The helicity amplitude approach to low energy theorems

It is shown that “low energy theorems” for charged vector and axial vector currents have a natural derivation in terms of helicity amplitudes. This is done by reconsidering the kinematic constraints as a function of the virtual photon mass, λ. The crucial point is that in general a certain limit of the longitudinal amplitudes is required as an input to the theorem. Two new νπ sum rules are also obtained.     

Does the glauber model fail in large angle πd scattering at high energies?

It is shown that, contrary to general belief, the uncertainties in the πN amplitudes are sufficient to account for the discrepancy between the Glauber model and the data for high-energy πd elastic scattering at large angles. The essential point is that the πd differential cross section in this kinematic region depends on the fourth power of the πN amplitudes and that, therefore, rather small changes in these amplitudes cause large effects in the πd cross section. Working with leading terms only it is found that more recent solutions for πN amplitudes (which are smaller in magnitude than those used in earlier analyses) may restore the agreement of theory and experiment at large angles.     

Complete and effectively complete inclusive experiments

The experiments required to meadure all the independent amplitudes in any single-particle inclusive process with experimentally available incident particles are determined, and the amplitude (or combination of amplitudes) obtained from each measurement is given. Various kinematic regions are considered, and the measurements which determine the subset of amplitudes expected to be important in each region are found. The prospects of a meaningful separation of exchanged naturalities are also investigated and found to be difficult, due to a kinematic suppression of certain amplitudes.     

Pionization structure function

We analyze the properties of a pionization structure function. Making some general assumptions about the analyticity structure of amplitudes describing inclusive processes (which are valid in a large class of models and are expected to be valid for the true amplitudes) we derive a general form of this structure function.     

Heuristic approach to non-abelian quantum kinematics and dynamics in configuration spacetime

New plausible kinematic foundations of quantum dynamics are discussed in a heuristic manner in which the quantum rule stems directly from the non-Abelian configuration symmetries of a system. Upon quantizing the ‘complete’ configuration symmetry group itself, irreducible generalized configuration-state representations can be calculated, whose transition amplitudes yield the propagation kernel. These states results from solving a set of ‘generalized Schrödinger equations’ corresponding to the superselection rules dictated by the quantized group. The propagation kernel of the system is thus obtained as an invariant Hurwitz integral, defined over the manifold of the complete symmetry group. A heuristic argument is given in favor of this approach to non-Abelian quantum kinematics, in which sums over physical world lines are evaluated instead of sums over arbitrary paths, for obtaining the propagation kernel of quantum systems having a classical Lagrangian analog. The attained quantum kinematic formalism, however, is completely general and does not depend on this particular interpretation. Nevertheless, the heuristic argument strongly suggests that non-Abelian quantum kinematics contains the formalism of standard nonrelativistic quantum mechanics as a very special case. No examples of the issues involved are presented in this paper.     

Reciprocal space-time and momentum-space singularities in the narrow resonance approximation

A general scheme is proposed which makes explicit the relationship between the singularities of off-shell amplitudes in position-space and momentum-space in the narrow resonnace approximation. In some ways this may be viewed as a duality scheme for amplitudes involving external quarks, in which narrow resonances in certain channels build the Fourier transform of power singularities in x² (x^μ being a position vector). This scheme is made precise by dual string off-shell amplitudes. As well as highlighting possible connections between the general dual framework and the structure of confined field theories we are able to pinpoint certain grave shortcomings of present dual models.     

Two-loop superstrings VII. Cohomology of chiral amplitudes

The relation between superholomorphicity and holomorphicity of chiral superstring N-point amplitudes for NS bosons on a genus 2 Riemann surface is shown to be encoded in a hybrid cohomology theory, incorporating elements of both de Rham and Dolbeault cohomologies. A constructive algorithm is provided which shows that, for arbitrary N and for each fixed even spin structure, the hybrid cohomology classes of the chiral amplitudes of the N-point function on a surface of genus 2 always admit a holomorphic representative. Three key ingredients in the derivation are a classification of all kinematic invariants for the N-point function, a new type of 3-point Green's function, and a recursive construction by monodromies of certain sections of vector bundles over the moduli space of Riemann surfaces, holomorphic in all but exactly one or two insertion points.     

Two-particle transfer reactions with heavy-deformed nuclei

Detailed calculations of two-particle transfer reactions on heavy, deformed nuclei are carried out within the framework of the macroscopic model for pair transfer and the sudden limit for rotational excitation. The marked structure that appears as a general feature of the angular distributions is explained as an interference of amplitudes that correspond to different orientations of the deformed nucleus. A comparison to recent data supports the existence of this structure.     

Dissolving N = 4 loop amplitudes into QCD tree amplitudes

We use the infrared consistency of one-loop amplitudes in N = 4 Yang-Mills theory to derive a compact analytic formula for a tree-level next-to-next-to-maximal helicity-violating gluon scattering amplitude in QCD, the first such formula known. We argue that the infrared conditions, coupled with recent advances in calculating one-loop box coefficients, can give a new tool for computing tree-level amplitudes in general. Our calculation suggests that many amplitudes have a structure which is even simpler than that revealed so far by current twistor-space constructions.     

X-ray Bragg diffraction with allowance for the second derivatives of amplitudes in dynamical diffraction equations

Asymmetrical Bragg diffraction in a perfect crystal with plane entrance surface is considered theoretically. In the dynamical diffraction equations the second derivatives of amplitudes in the direction, perpendicular to the diffraction plane are taken into account. Using the corresponding Green function, a general form for the amplitudes of waves in the crystal is presented. The sizes of the source in both directions as well as the source-crystal distance and non-monochromaticity of the radiation incident on the crystal are taken into account. On the basis of obtained formulas, the coherent properties of the field depending on the sizes of the source and on the width of spectrum of the incident radiation, are analized.     

Standard model effective field theory from on-shell amplitudes

We present a general method of constructing unfactorizable on-shell amplitudes (amplitude basis) and build up their one-to-one correspondence to the independent and complete operator basis in effective field theory (EFT). We apply our method to the Standard Model EFT and identify the amplitude basis in dimensions 5 and 6, which correspond to the Weinberg operator and operators in the Warsaw basis, except for some linear combinations.     

Raynal–Revai coefficients for a general kinematic rotation

In a three-body system, transitions between different sets of normalized Jacobi coordinates are described as general kinematic transformations that include an orthogonal or a pseudoorthogonal rotation. For such rotations, the Raynal–Revai coefficients execute a unitary transformation between three-body hyperspherical functions. Recurrence relations that make it possible to calculate the Raynal–Revai coefficients for arbitrary angular momenta are derived on the basis of linearized representations of products of hyperspherical functions.     

Scattering Amplitudes Interpolating Between Instant Form and Front Form of Relativistic Dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the front form has the largest number of kinematic generators. This distinction provides useful consequences in the analysis of physical observables in hadron physics. Using the method of interpolation between the instant form and the front form, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. We discuss the rationale for using front form dynamics, nowadays known as light-front dynamics (LFD), and present a few explicit examples of hadron phenomenology that LFD uniquely can offer from first-principles quantum chromodynamics. In particular, model-independent constraints are provided for the analyses of deuteron form factors and the N Δ transition form factors at large momentum transfer squared Q ². The swap of helicity amplitudes between the collinear and non-collinear kinematics is also discussed in deeply virtual Compton scattering.     

Solution of a one-dimensional torsion Schrödinger equation with a general periodic potential

Relations are found for the calculation of eigenvalues and eigenfunctions of the Hamiltonian of internal rotational motion in molecules in the basis of plane waves. The dependences of kinematic coefficient F(φ) and potential V(φ) on dihedral angle φ are represented by Fourier series for both symmetric and asymmetric functions, as well as for general periodic functions. If a molecule has symmetry elements, the found solution transforms to that previously known.     

Non-archimedean string dynamics

Explicit formulas for the N-point tree amplitudes of the non-archimedean open string are derived. These amplitudes can be generated from a simple non-local lagrangian involving a single scalar field (the tachyon) in ambient space-time. This lagrangian is studied and is found to possess a tachyon free vacuum with no “particles” but with soliton solutions. The question of generalizing the adelic product formular to N-point amplitudes is taken up. The infinite product of 5-point amplitudes is shown to converge in a suitably chosen kinematic region whence it can be analytically continued. Though the precise form of the product formula for the 5-point (and N-point)amplitudes is not found, it is shown that the product is not equal to one as it is for the 4-point amplitudes but rather involves the famous zeros of the Riemann zeta function. Chan-Paton rules for non-archimedean open strings are given. A string over the (global) field of rational numbers is constructed. Other problems that are addressed are the introduction of supersymmetry, the nature of a p-adic string lagrangian, and the possibility of strings over other locally compact fields.     

On Fliessbach's approaches to direct reactions

The conventional models of direct cluster reactions treat the nuclear wave-function overlaps or reduced-width amplitudes as single-particle wave functions, which is contrary to the Pauli principle. The motivation of Fliessbach's two approaches reviewed in this paper is to improve on these models by a proper treatment of antisymmetrization. Fliessbach's approaches involve redefined reduced-width amplitudes, which can be regarded as single-particle wave functions. We show, however, that in the approach specialized to transfer reactions the antisymmetrization is in fact treated incorrectly, and the more general approach seems applicable only to processes that involve just two nuclear fragments, like a decay or radiative capture. We outline how single-particle wave functions can be used correctly in approximating reduced-width amplitudes. We show that our approach helps to bring the phenomenological spectroscopic factors into agreement with the nuclear structure models.     

On the analytic properties of the reggeon-reggeon amplitude

The analytic properties of the reggeon-reggeon amplitude in the missing-mass like variable are discussed. (This amplitude is defined through the suitable high-energy limit of the eight-point amplitude). It is shown on the basis of simple Feynman diagrams that it is possible to define reduced amplitudes which are free from kinematical singularities provided that the eight-point amplitude is expressed in a form explicitly consistent with Steinmann relations. In a simple model which is considered in this paper, the reduced amplitudes have the singularity structure of ordinary two-body scattering amplitudes. The finite energy sum rules and four reggeon vertices are also briefly discussed.     

The Holomorphic Quadratic Differentials of Amplitudes for Strings with Boundaries

We show that the amplitudes for strings with boundaries can be written as complex structure forms. The C, curves used by Krichever and Novikov to parametrize compact Riemann surfaces satisfy the string boundary conditions. Thus they can be regarded as the initial and final states of the atrings. Using Krichever-Novikov bases, we explicitly construct a basis of holomorphic quadratic differentials for strings with boundaries.