Effective potential for local composite operators and the problem of factorization of multi-field condensates

A new formulation of effective potential for local composite operators is given. The two-fermion condensate \(\langle \bar \Psi \Psi \rangle \) and four-fermion condensate \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle \) are calculated simultaneously in the Gross-Neveu model up to next-to-the-leading order in 1/N expansion. It is shown that factorization \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle = C_1 \langle \bar \Psi \Psi \rangle ^2 \) holds only in theN→∞ limit and the non-factorized part of \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle \) contributed by the order-1/N terms is comparable to \(C_1 \langle \bar \Psi \Psi \rangle ^2 \) when takingN=3.     

On strange quark scalar condensate in the nucleon

A well known difficulty with a large value of the σ term in πN scattering is analysed from positions of the QCD sum rules approach. The matrix element \(\left\langle {p\left| {\bar ss} \right|p} \right\rangle\) is related to flavour singlet correlation function of two quark condensates at zero momentum. The splittings \(\left\langle {p\left| {\bar uu - \bar ss} \right|p} \right\rangle\) and \(\left\langle {p\left| {\bar dd - \bar ss} \right|p} \right\rangle\) are calculated and turn to be in agreement withSU ₃ relations.     

Production of π0 mesons and charged hadrons in\bar v neon and ν neon charged current interactions

The average multiplicities of charged hadrons and of π⁺, π^? and π⁰ mesons, produced in \(\bar v\) Ne and νNe charged current interactions in the forward and backward hemispheres of theW ^±-nucleon center of mass system, are studied with data from BEBC. The dependence of the multiplicities on the hadronic mass (W) and on the laboratory rapidity (y _Lab) and the energy fraction (z) of the pion is also investigated. Special care is taken to determine the π⁰ multiplicity accurately. The ratio of average π multiplicities \(\frac{{2\left\langle {n_{\pi ^O } } \right\rangle }}{{[\left\langle {n_{\pi ^ + } } \right\rangle + \left\langle {n_{\pi ^ - } } \right\rangle ]}}\) is consistent with 1. In the backward hemisphere \(\left\langle {n_{\pi ^O } } \right\rangle \) is positively correlated with the charged multiplicity. This correlation, as well as differences in multiplicities between \(\mathop v\limits^{( - )} \) and \(\mathop v\limits^{( - )} \) , \(\mathop v\limits^{( - )} \) scattering, is attributed to reinteractions inside the neon nucleus of the hadrons produced in the initial \(\mathop v\limits^{( - )} \) interaction.     

Chiral symmetry breaking in the colour dielectric model

Approximating the long-distance gluon dynamics ofSU(3)_colour by colour-dielectric block-spin variables, we obtain an effective QCD theory of a scalar colour-dielectric field and a massive colour-bleached gluon field coupled to light quarks. The massive vector field produces a strong attraction betweenq \(\bar q\) pairs, which leads toq \(\bar q\) condensation when the colour-dielectric field becomes small. We calculate \(\left\langle {\bar \psi \psi } \right\rangle\) and the pion decay constantf _n as a function of the dielectric field expectation value, by evaluating the fermion determinant in a derivative expansion, and integrating out the bosonic variables. We find that the effective quark-gluon coupling,α _s ^eff , including quark effects, is large on the surface of bags, where \(\left\langle {\bar \psi \psi } \right\rangle\) ±0, but decreases inside hadronic bags, where | \(\left\langle {\bar \psi \psi } \right\rangle\) | is decreasing.     

A comparison of\bar pp annihilations into charged particles,e + e −→hadrons ande + e −→Ψ, Γ→hadrons

A comparison of multiplicity distributions and \(\left\langle {P_T^2 } \right\rangle of \bar pp\) annihilation reactions at two energies ande ⁺ e ^?→hadrons leads to a model for \(\bar pp\) annihilation into gluons. The \(\bar pp\) data are consistent with the QCD predictions for the ratio of the moments of the fragmentation functions given for isolated gluon jets. The energy dependence of the ratio of the moments is also consistent with the predictions.     

Some implications of inclusive electro- and neutrino production data

We systematically exploit the reported data on \(F_2^{\gamma p} ,F_2^{\gamma n} ,\sigma ^{vN} ,\sigma ^{\bar vN} ,\left\langle {xy} \right\rangle _{vN} ,\left\langle {xy} \right\rangle _{\bar vN} ,\left\langle {1 - y} \right\rangle _{vN} \) and \(\left\langle {1 - y} \right\rangle _{\bar vN} \) in order to test various versions of the quark parton model and to obtain further predictions.     

Heavy and heavy to light quark expansions

We analyze the phenomenon of heavy quark condensation within the framework of the QCD sum rule approach. We discuss two alternative expansions for massive quark condensates. The first one (heavy to light quark expansion), introduced by Broadhurst and Generalis, establishes a connection between the heavy and light quark worlds. The other one (heavy quark expansion) is valid when only heavy quark systems are considered. As a byproduct we have obtained the coefficients of \(\left\langle {\bar qq} \right\rangle \) , \(\left\langle {\bar qGq} \right\rangle \) , 〈G ²〉 and 〈G ³〉 for all bilinear currents.     

Quark-diagram estimates ofCP violation in two-body baryonicB_d^0 - \bar B_d^0 decays

CP violation in partial-decay-rate asymmetries are examined for some two-body baryonic decays of \(B_d^0 - \bar B_d^0 \) system. We discuss two feasible experimental circumstances: the symmetrice ⁺ e ^? collisions (i) on theZ ⁰ resonance to produce incoherent \(B_d^0 \bar B_d^0 \) states, and (ii) just above the ?(4S) resonance to produceC=even \(B_d^0 \bar B_d^0 \) states. Using the quark-diagram scheme, we estimate the branching ratios of those decays, and the numbers ofb \(\bar b\) pairs needed for testing theCP-violating effects for 3σ signature. We find that the promising channels may beB _d ⁰ , \(\bar B_d^0 \to p\bar p\) , \(\Delta ^ + \bar \Delta ^ - \) , \(p\bar \Delta ^ - \) , \(\Delta ^ + \bar p\) , \(n\bar n\) , \(\Delta ^0 \bar \Delta ^0 \) , \(n\bar \Delta ^0 \) , \(\Delta ^0 \bar n\) , \(\Sigma _c^ + \bar \Sigma _c^ - \) , \(\Lambda _c^ + \bar \Lambda _c^ - \) , \(\Sigma _c^ + \bar \Lambda _c^ - \) , \(\Lambda _c^ + \bar \Sigma _c^ - \) , \(\Sigma _c^0 \bar \Sigma _c^0 \) , \(\Xi _c^0 \bar \Xi _c^0 \) , which should be interesting for experimental observation.     

Comparison of strange antibaryon and strange meson production inK + p interactions at 32 GeV/c

New experimental results are presented on inclusive production properties of \(\bar \Sigma ^{ * + } \) (1385) and \(\bar \Sigma ^{ * + } \) (1385) inK ⁺ p interactions at 32 GeV/c. The analysis is based on significantly larger statistics than previously available. A comparison is also made of invariantx-distributions ofK ⁰/ \(\bar K^0 \) , \(\bar \Lambda \) and \(\bar \Xi ^ + \) and of \(\bar \Sigma ^{ * \pm } \) (1385) andK ^*+(892). These spectra exhibit regularities expected from the quark-recombination picture when it is assumed that the strange mesons and antibaryons are produced off the strange \(\bar s\) -valence-quark in the incidentK ⁺ meson. Transverse momentum distributions are also presented forK ^*+(892) and \(\bar \Sigma ^{ * \pm } \) (1385) and found to be very similar. The results on strange antibaryon average multiplicities disagree strongly with a recent version of the additive quark model.     

\left\langle {\bar \Psi \Psi } \right\rangle in the Schwinger model with Wilson and naive fermions

The coefficients of an expansion series in the hopping coefficients are determined. This allows to calculate \(\left\langle {\bar \Psi \Psi } \right\rangle\) analytically for any coupling constant and fermion mass in 1+1 dimensions.     

Very high energy nucleus-nucleus collisions and multi-chain model

Inclusive and semi-inclusive production of Λ and \(\bar \Lambda\) inK ⁺ p interactions is studied at an incident momentum of 70 GeV/c. Cross sections and single particle distributions are presented and compared with data at lower energies. Scaling is observed between 32 and 70 GeV/c in the Feynmanx variable in the target and the beam fragmentation regions for Λ and \(\bar \Lambda\) inclusive production respectively. An increase of Λ ( \(\bar \Lambda\) ) production is observed in the beam (target) fragmentation regions, whereas the data at 70 and 32 GeV/c are reasonably close in the central region. The dependence of the Λ( \(\bar \Lambda\) ) polarization as a function ofx is measured and found to be in general agreement with the results at 32 GeV/c. The (Λ \(\bar \Lambda\) ) pair production cross section increases significantly from 32 to 70 GeV/c. The Λ and \(\bar \Lambda\) production associated with an identified proton is also studied.     

Double hypernuclei and the λ-gL interaction

The binding energy of the double hypernuclei \(\mathop \Lambda \limits^6 \Lambda\) He, \(\mathop {\Lambda \Lambda }\limits^{10}\) Be, and \(\mathop {\Lambda \Lambda }\limits^{11}\) Be and of the corresponding hypernuclei are calculated using the λ+λ+ core model. The parameters of the λ-λ interaction are found and compared to those of the λ-N interaction.     

Covariant partition temperature model ande + e − annihilation

The rapidity distributions of inclusive \(e^ + e^ - \to h\bar h + \cdot \cdot \cdot\) of PEP and DESY experiments are analyzed in terms of the covariant partition temperatureT _p model. The estimates ofT _p ^* in the fireball system are comparable to the conventional temperature, the energy dependence follows approximately Stefan's law, the radius of the specific volume ralative to the energy density being ～1.18 fm. In the c.m.s. of collision, \(T_p = AW^a (W = \sqrt s in GeV)\) witha=0.60±0.05 andA=0.256±0.006, it is found \(T_p \cong {W \mathord{\left/ {\vphantom {W {\tfrac{3}{2}\left\langle {n_ \pm } \right\rangle }}} \right. \kern-0em} {\tfrac{3}{2}\left\langle {n_ \pm } \right\rangle }}\) . These properties hold also for \(\bar pp\) collision, but not forpp→π^?+...     

Isgur-Wise functions from the MIT bag model

The Isgur-Wise functions for the ground state to ground state semileptonic decays involvingb→c transitions are calculated from the (modified) MIT bag model. It is checked that the results for the decays \(\bar B \to Dl\bar v\) and \(\bar B \to D^* l\bar v\) agree well with experiment. Predictions for the decays \(\Lambda _b \to \Lambda _c l\bar v,\bar B_s \to D_s^* l\bar v\) and \(\bar B_s \to D_s^* l\bar v\) are given and discussed.     

Multi-quark structure ofU(3.1)

We interpret the recently observedU(3.1) mesons with the \(\Lambda \bar p\) + pions decays as the bound state of \(\Lambda ,\bar p\) andX ₀(1480). TheX ₀(1480) is a mesonium with \(Q^2 \bar Q^2 \) structures observed in γγ reactions and \(\bar pn\) annihilations. With this interpretation, we can understand its decay modes. Furthermore, we predict the ratio of \(\sigma (\Lambda \bar p\pi ^ + \pi ^ - )/\sigma (\Lambda \bar p\pi ^ + \pi ^ + )\) to be ?3.1 for centrally produced events and that the width of \(U^ - (\Lambda \bar p\pi ^ + \pi ^ - )\) to be greater than that of \(U^ + (\Lambda \bar p\pi ^ + \pi ^ + )\) . Both predictions seem to be in reasonable accord with the available data. We call for the detection of the \(\Lambda \bar p\pi ^ - \pi ^ - \) mode to verify the present interpretation.     

Gluon condensate and the effective gluon mass

Using massive gauge invariant QCD we show explicity how power like corrections to \(\Pi _{\mu v} \left( q \right) = i\int {dx} e^{iq'x} \left\langle {0\left| {j_\mu ^{em} \left( x \right)\bar j_v^{em} \left( 0 \right)} \right|0} \right\rangle \) arise. Using our result for the 1/q ⁴ contribution, a one to one correspondence is made between the gluon condensate and the effective gluon mass. By relating this mass to, \(\langle 0|\frac{{\alpha _s }}{\pi }G_{\mu v}^2 |0\rangle \) a value ofm _gluon=750 MeV is found at ?q ²=10 GeV². In addition, within the context of dimensional regularization, a new technique for evaluating two loop momentum integrals with massive propagators is introduced. This method is a derivative of the Mellin transform technique that was applied to ladder diagrams in the days of Reggeisation.     

TheN\bar N and ππ decay modes of baryonium

A non-relativistic quark model is used to calculate the decay widths of baryonium states to \(N\bar N,N\bar \Delta \) , \(N\bar N,N\bar \Delta \) and \(\Delta \bar \Delta \) . Large widths are found and used to estimate the \(\bar pp\) and \(\bar pn\) elastic cross-sections. The couplings of baryonium states to two identical mesons are also investigated.     

Surface incompressibility of semi-infinite nuclear matter via constrained Hartree-Fock calculations

With a view to calculating the incompressibility \(\ddot \sigma \) of the nuclear surface, we develop a constrained Hartree-Fock treatment of semi-infinite nuclear matter. Our approach leads first to a proof of the “ \(\dot \sigma = 0\) ” theorem of Myers and Swiatecki, and then to a corroboration of a simple expression for \(\ddot \sigma \) , previously obtained in an intuitive way by Stocker. This expression is used to calculate \(\ddot \sigma \) for theS3, SkM and Gogny forces. The results are significantly different from those of a scaled HF calculation, but in very good agreement with the values of \(\ddot \sigma \) that are implied by RPA calculations of the breathing mode in various finite nuclei.