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.     

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.     

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.     

Taylor expansion of effective Hamiltonians by Monte Carlo simulations with fixed block spins

Monte Carlo simulations with fixed block spins allow the computation of Taylor expansion kernels for effective Hamiltonians. The expansion can be performed around arbitrary block spin configurations \(\bar \phi\) and does not suffer from truncation errors. Monte Carlo calculation of the Taylor kernels offers a ready possibility to check whether the effective Hamiltonian has good locality properties in the neighborhood of a given configuration \(\bar \phi\) . The method is applied in a renormalization group study of the 2-dimensional critical Ising model. The results show that one has to deal with a “large field problem”, as had been expected from rigorous renormalization group studies.     

How does anticommutator\left\{ {Q_\alpha \bar Q_\beta } \right\} realize energy-momentumP μ in quantum supergravity?

It is investigated to what extent the well-known algebra \(\left\{ {Q^S ,\bar Q^S } \right\} = \gamma ^\mu P_\mu \) in the rigid supersymmetry theory holds in quantum supergravity: The anti-commutator \(\left\{ {Q_\alpha ^S ,\bar Q_\beta ^S } \right\} = \gamma ^m \tilde P_m \) defines an “internal” translation generator \(\tilde P_m \) , quite another from the “external” translation generatorP _μ. It is, however, shown that those two operators give the same matrix elements between any two physical states aside from a proportional factor. Such a “miracle” is caused by some particular properties of global gauge transformation charge universal in gauge theories. These properties are fully clarified in a general manner.     

The process\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma as an alternative to\pi ^0 \to v\bar v

The process \(\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma \) is investigated as an alternative to \(\pi ^0 \to v\bar v\) . It is shown that the experimental bound on the branching fraction for missing energy (in the form of \(\lambda _\gamma \bar \lambda _\gamma \) and/or \(v\bar v\) ) may be understood in terms of \(\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma \) for the kinematically allowed photino mass, if the squark mass is >8 GeV.     

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.     

A modified large number theory withconstant G

The inspiring “numerology” uncovered by Dirac, Eddington, Weyl,et al. can be explained and derived when it is slightly modified so to connect the “gravitational world” (cosmos) with the “strong world” (hadron), rather than with the electromagnetic one. The aim of this note is to show the following. In the present approach to the “Large Number Theory,” cosmos and hadrons are considered to be (finite)similar systems, so that the ratio \({{\bar R} \mathord{\left/ {\vphantom {{\bar R} {\bar r}}} \right. \kern-0em} {\bar r}}\) of the cosmos typical length \(\bar R\) to the hadron typical length \(\bar r\) is constant in time (for instance, if both cosmos and hadrons undergo an expansion/contraction cycle—according to the “cyclical bigbang” hypothesis—then \(\bar R\) and \(\bar r\) can be chosen to be the maximum radii, or the average radii). As a consequence, then gravitational constantG results to be independent of time. The present note is based on work done in collaboration with P. Caldirola, G. D. Maccarrone, and M. Pav?i?.     

Renormalization group study of a critical lattice model

We start a nonperturbative study of the Wilson-Kadanoff renormalization group (RG) in weakly coupled massless lattice models. Nonlocal hierarchical models are introduced to mimic the infrared behaviour of the \(\tfrac{1}{2}(\nabla \phi )^2 + \lambda (\nabla \phi )^4\) model and the like. The RG is shown to drive these to the line of fixed points corresponding to the massless \(\tfrac{1}{2}c_\infty (\lambda )(\nabla \phi )^2\) models.     

The tomography of quark-gluon plasma by vector mesons

The fireball formed in a heavy ion collision is characterized by the impact parameter vector $\vec b$ , which is orthogonal to the beam direction and can be determined from the multiplicity and the angular distribution of the reaction products. By appropriate rotations the $\vec b$ vectors of each collision can be oriented into a fixed direction. Using the measured values of the momentum distributions of the vector mesons an integral equation can be formulated for the unknown emission densities $(E_M (\vec r))$ and for the unknown absorption densities $(\Delta \mu _M (\vec r,p))$ of the different vector mesons $M( \equiv \omega ^0 ,\rho ^0 ,\phi ^0 ,\psi ^0 ,\psi ^{0'} ,\Upsilon )$ .     

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.     

Benchmark cross sections forp \bar p collisions at 1.8 TeV

High-energyp \(\bar p\) collisions provide many quantitative tests of the standard model. Of particular interest are “hard scattering” processes, which test not only standard model matrix elements and higher order perturbative corrections, but also the distributions of quarks and gluons in the colliding hadrons. We present detailed comparisons of data from the CERNSp \(\bar p\) S collider with theory, incorporating up-to-date parton distributions derived from recent deep inelastic scattering data. Encouraged by the excellent agreement between data and theory at \(\sqrt s \) =630GeV, we present a complete set of “benchmark” predictions for the FNALp \(\bar p\) collider at \(\sqrt s \) =1.8TeV.     

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.     

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.     

String-like solutions and regge trajectories in a cylindrically deformed quark bag model

With the string picture in mind, we study quark bags of a simple fixed geometry: cylindrical. It is shown that the Dirac boundary value problem \(i\not n\psi = \psi\) of the M.I.T. bag model has no solutions, if this quark confinement condition is applied simultaneously on the radial walls as well as on the edges of the cylinder. By introducing a cruder condition, \(\bar \psi \psi = 0\) , instead, but now only on the side walls, we calculate properties of non-strange baryons. A justification for the use of this cruder condition, \(\bar \psi \psi = 0\) , on the side walls, instead of the proper M.I.T. condition, is then provided by showing that the M.I.T. “cylindrical” bag with smooth rounded corners gives essentially the same results, while being computationally more involved. Notwithstanding this departure from the M.I.T. confinement condition on the side walls, we find the following curious results: for high excitations, this bag attains string-like shapes. the sequence of baryonic states corresponding to pure single quark excitations fall on a linear Regge trajectory with a slope of ≈0.85 GeV^?2. These trajectories hold at low-angular momenta.     

Indecomposable representations with invariant inner product

Consequences of the existence of an invariant (necessarily indefinite) non-degenerate inner product for an indecomposable representation π of a groupG on a space \(\mathfrak{H}\) are studied. If π has an irreducible subrepresentation π₁ on a subspace \(\mathfrak{H}_1 \) , it is shown that there exists an invariant subspace \(\mathfrak{H}_2 \) of \(\mathfrak{H}\) containing \(\mathfrak{H}_1 \) and satisfying the following conditions: (1) the representation π ₁ ^# =π mod \(\mathfrak{H}_2 \) on \(\mathfrak{H}\) mod \(\mathfrak{H}_2 \) is conjugate to the representation (π₁, \(\mathfrak{H}_1 \) ), (2) \(\mathfrak{H}_1 \) is a null space for the inner product, and (3) the induced inner product on \(\mathfrak{H}_2 \) mod \(\mathfrak{H}_1 \) is non-degenerate and invariant for the representation $$\pi _2 = (\pi _2 |_{\mathfrak{H}_2 } )\bmod \mathfrak{H}_1 ,$$ a special example being the Gupta-Bleuler triplet for the one-particle space of the free classical electromagnetic field with \(\mathfrak{H}_1 \) =space of longitudinal photons and \(\mathfrak{H}_2 \) =the space defined by the subsidiary condition.     

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.     

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.     

Three-loop relation of quark\overline {MS} and pole masses

We calculate, exactly, the next-to-leading correction to the relation between the \(\overline {MS} \) quark mass, \(\bar m\) , and the scheme-independent pole mass,M, and obtain $$\begin{gathered} \frac{M}{{\bar m(M)}} \approx 1 + \frac{4}{3}\frac{{\bar \alpha _s (M)}}{\pi } + \left[ {16.11 - 1.04\sum\limits_{i = 1}^{N_F - 1} {(1 - M_i /M)} } \right] \hfill \\ \cdot \left( {\frac{{\bar \alpha _s (M)}}{\pi }} \right)^2 + 0(\bar \alpha _s^3 (M)), \hfill \\ \end{gathered} $$ as an accurate approximation forN _F?1 light quarks of massesM _i <M. Combining this new result with known three-loop results for \(\overline {MS} \) coupling constant and mass renormalization, we relate the pole mass to the \(\overline {MS} \) mass, \(\bar m\) (μ), renormalized at arbitrary μ. The dominant next-to-leading correction comes from the finite part of on-shell two-loop mass renormalization, evaluated using integration by parts and checked by gauge invariance and infrared finiteness. Numerical results are given for charm and bottom \(\overline {MS} \) masses at μ=1 GeV. The next-to-leading corrections are comparable to the leading corrections.