arXiv subjects

C. Weiss

Publications and source records attributed to C. Weiss.

At least 127 records · Page 7Linked to original sources

arXiv1998

Pion and photon light-cone wave functions from the instanton vacuum

The leading-twist wave functions of the pion and the photon at a low normalization point are calculated in the effective low--energy theory derived from the instanton vacuum. The pion wave function is found to be close to the asymptotic one, consistent with the recent CLEO measurements. The photon wave function is non-zero at the endpoints. This different behavior is a consequence of the momentum dependence of the dynamical quark mass suggested by the instanton vacuum. We comment on the relation of meson wave functions and off-forward parton distributions in this model.

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arXiv1998

Two-pion light-cone distribution amplitudes from the instanton vacuum

We calculate the two-pion light-cone distribution amplitudes in the effective low-energy theory based on the instanton vacuum. These generalized distribution amplitudes describe the soft (non-perturbative) part of the process $γ^*γ\to ππ$ in the region where the c.m. energy is much smaller than the photon virtuality. They can also be used in the analysis of exclusive processes such as $γ^* p \to p + 2π, 3π$ etc.

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arXiv1998

Isovector unpolarized quark distribution in the nucleon in the large-N_c limit

We calculate the isovector (flavor-nonsinglet) unpolarized quark- and antiquark distributions in the nucleon at a low normalization point in the large-N_c limit. The nucleon is described as a soliton of the effective chiral theory. The isovector distribution appears in the next-to-leading order of the 1/N_c-expansion. Numerical results for the quark- and antiquark distributions compare well with the parametrizations of the data at a low normalization point. This large-N_c approach gives a flavor asymmetry of the antiquark distribution (violation of the Gottfried sum rule) in good agreement with the measurements.

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arXiv1997

Nucleon parton distributions in the large $N_c$ limit

We review recent progress in calculating the twist--2 parton distribution functions at a low normalization point in the large--$N_c$ limit, where the nucleon can be described as a soliton of the effective chiral lagrangian. This field-theoretic approach preserves all general requirements on the distribution functions (positivity, normalization etc.). In particular, it allows to calculate the polarized and unpolarized antiquark distributions at the low normalization point.

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arXiv1997

Self-consistent calculation of parton distributions at low normalization point in the chiral quark-soliton model

We calculate the isosinglet unpolarized quark-- and antiquark distributions at a low normalization point in the large--$N_c$ limit. The nucleon is described as a self-consistent soliton solution of the effective chiral theory. The ultraviolet cutoff is implemented by a Pauli-Villars subtraction. The quark and antiquark distributions satisfy the momentum as well as the baryon number sum rule, corresponding to ``constituent'' quarks whose structure is not yet resolved at the low scale. Already at this level a sizable number of antiquarks is present.

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arXiv1997

Nucleon structure functions from the instanton vacuum: Leading and non-leading twists

We review the description of nucleon structure functions in the instanton vacuum. This includes the calculation of the twist-2 parton distributions at a low normalization point as well as higher-twist matrix elements. The instanton vacuum with its inherent small parameter, the packing fraction of the instanton medium, $\barρ/ R$, provides a consistent picture of the non-perturbative gluon degrees of freedom at the scale $\barρ^{-1} \simeq 600 MeV$. The twist-2 quark and antiquark distributions are of order unity, while the twist-2 gluon distribution is of order $(\barρ/ R)^4$. Twist-4 matrix elements determining power corrections to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules are found to be of order $(\barρ/ R)^0$. We present numerical estimates for the parametrically large quantities.

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arXiv1997

Estimates of higher-dimensional vacuum condensates from the instanton vacuum

We calculate the values of non-factorizable dimension-7 vacuum condensates in the instanton vacuum. We comment on a method, recently proposed by Oganesian, to estimate the dimension-7 condensates by factorization of dimension-10 condensates in various inequivalent ways. The instanton estimates could be used to analyze the stability of QCD sum rules with increasing dimensions.

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arXiv1997

Off-forward quark distributions of the nucleon in the large N_c limit

We study the off-forward quark distributions (OFQD's) in the chiral quark-soliton model of the nucleon. This model is based on the large-N_c picture of the nucleon as a soliton of the effective chiral lagrangian and allows to calculate the leading twist quark- and antiquark distributions at a low normalization point. We demonstrate the consistency of the approach by checking various sum rules for the OFQD's. We present numerical estimates of the isosinglet distribution H(x,ξ,Δ^2). In contrast to other approaches we find a strong qualitative dependence on the longitudinal momentum transfer, ξ. In particular, H(x,ξ,Δ^2) as a function of x exhibits fast crossovers at |x| = ξ/2. Such behaviour could lead to a considerable enhancement of the deeply-virtual Compton scattering cross section.

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arXiv1997

Nucleon matrix elements of higher-twist operators from the instanton vacuum

We compute the nucleon matrix elements of QCD operators of twist 3 and 4 in the instanton vacuum. We consider the operators determining 1/Q^2-power corrections to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules. The nucleon is described as a soliton of the effective chiral theory derived from instantons in the 1/N_c-expansion. QCD operators involving the gluon field are systematically represented by effective operators in the effective chiral theory. We find that twist-3 matrix elements are suppressed relative to twist-4 by a power of the packing fraction of the instanton medium. Numerical results for the spin-dependent (d^(2), f^(2)) and spin-independent twist-3 and 4 matrix elements are compared with results of other approaches and with experimental estimates of power corrections. The methods developed can be used to evaluate a wide range of matrix elements relevant to DIS.

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arXiv1997

Unpolarized and polarized quark distributions in the large-Nc limit

The isosinglet unpolarized and isovector polarized twist-2 quark distributions of the nucleon at low normalization point are calculated in the large-Nc limit. The nucleon is described as a soliton of the effective chiral theory. We derive the expressions for the distribution functions in the large-Nc limit starting from their definition as numbers of partons carrying momentum fraction x in the infinite momentum frame. We develop a numerical method for computation of the quark and antiquark distributions as sums over the quark single-particle levels in the pion field of the soliton. The contributions of the discrete bound-state level as well as the Dirac continuum are taken into account. The quark- and antiquark distributions obtained explicitly satisfy all general requirements. Results are in reasonable agreement with parametrizations of the data at low normalization point.

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arXiv1996

A chiral Lagrangian for excited pions

We construct a chiral Lagrangian containing besides the usual pion field (pi) also its first radial excitation (pi'). The Lagrangian is derived by bosonization of a Nambu--Jona-Lasinio quark model with separable non-local interactions, with form factors corresponding to 3-dimensional ground and excited state wave functions. Chiral symmetry breaking is governed by the NJL gap equation. The effective Lagrangian for pi- and pi'-mesons shows the decoupling of the Goldstone pion and the vanishing of the pi' leptonic decay constant, f_pi', in the chiral limit, as required by axial current conservation. We derive the excited states' contribution to the axial current of the model using Noether's theorem. For finite pion mass and pi' masses in the range of 750 MeV -- 1300 MeV, f_pi' / f_pi is found to be of the order of 1 percent.

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arXiv1996

Mixed quark-gluon condensate from instantons

We calculate the vacuum expectation value of the dimension-5 "mixed" quark-gluon operator, $O_σ= \barψ(λ^a /2) σ_{μν} ψF_{μν}^a$, in the instanton vacuum. Within the $1/N_c$--expansion the QCD operator is replaced by an effective many-fermion operator, which is averaged over the effective theory of massive quarks derived from instantons. We find $m_0^2 \equiv \langle O_σ\rangle / \langle \barψψ\rangle \approx 4 \barρ^{-2} = 1.4 GeV^2$, somewhat larger than the estimate from QCD sum rules for the nucleon.

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arXiv1996

Nucleon Parton Distributions at Low Normalization Point in the Large N_c Limit

At large N_c the nucleon can be viewed as a soliton of the effective chiral lagrangian. This picture of nucleons allows a consistent nonperturbative calculation of the leading-twist parton distributions at a low normalization point. We derive general formulae for the polarized and unpolarized distributions (singlet and non-singlet) in the chiral quark-soliton model. The consistency of our approach is demonstrated by checking the baryon number, isospin and total momentum sum rules, as well as the Bjorken sum rule. We present numerical estimates of the quark and antiquark distributions and find reasonable agreement with parametrizations of the data at a low normalization point. In particular, we obtain a sizeable fraction of antiquarks, in agreement with the phenomenological analysis.

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arXiv1996

Nucleon spin structure from the instanton vacuum

We discuss the evaluation of the nucleon isoscalar axial coupling, $g_A^{(0)}$, in the instanton vacuum, using the $1/N_c$ expansion. This approach allows a fully consistent treatment of the $U(1)_A$ anomaly. We compute the nucleon matrix element of the topological charge density, $\langle N | F\widetilde{F} | N \rangle$, and show that it reduces to the matrix element of the divergence of the isoscalar axial quark current. Our arguments show that the usual evaluation of $g_A^{(0)}$ in the chiral quark soliton model is consistent with the $U(1)_A$ anomaly in leading order of $1/N_c$. Such calculations give $g_A^{(0)} = 0.36$, which is in agreement with the recent estimate by Ellis and Karliner.

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arXiv1996

Hadronic matrix elements of gluon operators in the instanton vacuum

We propose a method to evaluate hadronic matrix elements of QCD gluon operators in the instanton vacuum. We construct the ground state of the interacting instanton ensemble for non-zero $\vartheta$--angle using a variational principle. A method to study the $\vartheta$--dependence of observables on the lattice is suggested. We then derive the effective fermion action, which allows to calculate hadronic correlation functions in a $1/N_c$--expansion (Nambu--Jona-Lasinio type effective fermion theory). Gluon operators are systematically represented as effective fermion operators. Physical matrix elements are obtained after integrating the correlation functions over fluctuations of the numbers of instantons. The influence of the fermion determinant on the topological susceptibility is taken into account. Our effective description gives matrix elements fully consistent with the trace and $U(1)_A$ anomalies. The approach allows to consistently evaluate the nucleon matrix elements of various gluon and mixed quark--gluon operators in a chiral soliton picture of the nucleon.

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arXiv1995

Baryon form factors in a diquark-quark bound state description

Nucleon form factors are calculated in a relativistic diquark--quark picture based on the Nambu--Jona-Lasinio model. The nucleon wave function is obtained in a static approximation to the quark exchange interaction between the valence quark and the diquark. We evaluate the valence quark and $0^+$--diquark contribution to the nucleon electromagnetic and weak currents. We find reasonable electric charge radii, magnetic moments as in the additive diquark model, and $g_A \approx 1$. We discuss the dependence on the model parameters.

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arXiv1994

Off-shell pion electromagnetic form factor from a gauge-invariant Nambu-Jona-Lasinio model

The off--shell electromagnetic vertex function of pions and kaons is studied in a bosonized Nambu--Jona-Lasinio model with a gauge--invariant proper--time cutoff. The slope of the pion form factor with respect to the pion 4--momentum is found to be equal to the on--shell pion charge radius in the chiral limit. The off--shell slope of the $K^0$ form factor is zero, that of the $K^\pm$ about 15\% smaller than that of the pion. We compare our results with those of a recent calculation in chiral perturbation theory.

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arXiv1994

Heavy--light mesons in a bilocal effective theory

Heavy--light mesons are described in an effective quark theory with a two--body vector--type interaction. The bilocal interaction is taken to be instantaneous in the rest frame of the bound state, but formulated covariantly through the use of a boost vector. The chiral symmetry of the light flavor is broken spontaneously at mean field level. The framework for our discussion of bound states is the effective bilocal meson action obtained by bosonization of the quark theory. Mesons are described by 3--dimensional wave functions satisfying Salpeter equations, which exhibit both Goldstone solutions in the chiral limit and heavy--quark symmetry for $m_Q\rightarrow\infty$. We present numerical solutions for pseudoscalar $D$-- and $B$--mesons. Heavy--light meson spectra and decay constants are seen to be sensitive to the description of chiral symmetry breaking (dynamically generated vs.\ constant quark mass).

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