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.     

Spectral signs of the internal heavy-atom effect in aliphatic carbonyl compounds

The CNDO/S method has been applied to the internal effect of Si on the electronic spectrum of the acetone molecule; there is a considerable bathochromic shift and an increase in the \(S_0 \to S_{n\pi ^ * } \) intensity for theα-silyl ketones, while theβ-silyl ketons give only an increase in the intensity of \(S_0 \to S_{n\pi ^ * } \) absorption relative to acetone. The heavy atom substantially alters \(f_{S_0 \to T_{n\sigma ^* } } \) and \(\tau _{T_{n\sigma ^* } }^0 \) but has little effect on \(f_{S_0 \to T_{n\pi ^* } } \) and \(\tau _{T_{n\pi ^* } }^0 \) .     

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.     

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.     

Unfolding the singularities in superspace

A method is described for unfolding the singularities in superspace, \(\mathcal{G} = \mathfrak{M}/\mathfrak{D}\) , the space of Riemannian geometries of a manifoldM. This unfolded superspace is described by the projection $$\mathcal{G}_{F\left( M \right)} = \frac{{\mathfrak{M} \times F\left( M \right)}}{\mathfrak{D}} \to \frac{\mathfrak{M}}{\mathfrak{D}} = \mathcal{G}$$ whereF(M) is the frame bundle ofM. The unfolded space \(\mathcal{G}_{F\left( M \right)}\) is infinite-dimensional manifold without singularities. Moreover, as expected, the unfolding of \(\mathcal{G}_{F\left( M \right)}\) at each geometry [g _o] ∈ \(\mathcal{G}\) is parameterized by the isometry groupIg _o (M) of g₀. Our construction is natural, is generally covariant with respect to all coordinate transformations, and gives the necessary information at each geometry to make \(\mathcal{G}\) a manifold. This construction is a canonical and geometric model of a nonrelativistic construction that unfolds superspace by restricting to those coordinate transformations that fix a frame at a point. These particular unfoldings are tied together by an infinite-dimensional fiber bundleE overM, associated with the frame bundleF(M), with standard fiber \(\mathcal{G}_{F\left( M \right)}\) , and with fiber at a point inM being the particular noncanonical unfolding of \(\mathcal{G}\) based at that point. ThusE is the totality of all the particular unfoldings, and so is a grand unfolding of \(\mathcal{G}\) .     

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.     

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.     

On the energy-dependence of the mass-operator and the „effective-interaction“

We consider a microscopic system \(\mathfrak{S}\) coupled to a bath \(\mathfrak{B}\) and establish a non-Markoffian master equation for the reduced statistical operator of \(\mathfrak{S}\) , valid in theBorn approximation. Discussing in detail theBorn approximation we find as a general condition for its validity that a certain “strength function” should not degenerate to one or more extremly sharp and high lines.     

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.     

Independence of local algebras in Quantum Field Theory

It is shown that localC*-algebras \(\mathfrak{A}\) (O ₁) and \(\mathfrak{A}\) (O ₂) associated with spacelike separated regionsO ₁ andO ₂ in the Minkowski space are independent. The proof is accomplished by a theorem concerning the structure of theC*-algebra generated by \(\mathfrak{A}\) (O ₁) and \(\mathfrak{A}\) (O ₂).     

Rules of thumb for theZ line shape

In this paper the theoretical parameters of theZ line shape, such asM _Z andΓ _Z, and the one photon exchange diagram are related to a set of parameters characterizing the experimental line shape. The latter are the peak height σ_max, peak position \(\sqrt {s_{\max } } \) and half peak positions \(\sqrt {s_ \pm } \) . The rules of thumb are accurate within 10 MeV. As a result we obtain approximate formulae which expressM _Z and Γ_Z in the measured \(\sqrt {s_{\max } } \) and \(\sqrt {s_ + } - \sqrt {s_ - } \) .     

\bar \Lambda Production inK − p interactions at 32 GeV/c

Antilambda production is studied inK ^? p interactions at 32 GeV/c. Both total and differential cross sections are presented. The inclusive \(\bar \Lambda \) production cross section amounts to 109±7 μb. A remarkable energy dependence is observed, σ( \(\bar \Lambda \) ) increasing by a factor of four between 14.3 and 32 GeV/c. Thep _⊥ ² distribution exhibits an exponential fall-off with a slope of 3.3±0.2 (GeV/c)^?2. Most of the \(\bar \Lambda \) 's are emitted in the forward hemisphere. The invariantx distribution increases between 14.3 and 32 GeV/c. Data are presented for \(\bar \Lambda \) production inK ^- p→Λ \(\bar \Lambda \) +X K ^- p→ \(\bar \Lambda \) K ⁿ +X, andK ^- p→ \(\bar \Lambda \) p+X.     

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.     

The(cc) - (\overline {cc} ) (diquark-antidiquark) states ine + e − annihilation

The mass spectrum and decay modes of the \((cc) - (\overline {cc} )\) states are estimated in a quark-gluon model. We argue that the peculiar resonance-like structures ofR(e ⁺ e ^? →hadrons) for \(\sqrt s = 6 - 7\) GeV may be due to production of theP-wave \((cc) - (\overline {cc} )\) states. They are predicted to lie in the range 6.4–6.8 GeV and mainly decay into charmend mesons.     

Second order QCD corrections toq\bar q-anihilation into a lepton pair at large transverse momentum

The \(\mathcal{O}{\text{(}}\alpha _{\text{s}}^{\text{2}} )\) correction is presented to \(q\bar q\) -annihilation into a lepton pair at large transverse momentum. I calculate the corresponding hadron cross section difference \(\frac{{d\sigma }}{{d^4 q}}(p\bar p - pp) \to e^ + e^ - + x(q\) is the momentum of the lepton pair system). The correction to this cross section difference is found to be large. This essentially agrees with recently published results by Ellis, Martinelli and Petronzio. Two improtant approximations are used: the invariant mass of the two-gluon-system is put to zero, and only valence-valence quark scattering is considered.     

Neutral strange particle exclusive production in charged current high-energy antineutrino interactions

The cross section of the quasi-elastic reactions \(\bar v_\mu p \to \mu ^ + \Lambda (\Sigma ^0 )\) in the energy range 5–100 GeV is determined from Fermilab 15′ bubble chamber antineutrino data. TheQ ² analysis of quasi-elastic Λ events yieldsM _A=1.0±0.3 GeV/c² for the axial mass value. With zero µΛ K ⁰ events observed, the 90% confidence level upper limit \(\sigma (\bar v_\mu p \to \mu ^ + \Lambda {\rm K}^0 )< 2.0 \cdot 10^{ - 40} cm^2 \) is obtained. At the same time, we found that the cross section of reaction \(\bar v_\mu p \to \mu ^ + \Lambda {\rm K}^0 + m\pi ^0 \) is equal to \(\left( {3.9\begin{array}{*{20}c} { + 1.6} \\ { - 1.3} \\ \end{array} } \right) \cdot 10^{ - 40} cm^2 \) .     

Scattering length expansion of the coupled channels\bar pp \to \bar \Lambda \Lambda and\bar \Lambda \Lambda \to \bar \Lambda \Lambda near theΛ production threshold

We fit the scattering lengths in the triplets-,p- andd- waves for the two channels \(\bar pp \to \bar \Lambda \Lambda\) and \(\bar \Lambda \Lambda \to \bar \Lambda \Lambda\) near theΛ production threshold to the differential cross section \(\frac{{d\sigma }}{{d\Omega }}(\bar pp \to \bar \Lambda \Lambda )\) and to the polarization P.     

Mixings and CP violations of theB^0 - \bar B^0 system in the four-generation model

We study the mixings and CP violations in the \(B^0 - \bar B^0 \) system together with the \(K^0 - \bar K^0 \) one in the four-generation model, taking into account the ARGUS data for the \(B_d^0 - \bar B_d^0 \) mixing. We take typical six cases of the mixing hierarchy and search for the allowed regions of three phases in the 4×4KM matrix. The CP violating parameter ? _K in the \(K^0 - \bar K^0 \) system gives a severe constraint for the phases, and the smaller mixing than that in the three-generation model is predicted for the \(B_s^0 - \bar B_s^0 \) system. The asymmetry parameters for the two-body non-leptonic decays of theB ⁰ and \(\bar B^0 \) mesons are also predicted.     

Ξ Resonances in Ξ− Be interactions II. Properties of Ξ(1820) and Ξ(1960) in the\Lambda \bar K^0 and\Sigma ^0 \bar K^0 channels

In an experiment at the CERN-SPS charged hyperon beam, we have investigated the inclusive \(\Lambda \bar K^0 \) and \(\Sigma ^0 \bar K^0 \) final states formed in Ξ^? Be interactions. In the \(\Lambda \bar K^0 \) channel, we observe a signal at 1826 MeV/c² which can be identified with the known Ξ(1820) resonance. We determine its mass and width to be:M=1826±4 MeV/c², Г=12±14 MeV/c². A moment analysis is consistent with a spin of 3/2 and indicates a negative parity for this spin assignment. Also in the \(\Lambda \bar K^0 \) channel, we observe a 3.6σ signal with the following parameters:M=1963±5 MeV/c², Г=25±15 MeV/c². This state, which we call Ξ(1960), is not observed in the \(\Sigma ^0 \bar K^0 \) channel, leading to an upper limit on the ratio of partial widths \(\Sigma \bar K/\Lambda \bar K\) of 2.3 (90% confidence level). A moment analysis of the \(\Lambda \bar K^0 \) final state indicates a spin of 5/2 or greater in the natural spin-parity series 5/2⁺, 7/2^?, etc.