Studying the possibility of recovering np and nn helicity amplitudes on the basis of \vec p + \vec d and \vec n + \vec d scattering data at intermediate energies

In this work, we study the possibility of direct recovery of np helicity amplitudes, which are unknown at incident neutron energies T _n > 1.1 GeV, and nn helicity amplitudes, which are unknown at any energy, from data on $\vec p + \vec d$ and $\vec n + \vec d$ scattering. For the inversion of $\vec N + \vec d$ data, we use formulas that relate N _d- and NN amplitudes derived in terms of a refined Glauber model. It is found that the critical factors for solving the inverse problem under study are the accuracy and completeness of the set of input $\vec N + \vec d$ observables.     

Investigation of the deuteron spin structure at short nucleon-nucleon distances in the reaction of polarized-deuteron fragmentation to cumulative pions

Experimental results on the vector (A _y ) and tensor (A _yy ) analyzing powers in the fragmentation of 5- and 9-GeV/c polarized deuterons to high-momentum pions in the kinematical region corresponding to pion production on a strongly correlated nucleon pair (cumulative meson production) are presented. The angular and momentum dependences of A _yy are not described by calculations performed in the impulse approximation by using standard deuteron wave functions. An explanation for our data should be sought on the basis of models that treat the deuteron at short distances (deuteron-core region) as a multiquark state—for example, a 6q cluster, whose high orbital angular momentum (D wave) leads to the observed strong dependence of the reaction tensor analyzing power A( $\vec d$ , π)X on the pion transverse momentum.     

Probing the mesonic structure of the nucleon by means of exclusive quasielastic pion knockout in (e, e′π) reactions at high energies

By including the Z diagram in an analysis performed in the laboratory frame (instantaneous form of dynamics), the notion of quasielastic pion knockout by protons and electrons [(p, 2p) and (e, e′p) reactions treated in terms of the relevant pole diagrams] is generalized to the relativistic case where a meson is quasielastically knocked out of a nucleon by an electron having an energy of a few GeV. The concept of the wave function is introduced for the pion (and for other mesons), and its relation to the vertex constant G _πNN and the vertex function g _πNN(k ²) is indicated. The spectroscopic factor S _N ^B? is defined as the normalization of the wave function for the meson ?. It is shown by two methods that, under the kinematical conditions of quasielastic knockout that include the condition E _π?m _π (E _π is the energy of the knock-on pion) and the condition that the square Q ² of the virtual pion mass is large, the competing tree diagram is suppressed in relation to the pole diagram (this is not so in the case of pion photoproduction). From data of a p(e, e′π ⁺)n experiment involving longitudinal virtual photons γ _L ^* , the momentum distribution |Ψ _p ^nπ (k)|² of pions in the nucleon is extracted for the first time over the entire range of significant momenta k, and this result is used to determine the cutoff constant Λ_π and the value of S _p ^nπ ≈0.2. The momentum distribution of positive rho mesons in the soft section of the spectrum is determined from experimental data on the process p(e, e′π ⁺)n proceeding through the mechanism ρ ⁺+γ _T ^* → π ⁺ involving transverse photons. A way to determine the momentum distribution of omega mesons through data on the process p(e, e′π ⁰)p is indicated. Two forms of dynamics—instantaneous form and that of light-front dynamics (the latter does not involve the Z diagram)—are compared for the example where the calculations are performed for the spectroscopic factor S _N ^B? .     

The possibility that the triple-Pomeron coupling vanishes at q t =0

We study the case when the triple-Pomeron vertex is assumed to have a vectorial form, that is, the amplitude of high-mass diffractive dissociation vanishes as $V\propto \vec{q}_{t}\cdot\vec{e}$ as q _t →0. We find that the available data in the triple-Reggeon region may be well described in such a ‘weak’ coupling scenario, providing that absorptive effects are taken into account. We compare this weak-vector coupling scenario with the strong and weak-scalar coupling scenarios. Corresponding predictions are presented for an LHC energy of 14 TeV.     

Off-shell effects in nucleon-deuteron polarization observables

A separable representation of theS-wave Paris potential and a phase-shift equivalent Yamaguchi-type potential significantly differing in their off-shell behaviours are used to calculate second-order polarization observables of elastic nucleon-deuteron scattering atE _D=10 and 20MeV. Off-shell effects are found that stem from differences in the nuclear interaction in the inner regionr?1.2 fm. Adding approximate Coulomb-distortion contributions to the purely nuclear Faddeev amplitudes proton-deuteron predictions are obtained. Coulomb effects are not found to be negligible. Comparison with experimental data, in particular, the spin-correlation parameterC _y,y of the reaction \({}^1\vec H(\vec d,d)^1 H\) forE _D=10MeV vector-polarized deuterons and the spin-transfer coefficientsK _y ^y′ ,K _x ^x′ andK _z ^x′ for \({}^2H(\vec p,\vec p)^2 H\) atE _p=10MeV, prefer the interaction model that contains an intermediate-range repulsion.     

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 new model forN \bar N annihilation

A new quark model forN \(\bar N\) annihilation is proposed. It is argued that a linear superposition of the so-called³P₀ and³S₁ models is more consistent with QCD and the inclusion of quark degrees of freedom inNN scattering, and is also suggested by the data. A comparison is made, in Born approximation, with the angular distribution for \(p\bar p \to \Lambda \bar \Lambda \) .     

Altarelli-parisi equation in non-equilibrium QCD

The Q ² evolution of fragmentation function in non-equilibrium QCD by using DGLAP evolution equation may be necessary to study hadron formation from quark-gluon plasma at RHIC and LHC. In this paper we study splitting functions in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. For quarks and gluons with arbitrary non-equilibrium distribution functions f _q ( $\vec p$ ) and f _g ( $\vec p$ ), we derive expressions for quark and gluon splitting functions in non-equilibrium QCD at leading order in ?? _s . We make a comparison of these splitting functions with that obtained by Altarelli and Parisi in vacuum.     

Unnatural parity states in nuclei and pion condensation

This is a systematic study to assess a lower limit on the threshold density for pion condensation on the basis of empirical nuclear data. It turns out that the isovector unnatural parity states in ⁴He, ¹⁶O and ⁴⁰Ca, and quantities related to them are best suited for a quantitative test. Assuming for the interactions parameters in the nucleon-hole and Δ-isobar-hole channels g′: = g′_NN = g′_NΔ = g′_ΔΔ, a value g′ = 0.7±0.1 is obtained from the measured energy shifts of unnatural parity states. Taking also into account results by Oset and Rho who obtain g′_ΔΔ = 0.6?0.7 from the observed quenching of Gamov-Teller matrix elements of (A±1) nuclei around ¹⁶O and ⁴⁰Ca, one finds the onset of pion condensation in nuclear matter at densities considerably larger than twice normal nuclear density, if at all. We discuss the work of Migdal et al. who prefer the assumption g′_NΔ = g′_ΔΔ = 0 and obtain lower critical densities. Also the question of (pre)critical behaviour in finite nuclei is investigated in terms of a quantitative example. It is found that a genuine signal for proximity to pion condensation would be the appearance of a strongly collective spin-isospin mode which has, however, not been observed experimentally so far.     

The Adler-Weisberger sum rule and the σ-commutator for the kaon-neutron system

The axial coupling constant is determined from Kp and Kn Adler-Weisberger sum rule, in correspondence with different \(\bar K\) N unphysical region parametrizations. Moreover a new calculation of the sigma-term is presented. It is shown that by usingKn data it is possible to reduce considerably the error on σ _NN ^KK with respect to the analogous calculation forKp, but that an accurate determination requires a good value for thep _3/2 \(\bar K\) N scattering length. By preferring the solutions which lead to a positive sigma-term, one obtains _NN ^KK =638±438 MeV     

Strong magnetic fields,Dirichlet boundaries,and spectral gaps

We consider magnetic Schrödinger operators $$H(\lambda \vec a) = ( - i\nabla - \lambda \vec a(x))^2$$ inL ₂(R ⁿ ), where $\vec a \in C^1 (R^n ;R^n )$ and λεR. LettingM={x;B(x)=0}, whereB is the magnetic field associated with $\vec a$ , and $M_{\vec a} = \{ x;\vec a(x) = 0\}$ , we prove that $H(\lambda \vec a)$ converges to the (Dirichlet) Laplacian on the closed setM in the strong resolvent sense, as λ→∞,provided the set $M\backslash M_{\vec a}$ has measure zero. In various situations, which include the case of periodic fields, we even obtain norm resolvent convergence (again under the condition that $M\backslash M_{\vec a}$ has measure zero). As a consequence, if we are given a periodic fieldB where the regions withB=0 have non-empty interior and are enclosed by the region withB≠0, magnetic wells will be created when λ is large, opening up gaps in the spectrum of $H(\lambda \vec a)$ . We finally address the question of absolute continuity of $\vec a$ for periodic $H(\vec a)$ .     

Spin Physics at ANKE-COSY

The COSY accelerator (Jülich, Germany) provides beams of polarised protons and deuterons. The ANKE facility at COSY is equipped with polarised hydrogen and deuterium atomic gas targets. The reactions investigated with polarised probes at ANKE include the deuteron break-up at small and large momentum transfer, the pion production processes in pp and pn collisions and the near-threshold η meson production in dip $\vec dp \to ^3 He\eta$ process. Use of the polarised deuteron beam properties allowed a precision measurement of the η meson mass. The future experimental program covers the study of the elementary pp and pn-interaction with polarised beams up to the maximal COSY energy, and a double polarised measurement of the A _{x, z} spin correlation parameter in the pN → {pp} _s π process.     

Exclusive semi-leptonic decays of bottom mesons in the spectator quark model

We calculate the exclusive semileptonic bottom meson decays \(B \to D(D*) + l^ - + \bar v_l \) in the spectator quark model. The helicity structure of the mesonic current transitionsB→D(D ^*) is matched to the helicity structure of the free quark current transitionsb→c at minimum momentum transferq ²=0. The results are continued toq ²≠=0 by pole-dominated form factors. Our results are compared to recent calculations that use quark model dynamics at maximum momentum transferq _max ² = (M ₁ ?M ₂)². We find agreement atq _max ² . Atq ²=0 there are significant differences between the predictions of the two approaches leading to marked differences in the predictions for the shape of the lepton energy spectrum, the shape of theq ²-distribution, and the helicity composition of the transition measurable in the angular distributions of the decaysD ^*→Dπ and \(W_{virtual}^ - \to l^ - + \bar v_l \) .     

Meson-loop effects in the NJL model at zero and nonzero temperature

We compare two different possibilities of including meson-loop corrections in the Nambu-Jona-Lasinio model: a strict 1/N _c expansion in the next-to-leading order and a nonperturbative scheme corresponding to a one-meson-loop approximation to the effective action. Both schemes are consistent with chiral symmetry, in particular, with the Goldstone theorem and the Gell-Mann-Oakes-Renner relation. The numerical part at zero temperature focuses on the pion and the ρ-meson sector. For the latter, meson-loop corrections are crucial in order to include the dominant ρ → ππ-decay channel, while the standard Hartree + RPA approximation only contains unphysical $m_\pi ,f_\pi ,\left\langle {\bar \psi \psi } \right\rangle $ -decay channels. We find that $q\bar q$ , and quantities related to the ρ-meson self-energy can be described reasonably with one parameter set in the 1/N _c-expansion scheme, whereas we did not succeed in obtaining such a fit in the nonperturbative scheme. We also investigate the temperature dependence of the quark condensate. Here, we find consistency with the chiral perturbation theory to the lowest order. Similarities and differences of both schemes are discussed.     

Hadroproduction of ψ and Υ

We show that inclusive ψ hadroproduction cross sections andx _F -distributions are quantitatively consistent with calculations based on the lowest order \(q\bar q \to c\bar c\) andgg→ \(c\bar c\) QCD subprocesses using a duality ansatz. Data in the πN, KN, NN and \(\bar NN\) channels are considered. They provide determinations of the gluon distributions within the nucleon, the pion, and the kaon at the ψ mass scale. AvailableNN→ΥX data aty=0 are consistent with the same model, using gluon distributions appropriate to the Υ mass: predictions ofx _F -distributions are made.     

Calculation of Feynman diagrams with zero mass threshold from their small momentum expansion

A method of calculating Feynman diagrams from their small momentum expansion [1] is extended to diagrams with zero mass thresholds. We start from the asymptotic expansion in large masses [2] (applied to the case when all $M_i^2$ are large compared to all momenta squared). Using dimensional regularization, a finite result is obtained in terms of powers of logarithms (describing the zero-threshold singularity) times power series in the momentum squared. Surprisingly, these latter ones represent functions, which not only have the expected physical “second threshold” but have a branchcut singularity as well below threshold at a mirror position. These can be understood as pseudothresholds corresponding to solutions of the Landau equations. In the spacelike region the imaginary parts from the various contributions cancel. For the two-loop examples with one mass M, in the timelike region for q² ≈ M² we obtain approximations of high precision. This will be of relevance in particular for the calculation of the decay Z → bb?in the m _b = 0 approximation.     

Quasielastic knockout of light fragments from 12C and 16O nuclei by intermediate-energy pions

Quasielastic deuteron and triton knockout from ¹²C and ¹⁶O nuclei has been studied infull kinematics using a 0.72-GeV/c pion beam. The momentum distributions of the intranuclear quasideuteron motion, excitation-energy spectra of the residual nuclei, and the effective numbers N _d ^eff of quasideuterons are determined. The parameters of the quasideuteron intranuclear motion are in reasonable agreement with the results obtained in other beams. The N _d ^eff in the nuclei from ⁶Li to ¹⁶O measured in full kinematics are virtually independent of the atomic number in contrast to the analogous values in the inclusive deuteron-knockout reaction induced by protons. The phenomenon of triton knockout from these nuclei is observed, which makes possible estimation of the cross section of backward pion-triton elastic scattering in yet unexplored regions of energy and momentum transfer.     

Calculation of the binding energy and of the parameters of low-energy scattering in the Λnp system

The cluster-reduction method is used to solve the differential Faddeev equations for S=1/2, T=0 and S=3/2, T=0 spin-isospin states of the Λnp system in the s-wave approximation. The NN interaction is simulated on the basis of the MT I–III potential model, and the ΛN potential is set to V _ΛN =V _NN /2. This simple option makes it possible to reproduce faithfully the binding energy of the hypertriton _Λ ³ H. The doublet and quadruplet Λd scattering lengths and the low-energy phase shifts are calculated. It is shown that the effective-range approximation is applicable to the cases of doublet and quadruplet scattering.     

φ meson production fromp\bar p collisions at\sqrt s = 1.8 TeV

Fermilab experiment E735 located at the CO intersection region of the $\sqrt s = 1.8$ TeV $p\bar p$ collider analysed over 900 Φ→K ⁺ K ^? events. Measured were the transverse momentum spectrum, the correlation between the average transverse momentum <pt> and the charged particle multiphcityN _c , as well as the probability of Φ production per charged track,N _Φ /N _c , versusN _c . We have also made an estinate of the total inclusive cross section for Φ mesons, $\sigma (p\bar p \to \phi X) = 7.3 \pm 2.2 mb$ .