Limit Of Large Momentum Transfer Research Articles

Flavor-singlet meson decay constants from Nf=2+1+1 twisted mass lattice QCD

We present an improved analysis of our lattice data for the $\eta$--$\eta'$ system, including a correction of the relevant correlation functions for residual topological finite size effects and employing consistent chiral and continuum fits. From this analysis we update our physical results for the masses $M_\eta=557(11)_\mathrm{stat}(03)_{\chi\mathrm{PT}}\,\mathrm{MeV}$ and $M_{\eta'}=911(64)_\mathrm{stat}(03)_{\chi\mathrm{PT}}\,\mathrm{MeV}$, as well as the mixing angle in the quark flavor basis $\phi=38.8(2.2)_\mathrm{stat}(2.4)_{\chi\mathrm{PT}}^\circ$ in excellent agreement with other results from phenomenology. Similarly, we include an analysis for the decay constant parameters, leading to $f_l=125(5)_\mathrm{stat}(6)_{\chi\mathrm{PT}}\,\mathrm{MeV}$ and $f_s=178(4)_\mathrm{stat}(1)_{\chi\mathrm{PT}}\,\mathrm{MeV}$. The second error reflects the uncertainty related to the chiral extrapolation. The data used for this study has been generated on gauge ensembles provided by the European Twisted Mass Collaboration with $N_f=2+1+1$ dynamical flavors of Wilson twisted mass fermions. These ensembles cover a range of pion masses from $220\,\mathrm{MeV}$ to $500\,\mathrm{MeV}$ and three values of the lattice spacing. Combining our data with a prediction from chiral perturbation theory, we give an estimate for the physical $\eta,\eta' \rightarrow \gamma\gamma$ decay widths and the singly-virtual $\eta,\eta'\rightarrow\gamma\gamma^*$ transition form factors in the limit of large momentum transfer.

Effective field theory for large logarithms in radiative corrections to electron proton scattering

Radiative corrections to elastic electron-proton scattering are analyzed in effective field theory. A new factorization formula identifies all sources of large logarithms in the limit of large momentum transfer, $Q^2\gg m_e^2$. Explicit matching calculations are performed through two-loop order. A renormalization analysis in soft-collinear effective theory is performed to systematically compute and resum large logarithms. Implications for the extraction of charge radii and other observables from scattering data are discussed. The formalism may be applied to other lepton-nucleon scattering and $e^+e^-$ annihilation processes.

Analytic formulae for occupation probabilities of atomic states in strong short laser pulses

Explicit analytic expressions, involving elementary functions, are given for occupation probabilities of atomic states after one or a few cycles of a strong short laser pulse. These formulae are strictly valid in the asymptotic limit of large momentum transfer from the field to the atom during a half cycle of the pulse. The cases of a hydrogenic atom, of a negative ion and of multielectron atoms in the independent-electron approximation are considered. The asymptotic expressions, derived in the limit of infinite momentum transfer from the field, have also the correct limit for vanishingly small momentum transfers, so that fortuitously they are valid for arbitrary momentum transfer.

Elastic and inelastic scattering in electron momentum spectroscopy of amorphous Ge films

Electron momentum spectroscopy (an (e, 2e) experiment in the high-energy and large momentum transfer limit) is a scattering approach to the study of the electronic structure. The intensity observed in these experiment is, for an infinitely thin film, simply proportional to the spectral momentum density. For experiments using free-standing films of a more realistic thickness (100 Å or so), elastic and inelastic multiple scattering events are frequent and their influence on the observed intensity cannot be neglected. Here we study germanium films where the sp derived valence band can be measured simultaneously with the shallow, non-dispersing, 3d level. Somewhat surprisingly, the intensity of the 3d level, relative to that of the valence band, increases with film thickness. This effect is attributed to elastic multiple scattering. Monte Carlo simulations reproduce the changes in the observed intensity distributions with increasing film thickness.

Erratum: Skewed quark distribution of the pion at large momentum transfer [Phys. Rev. D64, 057501 (2001)

We derive an explicit and model-independent representation for the skewed quark distribution of the pion in the limit of large momentum transfer. Our result is expressed in terms of the conventional pion distribution amplitudes and complies with known properties of skewed parton distributions such as symmetry and polynomiality conditions. The continuity of the result at the points \pm \xi is manifest, whereas its derivatives exhibit discontinuities.

Probing quark-distribution amplitudes through generalized parton distributions at large momentum transfer.

In the large momentum transfer limit, generalized parton distributions can be calculated through a QCD factorization theorem which involves perturbatively calculable hard kernels and light-cone parton distribution amplitudes of hadrons. We illustrate this through the H(q)(x,xi,t) distribution for the pion and the proton, presenting the hard kernels at leading order. As a result, experimental data on the generalized parton distributions in this regime can be used to determine the functional form of the parton distribution amplitudes which has thus far been quite challenging to obtain. Our result can also be used as a constraint in phenomenological generalized parton distribution parametrizations.

Skewed quark distribution of the pion at large momentum transfer

We derive an explicit and model-independent representation for the skewed quark distribution of the pion in the limit of large momentum transfer. Our result is expressed in terms of the conventional pion distribution amplitudes and complies with known properties of skewed parton distributions such as symmetry and polynomiality conditions. The continuity of the result at the points $\ifmmode\pm\else\textpm\fi{}\ensuremath{\xi}$ is manifest, whereas its derivatives exhibit discontinuities.

Determining Color-Octet ψ-Production Matrix Elements from γp and ep Processes

We calculate, within the NRQCD factorization formalism, the leading color-octet contributions to ψ production in photon-nucleon and electron-nucleon collisions. The expressions we obtaine depend on the NRQCD matrix elements [Formula: see text] and [Formula: see text]. These matrix elements can be determined by fitting to experimental data. The color-octet contribution to ψ photoproduction is in the forward region of phase space, where there may be large corrections to the NRQCD result from higher twist terms. As to ψ leptoproduction we point out that the theoretical uncertainties plaguing the photoproduction calculation vanish in the large momentum transfer limit. In this region of phase space the NRQCD formalism should be valid, making ψ leptoproduction an ideal laboratory for testing the theory.

The asymptotics of 3 ladder diagrams in six dimensions: high energy and large momentum transfer

The first three leading terms of the asymptotic form of the scattering amplitude for the n -rung 3 ladder diagram in six dimensions are derived in the high-energy, large-momentum transfer limit. The behavior of these terms is qualitatively different from that of the same diagram in four dimensions.

The asymptotics of ladder diagrams involving massless scalars

The asymptotic form of the scattering amplitude for n-rung φ 3 ladder diagrams is derived in the high energy, large momentum transfer limit. When the internal lines are massless, the result is shown to be analytic in γ = log s log |t| .

The high-energy, large-transfer-momentum limit: The asymptotics of ø 3 ladder diagrams

We derive the asymptotic form of the scattering amplitude for arbitrary ø 3 ladder diagram in the high-energy, large-momentum transfer limit.

A new technique for the evaluation of Feynman diagrams in the high energy, large momentum transfer limit

The problem of finding scattering amplitudes in the high energy, large momentum transfer limit is reconsidered. We propose a novel technique of evaluating Feynman diagrams in this regime with higher order perturbative corrections in mind. The relation to other methods is discussed and the ladder diagrams in φ3 theory, recalculated up to sixth order, serve as examples.

Asymptotic behavior of the Sudakov form factor in quantum chromodynamics

In this paper we give an algorithm to compute the asymptotic behavior of the on-shell quark form factor in the limit of large momentum transfer (Sudakov form factor) in Abelian and non-Abelian gauge theories. We ignore terms which are suppressed by a power of momentum transfer, but keep all nonleading logarithms of the momentum transfer and all powers of the coupling constant.

Asymptotic behavior of composite-particle form factors and the renormalization group

Composite-particle form factors are studied in the limit of large momentum transfer $Q$. It is shown that in models with spinor constituents and either scalar or guage vector gluons, the meson electromagnetic form factor factorizes at large ${Q}^{2}$ and is given by independent light-cone expansions on the initial and final meson legs. The coefficient functions are shown to satisfy a Callan-Symanzik equation. When specialized to quantum chromodynamics, this equation leads to the asymptotic formula of Brodsky and Lepage for the pion electromagnetic form factor. The nucleon form factors ${G}_{M}({Q}^{2})$, ${G}_{E}({Q}^{2})$ are also considered. It is shown that momentum flows which contribute to subdominant logarithms in ${G}_{M}({Q}^{2})$ vitiate a conventional renormalization-group interpretation for this form factor. For large ${Q}^{2}$, the electric form factor ${G}_{E}({Q}^{2})$ fails to factorize, so that a renormalization-group treatment seems even more unlikely in this case.

Light cone, Regge contributions and large-angle scattering

The asymptotic behaviour of various three-particle vertices involving reggeons far off-mass-shell, and that of various exclusive reactions is found by using the light-cone algebra of the local and bilocal operators and supposing that the Regge contributions survive in the amplitude in the limit of large momentum transfer. The scaling behaviour (29), (34) is obtained in this way for the exclusive amplitudes. Besides, the asymptotic behaviour of hadronic form factors is obtained. The asymptotic behaviour of Regge-cut contributions and the region of applicability of the scaling behaviour (29) are found for the 2 → 2 amplitude. The relations between the dispersion contributions, Regge contributions, and those of quark diagrams, as well as the role of the signature are discussed. Predictions are given for the energy and the angular distributions for a number of two-particle reactions.

Inelastic Lepton-Nucleon Scattering and Lepton Pair Production in the Relativistic Quark-Parton Model

We discuss the interaction of hadrons with leptons in the limit of large momentum transfer. A special parton model will be used for the hadrons in which the partons are identified with quarks. The relativistic quark model with which we interpret recent observations is formulated as follows: (1) The baryons are composed of three valence quarks and a core of an indefinite number of quark-antiquark pairs. (2) The lepton sees the nucleon in the limit of large momenta in the c.m. frame as an assembly of freely moving constitutents with point charges. (3) The scattering of the valence quarks is interpreted as the nondiffractive component, the scattering of the core is interpreted as the diffractive component of the cross section. (4) The nondiffractive scattering is assumed to be mediated by suitable meson exchanges, and this assumption determines the momentum distribution of the valence quarks. The ($q\overline{q}$) pairs in the core are assumed to be distributed statistically in the available phase space. (5) It will be necessary to include among the constituents of the nucleon. They are supposed to be the uncharged quanta of the force field between quarks and are assumed to be distributed statistically over the momentum space. There is only one constant adjustable in this model, which is the ratio of gluons to core pairs. All other constants are fixed by simple considerations. This model is used to calculate the deep-inelastic scattering of electrons by protons and neutrons and its dependence on the relative spin orientations, the inelastic scattering of neutrinos by nucleons, and the creation of massive muon pairs by proton-proton collisions. After adjusting the open constant to the data of electron-proton scattering, the theory predicts unambiguously the other results. They are in reasonably good agreement with the observations as far as they are known.

High‐Energy Neutron Scattering from Liquid He4

AbstractIn the limit of large momentum transfer, κ, the cross section for the scattering of neutrons from a macroscopic system is given by the impulse approximation, in which the scattering atom recoils as if it were free, and the energy distribution of the scattered neutrons is the Doppler profile characteristic of the momentum distribution in the initial state. In particular, the zero‐momentum condensate in liquid He4 below the λ‐point will produce a sharp peak in the spectrum of the scattered neutrons at the position of the free‐particle recoil energy and the relative intensity of this peak equals the fraction of atoms in the condensate. For finite momentum transfers the condensate peak tends to be smeared out by final‐state interactions and it is estimated that values of κ ≳ 80 Å−1 are required for the appearance of a well‐defined condensate peak. Available neutron data in the range 4 ≲κ≲ 20 Å−1 show no condensate peak and the main features of the observed scattering can be understood in terms of a truncated expansion of the scattering function as a series of Hermite polynomials.

High-Energy Neutron Scattering from LiquidHe4

The scattering of high-energy neutrons from liquid ${\mathrm{He}}^{4}$ is discussed in terms of the Gram-Charlier series expansion of the incoherent scattering function. It is shown that the series falls naturally into two parts. The first part, which corresponds to keeping only the leading term in each coefficient in the limit of large momentum transfer $\ensuremath{\kappa}$ can be summed exactly and gives the impulse approximation (IA). The second part, which vanishes in the limit $\ensuremath{\kappa}\ensuremath{\rightarrow}\ensuremath{\infty}$, describes the effect of final-state interactions which are neglected in the IA. The first two coefficients in the latter series are evaluated and indicate that final-state interactions are not negligible in the recent experiments of Cowley and Woods, a fact which probably explains why these authors failed to see a sharp peak, due to the condensate, which had been predicted by Hohenberg and Platzman on the basis of the IA. It is also shown that final-state interactions produce a shift in the position of the maximum of the energy distribution of scattered neutrons, and the calculated value is in rough agreement with the value observed by Cowley and Woods.

Complex Angular Momentum in Spinor Bethe-Salpeter Equation

A model of fermion-antifermion scattering, mediated by pseudoscalar neutral bosons, is described by the corresponding spinorial Bethe-Salpeter equation in the ladder approximation. The decomposition of the equation into partial waves by means of fusion amplitudes and conventional spherical harmonics is discussed in detail; various important symmetries of the resulting kernel and Born amplitudes are pointed out. The resulting set of coupled equations is continued into the complex angular momentum ($J$) plane, and it is shown that Fredholm theory is inapplicable for any $J$. The equations are solved in a weak coupling, low-energy limit by an iterative scheme. The resulting solutions exhibit a cut of the square-root type extending along the real axis to $\frac{G}{2\ensuremath{\pi}}$ ($G=\mathrm{coupling}\mathrm{constant}$) in the right-hand plane; other cuts and poles prevent the extension of our solutions into the left-hand $J$ plane. The dominance of the cut is used to extract the large momentum transfer limit and obtain certain results for the high-energy limit in the cross channel. The total cross section for fermion-antifermion annihilation is extracted by means of the optical theorem and is found to exhibit an energy dependence of the form ${t}^{(\frac{G}{2\ensuremath{\pi}})\ensuremath{-}1}{[\mathrm{ln}t]}^{\ensuremath{-}\frac{3}{2}}$, where $t$ is the c.m. energy squared.