41 research outputs found
Exclusive processes in position space and the pion distribution amplitude
We suggest to carry out lattice calculations of current correlators in
position space, sandwiched between the vacuum and a hadron state (e.g. pion),
in order to access hadronic light-cone distribution amplitudes (DAs). In this
way the renormalization problem for composite lattice operators is avoided
altogether, and the connection to the DA is done using perturbation theory in
the continuum. As an example, the correlation function of two electromagnetic
currents is calculated to the next-to-next-to-leading order accuracy in
perturbation theory and including the twist-4 corrections. We argue that this
strategy is fully competitive with direct lattice measurements of the moments
of the DA, defined as matrix elements of local operators, and offers new
insight in the space-time picture of hard exclusive reactions.Comment: 15 pages, 10 figure
Power corrections to the transition form factor and pion distribution amplitudes
Employing the standard hard-scattering approach and the running coupling
method we calculate a class of power-suppressed corrections to the electromagnetic transition form
factor (FF) arising from the end-point
integration regions. In the investigations we use a hard-scattering amplitude
of the subprocess , symmetrized under
exchange important for exclusive
processes containing two external photons. In the computations the pion model
distribution amplitudes (DA's) with one and two non-asymptotic terms are
employed. The obtained predictions are compared with the CLEO data and
constraints on the DA parameters and at the
normalization point are extracted. Further restrictions on
the pion DA's are deduced from the experimental data on the electromagnetic FF
.Comment: 23 pages, 6 figures; the version published in Phys. Rev. D69, 094010
(2004
Pion light cone wave function in the non-local NJL model
We use the simple instanton motivated NJL-type model to calculate the leading
twist pion light cone wave function. The model consists in employing the
momentum dependent quark mass in the quark loop entering the definition of the
wave function. The result is analytical up to a solution of a certain algebraic
equation. Various properties including the kT dependence of the pion wave
function are discussed. The resulting kT integrated wave function is not
asymptotic and is in agreement with recent analysis of the CLEO data.Comment: 9 pages, 12 figures, formulas (23-25) corrected, typos correcte
Unbiased analysis of CLEO data at NLO and pion distribution amplitude
We discuss different QCD approaches to calculate the form factor
F^{\gamma^*\gamma\pi}(Q^2) of the \gamma^*\gamma\to\pi^{0} transition giving
preference to the light-cone QCD sum rules (LCSR) approach as being the most
adequate. In this context we revise the previous analysis of the CLEO
experimental data on F^{\gamma^*\gamma\pi}(Q^{2}) by Schmedding and Yakovlev.
Special attention is paid to the sensitivity of the results to the (strong
radiative) \alpha_s-corrections and to the value of the twist-four coupling
\delta^2. We present a full analysis of the CLEO data at the NLO level of
LCSRs, focusing particular attention to the extraction of the relevant
parameters to determine the pion distribution amplitude, i.e., the Gegenbauer
coefficients a_2 and a_4. Our analysis confirms our previous results and also
the main findings of Schmedding and Yakovlev: both the asymptotic, as well as
the Chernyak--Zhitnitsky pion distribution amplitudes are completely excluded
by the CLEO data. A novelty of our approach is to use the CLEO data as a means
of determining the value of the QCD vacuum non-locality parameter \lambda^2_q =
/ =0.4 GeV^2, which specifies the average virtuality of
the vacuum quarks.Comment: 25 pages, 5 figures, 4 tables; format and margins corrected to fit
page size; small changes in the text and correction of misprint
Spectral quark model and low-energy hadron phenomenology
We propose a spectral quark model which can be applied to low energy hadronic
physics. The approach is based on a generalization of the Lehmann
representation of the quark propagator. We work at the one-quark-loop level.
Electromagnetic and chiral invariance are ensured with help of the gauge
technique which provides particular solutions to the Ward-Takahashi identities.
General conditions on the quark spectral function follow from natural physical
requirements. In particular, the function is normalized, its all positive
moments must vanish, while the physical observables depend on negative moments
and the so-called log-moments. As a consequence, the model is made finite,
dispersion relations hold, chiral anomalies are preserved, and the twist
expansion is free from logarithmic scaling violations, as requested of a
low-energy model. We study a variety of processes and show that the framework
is very simple and practical. Finally, incorporating the idea of vector-meson
dominance, we present an explicit construction of the quark spectral function
which satisfies all the requirements. The corresponding momentum representation
of the resulting quark propagator exhibits only cuts on the physical axis, with
no poles present anywhere in the complex momentum space. The momentum-dependent
quark mass compares very well to recent lattice calculations. A large number of
predictions and relations can be deduced from our approach for such quantities
as the pion light-cone wave function, non-local quark condensate, pion
transition form factor, pion valence parton distribution function, etc.Comment: revtex, 24 pages, 3 figure
Pion light-cone wave function and pion distribution amplitude in the Nambu-Jona-Lasinio model
We compute the pion light-cone wave function and the pion quark distribution
amplitude in the Nambu-Jona-Lasinio model. We use the Pauli-Villars
regularization method and as a result the distribution amplitude satisfies
proper normalization and crossing properties. In the chiral limit we obtain the
simple results, namely phi_pi(x)=1 for the pion distribution amplitude, and
= -M / f_pi^2 for the second moment of the pion light-cone
wave function, where M is the constituent quark mass and f_pi is the pion decay
constant. After the QCD Gegenbauer evolution of the pion distribution amplitude
good end-point behavior is recovered, and a satisfactory agreement with the
analysis of the experimental data from CLEO is achieved. This allows us to
determine the momentum scale corresponding to our model calculation, which is
close to the value Q_0 = 313 MeV obtained earlier from the analogous analysis
of the pion parton distribution function. The value of is, after the
QCD evolution, around (400 MeV)^2. In addition, the model predicts a linear
integral relation between the pion distribution amplitude and the parton
distribution function of the pion, which holds at the leading-order QCD
evolution.Comment: mistake in Eq.(38) correcte
Transverse lattice calculation of the pion light-cone wavefunctions
We calculate the light-cone wavefunctions of the pion by solving the meson
boundstate problem in a coarse transverse lattice gauge theory using DLCQ. A
large-N_c approximation is made and the light-cone Hamiltonian expanded in
massive dynamical fields at fixed lattice spacing. In contrast to earlier
calculations, we include contributions from states containing many gluonic
link-fields between the quarks.The Hamiltonian is renormalised by a combination
of covariance conditions on boundstates and fitting the physical masses M_rho
and M_pi, decay constant f_pi, and the string tension sigma. Good covariance is
obtained for the lightest 0^{-+} state, which we identify with the pion. Many
observables can be deduced from its light-cone wavefunctions.After perturbative
evolution,the quark valence structure function is found to be consistent with
the experimental structure function deduced from Drell-Yan pi-nucleon data in
the valence region x > 0.5. In addition, the pion distribution amplitude is
consistent with the experimental distribution deduced from the pi gamma^* gamma
transition form factor and diffractive dissociation. A new observable we
calculate is the probability for quark helicity correlation. We find a 45%
probability that the valence-quark helicities are aligned in the pion.Comment: 27 pages, 9 figure