Soft-pion Production Research Articles

Studies of X(3872) and ψ(2S) production in pp¯ collisions at 1.96 TeV

We present various properties of the production of the $X(3872)$ and $\psi(2S)$ states based on 10.4 fb$^{-1}$ collected by D0 experiment in Tevatron $p \bar p$ collisions at $\sqrt{s}$ = 1.96 TeV. For both states, we measure the nonprompt fraction $f_{NP}$ of the inclusive production rate due to decays of $b$-flavored hadrons. We find the $f_{NP}$ values systematically below those obtained at the LHC. The $f_{NP}$ fraction for $\psi(2S)$ increases with transverse momentum whereas for the X(3872) it is constant within large uncertainties, in agreement with the LHC results. The ratio of prompt to nonprompt $\psi(2S)$ production, $(1 - f_{NP}) / f_{NP}$, decreases only slightly going from the Tevatron to the LHC, but for the $X(3872)$ this ratio decreases by a factor of about 3. We test the soft-pion signature of the $X(3872)$ modeled as a weakly-bound charm-meson pair by studying the production of the $X(3872)$ as a function of the kinetic energy of the $X(3872)$ and the pion in the $X(3872)\pi$ center-of-mass frame. For a subsample consistent with prompt production, the results are incompatible with a strong enhancement in the production of the $X(3872)$ at small kinetic energy of the $X(3872)$ and the $\pi$ in the $X(3872)\pi$ center-of-mass frame expected for the $X$+soft-pion production mechanism. For events consistent with being due to decays of $b$ hadrons, there is no significant evidence for the soft-pion effect but its presence at the level expected for the binding energy of 0.17 MeV and the momentum scale $\Lambda=M(\pi)$ is not ruled out.

MARS Code Developments, Benchmarking and Applications

Recent developments of the MARS Monte Carlo code system for simulation of hadronic and electromagnetic cascades in shielding, accelerator and detector components in the energy range from a fraction of an electronvolt up to 100 TeV are described. The physical model of hadron and lepton interactions with nuclei and atoms has undergone substantial improvements. These include a new nuclear cross section library, a model for soft pion production, a cascade-exciton model, a dual parton model, deuteron-nucleus and neutrino-nucleus interaction models, a detailed description of negative hadron and muon absorption, and a unified treatment of muon and charged hadron electromagnetic interactions with matter. New algorithms have been implemented into the code and benchmarked against experimental data. A new Graphical-User Interface has been developed. The code capabilities to simulate cascades and generate a variety of results in complex systems have been enhanced. The MARS system includes links to the MCNP code for neutron and photon transport below 20 MeV, to the ANSYS code for thermal and stress analyses and to the STRUCT code for multi-turn particle tracking in large synchrotrons and collider rings. Results of recent benchmarking of the MARS code are presented. Examples of non-trivial code applications are given for the Fermilab Booster and Main Injector, for a 1.5 MW target station and a muon storage ring.

Multiple soft pion production in nonlinear chiral sigma model

Multiple soft pion production in the baryon scattering reactions is considered in the framework of chiral nonlinear sigma model neglecting the pion mass. Treating baryons in the eikonal approximation as classical sources, a set of analytical solutions for the pion field is found. A tree S-matrix is constructed on the basis of these solutions describing the emission (or absorption) of any number of soft pions. Then the contribution of soft virtual pions is taken into account in a closed form. It is shown that the loop corrections strongly suppress the pion radiation, and for the two limiting cases of nonrelativistic and ultra-relativistic baryon scatterings there is no pion emission from the "ends". Thus, the mechanism similar to the soft photon bremsstrahlung in the quantum electrodynamics seems to be unable to create a state with a large number of the soft pions.

Measurement of the branching fraction for D0 → K−π+

Abstract The branching fraction for D0 → K−π+ is measured with the statistics collected by ALEPH from 1991 to 1994. The method is based on the comparison between the rate for the reconstructed D ∗+ → D 0 π + , D0 → K−π+ decay chain and the rate for inclusive soft pion production at low transverse momentum with respect to the nearest jet. The result is B(D0 → K−π+0 = (3.90 ± 0.09 ± 0.12)%

Rapidity dependence of soft mesons as a signature of resonance matter production in nucleus-nucleus collisions.

Enhanced production of soft---i.e., low transverse momentum---pions has been experimentally observed in nucleus-nucleus collisions at beam energies of 14.5{ital A} GeV [the Brookhaven National Laboratory Alternating Gradient Synchrotron (AGS)] and 200{ital A} GeV (CERN Super Proton Synchrotron). Here the rapidity dependence of soft pion and kaon production for the reaction Si(14.5{ital A} GeV)+Au is studied in the framework of the relativistic quantum molecular dynamics (RQMD) approach. The softest mesons from decaying resonance matter, which turns out to be the main production mechanism in RQMD, show a peculiar rapidity dependence, a weakening of the signal in the central rapidity region of the participant nucleons. This is in striking contrast to expectations from all other suggested mechanisms like mean fields, collective flow, and quantum statistical effects. The prediction can be tested by forthcoming experiments at the AGS in the near future. It is also predicted that a similar, though quantitatively much weaker, signal can be observed in the kaon spectra.

Analysis of Photoproduction Sum Rules from the Current Anticommutator on the Null-Plane: A Role of Soft-Pion Production at High Energy

It is shown that the sum rules in photoproductlon derived from the current anticommutator on the null-plane are well satisfied. The fact that the soft-pion production at high energy is asymmetric between the proton target and the neutron one plays an important role in this saturation.

A FULL-ACCEPTANCE DETECTOR FOR SSC PHYSICS AT LOW AND INTERMEDIATE MASS SCALES: AN EXPRESSION OF INTEREST TO THE SSC

A FULL-ACCEPTANCE DETECTOR FOR SSC PHYSICS AT LOW AND INTERMEDIATE MASS SCALES: AN EXPRESSION OF INTEREST TO THE SSC

Soft-pion emission in high-energy heavy-ion collisions.

We revive Heisenberg's approach to multiparticle production in the context of soft-pion emission in heavy-ion collisions. Adopting appropriate boundary conditions, we find a general analytic solution of the classical equations of motion for the nonlinear $\ensuremath{\sigma}$ model (for soft pions this model is an approximation to QCD). The solution is used to discuss various features of soft pion production in nuclear collisions.

Inclusive soft-pion production in e+e- annihilation and PCAC

Inclusive soft-pion production in e+e- annihilation and PCAC

Quantum statistics and the uncorrelated jet model at high energy

We show that the explicit introduction of quantum statistics in the uncorrelated jet model provides an enhancement of soft pion production. With increasing c.m. energy √ s, this results in a log s violation of Feynman scaling, a triangular rapidity distribution in place of the plateau, and a multiplicity growing as (log s) 2. Our predictions are found to be in good agreement with the behaviour observed in high-energy hadronic collisions.

Application of current-algebra techniques to soft-pion production by the weak neutral current:S,P,Tcase

We develop the cross-section formulas needed to correlate information on neutral currents obtained from deep-inelastic neutrino scattering, neutrino-proton elastic scattering, and neutral-current-induced soft-pion production, in the case of neutral currents with $S$, $P$, $T$ spatial structure. (The necessary $S$, $P$, $T$ current renormalization constants were estimated by us in a previous paper.) The pion-emission amplitude is obtained by current-algebra soft-pion techniques, with the effects of (3,3)-resonance excitation taken into account to leading nonvanishing order in the static approximation. We analyze recently reported Brookhaven National Laboratory results for neutral-current-induced soft-pion production under the simplifying assumption of a purely isoscalar $S$, $P$, $T$ neutral current, while simultaneously imposing existing bounds on neutrino-proton elastic scattering and fitting existing data on neutral-current-induced deep-inelastic scattering. If all $S$, $P$, $T$ renormalization constants are given their central quark-model values, the elastic-scattering and deep-inelastic restrictions constrain the pion-production cross section to be too low compared with experiment; if apparently reasonable deviations of the parameters from the quark-model values are permitted, satisfactory fits to all data are obtained with $S$, $T$, with $P$, $T$ or with $S$, $P$, $T$ mixtures. An isovector tensor or pseudoscalar neutral current is found to lead to a strong (3,3) peak in $\ensuremath{\pi}N$ invariant-mass plots, but an isovector scalar neutral current can be present without producing a visible (3,3) peak, even when ratios of the various $\ensuremath{\pi}N$ charge states produced by the neutral current are appreciably changed from the values which they have in the isoscalar-current case. Two other interesting qualitative features of $\mathrm{CP}$-conserving $S$, $P$, $T$ structures are the following: (1) constructive $T$ interference with $S$ (or $S$ and $P$) in $\ensuremath{\nu}+N\ensuremath{\rightarrow}\ensuremath{\nu}+N+\ensuremath{\pi}$ can accompany destructive interference in $\ensuremath{\nu}+p\ensuremath{\rightarrow}\ensuremath{\nu}+p$, and vice versa, and (ii) observation of unequal neutrino- and antineutrino-induced neutral-current cross sections would not be accompanied by neutral-current-induced parity-violating effects in the $\mathrm{pp}$, $\mathrm{ep}$, and $\ensuremath{\mu}p$ interactions.

Application of current algebra to soft-pion production induced by the weak neutral current: Second-classV,Acase

We apply current-algebra techniques to study neutrino--proton elastic scattering and neutral-current--induced soft-pion production in the case of second-class vector and axial-vector currents. (Such currents are CP-violating if the final and incident neutrinos are identical, but can be CP-conserving if the final and incident neutrinos are different particles.) The second-class currents are constructed phenomenologically from meson fields and the usual first- class V, A quark currents. The matrix elements of the second-class currents between one-nucleon states are estimated by inserting a complete set of intermediate states and saturating the sum with one-nucleon states. In this way the second-class matrix elements are expressed in terms of the experimentally measured renormalization constant of the first-class V, A currents and the pion-- nucleon coupling constants. Using standard soft-pion techniques, we analyze recently reported Brookhaven National Laboratory results for neutral-current-- induced soft-pion production under the simplifying assumption of a purely isoscalar second-class V, A neutral current. We find in this case that a second- class V--A current is consistent with the reported results. Some qualitative features of second-class neutral currents are equal cross sections for $nu$p and nu-barp elastic scattering, with only the axial-vector current contributing, and very small $nu$p and nu-barp elastic cross sectionsmore » at energies of order 50 MeV, which are relevant for possible neutrino experiments of the Los Alamos Meson Physics Facility. (AIP)« less

Application of current-algebra techniques to soft-pion production by the weak neutral current:V,Acase

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Inclusive soft-pion production in inelastic eγ scattering

The differential cross-section for producing one or two soft pions in inelastic eγ scattering is related to the structure functions describing the Fourier transformed forward matrix elements of the products of two strangeness-conserving weak axial vector or vector currents respectively between spin-averaged identical photon states.

Soft pion production in deep inelastic electromagnetic and weak processes

On the basis of the PCAC hypothesis and current algebra, we calculate the cross section of one and two soft pion production in the deep inelastic scattering of electrons and neutrinos on nucleons. The experimental measurement of these processes would make it possible to investigate the one-nucleon matrix elements of the axial and isovector current commutators and contribute to elucidation of the scale invariance mechanism.

Uncertainties in tests of long-range charge independence

It is pointed out that determinations of the pion-nucleon coupling constant g based on distant collisions in proton-proton (p-p) and neutron-proton (n-p) scattering employing pseudoscalar (ps) theory have questionable validity because the physical particles are not the idealized undressed particles to which the one-pion exchange (OPE) considerations really apply. Neither the pion-pion (π-π) interaction nor the electromagnetic form factors of nucleons (N) and the π's are explained by the derivation of the OPE interaction. Furthermore the Fermi-Yang pion model suggests directly the entrance of derivatives in the π-N interaction energy even though it had to be modified through the years. Although the literal applicability of the ps theory to the calculation of OPE effects is doubtful the exponential dependence of the equivalent OPE potential (OPEP) on the N-N separation is on the other hand a consequence of the tunneling phenomenon in the transfer of a π from one N to another, such as is present in the theory of nucleon-transfer reactions in low energy nuclear physics. The qualitative support for the mathematical form of the OPE from N-N scattering data is thus not a convincing argument for any one detailed mathematical form of OPE theory. It is pointed out that the presence of the factor ( m π/M) 2) in the OPE phase shift formula is of questionable validity. Estimates are made of the effect of disregarding the variation of the factor with m π. The estimates indicate that the π-N coupling constants derived from p-p and n-p data will agree appreciably better with each other as a result. This modification does not destroy the highly probable dependence of the OPE phase shifts on m π expected from the picture of π-tunneling through the region of negative kinetic energy between the nucleons. The modification is equivalent to the replacement of the ps coupling theory by the pv theory employing the factor ƒ/ m π in the interaction energy with actual values of m π corresponding to π +, π −, and π O . It is suggested that tests of long-range charge independence performed by comparing ( g 2) p- p with ( g 2) n- p do not emphasize sufficiently the rather likely possibility of differences in the coupling of the charged pions to both n and p as compared with that of the neutral pion. Possible uncertainties in the coupling constant determinations caused by the characteristics of experimental data are mentioned and briefly discussed. Different forms of the π-N interaction energy are considered. It is pointed out that there is no compelling reason for considering only local forms in necessarily phenomenological formulations of the theory, because the nucleon, pions, and other mesons involved (ϱ, η, μ, ϕ) are not definitely elementary particles and are coupled to each other. The limited meaning of charge independence of the π-N interaction without the incorporation of a quantitative explanation of the pion mass differences is emphasized. It is pointed out that the employment of the pv coupling theory made in this paper is consistent with relatively recent generalizations of that theory made by S. Weinberg and J. Schwinger in connection with PCAC, soft pion production, π-π interaction, nucleon magnetic moments, and related questions. The relationship of matters discussed to theories of electromagnetic mass differences is briefly considered.

Soft-pion production and algebra of currents

The production of two soft pions in collision processes are here investigated under the hypotheses of the algebra of currents and the partially-conserved axial-vector current. The condition of softness is made to meet with the experimental situation. A general formula to estimate the two soft-pion production is derived. A scalar part as well as the normal isospin part of the reduction amplitude are included in this formula. The calculated cross section is large enough to be measured experimentally.The baryon-baryon collision and the production of double soft pions are studied in detail. Assuming the SU(3) symmetry for baryon systems, we get many sum rules and selection rules. The non-go selection rules are classified into three classes according to the forbiddenness of the scalar and isospin part of the reaction amplitude, viz. (i) no scalar part and forbidden isospin part, (ii) allowed scalar part but forbidden by the isospin part, (iii) completely forbidden by both scalar and isospin part.