Factorization Ansatz Research Articles

Comparison of the electromagnetic responses of C12 obtained from the Green's function Monte Carlo and spectral function approaches

The electromagnetic responses of carbon obtained from the Green's function Monte Carlo and spectral function approaches using the same dynamical input are compared in the kinematical region corresponding to momentum transfer in the range 300-570 MeV. The results of our analysis, aimed at pinning down the limits of applicability of the approximations involved in the two schemes, indicate that the factorization ansatz underlying the spectral function formalism provides remarkably accurate results down to momentum transfer as low as 300 MeV. On the other hand, it appears that at 570 MeV relativistic corrections to the electromagnetic current not included in the Monte Carlo calculations may play a significant role in the transverse channel.

Slave rotor approach to dynamically screened Coulomb interactions in solids

Recent studies of dynamical screening of the electronic Coulomb interactions in solids have revived interest in lattice models of correlated fermions coupled to bosonic degrees of freedom (Hubbard-Holstein-type models). We propose a dynamical mean-field-based approach to dynamically screened Coulomb interactions. In the effective Anderson-Holstein model, a transformation to slave rotors [S. Florens and A. Georges, Phys. Rev. B 66, 165111 (2002)] is performed to decouple the dynamical part of the interaction. This transformation allows for a systematic derivation and analysis of recently introduced approximate schemes for the solution of dynamical impurity problems, in particular, the Bose factor ansatz within the dynamic atomic limit approximation (DALA) with and without Lang-Firsov correction. More importantly still, it suggests an optimized choice for a Bose factor in the sense of the variational principle of Feynman and Peierls. We demonstrate the accuracy of our scheme and present a comparison to calculations within the DALA.

Determination of the axial nucleon form factor from the MiniBooNE data

Both neutrino and antineutrino charged-current quasielastic scattering on a carbon target are studied to investigate the nuclear effect on the determination of the axial form factor ${F}_{A}({Q}^{2})$. A method for extraction of ${F}_{A}({Q}^{2})$ from the flux-integrated $d\ensuremath{\sigma}/d{Q}^{2}$ cross section of (anti)neutrino scattering on nuclei is presented. Data from the MiniBooNE experiment are analyzed in the relativistic distorted-wave impulse approximation, the Fermi gas model, and the Fermi gas model with enhancements in the transverse cross section. We found that the values of the axial form factor, extracted in the impulse approximation and predicted by the dipole approximation with the axial mass ${M}_{A}\ensuremath{\approx}1.37\text{ }\mathrm{GeV}$, are in good agreement. The agreement between the extracted form factor and meson-dominance ansatz also is good. On the other hand, the ${Q}^{2}$ dependence of ${F}_{A}$ extracted in the approach with the transverse enhancement is found to differ significantly from the dipole approximation.

Sum rules for nucleon generalized parton distributions and border function formulation

The newy developed approach to model nucleon generalized parton distributions (GPDs) H and E$ is based on two types of their representation in terms of double distributions. Within this approach, we re-consider the derivation of GPD sum rules that allow to use border functions H(x,x) and E(x,x) instead of full GPDs H(x,\xi) and E(x,\xi) in the integrals producing Compton form factors of deeply virtual Compton scattering. Using factorized DD Ansatz to model GPDs, we discuss the relation between the border functions and underlying parton densities. We find that a substantial contribution to H(x,x) border function comes from the extra term required by new DD representations and related to E(x,\xi) GPD.

Network inference with hidden units

We derive learning rules for finding the connections between units in stochastic dynamical networks from the recorded history of a "visible'' subset of the units. We consider two models. In both of them, the visible units are binary and stochastic. In one model the "hidden'' units are continuous-valued, with sigmoidal activation functions, and in the other they are binary and stochastic like the visible ones. We derive exact learning rules for both cases. For the stochastic case, performing the exact calculation requires, in general, repeated summations over an number of configurations that grows exponentially with the size of the system and the data length, which is not feasible for large systems. We derive a mean field theory, based on a factorized ansatz for the distribution of hidden-unit states, which offers an attractive alternative for large systems. We present the results of some numerical calculations that illustrate key features of the two models and, for the stochastic case, the exact and approximate calculations.

Dynamical screening in strongly correlated metal SrVO3

The consequences of dynamical screening of Coulomb interaction among correlated electrons in realistic materials have not been widely considered before. In this letter we try to incorporate a frequency-dependent Coulomb interaction into the state-of-the-art ab initio electronic structure computing framework of local density approximation plus dynamical mean-field theory, and then choose SrVO3 as a prototype material to demonstrate the importance of dynamical screening effect. It is shown to renormalise the spectral weight near the Fermi level, to increase the effective mass, and to suppress the t2g quasiparticle bandwidth apparently. The calculated results are in accordance with very recent angle-resolved photoemission spectroscopy experiments and Bose factor ansatz calculations.

SU(3) symmetry breaking andCPviolation inD→PPdecays

Evidence of CP violation in the charm sector has been observed recently by the LHCb and CDF Collaborations. Adopting the topological diagram approach, we study flavor SU(3) symmetry breaking effects in the weak decay tree amplitudes of singly Cabibbo-suppressed $D\to PP$ decays. The symmetry breaking in the color-allowed and color-suppressed amplitudes is estimated with the help of the factorization ansatz, while that in the $W$-exchange amplitude is done by fitting to related branching fraction data. We find that the $W$-exchange amplitudes stay in the second quadrant relative to the color-allowed tree amplitude, albeit there are two possibilities for one type of $W$-exchange amplitude. The weak decay penguin amplitudes, on the other hand, are evaluated within the framework of QCD factorization. Using the input of topological tree amplitudes extracted from the Cabibbo-favored decay modes and the perturbative results for QCD penguin amplitudes, we make predictions for the branching fractions and CP asymmetries of singly Cabibbo-suppressed modes. The predictions of branching fractions are generally improved from those in the SU(3) limit. We conclude that the direct CP asymmetry difference between $D^0 \to K^+ K^-$ and $D^0 \to \pi^+ \pi^-$ is about $-(0.139\pm 0.004)%$ and $-(0.151\pm 0.004)%$ for the two solutions of $W$-exchange amplitudes, respectively. We also find that the CP asymmetry of $D^0\to K^0\ov K^0$ dominated by the interference between $W$-exchange amplitudes ranges from $-0.62\times 10^{-3}$ to $-1.82\times 10^{-3}$. We study phenomenological implications of two new physics scenarios for explaining the observed CP asymmetry in the charm sector, one with large penguin amplitudes and the other with a large chromomagnetic dipole operator. We find that the two scenarios can be discriminated by the measurements of CP asymmetries of a set of decay modes.

Jet physics in electron–proton scattering

Hadronic jets in electron–proton collisions at HERA have been used for some considerable time as a tool for tests of the theory of strong interactions, quantum chromodynamics. Using jet final states, basic concepts like the factorisation ansatz for cross-section calculations, the perturbative approach to the cross section and the universality of the proton parton distribution functions can be examined. More concretely, jet measurements provide ready access to the strong coupling of QCD, α s , and to the parton distributions. In this report, an overview of jet results from the HERA experiments H1 and ZEUS and their interpretation is given together with a description of the theoretical foundations of jet physics in electron–proton collisions and of the experimental environment at HERA. Special emphasis is put on extractions of α s values and on the influence of jet data on fits of the proton parton distribution functions. Where useful, the HERA results are also discussed in the light of results from other colliders like LEP, the Tevatron or the LHC. The central message from these studies is that QCD does not only describe most of the measurements very well, but that QCD at HERA has achieved the status of a precision theory. On the other hand it is shown that further understanding of problematic issues relies critically on theoretical progress in the form of improved models or of increased precision in analytical calculations.

Consistent model forπNtransition distribution amplitudes and backward pion electroproduction

The extension of the concept of generalized parton distributions leads to the introduction of baryon to meson transition distribution amplitudes (TDAs), non-diagonal matrix elements of the nonlocal three quark operator between a nucleon and a meson state. We present a general framework for modelling nucleon to pion ($\pi N$) TDAs. Our main tool is the spectral representation for \pi N TDAs in terms of quadruple distributions. We propose a factorized Ansatz for quadruple distributions with input from the soft-pion theorem for \pi N TDAs. The spectral representation is complemented with a D-term like contribution from the nucleon exchange in the cross channel. We then study backward pion electroproduction in the QCD collinear factorization approach in which the non-perturbative part of the amplitude involves \pi N TDAs. Within our two component model for \pi N TDAs we update previous leading-twist estimates of the unpolarized cross section. Finally, we compute the transverse target single spin asymmetry as a function of skewness. We find it to be sizable in the valence region and sensitive to the phenomenological input of our \pi N TDA model.

Semi-inclusive charged-pion electroproduction off protons and deuterons: Cross sections, ratios, and access to the quark-parton model at low energies

A large set of cross sections for semi-inclusive electroproduction of charged pions (π±) from both proton and deuteron targets was measured. The data are in the deep-inelastic scattering region with invariant mass squared W2>4 GeV2 (up to ≈7 GeV2) and range in four-momentum transfer squared 2<Q2<4 (GeV/c)2, and cover a range in the Bjorken scaling variable 0.2<x<0.6. The fractional energy of the pions spans a range 0.3<z<1, with small transverse momenta with respect to the virtual-photon direction, Pt2<0.2 (GeV/c)2. The invariant mass that goes undetected, Mx or W′, is in the nucleon resonance region, W′<2 GeV. The new data conclusively show the onset of quark-hadron duality in this process, and the relation of this phenomenon to the high-energy factorization ansatz of electron-quark scattering and subsequent quark→pion production mechanisms. The x, z, and Pt2 dependences of several ratios (the ratios of favored-unfavored fragmentation functions, charged pion ratios, deuteron-hydrogen and aluminum-deuteron ratios for π+ and π−) have been studied. The ratios are found to be in good agreement with expectations based upon a high-energy quark-parton model description. We find the azimuthal dependences to be small, as compared to exclusive pion electroproduction, and consistent with theoretical expectations based on tree-level factorization in terms of transverse-momentum-dependent parton distribution and fragmentation functions. In the context of a simple model, the initial transverse momenta of d quarks are found to be slightly smaller than for u quarks, while the transverse momentum width of the favored fragmentation function is about the same as for the unfavored one, and both fragmentation widths are larger than the quark widths.19 MoreReceived 7 March 2011DOI:https://doi.org/10.1103/PhysRevC.85.015202©2012 American Physical Society

Inelastic production of J/ψ mesons in photoproduction and deep inelastic scattering at HERA

A measurement is presented of inelastic photo- and electroproduction of J/psi mesons in ep scattering at HERA. The data were recorded with the H1 detector in the period from 2004 to 2007. Single and double differential cross sections are determined and the helicity distributions of the J/psi mesons are analysed. The results are compared to theoretical predictions in the colour singlet model and in the framework of non-relativistic QCD. Calculations in the colour singlet model using a k_T factorisation ansatz are able to give a good description of the data, while colour singlet model calculations to next-to-leading order in collinear factorisation underestimate the data.

Many-body approach for quartet condensation in strong coupling

The theory for condensation of higher fermionic clusters is developed. Fully selfconsistent nonlinear equations for the quartet order parameter in strongly coupled fermionic systems are established and solved. The breakdown of the quasiparticle picture is pointed out. Derivation of numerically tractable approximation is described. The momentum projected factorisation ansatz of Ref. \cite{slr09} for the order parameter is employed again. As a definite example the condensation of $\alpha$ particles in nuclear matter is worked out.

Partonic transverse momenta in non-relativistic hyper-central quark potential models

We investigate the impact of three-body forces on the transverse-momentum distribution of partons inside the proton. This is achieved by considering the three-body problem in a class of hyper-central quark potential models. Solving the corresponding Schrödinger equation, we determine the quark wave function in the proton and with appropriate transformations and projections we find the transverse-momentum distribution of a single quark. In each case the parameters of the quark potentials are adjusted in order to sufficiently describe observable properties of the proton. Using a factorization ansatz, we incorporate the obtained transverse-momentum distribution in a perturbative QCD scheme for the calculation of the cross-section for prompt photon production in pp collisions. A large set of experimental data is fitted using as a single free parameter the mean partonic transverse momentum. The dependence of 〈k T〉 on the collision characteristics (initial energy and transverse momentum of the final photon) is much smoother when compared with similar results found in the literature using a Gaussian distribution for the partonic transverse momenta. Within the considered class of hyper-central quark potentials the one with the weaker dependence on the hyper-radius is preferred for the description of the data since it leads to the smoothest mean partonic transverse-momentum profile. We have repeated all the calculations using a two-body potential of the same form as the optimal (within the considered class) hyper-central potential in order to check if the presence of three-body forces is supported by the experimental data. Our analysis indicates that three-body forces influence significantly the form of the parton transverse-momentum distribution and consequently lead to an improved description of the considered data.

Generalized-gradient exchange-correlation hole obtained from a correlation factor ansatz

The Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy is employed as reference point for the construction of an angle-averaged exchange-correlation hole. First, we develop a new model for the PBE exchange hole. In contrast to the previous model [Ernzerhof and Perdew, J. Chem. Phys. 109, 3313 (1998)], it contains an atomic exchange hole, similar to the Becke-Roussel model [Becke and Roussel, Phys. Rev. A 39, 3761 (1989)]. A correlation factor, i.e., a function multiplying the exchange hole, is proposed that turns the exchange into an exchange-correlation hole. The correlation factor has a simple form and is determined through a number of known conditions that should be satisfied by a generalized-gradient exchange-correlation hole.

A method of experimentally probing transverse momentum dependent distributions

We calculate the double spin asymmetry ALL for the π0 production in semi-inclusive deep inelastic lepton–proton scattering with a spectator model of power-law and a model based on the factorization ansatz. We also calculate the double spin asymmetry for the integration over parts of the kinematic range for the setups of the experiments of COMPASS, HERMES, and JLab. We find that the results are characteristically dependent on the model used. Therefore, we suggest that the measurements of the double spin asymmetry provides a method of experimentally probing the transverse momentum dependent distributions.

Onset of Quark-Hadron Duality in Pion Electroproduction

A large data set of charged-pion (pi+/-) electroproduction from both hydrogen and deuterium targets has been obtained spanning the low-energy residual-mass region. These data conclusively show the onset of the quark-hadron duality phenomenon, as predicted for high-energy hadron electroproduction. We construct several ratios from these data to exhibit the relation of this phenomenon to the high-energy factorization ansatz of electron-quark scattering and subsequent quark-->pion production mechanisms.

LIOUVILLE THEORY AND LOGARITHMIC SOLUTIONS TO KNIZHNIK–ZAMOLODCHIKOV EQUATION

We study a class of solutions to the SL (2, ℝ)k Knizhnik–Zamolodchikov equation. First, logarithmic solutions which represent four-point correlation functions describing string scattering processes on three-dimensional anti-de Sitter space are discussed. These solutions satisfy the factorization ansatz and include logarithmic dependence on the SL (2, ℝ)-isospin variables. Different types of logarithmic singularities arising are classified and the interpretation of these is discussed. The logarithms found here fit into the usual pattern of the structure of four-point function of other examples of AdS/CFT correspondence. Composite states arising in the intermediate channels can be identified as the phenomena responsible for the appearance of such singularities in the four-point correlation functions. In addition, logarithmic solutions which are related to nonperturbative (finite k) effects are found. By means of the relation existing between four-point functions in Wess–Zumino–Novikov–Witten model formulated on SL (2, ℝ) and certain five-point functions in Liouville quantum conformal field theory, we show how the reflection symmetry of Liouville theory induces particular ℤ2 symmetry transformations on the WZNW correlators. This observation allows to find relations between different logarithmic solutions. This Liouville description also provides a natural explanation for the appearance of the logarithmic singularities in terms of the operator product expansion between degenerate and puncture fields.

Formula omitted] and tests of factorization for two-body non-leptonic B decays with axial-vector mesons

The large branching ratio for B→K1γ recently measured at Belle implies a large B→K1 transition form factor and large branching ratios for non-leptonic B decays involving an axial-vector meson. In this Letter we present an analysis of two-body B decays with an axial-vector meson in the final state using naive factorization and the B→K1 form factors obtained from the measured radiative decays. We find that the predicted B→J/ψK1 branching ratio is in agreement with experiment. We also suggest that the decay rates of B→K1π, B→a1K and B→b1K could be used to test the factorization ansatz.

Asymptotics for Selfdual Vortices on the Torus and on the Plane: A Gluing Technique

We consider multivortex solutions for the selfdual Abelian Higgs model, as the ratio of the vortex core size to the separation distance between vortex points (the scaling parameter) tends to zero. To this end, we use a gluing technique (a shadowing lemma) for solutions to the corresponding semilinear elliptic equation on the plane, allowing any number (finite or countable) of arbitrarily prescribed singular sources. Our approach is particularly convenient and natural for the study of the asymptotics. In particular, in the physically relevant cases where the vortex points are either finite or periodically arranged in the plane, we prove that a frequently used factorization ansatz for multivortex solutions is rigorously satisfied, up to an error which is exponentially small.

Diamagnetic shift and localization of excitons in disordered quantum wells

Calculations of exciton absorption spectra and wave functions in quantum wells with alloy and interface disorder under the influence of a perpendicular magnetic field are presented. The four-coordinate Schrödinger equation is solved in electron–hole in-plane coordinates thus going beyond the standard factorization ansatz. It is shown that the diamagnetic shift varies remarkably among different states and is not monotonic in energy, which is in agreement with recent experiments. The stronger the localization of the wave function the smaller the diamagnetic shift. Therefore, the diamagnetic shift analysis gives additional information about the local potential landscape in quantum wells.