3 research outputs found
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
Vacuum condensates and the pion wave functions in the nonlocal chiral model
We use the simple instanton motivated Nambu Jona-Lasinio - type model to
calculate a twist 3 pseudoscalar pion light cone wave function. Using
normalisation condition for this wave function we calculate the quark
condensate and also the gluon condensate, which agree with the phenomenological
values for these quantities. Since we can compute also the k_T^2 dependence of
the light cone wave functions, we calculate k_T^2 moments of the pseudo-scalar
and axial-vector wave functions which are related to the mixed vacuum
condensates. This allows us to extract the condensates and compare them with
existing estimates.Comment: 12 pages, 7 figures; three new paragraphs added: one (in sec. IV)
discusses the relation between quark and gluon condensates, the other two (in
secs. I and VI) clarify the difference between the normalisation scale Q_0,
at which the condensates are evaluated, and the model parameter Lambda; new
references added; to be published in Phys. Rev.