be dominant. Angular momentum conservation allows us to describe the concerned decays by four independent complex helicity amplitudes. It is observed that the negative-helicity states for the $\mathrm{\ensuremath{\Lambda}}$ baryon are preferred as expected in the left-handed nature of the charged-current interaction. The obtained results for the helicity amplitudes are used to compute the branching ratios and various observable parameters, which are then compared to the existing theoretical predictions and experimental data. In particular, we predict the ratio $\mathcal{R}=\frac{\mathcal{B}({\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\ensuremath{\psi}(2S))}{\mathcal{B}({\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}J/\ensuremath{\psi})}=0.4{7}_{\ensuremath{-}0.00}^{+0.02}$ in comparison with $0.508\ifmmode\pm\else\textpm\fi{}0.023$ from the Particle Data Group at the level of 1 standard deviation. We also briefly explore the long-distance contributions to the semileptonic ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}{l}^{+}{l}^{\ensuremath{-}}$ decays in the kinematic regions where the dilepton invariant masses are around the $J/\ensuremath{\psi}$ and $\ensuremath{\psi}(2S)$ resonances.

Simplification of the complete-experiment problem for photoproduction of two pseudoscalar mesons on a nucleon in a truncated partial-wave analysis

It is shown that within a truncated partial-wave analysis for photoproduction of two pseudoscalar mesons, it is possible to halve the number of independent partial amplitudes by taking into account parity conservation. In addition, within the framework of the proposed formalism, one can rather easily resolve the double discrete ambiguity arising from the symmetry under complex conjugation of the helicity amplitudes. This leads to essential simplifications of the complete experiment problem, at least, as far as mathematical aspects are concerned.

Shifts in the BCFW method for QED * *Supported by the Natural Science Foundation of China (11475180, 11875260); X. Zhao's work is Supported by the Italian Ministry of Research (MUR) (PRIN 20172LNEEZ)

We study the application of BCFW recursion relations to the QED process . Based on 6-point amplitudes (both MHVA and NMHVA) computed from Feynman diagrams in the Berends-Giele gauge, we conduct a comprehensive study on different shifts. Subsequently, we propose a new shift (LLYZ shift), which can lead to the full amplitudes of these processes and have several realistic computational advantages. We compare the number of terms and independent amplitudes of this novel shift with those of a few typical shifts.

Efficient Implementation of Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Strongly Correlated Systems

An optimized implementation of block-correlated coupled cluster theory based on the generalized valence bond wave function (GVB-BCCC) for the singlet ground state of strongly correlated systems is presented. The GVB-BCCC method with two-pair correlation (GVB-BCCC2b) or up to three-pair correlation (GVB-BCCC3b) will be the focus of this work. Three major techniques have been adopted to dramatically accelerate GVB-BCCC2b and GVB-BCCC3b calculations. First, the GVB-BCCC2b and GVB-BCCC3b codes are noticeably optimized by removing redundant calculations. Second, independent amplitudes are identified by constraining excited configurations to be pure singlet states and only independent amplitudes need to be solved. Third, an incremental updating scheme for the amplitudes in solving the GVB-BCCC equations is adopted. With these techniques, accurate GVB-BCCC3b calculations are now accessible for systems with relatively large active spaces (50 electrons in 50 orbitals) and GVB-BCCC2b calculations are affordable for systems with much larger active spaces. We have applied GVB-BCCC methods to investigate three typical kinds of systems: polyacenes, pentaprismane, and [Cu2O2]2+ isomers. For polyacenes, we demonstrate that GVB-BCCC3b can capture more than 94% of the total correlation energy even for 12-acene with 50 π electrons. For the potential energy curve of simultaneously stretching 15 C-C bonds in pentaprismane, our calculations show that the GVB-BCCC3b results are quite close to the results from the density matrix renormalization group (DMRG) over the whole range. For two dinuclear copper oxide isomers, their relative energy predicted by GVB-BCCC3b is also in good accord with the DMRG result. All calculations show that the inclusion of three-pair correlation in GVB-BCCC is critical for accurate descriptions of strongly correlated systems.

General Analysis of the Reaction e^+ + e^- → N + Ñ + π^0

The general analysis of the reaction , in the case of longitudinally polarized electron beam, has been performed in the one-photon-nnihilation approximation, accounting for the polarization states of the final nucleon. This analysis is useful for the description of the continuum (non-resonant) and resonant (with different possible vector mesons or excited baryons in the intermediate virtual states of the Feynman diagrams) contributions. The conservation of the hadron electromagnetic currents and P-invariance of the hadron electromagnetic interaction were used to express the matrix element in terms of the six complex independent invariant amplitudes. The general structure of the hadronic tensor for the case of unpolarized final hadrons and polarized nucleon has been derived. The spin-independent part of the hadronic tensor is determined by five structure functions and the spin-dependent one by 13 structure functions. The transversal, longitudinal and normal components of the nucleon polarization four-vector are expressed by means of the four-vectors of the particle momenta. The five independent invariant variables which describe the reaction have been introduced. The limits of the changing of these variables have been considered. The kinematical double invariant variables regions are given in the figure. The kinematics, suitable to study the invariant mass distributions, is investigated.

Two-loop mixed QCD-EW corrections to qoverline{q} → Hg, qg → Hq, and overline{q}g → Hoverline{q}

We compute the two-loop mixed QCD-Electroweak corrections to qoverline{q} → Hg and its crossed channels qg → Hq, overline{q}g → Hoverline{q} , limiting ourselves to the contribution of light virtual quarks. We compute the independent helicity amplitudes as well as the form factors for this process, expressing them in terms of hyperlogarithms with algebraic arguments. The Feynman integrals are computed by direct integration over Feynman parameters and the results are expressed in terms of a basis of rational prefactors.

Interpretable Deep Probabilistic Model for HRR Radar Signal and its Application to Target Recognition

With the advent of neural network, unprecedented advancements have been achieved in many tasks, including radar signal processing. However, a key disadvantage of the current methods is the black-box structure, which makes it hard to interpret or assess the hidden representations of data. In this paper, by combining the physical generative mechanism of the high range resolution (HRR) radar signal with neural network, we develop an interpretable deep probabilistic model to learn the latent features from HRR radar signals that can characterize the physical structure of targets. In detail, based on the radar target's scattering center model which describes the HRR radar signal as the summation of echoes from the scattering centers, a deep probabilistic model is constructed to depict the generative process from the scattering centers to observations, where the latent features comprise the locations and amplitudes of scattering centers. Considering that the locations of scattering centers are nearly invariable and the amplitudes of them are fluctuant for the signals within a small angular range, our model defines the shared locations and independent amplitudes of scattering centers for the signals in a small angular range, aiming to improve the robustness of interpretable feature extraction model. In addition, our model performs probabilistic inference on the posterior distribution of latent features with high preciseness. With the proposed model, we further design a recognition scheme based on the minimum reconstruction error criterion. Experiments on the measured HRR radar dataset validate the effectiveness of our model on learning interpretable features and superior recognition performance.

KK-like relations of α′ corrections to disk amplitudes

Inspired by the definition of color-dressed amplitudes in string theory, we define analogous color-dressed permutations replacing the color-ordered string amplitudes by their corresponding permutations. Decomposing the color traces into symmetrized traces and structure constants, the color-dressed permutations define BRST-invariant permutations, which we show are elements of the inverse Solomon descent algebra and we find a closed formula for them. We then present evidence that these permutations encode KK-like relations among the different α′ corrections to the disk amplitudes refined by their MZV content. In particular, the number of linearly independent amplitudes at a given α′ order and MZV content is given by (sums of) Stirling cycle numbers. In addition, we show how the superfield expansion of BRST invariants of the pure spinor formalism corresponding to α′2ζ2 corrections is encoded in the descent algebra.

Theory of deeply virtual Compton scattering off the unpolarized proton

Using the helicity amplitudes formalism, we study deeply virtual exclusive electron photoproduction off an unpolarized nucleon target, $ep\ensuremath{\rightarrow}{e}^{\ensuremath{'}}{p}^{\ensuremath{'}}\ensuremath{\gamma}$, through a range of kinematics both in the fixed target setting with initial electron energies of 6, 11, and 24 GeV and for an electron ion collider. We reformulate the cross section bringing to the forefront the defining features of the $ep\ensuremath{\rightarrow}{e}^{\ensuremath{'}}{p}^{\ensuremath{'}}\ensuremath{\gamma}$ process, where the observables are expressed as bilinear products of the independent helicity amplitudes which completely describe it in terms of the electric, magnetic, and axial currents of the nucleon. These contributions are checked against the Fourier harmonics-based formalism which has provided so far the underlying mathematical framework to study deeply virtual Compton scattering (DVCS) and related experiments. Using theoretical model calculations of the twist-two generalized parton distributions, $H$, $E$, $\stackrel{\texttildelow{}}{H}$, and $\stackrel{\texttildelow{}}{E}$, we uncover large discrepancies between the harmonic series and our proposed framework. Most importantly, these numerical differences appear in the intermediate ${Q}^{2}$ range which represents a sweet spot for extracting generalized parton distributions from data. We provide a framework that is ideal, on one side, to study and compare the different conventions that can be used to describe the leading order contribution to DVCS in QCD, while on the other it facilitates a quantitative extraction of physically meaningful information from experiment through traceable and controllable approximations in the intermediate ${Q}^{2}$ region.

Tensor decomposition for bosonic and fermionic scattering amplitudes

In this paper, we elaborate on a method to decompose multiloop multileg scattering amplitudes into Lorentz-invariant form factors, which exploits the simplifications that arise from considering four-dimensional external states. We propose a simple and general approach that applies to both fermionic and bosonic amplitudes and allows us to identify a minimal number of physically relevant form factors, which can be related one-to-one to the independent helicity amplitudes. We discuss explicitly its applicability to various four- and five-point scattering amplitudes relevant for LHC physics.

Group constraint relations for five-point amplitudes in gauge theories with SO(N) and Sp(2N) groups

Linear constraint relations among loop-order five-point color-ordered amplitudes in SO(N) and Sp(2N) gauge theories are derived with the group-theoretic method. These constrains are derived up to four-loop order. It is found that in both theories, there are n=6,22,34,44,50 linear constraint relations at L=0,1,2,3,4 loop orders. Then the numbers of independent color-ordered five-point amplitudes under group-theoretic constraints are respectively nind.=6,12,22,34,50. We find that the number of independent color-ordered amplitudes begins to diverge from SU(N) at four-loop order. This provides an evidence on the argument that group-theoretic constraint relations depend on properties of group algebras. Some comments are given on future study along this direction.

Constructing massive on-shell contact terms

The purely on-shell approach to effective field theories requires the construction of independent contact terms. Employing the little-group-covariant massive-spinor formalism, we present the first systematic derivation of independent four-point contact terms involving massive scalars, spin-1/2 fermions, and vectors. Independent three-point amplitudes are also listed for massive particles up to spin-3. We make extensive use of the simple relations between massless and massive amplitudes in this formalism. Our general results are specialized to the (broken-phase) particle content of the electroweak sector of the standard model. The (anti)symmetrization among identical particles is then accounted for. This work opens the way for the on-shell computation of massive four-point amplitudes.

Two-loop mixed QCD-EW corrections to gg \u2192 Hg

We compute the two-loop mixed QCD-Electroweak (QCD-EW) corrections to the production of a Higgs boson and a gluon in gluon fusion through a loop of light quarks. The relevant four-point functions with internal massive propagators are expressed as multiple polylogarithms with algebraic arguments. We perform the calculation by integration over Feynman parameters and, independently, by the method of differential equations. We compute the two independent helicity amplitudes for the process and we find that they are both finite. Moreover, we observe a weight drop when all gluons have the same helicity. We also provide a simplified expression for the all-plus helicity amplitude, which is optimised for fast and reliable numerical evaluation in the physical region.

Integer and half-integer channel spins for elastic scattering cross sections

We present analytical expressions for differential cross sections and independent partial amplitudes of elastic scattering of nuclear particles for channels with a spin value of 1/2, 1, 3/2, 2 and 5/2. The independent partial amplitudes are calculated taking into account the spin-orbit splitting for arbitrary orbital angular momentum l. The analytical expressions allow one to carry out full phase shift analysis using experimental data of differential cross sections for processes with channel spins 1/2, 1, 3/2, 2 and 5/2.

Planar two-loop five-parton amplitudes from numerical unitarity

We compute a complete set of independent leading-color two-loop five-parton amplitudes in QCD. These constitute a fundamental ingredient for the next-to-next-to-leading order QCD corrections to three-jet production at hadron colliders. We show how to consistently consider helicity amplitudes with external fermions in dimensional regularization, allowing the application of a numerical variant of the unitarity method. Amplitudes are computed by exploiting a decomposition of the integrand into master and surface terms that is independent of the parton type. Master integral coefficients are numerically computed in either finite-field or floating-point arithmetic and combined with known analytic master integrals. We recompute leading-color two-loop four-parton amplitudes as a check of our implementation. Results are presented for all independent four- and five-parton processes including contributions with massless closed fermion loops.