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 Kotko Piotr EPJ Web of Conferences , 2012, DOI: 10.1051/epjconf/20123708008 Abstract: Transition distribution amplitudes (TDAs) are non-perturbative quantities appearing in the description of certain exclusive processes, for instance hadron-anti-hadron annihilation HH → γ*γ or backward virtual Compton scattering. They are similar to generalized parton distributions (GPDs), except that the non-diagonality concerns not only the momenta, but also the physical states (they are defined in terms of hadron-photon matrix element of a non-local operator). For the case of hadronic states such as pions, there are two TDAs of interest: the vector and the axial one. They are straightforwardly related to the axial and vector form factors controlling weak pion decays π± → e±νγ. The value at zero momentum transfer of the vector form factor is fixed by the axial anomaly, while this is not the case for the axial one. Moreover, the vector form factor is related to the pion-photon transition form factor which was recently measured by Belle and BaBar giving contradictory results at high momentum transfers. We have studied pion-to-photon TDAs within the non-local chiral quark model using modified non-local currents satisfying Ward-Takahashi identities. We found that the value of the axial form factor at zero momentum transfer is shifted towards the experimental value due to the non-locality of the model (in the local quark models the values of both vector and axial form factors at zero momentum transfer are the same, what is not consistent with the data). We also calculate the pion-photon transition form factor and compare it with the data.
 Physics , 1999, DOI: 10.1103/PhysRevC.61.045202 Abstract: The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the dressed quark-photon vertex to study the low-momentum behavior of the pion electromagnetic form factor. With model gluon parameters previously fixed by the pion mass and decay constant, the pion charge radius $r_\pi$ is found to be in excellent agreement with the data. When the often-used Ball-Chiu Ansatz is used to construct the quark-photon vertex directly from the quark propagator, less than half of $r_\pi^2$ is generated. The remainder of $r^2_\pi$ is seen to be attributable to the presence of the $\rho$-pole in the solution of the ladder Bethe-Salpeter equation.
 High Energy Physics - Phenomenology , 2008, Abstract: We present a general representation for the nucleon distribution amplitudes and for the nucleon to pion transition distribution amplitudes in terms of light-cone wave functions. We apply our formalism to a light-cone constituent quark model giving some numerical results for both the classes of observables.
 Physics , 2008, Abstract: We present a general representation for the nucleon distribution amplitudes and for the nucleon to pion transition distribution amplitudes in terms of light-cone wave functions. We apply our formalism to a light-cone constituent quark model giving some numerical results for both the classes of observables.
 High Energy Physics - Phenomenology , 2007, DOI: 10.1103/PhysRevD.76.094026 Abstract: We define the pion-photon Transition Distribution Amplitudes (TDA) in a field theoretic formalism from a covariant Bethe-Salpeter approach for the determination of the bound state. We apply our formalism to the Nambu - Jona Lasinio model, as a realistic theory of the pion. The obtained vector and axial TDAs satisfy all features required by general considerations. In particular, sum rules and polynomiality condition are explicitly verified. We have numerically proved that the odd coefficients in the polynomiality expansion of the vector TDA vanish in the chiral limit. The role of PCAC and the presence of a pion pole are explicitly shown.
 Physics , 2014, Abstract: We study the quark-antiquark scattering phase shift and meson spectral function in the pion superfluid described by the Nambu--Jona-Lasinio model. The meson mixing in the pion superfluid changes dramatically the full scattering phase shift and spreads strongly the spectral function of some of the collective modes.
 High Energy Physics - Phenomenology , 2013, Abstract: The gauge-invariant, nonlocal, dynamical quark model is proved to generate the minimal vertices which satisfy the Ward-Takahashi identities. In the chiral limit, the momentum-dependent quark self-energy results in a flat-like form with some end point delta-funtions for the light-cone pion distribution amplitudes, similarly found in the Nambu Jona-Lasino model with constant constituent mass. The leading order nonzero pion and current quark masses corrections lead concave type asymptotic-like form modifications to twist-2 pion distribution amplitude with end point pillars and twist-3 tensor pion distribution amplitude above the flat-like form backgrounds. A by-product of our investigation shows that the variable u appearing in pion light-cone distribution amplitudes is just the standard Feynman parameter in the Feynman parameter integrals; also chiral perturbation works well for these amplitudes.
 Physics , 2013, DOI: 10.1088/0256-307X/30/8/081101 Abstract: The gauge-invariant, nonlocal, dynamical quark model is proved to generate the minimal vertices which satisfy the Ward-Takahashi identities. In the chiral limit, the momentum-dependent quark self-energy results in a flat-like form with some end point delta-funtions for the light-cone pion distribution amplitudes, similarly found in the Nambu Jona-Lasino model with constant constituent mass. The leading order nonzero pion and current quark masses corrections lead concave type asymptotic-like form modifications to twist-2 pion distribution amplitude with end point pillars and twist-3 tensor pion distribution amplitude above the flat-like form backgrounds. A by-product of our investigation shows that the variable u appearing in pion light-cone distribution amplitudes is just the standard Feynman parameter in the Feynman parameter integrals; also chiral perturbation works well for these amplitudes.
 Physics , 2010, DOI: 10.1364/OE.18.012915 Abstract: We test two-dimensional TPSA of biphoton light emitted via ultrafast spontaneous parametric down-conversion (SPDC) using the effect of group-velocity dispersion in optical fibres. Further, we apply this technique to demonstrate the engineering of biphoton spectral properties by acting on the pump pulse shape.
 Physics , 2012, Abstract: Baryon to meson transition distribution amplitudes (TDAs), non-diagonal matrix elements of the nonlocal three quark operator between a nucleon and a meson state, extend the concept of generalized parton distributions. These non-perturbative objects which encode the information on three quark correlations inside the nucleon may be accessed experimentally in backward meson electroproduction reactions. We suggest a general framework for modelling nucleon to pion (pi N) TDAs employing the spectral representation for pi N TDAs in terms of quadruple distributions. The factorized Ansatz for quadruple distributions with input from the soft-pion theorem for pi N TDAs is proposed. It is to be complemented with a D-term like contribution from the nucleon exchange in the cross channel. We present our estimates of the unpolarized cross section and of the transverse target single spin asymmetry for backward pion electroproduction within the QCD collinear factorization approach in which the non-perturbative part of the amplitude involves pi N TDAs. The cross section is sizable enough to be studied in high luminosity experiments such as J-lab@12GeV and EIC.
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