Projectile breakup dynamics for 6Li + 59Co : Kinematical analysis of \alpha - d coincidences

A study of the kinematics of the $ \alpha$ -d coincidences in the ⁶Li + ⁵⁹Co system at a bombarding energy of E _lab = 29.6 MeV is presented. With exclusive measurements performed over different angular intervals it is possible to identify the respective contributions of the sequential and direct projectile breakup components. The angular distributions of both breakup components are fairly well described by the Continuum-Discretized Coupled-Channels framework (CDCC). Furthermore, a careful analysis of these processes using a semiclassical approach provides information on both their lifetime and their distance of occurrence with respect to the target. Breakup to the low-lying (near-threshold) continuum is delayed, and happens at large internuclear distances. This suggests that the influence of the projectile breakup on the complete fusion process can be related essentially to the direct breakup to the ⁶Li high-lying continuum spectrum.     

Scaling multiplicities of h-p collisions toe + e −→π±+... by the Fermi-Landau law

The similarity of rapidity distributions of hadrons frompp and $\bar p$ p withe ⁺ e ^?→π^±+... implies a scaling forE _cm, reflecting the quark-quark interaction of particle production by $\bar p$ /p+p. This scaling relates the meson multiplicity fromh+p→m $\bar m$ +... to the Fermi-Landau law $n_{ch} = a\sqrt {E_{cm} } $ fore ⁺ e ^? collisions, without free-parameters, threshold energy being taken into account including the mass of quarks constituent of the projectile and the target, the coefficient behaves like bremsstrahlung a～1/m ².     

A semi-statistical model of high-energy collisions

The emission of particles directly created in high-energy collisions is considered to be only partly governed by statistical laws as in Fermi's model. The motion of the created particles is to some degree related to the former motion of the incoming colliding particles. In first approximation this intermediate state is built up of two extremes: two Lorentz systems are introduced from which the particles are emitted isotropically and according to statistical laws. In the centre-of-momentum system (CMS) of the collision these two systems move in the directions of the incoming particles after collision. This approximation corresponds to the two-fireball model which we regard as a representative of a mathematical method of dealing with correlations. In further approximation phase space distributions are replaced by the thermodynamic Fermi or Bose distributions for relativistic particles. Both experimental data such as the nearly constant mean transverse momentum¯p _t and phase space calculations with constant interaction volume show that the temperaturekT reaches an upper limit asymptotically at high energies; the asymptotic region begins at about 30 GeV. The comparison with experimental particle spectra from accelerators in the 10–30GeV region shows good agreement if one uses a smooth dependence ofkT on the collision energyE ₀ and, for each independent set of measurements, an individual choice of \(\bar \gamma _f \) , the mean Lorentz factor of the “fireballs” in the CMS, and of ¯n, the mean number of created particles. The p_t-distribution of pions and the dependence of¯p _t on the particle mass can also be successfully described. At very high energies the model gives production ratios of the various kinds of particles which lie within the range of the experimental determinations. The dependence of \(\bar \gamma _f \) onE ₀ is concluded to be of the form \(\bar \gamma _f \propto E_0^{1/2} /\bar n(E_0 ) \approx 0.5E_0^{1/4} \) , i.e. CMS anisotropy is related to multiplicity.     

Koba-Nielsen-Olesen scaling

A correct version of Koba-Nielsen-Olesen (KNO) scaling is described in detail for multiplicity distributions. Some statements on the violation of KNO scaling that are based on an erroneous interpretation of experimental data are discussed. An accurate comparison with data is presented for the distributions of negatively charged particles originating from electron-positron annihilation at $\sqrt s = 3 - 161GeV$ , from inelastic proton-proton collisions at p _lab=4.5–520 GeV/c, and from nucleus-nucleus collisions at p _lab=4.5–520 GeV/c per projectile nucleon. Data on proton-antiproton interactions at $\sqrt s = 546GeV$ are also considered.     

Probabilistic Time

The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions p _τ (t) at a given time t obtain by integrating out the past and future. We discuss all-time probability distributions that realize a unitary time evolution as described by rotations of the real wave function $q_{\tau}(t)=\pm \sqrt{p_{\tau}(t)}$ . We establish a map to quantum physics and the Schr?dinger equation. Suitable classical observables are mapped to quantum operators. The non-commutativity of the operator product is traced back to the incomplete statistics of the local-time subsystem. Our investigation of classical statistics is based on two-level observables that take the values one or zero. Then the wave functions can be mapped to elements of a Grassmann algebra. Quantum field theories for fermions arise naturally from our formulation of probabilistic time.     

Truncated Connectivities in a Highly Supercritical Anisotropic Percolation Model

We consider an anisotropic bond percolation model on $\mathbb{Z}^{2}$ , with p=(p _h ,p _v )∈[0,1]², p _v >p _h , and declare each horizontal (respectively vertical) edge of $\mathbb{Z}^{2}$ to be open with probability p _h (respectively p _v ), and otherwise closed, independently of all other edges. Let $x=(x_{1},x_{2}) \in\mathbb{Z}^{2}$ with 0<x ₁<x ₂, and $x'=(x_{2},x_{1})\in\mathbb{Z}^{2}$ . It is natural to ask how the two point connectivity function $\mathbb{P}_{\mathbf{p}}(\{0\leftrightarrow x\})$ behaves, and whether anisotropy in percolation probabilities implies the strict inequality $\mathbb{P}_{\mathbf{p}}(\{0\leftrightarrow x\})>\mathbb{P}_{\mathbf {p}}(\{0\leftrightarrow x'\})$ . In this note we give an affirmative answer in the highly supercritical regime.     

Inclusive\bar K^{0*} (892) andK 0*(892) production on silicon by 200 GeVK − andπ −

The production of the neutralK ^? (892) resonances by 200 GeVK ^? andπ ^? has been studied over the kinematic range 0.0<x _f<1.0 andp _t ² <5.0 GeV². Longitudinal and transverse momentum distributions are presented. In addition the decay angular distributions inK ^? fragmentation to \(\bar K^{0*} \) have been investigated.     

Chiral Expansion of Nucleon PDF at x ~ m π /M N

Based on the chiral perturbation theory, we investigate the low-energy dynamics of nucleon parton distributions. We show that in different regions of the momentum fraction x the chiral expansion is significantly different. For nucleon parton distributions these regions are characterized by x ~ 1, x ~ m _π /M _N and \({x \sim (m_{\pi}/M_{N})^2}\) . We derive extended counting rules for each region and obtain model-independent results for the nucleon parton distributions down to \({x \gtrsim m^{2}_{\pi}/M^2_{N} \approx 10^{-2} }\) .     

Single decay-lepton angular distributions in polarizede + e − →\overline {tt} and simple angular asymmetries as a measure of CP-violating top dipole couplingsand simple angular asymmetries as a measure of CP-violating top dipole couplings

In the presence of an electric dipole coupling of $\overline {tt} $ to a photon, and an analogous ‘weak’ dipole coupling to the Z, CP violation in the process e⁺e^? → $\overline {tt} $ results in modified polarization of the top and the anti-top. This polarization can be analyzed by studying the angular distributions of decay charged leptons when the top or anti-top decays leptonically. Analytic expressions are presented for these distributions when eithert or $\overline t $ decays leptonically, including $\mathcal{O}$ (α_s) QCD corrections in the soft-gluon approximation. The angular distributions are insensitive to anomalous interactions in top decay. Two types of simple CP-violating polar-angle asymmetries and two azimuthal asymmetries, which do not need the full reconstruction of thet or $\overline t $ , are studied. Independent 90% CL limits that may be obtained on the real and imaginary parts of the electric and weak dipole couplings at a linear collider operating at √ s = 500 GeV with integrated luminosity 500 fb^? and also at √s = 1000 GeV with integrated luminosity 1000 fb^? have been evaluated. The effect of longitudinal electron and/or positron beam polarizations has been included.     

Diffusion Effects on the Breakdown of a Linear Amplifier Model Driven by the Square of a Gaussian Field

We investigate solutions to the equation ? _t ?? $\mathcal{D}$ Δ?=λS ²?, where S(x, t) is a Gaussian stochastic field with covariance C(x?x′, t, t′), and x∈ $\mathbb{R}$ ^d . It is shown that the coupling λ _cN (t) at which the N-th moment <? ^N (x, t)> diverges at time t, is always less or equal for $\mathcal{D}$ >0 than for $\mathcal{D}$ =0. Equality holds under some reasonable assumptions on C and, in this case, λ _cN (t)=Nλ _c (t) where λ _c (t) is the value of λ at which <exp[λ ∫ ^t ₀ S ²(0, s) ds]> diverges. The $\mathcal{D}$ =0 case is solved for a class of S. The dependence of λ _cN (t) on d is analyzed. Similar behavior is conjectured when diffusion is replaced by diffraction, $\mathcal{D}$ →i $\mathcal{D}$ , the case of interest for backscattering instabilities in laser-plasma interaction.     

Indirect methods for determining heavy-neutrino masses

Within the two-flavor approximation, equations that relate the oscillation parameters for both light and heavy neutrinos to the Yukawa coupling constants and the vacuum expectation values of the Higgs fields are derived within the left-right model. The contributions from Higgs bosons to the muon anomalous magnetic moment, to the cross sections for lepton-flavor-violating processes, and to the cross sections for low-energy light-neutrino scattering are studied in order to determine the Yukawa coupling constants. It is shown that the heavy-neutrino masses $m_{N_{1,2} } $ can be expressed in terms of only the triplet Yukawa coupling constants and the mass of the gauge boson W ₂. Data on direct and inverse muon decay and constraints on the masses of the $\tilde \delta ^{( - )} , \Delta _{1,2}^{( - - )} $ and W ₂ bosons are used to obtain bounds on $m_{N_{1,2} } $ both in the absence of degeneracy and in the presence of mass degeneracy in the sector of heavy neutrinos. Only in the case of degeneracy are data concerning the explanation of the (g ? 2)_μ anomaly used to determine bounds on $m_{N_{1,2} } $ .     

Asymmetry of π− meson emission in nucleus-nucleus collisions as a measure of the target-to-projectile ratio of the numbers of interacting nucleons

Experimental data on the forward-backward asymmetry of π^- emission in (d,⁴He,¹²C)¹⁸¹Ta interactions atp/A=4.2 GeV/c are presented. The absolute value of the asymmetry coefficient of the inclusive π^- production in the nucleon-nucleonCMS decreases asA _p ^?0.35 with increasing atomic mass of projectile nucleus. A method of obtaining the target-to-projectile ratio of the numbers of participant nucleonsN _t /N _p through measuring the velocity of the symmetric pion emission system is proposed. It has been found that N_t/N_p～A _p ^?0.73 .     

Optimality of a Class of Entanglement Witnesses for 3⊗3 Systems

Let $\varPhi_{t,\pi}: M_{3}({\mathbb{C}}) \rightarrow M_{3}({\mathbb{C}})$ be a linear map defined by $\varPhi_{t,\pi}(A)=(3-t)\*\sum_{i=1}^{3}E_{ii}AE_{ii}+t\sum_{i=1}^{3}E_{i,\pi (i)}AE_{i,\pi(i)}^{\dag}-A$ , where 0≤t≤3 and π is a permutation of (1,2,3). We show that the Hermitian matrix $W_{\varPhi_{t,\pi}}$ induced by Φ _t,π is an optimal entanglement witness if and only if t=1 and π is cyclic.     

Invariant Measures for Dissipative Dynamical Systems: Abstract Results and Applications

In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit. Consider an arbitrary complete separable metric space X which is acted on by any continuous semigroup {S(t)} _{t ?? 0}. Suppose that {S(t)} _{t ?? 0} possesses a global attractor ${\mathcal{A}}$ . We show that, for any generalized Banach limit LIM _{T ?? ??} and any probability distribution of initial conditions ${\mathfrak{m}_0}$ , that there exists an invariant probability measure ${\mathfrak{m}}$ , whose support is contained in ${\mathcal{A}}$ , such that $$\int_{X} \varphi(x) {\rm d}\mathfrak{m}(x) = \underset{t \rightarrow \infty}{\rm LIM}\frac{1}{T} \int_0^T \int_X \varphi(S(t) x) {\rm d}\mathfrak{m}_0(x) {\rm d}t,$$ for all observables ?? living in a suitable function space of continuous mappings on X. This work is based on the framework of Foias et?al. (Encyclopedia of mathematics and its applications, vol 83. Cambridge University Press, Cambridge, 2001); it generalizes and simplifies the proofs of more recent works (Wang in Disc Cont Dyn Syst 23(1?C2):521?C540, 2009; Lukaszewicz et?al. in J Dyn Diff Eq 23(2):225?C250, 2011). In particular our results rely on the novel use of a general but elementary topological observation, valid in any metric space, which concerns the growth of continuous functions in the neighborhood of compact sets. In the case when {S(t)} _{t ?? 0} does not possess a compact absorbing set, this lemma allows us to sidestep the use of weak compactness arguments which require the imposition of cumbersome weak continuity conditions and thus restricts the phase space X to the case of a reflexive Banach space. Two examples of concrete dynamical systems where the semigroup is known to be non-compact are examined in detail. We first consider the Navier-Stokes equations with memory in the diffusion terms. This is the so called Jeffery??s model which describes certain classes of viscoelastic fluids. We then consider a family of neutral delay differential equations, that is equations with delays in the time derivative terms. These systems may arise in the study of wave propagation problems coming from certain first order hyperbolic partial differential equations; for example for the study of line transmission problems. For the second example the phase space is ${X= C([-\tau,0],\mathbb{R}^n)}$ , for some delay ?? > 0, so that X is not reflexive in this case.     

Target dependence of clan model parameter in 84 Kr 36 – Emulsion interactions at 1 GeV per nucleon

This article focusses on the study of clan model parameters and their target dependence in light of void probability scaling for heavy (Ag and Br) and light (C, N and O) groups of targets present in nuclear emulsion detector using ⁸⁴Kr₃₆ at ～1 A GeV. The variation of scaled rapidity-gap (rap–gap) probability with single moment combination has been studied. We found that experimental points lie approximately on the negative binomial distribution (NBD) curve, indicating a scaling behaviour. The increase in average clan multiplicities ( \(\bar {N}\) ) for interactions with the pseudorapidity interval (Δη) was also observed. The values of \(\bar {N}\) for AgBr targets are larger than those for C/N/O target and also average number of particles per clan ( \(\bar {n}_{\mathrm {c}}\) ) increases with increase in pseudorapidity interval. We further observed that for a particular target, the average number of particles per clan ( \(\bar {n}_{\mathrm {c}}\) ) increases with an increase in the size of projectile nucleus.     

The electromagnetic interaction in chiral perturbation theory

We investigate electromagnetic effects in the framework of chiral perturbation theory. Using a completely independent method, we confirm Urech’s results for the divergences of the one-loop functional in the electromagnetic sector. We perform a one-loop analysis of allP _t2 (P=π, K, η) and theK _t3 form factors $f_ + ^{K^ + \pi ^o } (0),f_ + ^{K^o \pi ^ - } (0)$ , including a systematic treatment of theO(e ² p ²) contributions in the mesonic part. We illustrate our results by several numerical estimates.     

Positivity and monotonicity properties ofC 0-semigroups. II

IfS _t =exp{?tH},T _t =exp{?tK}, are self-adjoint positivity preserving semigroups on a Hilbert space ?=L ²(X; dμ) we write (*) $$T_t \succ 0$$ ifT _t is positivity improving and (**) $$S_t \succ T_t $$ if the differenceS _t ?T _t is positivity improving. We derive a variety of characterizations of (*) and (**). In particular (*) is valid for allt>0 if, and only if,T _t ∪L ^∞ (X; dμ) is irreducible for somet>0. Similarly if the semigroups are ordered the strict order (**) is valid if, and only if, {S _t ?T _t }∪L ^∞(X; dμ) is irreducible for somet>0. These criteria are used to prove that if (*) is valid for allt>0 then $$e^{ - tf(K)} \succ 0,t > 0,$$ and if (**) is valid for allt>0 then $$e^{ - tf(H)} \succ e^{ - tf(K)} ,t > 0$$ for each non-constantf in the class characterized in the preceding paper. We discuss the decomposition of positivity preserving semigroups in terms of positivity improving semigroups on subspaces. Various applications to monotonicity properties of Green's functions are given.     

Single-Spin asymmetries in semi-inclusive pion production

For the first time single-spin asymmetries in semi-inclusive pion production are measured by the HERMES experiment with a transversely polarised hydrogen target. Two different sine-modulations are extracted which can be related to the transversity δq(x) and Sivers $f_{1T}^{ \bot q} (x)$ quark distribution functions. The extracted sine-moments still contain small sub-leading twist contributions which can be extracted from HERMES data combining the results from the transversely polarised hydrogen target with previously measured results from a longitudinally polarised hydrogen target.     

K S 0 , Λ and ≡ production at intermediate to high pT from Au+Au collisions at \sqrt {s_{NN} } = 39, 11.5 and 7.7 GeV

We report on the p _T dependence of nuclear modification factors (R _CP) for K _S ⁰ , ??, ?? and the $\bar NK_S^0 $ ratios at mid-rapidity from Au+Au collisions at $\sqrt {s_{NN} } $ = 39, 11.5 and 7.7 GeV. At $\sqrt {s_{NN} } $ = 39 GeV, the R _CP data show a baryon/meson separation at intermediate p _T and a suppression for K _S ⁰ for p _T up to 4.5 GeV/c; the $\bar \Lambda K_S^0 $ shows baryon enhancement in the most central collisions. However, at $\sqrt {s_{NN} } $ = 11.5 and 7.7 GeV, R _CP shows less baryon/meson separation and $\bar NK_S^0 $ shows almost no baryon enhancement. These observations indicate that the matter created in Au+Au collisions at $\sqrt {s_{NN} } $ = 11.5 or 7.7 GeV might be distinct from that created at $\sqrt {s_{NN} } $ = 39 GeV.     

A new analysis improving the evidence of a narrow peak in the invariant-mass distribution of the \Lambdap system observed in the \bar{{p}} annihilation at rest on 4He

The presence of a narrow peak in the $ \Lambda$ p invariant-mass distribution observed in the $ \bar{{p}}$ annihilation reaction at rest $\ensuremath \bar{p} {}^4\mathrm{He}\rightarrow p\pi^-p\pi^+\pi^-n X$ is discussed again through an analysis procedure which improves the ratio signal/background in comparison with the previous analysis. The peak is centred at 2223.2±3.2_stat±1.2_syst MeV and has a statistical significance of 4.7 $ \sigma$ , values compatible with those published previously. If interpreted as the result of the decay into $ \Lambda$ p of a $\ensuremath { }_{\bar{K}}{}^2\mathrm{H}$ bound system, the corresponding binding energy should be B = - 151.0±3.2_stat±1.2_syst MeV and the width $ \Gamma_{{FWHM}}^{}$ < 33.9±6.2 MeV. The production rate has a lower limit of 1.2 10^-4. Data on the $ \bar{{p}}$ annihilation reaction at rest $ \bar{{p}}$ ⁴He $ \rightarrow$ p $ \pi^{-}_{}$ p $ \pi^{-}_{}$ p _s X , analyzed for the first time, lead to a result in qualitative agreement with the previous one.