A study of Bose-Einstein correlations ine+e? annihilation at 91 GeV

This paper describes a study of Bose-Einstein correlations made using the ALEPH detector at LEP. The correlations are found to enhance the two particle differential cross section for pairs of identical pions by a factor which can be roughly parametrized byR(Q)=1+ exp(-Q²²), whereQ is the difference in the 3-momenta of the two pions in their centre of mass frame, =0.51±0.04±0.11 and =3.3±0.2±0.8 GeV^–1, which corresponds to a source size of 0.65±0.04±0.16 fm. The large systematic errors on these results reflect their strong dependence on the choice of the reference sample used in the analysis. This problem is believed to occur primarily because of uncertainties in the rates of resonance production and a lack of knowledge about the pion-pion strong interaction. No significant correlations are seen amongst like-charged pion-kaon pairs.Supported by CAICYT, Spain     

Meson production inp+U,O+U and S+U interactions at 200 GeV/nucleon

Meson production in proton, oxygen and sulphur interactions with uranium targets at 200 GeV/nucleon is studied. We measure the inclusive meson cross-section d /dP _T ² and its evolution fromp+U to S+U. The cross-section fitted with an exponential gives an inverse slopeP _T0 of the order of 210 MeV/c. As a function of the neutral transverse energy,P _T0 values show a slight rise followed by a plateau. The normalized difference (⁺–^–)/^– between positive and negative meson cross-sections is found to increase withE _T .also at ISEL     

Nuclear and electromagnetic fragmentation of 2.25-TeV197Au nuclei

We report the first measurement of the total charge-loss cross section _tot=_em+_nuc and partial cross sections (for Z=1, 2, ..., 9) of 11.4 A GeV¹⁹⁷Au nuclei in various targets. The large Coulomb barrier for Au reduces the electromagnetic contribution _em in a Pb target to only 18% of _nuc, compared with 70% for 14.5 A GeV²⁸Si and 120% for 200 A GeV³²S. With _em taken to be Z _T ^1.8 , _nuc can be fitted with _nuc=(A _P ^1/3 +A _T ^1/3 –b)², with b=0.83 and =59 mb, essentially the same as found at energies of 1 to 2 A GeV. Electromagnetic partial cross sections for Z=1 exceed 40 mb in the Pb, Sn, Cu, and Fe targets and are substantial for larger values ofZ in the heavier targets.We are indebted to D. Beavis and the staff of the Alternating Gradient Synchrotron at Brookhaven National Laboratory for producing the beam of 11.4 A GeV Au ions, to D. Snowden-Ifft for his efforts in developing the automated scanning system, and to S. Hirzebruch for a useful discussion. This work was supported in part by the Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics, of the Department of Energy under contract No. DEAC03-76SF00098.     

On the relative entropy

ForA any subset of () (the bounded operators on a Hilbert space) containing the unit, and and restrictions of states on () toA, ent _A (|)—the entropy of relative to given the information inA—is defined and given an axiomatic characterisation. It is compared with ent _A ^A (|)—the relative entropy introduced by Umegaki and generalised by various authors—which is defined only forA an algebra. It is proved that ent and ent ^S agree on pairs of normal states on an injective von Neumann algebra. It is also proved that ent always has all the most important properties known for ent ^S : monotonicity, concavity,w* upper semicontinuity, etc.     

Study of the centrally producer ππ andK \bar K systems at 85 and 300 GeV/c

We have studied the andK systems centrally produced in proton proton collisions at 300 GeV/c and ⁺/p proton collisions at 85 GeV/c using the CERN spectrometer. Clear evidence forS ^*/f _o(975) production is observed. An analysis performed on the ^{+ –} mass spectrum in the 1.0 GeV region, using a coupled channel formalism, shows that it is possible to describe theS ^*/f _o(975) effect with one single resonance once interference of theS ^*/f _o(975) with theS-wave background is introduced. The resultingS ^*/f _o(975) parameters arem _o =979±4MeV,g =0.28±0.04,g _K =0.56±0.18 corresponding to a pole position on sheet II at (1001±2)–i(36±4) MeV. Evidence is also found for a structure having a mass of 1472±12 MeV and a width of 195±33 MeV.     

Photon-deuteron diffractive scattering

One expects a similarity of the energy dependence of the difference _tot(*p)– _tot(*n) for virtual (deep inelastic scatteringQ ²m ²) and real (Q ²=0) photons. Previous analysis of D structure functions with allowence for nuclear shadowing (NS) in the deuteron has led to conclusion that _tot(*p)– _tot(*n)<0>x<0.015. the=" early=" evidence=" from=" the=" real=" photoproduction=" data="> _tot(p)– _tot(n)<0. we=" critically=" reexamine=" determinations=" of=" the="> _tot(p)– _tot(n), using more accurate calculations of NS correction to _tot(D), and discuss a possibility of _tot(n) _tot(p) at moderately high energies.     

Local particle densities and global multiplicities in central heavy ion interactions at 3.7, 14.6, 60 and 200A GeV

The energy and centrality dependence of local particle pseudorapidity densities as well as validity of various parametrizations of the distributions are examined. The dispersion, , of the rapidity density distribution of produced particles varies slowly with centrality and is 0.80, 0.98, 1.21 and 1.41 for central interactions at 3.7, 14.6, 60 and 200A GeV incident energy, respectively, is found to be independent of the size of the interacting system at fixed energy. A novel way of representing the window dependence of the multiplicity as normalized variance versus inverse average multiplicity is outlined.     

Pomeron-pomeron cross section from inclusive production of a central cluster in quasi-elastic π+ p andK + p scattering at 250 GeV/c

Meson-nucleon quasi-elastic scattering is studied with (semi) inclusive production of a central hadron cluster. The dominant mechanism of central cluster production is double pomeron exchange. The cross section is (39±5±8) b and (24±6±3) b for pion and kaon induced reactions, respectively. An estimate of the pomeron-pomeron total cross section _pp is extracted in the interval . While _pp=0.45±0.10mb is obtained in thef ₂(1270) region, an almost constant cross section with an average of _pp=0.16±0.02mb is observed outside thef ₂ region.Partially supported by grants from CPBP 01.06 and 01.09     

B* production in Z decays

The decayB ^*B has been observed with the DELPHI detector at LEP, where theB ^* meson is produced inZ boson decays. The combination of inclusively reconstructedB mesons with well-measured converted photons yields a measurement of the flavour-averagedB ^*-B mass difference of 45.5±0.3 (stat.) ±0.8 (syst.) MeV/c². 95% confidence level upper limits at 6 MeV/c² are placed on both the isospin (i.e.B ⁺-B ⁰) and theB _s -B _ud splitting of the mass difference. The production ratio ofB ^* toB mesons inZ decays is measured to be 0.72±0.03 (stat.) ±0.06 (syst.). Limits on the production cross-section of other hypothetical excitedB hadron states decaying radiatively are established. The differentialB ^* cross section has been measured to be in good agreement with the averageb fragmentation, yielding an average fractionalB ^* energy of x _E =0.695±0.009 (stat.) ±0.013 (syst.). From the decay angular distribution the relative contribution of longitudinalB ^* polarisation states is measured to be _L/(_L + _T) = 0.32 ± 0.04 (stat.) ±0.03 (syst.).CICYT_AEN93-0832     

Investigation of the fusion reaction27Al+236U→263105 at excitation energies of 57 MeV and 65 MeV

The neutron-deficient isotopes^257,258105 were produced in the reaction²⁷Al+²³⁶u in 6n and 5n evaporation channels, respectively. The evaporation residues emerging from the target were separated in-flight from the projectiles and from products of different nuclear reactions by the electrostatic separator VASSILISSA [1]. The isotopes were then implanted into position-sensitive silicon detectors and identified using the --correlation method. The measured production cross-section is (5n)=(0.45±0.20)nb atE _P =154 MeV and (6n)=(0.075±0.055) nb atE _P =163 MeV. These cross-sections are compared with data measured for the same isotopes in the more symmetrical reaction⁵⁰Ti+²⁰⁹Bi.     

Measurement ofR and determination of the charged-particle multiplicity ine+e? annihilation at 13-113-113-1around 10 GeV

We have measured theR value in non-resonante ⁺ e ^– annihilation using the ARGUS detector at the storage ring DORIS II. At a centre-of-mass energy GeV the ratio of the hadronic cross-section to the -pair cross section in lowest order QED has been determined to beR=3.46±0.03±0.13. In addition, we have measured the charged-particle multiplicities in non-resonant hadron production at GeV just below theB threshold and in (4S) resonance decays. For the average charged-particle multiplicities in continuum events and (4S)B decays we obtain n>_cont=8.35±0.02±0.20 and n>_(4s)=10.81±0.05±0.23.Supported by the German Bundesministerium für Forschung und Technologie, Contract no. 054DO51P     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Resistance to dislocation motion in copper-based solid solutions with a statistically disordered atomic distribution

The stress _F due to friction forces in copper-based solid solutions was determined. Under the conditions of the procedure used to measure _F, on the basis of the half-wave hysteresis with polycrystalline samples, the value of d: _F = _F0 + K_Fd^–(1/2) where _F0 is the resistance to dislocation motion in an alloy having an infinite grain size, and K_F is a constant. It is shown that _F0 is governed by the interaction of moving dislocations with impurity atoms in the case of a statistically disordered atomic distribution. A study was made of the effects of various factors on _F and of the nature of the changes in _F0 caused by alloying.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No.3, pp. 18–23, March, 1971.     

Ion mixing in Al,Si, and their oxides

The redistribution of thin metallic markers due to ion irradiation was studied by backscattering spectrometry in Al, Al₂O₃, Si, and SiO₂. Marker species were selected for their similar masses and different chemical reactivities with the host media and included Ti, Fe, W, Pt, and Au. It was found that the marker signals are Gaussian and that the variance ² of the marker atom distributions increases linearly with the dose of the irradiation, is insensitive to the temperature of irradiation in the range of 80–300 K, and depends linearly on the nuclear stopping power of the incident ions. The absolute values of ² for Ti, Fe, W, Pt, and Au markers in Al and Al₂O₃, W, and Pt in SiO₂ and W in Si is, within±50 %, of 6.5×10³Å² for 300 keV, 8×10¹⁵ Xe ions/cm². These observations suggest that collisional cascade mixing is a dominant mechanism in this type of impurity-matrix combinations. Only Au and Pt in Si mix at a larger rate: ² for Pt is about 3 and for Au about 5 times larger than ² for all other markers. Lower threshold displacement energies and/or the contribution of processes other than cascade mixing are possible considered reasons. In polycrystalline Al, a rapid migration of Au and Pt atoms throughout the Al layer, similar to grain boundary diffusion, is observed.     

How effective is the weak mixing angle?

The usefulness of an effective weak mixing angle to parameterise the electroweak couplings of quarks and leptons measured at LEP is discussed. After a review of the theoretical formalism used to handle the electroweak radiative corrections to LEP processes, some suggestions for procedures to be used to extract the mixing angle are given and the various definitions of the effective weak mixing angle used by the experiments are examined. This is followed by an attempt to extract a coherent set of mixing angle values from the four experiments with the published 1989/90 (and some 1991) measurements of the Z⁰ line-shapes, asymmetries and polarisation. These results are updated with preliminary results from the 1991 data presented at the XXVI International Conference on High Energy Physics, in Dallas, USA, in August 1992, including the preliminary measurement ofA _LR at the SLC. The average value found for the effective weak mixing angle, defined for leptons, is sin² _eff ^lept =02322±0.0010. The error on sin² _eff ^lept can be further reduced by imposing the constraints between the parameters implicit in the MSM. With the additional constraint _s=0.123±0.006 imposed in the fit, the result is sin² _eff ^lept , where the central value is form _H =300 GeV, and the second error is the variation ifm _H is changed to 50 GeV (lower error) and 1000 GeV (upper error). Within the MSM, sin² _lept ^eff is directly related to the top-quark mass, and the corresponding value ism _t =153 _–25–23 ⁺²²⁺¹⁹ GeV, where the errors have the same meaning as those for sin² _eff ^lept . Finally, the prospects for improved precision are discussed.     

An algebraic approach to quantum field theory and commutation relations for energy momentum in the framework of general relativity

We present a consistent set of commutation relations (C.R.) for a quantum system immersed in a classical gravitational field. The gravity field is described by metric tensorg _ik (x) andg ₀₀(x) with coordinate gaugeg _i0=0. The Hamiltonian of the system is found to be a linear function of [–g ₀₀(x)]^1/2. Its properties we define by C.R. avoiding explicit expression in terms of fields, as well as its splitting into free and interaction parts. In this way a consistent set of C.R., which are equally simple for a flat and curvilinear space, can be established. To stress the main idea of our approach, we consider the simple but still nontrivial example of a scalar electrodynamics immersed in a gravity field. The electromagnetic current operator we define by its C.R. and not explicitly. An interesting feature of this approach is that the Poisson equation follows from the consistency of the C.R. The C.R. for the energy and momentum operators of the system in a gravity field are established which generalize the usual Poincare group generators C.R. For example, we find (i/hc ²)[H _(x) ,H _(x) ]=P _– , whereH _(x) is the Hamiltonian of the system, which is a linear functional of (x)[–g ₀₀(x)]^1/2 andP _s(x) represents the momentum-density operator [averaged with the classical functions(x)].     

Random walks on cubic lattices with bond disorder

We consider diffusive systems with static disorder, such as Lorentz gases, lattice percolation, ants in a labyrinth, termite problems, random resistor networks, etc. In the case of diluted randomness we can apply the methods of kinetic theory to obtain systematic expansions of dc and ac transport properties in powers of the impurity concentrationc. The method is applied to a hopping model on ad-dimensional cubic lattice having two types of bonds with conductivity and ₀=1, with concentrationsc and 1–c, respectively. For the square lattice we explicitly calculate the diffusion coefficientD(c,) as a function ofc, to O(c²) terms included for different ratios of the bond conductivity. The probability of return at long times is given byP ₀(t) [4D(c,)t]^–d/2, which is determined by the diffusion coefficient of the disordered system.     

Insensitivity of Quantized Hall Conductance to Disorder and Interactions

A two-dimensional quantum Hall system is studied for a wide class of potentials including single-body random potentials and repulsive electron–electron interactions. We assume that there exists a nonzero excitation gap above the ground state(s), and then the conductance is derived from the linear perturbation theory with a sufficiently weak electric field. Under these two assumptions, we prove that the Hall conductance _xy and the diagonal conductance _yy satisfy | _xy+e ² /h|const·L ^–1/2 and | _yy|const·L ^–1/12. Here e ²/h is the universal conductance with the charge –e of the electron and the Planck constant h; is the filling factor of the Landau level; and L is the linear dimension of the system. In the thermodynamic limit, our results show _xy=–e ² /h and _yy=0. The former implies that integral and fractional filling factors with a gap lead to, respectively, integral and fractional quantizations of the Hall conductance.     

Convexity and concavity of eigenvalue sums

It is well known that(H), the sum of the negative eigenvalues of a Hermitian matrixH, is a concave and increasing function ofH. In contrast to this, we prove that forA nonsingular Hermitian andP positive definite, the functionP(AP)=(P ^1/2 AP ^1/2) is convex and decreasing. Several other results of this nature are also proved.