Behavior Of Form Factors Research Articles

Supersymmetric Spectral Form Factor and Euclidean Black Holes.

The late-time behavior of spectral form factor (SFF) encodes the inherent discreteness of a quantum system, which should be generically nonvanishing. We study an index analog of the microcanonical spectrum form factor in four-dimensional N=4 super Yang-Mills theory. In the large N limit and at large enough energy, the most dominant saddle corresponds to the black hole in the AdS bulk. This gives rise to the slope that decreases exponentially for a small imaginary chemical potential, which is a natural analog of an early time. We find that the "late-time" behavior is governed by the multicut saddles that arise in the index matrix model, which are nonperturbatively subdominant at early times. These saddles become dominant at late times, preventing the SFF from decaying. These multicut saddles correspond to the orbifolded Euclidean black holes in the AdS bulk, therefore giving the geometrical interpretation of the "ramp". Our analysis is done in the standard AdS/CFT setting without ensemble average or wormholes.

Late time behavior of n-point spectral form factors in Airy and JT gravities

We study the late time behavior of n-point spectral form factors (SFFs) in two-dimensional Witten-Kontsevich topological gravity, which includes both Airy and JT gravities as special cases. This is conducted in the small ħ expansion, where hbar sim {e}^{-1/{G}_{textrm{N}}} is the genus counting parameter and nonperturbative in Newton’s constant GN. For one-point SFF, we study its absolute square at two different late times. We show that it decays by power law at t ~ ħ−2/3 while it decays exponentially at t ~ ħ−1 due to the higher order corrections in ħ. We also study general n(≥2)-point SFFs at t ~ ħ−1 in the leading order of the ħ expansion. We find that they are characterized by a single function, which is essentially the connected two-point SFF and is determined by the classical eigenvalue density ρ0(E) of the dual matrix integral. These studies suggest that qualitative behaviors of n-point SFFs are similar in both Airy and JT gravities, where our analysis in the former case is based on exact results.

Features of determining the charge deuteron form factor G C (p)

Abstract The main features of obtaining the asymptotic behavior of the charge deuteron form factor G C (p) at large values of the momentum have been analyzed. The asymptotic behavior of the charge form factor G C (p) was determined by taking into account the analytic form of deuteron wave function in the coordinate representation and the original dipole fit for the nucleon form factors. Asymptotic values of charge form factor G C (p) has been obtained for the nucleon-nucleon phenomenological potential Reid93 and compared with the calculations for eight different nucleon form factors models and their approximations. In the wide range up to 10.5 fm−1 of transmitted momentum, the basic forms of the asymptotic behavior of the charge deuteron form factor have been demonstrated and compared with the experimental data of the leading modern collaborations and reviews. The secondary maximum for G C (p) for the potential Reid93 will be located at the momentum range at 5.45–5.70 fm−1. The calculated position of the zero p 0 is located at the momentum interval 4.60–4.65 fm−1. The position of the zero for one potential coincides regardless of the choice of models and approximations for the nucleon form factors. As the analysis shows, the value of the mean-square charge radius of the deuteron takes the value of r ch = 2.02876–2.14695 fm depending on the chosen deuteron wave function and nucleon form factors.

Timelike behavior of the pion electromagnetic form factor in the functional formalism

The electromagnetic form factor of the pion is calculated within the use of functional formalism. We develop integral representation for the minimal set of Standard Model Green's functions and derive the dispersion relation for the form factor in the two-flavor QCD isospin limit ${m}_{u}={m}_{d}$. We use the dressed quark propagator as obtained from the gap equation in Minkowski space and within the Dyson-Schwinger equations formalism to derive the approximate dispersion relation for the form factor for the first time. We evaluate the form factor for the spacelike as well as for the timelike momentum in the presented formalism. A new Nakanishi-like form of integral representation is proved on the basis of the vector Bethe-Salpeter equation for the quark-photon vector with a ladder-rainbow kernel. The gauge technique turns out to be a part of the entire structure of the vertex. In the analytic approach presented here, it is shown that a large amount of the $\ensuremath{\rho}$-meson peak in the cross section ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ is governed by the gauge invariance of QED/QCD---i.e., by a gauge-technique-constructed quark-photon vertex. This approximation naturally explains the broad shape of the $\ensuremath{\rho}$-meson peak.

Relativistic description of the semileptonic decays of bottom mesons

The form factors of the semileptonic $B$, $B_s$ and $B_c$ meson decays are calculated in the framework of the relativistic quark model based on the quasipotential approach in QCD. They are expressed through the overlap integrals of the meson wave function. All relativistic effects are consistently taken into account. The momentum transfer $q^2$ behavior of form factors is determined in the whole accessible kinematical range. We do not use any extrapolations, heavy quark $1/m_Q$ expansion or model assumptions about the shape of form factors. Convenient analytic expressions of the form factors are given, which very accurately reproduce the numerical results of our calculation. On the basis of these form factors and helicity formalism, the differential and total branching fractions of various semileptonic decays of bottom meson are calculated. The mean values of the forward-backward asymmetry $\langle A_{FB}\rangle$, lepton-side convexity parameter $\langle C^\ell_{F}\rangle$, longitudinal $\langle P^\ell_{L}\rangle$ and transverse $\langle P^\ell_{T}\rangle$ polarization of the charged lepton, and the longitudinal polarization fraction $\langle F_{L}\rangle$ for final-state vector meson are also evaluated. We present a detailed comparison of the obtained predictions with the calculations based on the covariant light-front quark model and confront them to available lattice QCD and experimental data. It is found that although both models predict close values of the total branching fractions, the differential distributions and forward-backward asymmetry and polarization parameters differ significantly, especially for the heavy-to-light semileptonic decays. We identify observables which measurement can help to discriminate between models.

Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos.

We propose a measure, which we call the dissipative spectral form factor (DSFF), to characterize the spectral statistics of non-Hermitian (and nonunitary) matrices. We show that DSFF successfully diagnoses dissipative quantum chaos and reveals correlations between real and imaginary parts of the complex eigenvalues up to arbitrary energy scale (and timescale). Specifically, we provide the exact solution of DSFF for the complex Ginibre ensemble (GinUE) and for a Poissonian random spectrum (Poisson) as minimal models of dissipative quantum chaotic and integrable systems, respectively. For dissipative quantum chaotic systems, we show that the DSFF exhibits an exact rotational symmetry in its complex time argument τ. Analogous to the spectral form factor (SFF) behavior for Gaussian unitary ensemble, the DSFF for GinUE shows a "dip-ramp-plateau" behavior in |τ|: the DSFF initially decreases, increases at intermediate timescales, and saturates after a generalized Heisenberg time, which scales as the inverse mean level spacing. Remarkably, for large matrix size, the "ramp" of the DSFF for GinUE increases quadratically in |τ|, in contrast to the linear ramp in the SFF for Hermitian ensembles. For dissipative quantum integrable systems, we show that the DSFF takes a constant value, except for a region in complex time whose size and behavior depend on the eigenvalue density. Numerically, we verify the above claims and additionally show that the DSFF for real and quaternion real Ginibre ensembles coincides with the GinUE behavior, except for a region in the complex time plane of measure zero in the limit of large matrix size. As a physical example, we consider the quantum kicked top model with dissipation and show that it falls under the Ginibre universality class and Poisson as the "kick" is switched on or off. Lastly, we study spectral statistics of ensembles of random classical stochastic matrices or Markov chains and show that these models again fall under the Ginibre universality class.

Electroweak effective theory and beyond Standard Model resonances

We consider a non-linear realization of the electroweak symmetry-breaking pattern S U(2)L × S U(2)R/S U(2)L+R to construct a low-energy effective theory, later extended by the inclusion of heavy new-physics resonances. After assuming appropriate high-energy constraints given by Weinberg sum-rules and the asymptotic behaviour of form-factors, we obtain relations between resonance masses and some low-energy effective couplings. These predictions are compared with current experimental data and some resonance mass bounds are inferred.

Gluon parton densities in soft-wall AdS/QCD

We study the gluon parton densities [parton distribution functions (PDFs), transverse momentum distributions (TMDs), generalized parton distributions (GPDs)] and form factors in soft-wall AdS/QCD. We show that the power behavior of gluon parton distributions and form factors at large values of the light-cone variable and large values of square momentum is consistent with quark counting rules. We also show that the transverse momentum distributions derived in our approach obey the model-independent Mulders-Rodrigues inequalities without referring to specific model parameters. All gluon parton distributions are defined in terms of the unpolarized and polarized gluon PDFs and profile functions. The latter are related to gluon PDFs via differential equations.

Toward accurate form factors for B -to-light meson decay from lattice QCD

We present the results of a lattice QCD calculation of the scalar and vector form factors for the unphysical $B_s\to\eta_s$ decay, over the full physical range of $q^2$. This is a useful testing ground both for lattice QCD and for our wider understanding of the behaviour of form factors. Calculations were performed using the highly improved staggered quark (HISQ) action on $N_f = 2 + 1 + 1$ gluon ensembles generated by the MILC Collaboration with an improved gluon action and HISQ sea quarks. We use three lattice spacings and a range of heavy quark masses from that of charm to bottom, all in the HISQ formalism. This permits an extrapolation in the heavy quark mass and lattice spacing to the physical point and nonperturbative renormalisation of the vector matrix element on the lattice. We find results in good agreement with previous work using nonrelativistic QCD $b$ quarks and with reduced errors at low $q^2$, supporting the effectiveness of our heavy HISQ technique as a method for calculating form factors involving heavy quarks. A comparison with results for other decays related by SU(3) flavour symmetry shows that the impact of changing the light daughter quark is substantial but changing the spectator quark has very little effect. We also map out form factor shape parameters as a function of heavy quark mass and compare to heavy quark effective theory expectations for mass scaling at low and high recoil. This work represents an important step in the progression from previous work on heavy-to-heavy decays ($b\to c$) to the numerically more challenging heavy-to-light decays.

Study of Non-standard Neutrino Interactions in Future Coherent Elastic Neutrino-Nucleus Scattering Experiments

Non-standard interactions (NSI) of the neutrino sector is studied in the framework of coherent elastic neutrino-nucleus scattering (CE $$\nu$$ NS). Differential and total cross sections of the CE $$\nu$$ NS process for several nuclei are presented for different scale of incoming neutrino energy. Behavior of form factor in accordance with the criteria of coherency process is also shown as a function of momentum transfer. Several benchmarks were implemented according to the proposed advancement of CE $$\nu$$ NS experiments. Using recently analyzed bound, we forecast that the NSI cross section spectrum is larger than the standard model (SM) ones and increased for heavier nuclei. Prediction of the NSI bounds is also given in the parameter space of the new interaction strengths by utilizing the deviation of NSI and SM spectrum ratio. All possibilities of non-universal flavor conserving (FC) and flavor violating (FV) process are considered as neutrino interact with the quark constituent of nucleus.

Forced Soliton Equation and Semiclassical Soliton Form Factors

We show that the leading semiclassical behavior of soliton form factors at arbitrary momentum transfer is controlled by solutions to a new wavelike integro-differential equation that describes solitons undergoing acceleration. We work in the context of two-dimensional linear σ models with kink solitons for concreteness, but our methods are purely semiclassical and generalizable.

Asymptotic behavior of meson transition form factors

One of the open issues in evaluations of the contribution from hadronic light- by-light scattering to the anomalous magnetic moment of the muon (g − 2)μ concerns the role of heavier scalar, axial-vector, and tensor-meson intermediate states. The coupling of axial vectors to virtual photons is suppressed for small virtualities by the Landau-Yang theorem, but otherwise there are few rigorous constraints on the corresponding form factors. In this paper, we first derive the Lorentz decomposition of the two-photon matrix elements into scalar functions following the general recipe by Bardeen, Tung, and Tarrach. Based on this decomposition, we then calculate the asymptotic behavior of the meson transition form factors from a light-cone expansion in analogy to the asymptotic limits for the pseudoscalar transition form factor derived by Brodsky and Lepage. Finally, we compare our results to existing data as well as previous models employed in the literature.

Transition form factors and helicity amplitudes for electroexcitation of negative and positive parity nucleon resonances in a light-front quark model

A workable basis of quark configurations $s^3$, $s^2p$ and $sp^2$ at light front has been constructed to describe the high-$Q^2$ behavior of transition form factors and helicity amplitudes in the electroproduction of the lightest nucleon resonances, $N_{1/2^-}(1535)$ and $N_{1/2^+}(1440)$. High-quality data of the CLAS Collaboration are described in the framework of a model which takes into account mixing of the quark configurations and the hadron-molecular states. The model allows for a rough estimate of the quark core weight in the wave function of the resonance in a comparison with high momentum transfer data on resonance electroproduction.

Colloquium : Roper resonance: Toward a solution to the fifty year puzzle

Discovered in 1963, the Roper resonance appears to be an exact copy of the proton except that its mass is 50% greater and it is unstable. These features of the Roper have been very difficult to explain so that for half a century this lightest excited state of the proton has defied understanding. The last decade has presented a new challenge, viz. precise information on the proton-to-Roper electroproduction transition form factors. Reaching to momentum transfer Q2≈4.5 GeV2, the data probe a domain within which hard valence-quark degrees of freedom could be expected to determine form factor behavior. An explanation of the Roper should combine an understanding of all these things. This is a prodigious task, but a ten-year international collaborative effort, involving experimentalists and theorists, has presented a candidate solution to the puzzle. Namely, the observed Roper is at the heart of the proton’s first radial excitation, consisting of a dressed-quark core augmented by a meson cloud that reduces the core mass by approximately 20% and materially alters its electroproduction form factors on Q2<2mN2, where mN is the proton’s mass. This Colloquium describes the experimental developments which enabled electroproduction data to be procured within a domain that is the purview of strong quantum chromodynamics, thereby providing challenges and opportunities for modern theory, and surveys the developments in reaction models and QCD theory that have enabled this picture of the Roper resonance to be drawn.

Asymptotic behavior of the heavy quark form factors at higher order

In the asymptotic limit $Q^2 \gg m^2$, the heavy quark form factors exhibit Sudakov behavior. We study the corresponding renormalization group equations of the heavy quark form factors which do not only govern the structure of infrared divergences, but also control the high energy logarithms. This enables us to obtain the complete logarithmic three--loop and partial four--loop contributions to the heavy quark form factors in perturbative Quantum Chromodynamics.

On the large-Q2 behavior of the pion transition form factor

We study the transition of non-perturbative to perturbative QCD in situations with possible violations of scaling limits. To this end we consider the singly- and doubly-virtual pion transition form factor π0→γγ at all momentum scales of symmetric and asymmetric photon momenta within the Dyson–Schwinger/Bethe–Salpeter approach. For the doubly virtual form factor we find good agreement with perturbative asymptotic scaling laws. For the singly-virtual form factor our results agree with the Belle data. At very large off-shell photon momenta we identify a mechanism that introduces quantitative modifications to Efremov–Radyushkin–Brodsky–Lepage scaling.

High energy behaviour of form factors

We solve renormalization group equations that govern infrared divergences of massless and massive form factors. By comparing to recent results for planar massive three-loop and massless four-loop form factors in QCD, we give predictions for the high-energy limit of massive form factors at the four- and for the massless form factor at five-loop order. Furthermore, we discuss the relation which connects infrared divergences regularized dimensionally and via a small quark mass and extend results present in the literature to higher order.

Influence of confining gluon configurations on the P→γ*γ transition form factors

Transition form factors $F_{P\gamma^*\gamma^{(*)}}$ of pseudoscalar mesons are studied within the framework of the domain model of confinement, chiral symmetry breaking and hadronization. In this model, the QCD vacuum is described by the statistical ensemble of domain wall networks which represents the almost everywhere homogeneous Abelian (anti-)self-dual gluon field configurations. Calculations of the form factors are performed consistently with mass spectra of light, heavy-light and double-heavy mesons, their weak and strong decay constants. Influence of the nonperturbative intermediate range gluon fields on asymptotic behaviour of pion transition form factor is of particular interest, as it can potentially lead to the growth of $Q^2F_{\pi\gamma^*\gamma}(Q^2)$. It is found that $Q^2F_{\pi\gamma^*\gamma}(Q^2)$ approaches a constant value at asymptotically large $Q^2$. However, this limit differs from the standard factorization bound, though for pion form factor complies with Belle data more likely than with BaBar ones. At the same time the generally accepted factorization bound is shown to be satisfied for the case of the symmetric kinematics, $Q^2F_{P\gamma^*\gamma^*}(Q^2)$. Peculiarities of description of $\eta$, $\eta'$ and $\eta_c$ form factors within the model are discussed in detail.

Form factors of bound states in the XXZ chain

This work focuses on the calculation of the large-volume behaviour of form factors of local operators in the XXZ spin-1/2 chain taken between the ground state and an excited state containing bound states. The analysis is rigorous and builds on various fine properties of the string solutions to the Bethe equations and certain technical hypotheses. These technical hypotheses are satisfied for a generic excited state. The results obtained in this work pave the way for extracting, starting from the first principles, the large-distance and long-time asymptotic behaviour of the XXZ chain’s two-point functions just as the so-called edge singularities of their Fourier transforms.

Form factors in the N=4 maximally supersymmetric Yang–Mills theory, soft theorems, and integrability

We discuss the universal soft behavior of form factors in the N=4 maximally supersymmetric Yang–Mills theory in the limit where the momentum of one of the particles tends to zero. We present details of how the tree-level form factors of this theory are related to eigenfunctions of a gl(4|4) integrable spin chain.