A phenomenological investigation of the shower particle pseudorapidity fluctuations in hadron-nucleus collisions

From the experimental matrix $\text{?(N}{}_{\mathrm{<mtext>g</mtext>}}\text{; n}{}_{\mathrm{<mtext>s</mtext>}}\text{, Δη}{}_{\mathrm{i}}\text{)}$ (the number of events with a given number N_g of particles with velocity 0.3c<v<0.7c, and n_s, the number of shower particles (v > 0.7c) in a pseudo-rapidity interval Δη_i) obtained from the Heidelberg-Igel hadron-nucleus experiment at CERN, we extract the shower particle multiplicity distributions as a function of ν, the number of nucleons that interacted with the projectile. We use a theoretically justified statistical correlation between ν and N_g (recoil protons) and the assumption that the correlation between n_s and N_g is given merely through ν. The data used are for incoming energies 50 and 150 GeV with a proton or pion as the projectile and Cu or Pb as the target. We find that the shower particle multiplicity distributions are of a Poissonian character in each η bin and for each value of ν. The average multiplicities $\text{〈n}{}_{\mathrm{<mtext>s</mtext>}}\text{〉(ν)}\text{Δη}{}_{\mathrm{i}}$ are approximately the same for the two targets and for the different projectile, possibly with a small excess for the pion projectile.The results are compared to a rather general theoretical model of the soft interaction type. The predictions from this model for the shower particle pseudorapidity distributions are very close to the derived values.     

Multiplicity of charged particles π− interactions on nuclei at 40 GeV/c

Multiparticle production in π^?-nucleus interactions at 40 GeV/c (Fifth Joint CERN-Serpukhov Experiment) has been studied using a spark-chamber technique at the Serpukhov accelerator. The mean multiplicities, the pseudorapidity distributions and the dispersion of the multiplicity distributions of charged particles produced on C, Al, Cu and Pb targets are presented. The data have been analysed, both subtracting and including secondary protons with p < 1 GeV/c. In the region of pseudorapidity η > 3.4 the average multiplicity is nearly independent of the size ($\text{ν}$) of the target nucleus, while it increases for η < 3.4. In the forward direction (η > 4) the mean multiplicity on nuclei is smaller than the mean multiplicity on hydrogen. The dependence upon $\text{ν}$ in the target fragmentation region is stronger when the emitted protons are included in the pseudorapidity distributions of the secondary particles. The dispersion of the multiplicity distributions for the different nuclear targets versus the mean multiplicity shows the same slope as found by the world statistics on hydrogen and by other experiments on nuclei at different energies. The results are compared with the predictions of the coherent tube model and with the soft hadron-nucleus collision model.     

Inelastic hadron-nucleus interactions at 20 and 37 GeV/c

The experiment studies charged particle production for π^?, K^?, and $\text{p}$ interactions on nuclei at 20 and 37 GeV/c at the CERN SPS. A non-magnetic detector, consisting of CsI(Tl) scintillation and lucite ?erenkov counters, distinguishes between fast particles, mainly pions, and slow particles, mainly nucleons, with a cut at velocity β ≈ 0.7. Angular distributions, multiplicity distributions and correlations of slow and fast particles were analysed. It is shown that the measurement of the correlations can provide a critical test for different theoretical models of the hadron-nucleus interaction. At the energies studied so far a systematic deviation from KNO scaling is observed. This gives further support to the “standard picture” of the hadron-nucleus interaction and it contrasts with predictions of the coherent-tube model. The regularity observed for the angular distribution of fast secondaries as a function of the number of slow particles can only be explained by combining features predicted by different models.     

Hydrodynamics of an n-component phonon system

The dynamic properties of an n-component phonon system in d dimensions, which serves as a model for a structural phase transition of second order, are investigated. The symmetry group of the hamiltonian is the group of orthogonal transformations $\text{O}$(n). For n ≥ 2 a continuous symmetry is broken for T<T_c, where T_c is the transition temperature. We derive the hydrodynamic equations for the generators of this group, the $\text{1}\text{2}\text{n (n ? 1)}$ angular-momentum variables. Besides the usual hydrodynamics of a phonon system, there are $\text{1}\text{2}\text{n (n ? 1)}$ additional independent diffusive modes for T > T_c. In the ordered phase we find 2 (n ? 1) propagating modes with linear dispersion and quadratic damping. Formally the hydrodynamics is similar in the isotropic Heisenberg ferromagnet (n = 2) or the isotropic antiferromagnet (n ≥ 3). The relaxing modes for T < T_c require special care. We study the critical dynamics by means of the dynamical scaling hypothesis and by a mode-coupling calculation, both of which give the critical dynamical exponent $\text{z =}\text{1}\text{2}\text{d}$. The results are compared with the 1/n expansion. It is shown that for large n there is a non-asymptotic region characterized by an effective exponent $\text{z}\text{?}\text{= φ/2ν}$, where φ is the crossover exponent for a uniaxial perturbation, and ν the critical exponent of the correlation length.     

The production of charged particles with high transverse momentum in proton-proton collisions at the CERN ISR

Results are given on the inclusive production of charged pions, kaons and nucleons in high-energy proton-proton collisions in the centre-of-mass rapidity range |y_cm| < 1 and for transverse momenta up to 4.8 GeV/c. The dependence of the composition of produced particles on y_cm, the total energy $\text{s}$, and transverse momentum p_T is discussed.     

Determination of the one-pion exchange potential from pn and pp charge exchange scattering

The πNN vertex function is determined from $\text{d}\text{σ}\text{d}\text{t}$ for pn → np and $\text{p}\text{p →}\text{n}\text{n}$ at 8 GeV/c in the interval 0 < ? t < 0.1 GeV². A “regularor mass” of 3.5m_π=488 MeV is found, corresponding to an “extension” of 0.40 fm of the πNN vertex. The resulting OPE potential is discussed.     

Dynamics of the infinite-range ising spin glass

The Glauber dynamics of an Ising spin glass with infinite-range interactions and additional static field, h, is investigated near the freezing temperature, T_f. We obtain critical slowing down at and below the de Almeida-Thouless instability line, h_c(T), to order (1?T/T_f)³ with algebraic decay of the spin correlations ～t^?ν, where $\text{ν=}\text{1}\text{2}$ at T_f and $\text{ν≤}\text{1}\text{2}$ for T<T_f.     

On the difference between pp and pp topological cross sections up to 100 GeV/c

New 100 GeV/c$\text{p}$p data are used to find moments of the difference between the $\text{p}$p and pp topological cross sections. The mean multiplicity for annihilations at 100 GeV/c is estimated to be 9.06 ± 0.56, and the value of the quantity 〈n〉/D to be 2.75 ± 0.33. It is shown that $\text{R}{}_{\mathrm{n}}\text{= {σ}{}_{\mathrm{n}}\text{(}\text{p}\text{p) ? σ}{}_{\mathrm{n}}\text{(pp)}/σ}{}_{\mathrm{n}}\text{(pp)}$ appears at 100 GeV/c to have acquired an asymptotic form, R_n = s^?αβⁿ, with α and β constant.     

Nuclear effects in 800 GeV proton interactions

We discuss here the nuclear effects in multiparticle production processes in 800 GeV proton-emulsion nuclei interactions. The multiplicity of medium energy particles (N _g ) was used as a measure of the average number of projectile collisions (<v(N _g )>). To study nuclear effects, we determined <v(N _g )> and ratio of normalized rapidity density of all produced charged particles in hadron-nucleus to hadron-hadron interaction,R(N _η ). It was found that the average multiplicity of shower particles increases with <v(N _g )>. From theR(N _η ) distribution, we find; a strong maxima in the target fragmentation region, a plateau in the central region and depletion of particle density in the projectile fragmentation region.     

Regeneration amplitude of KS0 from KL0 in carbon

We have measured the transmission regeneration amplitude for carbon. The invariant amplitude $\text{[?(0) ?}\text{?}\text{(0)]/P}$ varies from 5.909 ± 0.066 mb at 4.5 GeV/c to 3.933 ± 0.152 mb at 9.5 GeV/c. The results agree with optical model calculations using measured kaon-nucleon total cross sections. The data also provide a value for the ω trajectory intercept α_ω(0) = 0.42 ± 0.04.     

Large angle production of stable particles heavier than the proton and a search for quarks at the CERN intersecting storage rings

Measurements have been performed on production of particles with mass 1.5 GeV/c² and charge $\text{?}\text{2}\text{3}$ for θ_lab = 62.5° and $\text{s}\text{= 53}\text{GeV}$. At p_T = 0.7 GeV/c the relative rate of production of antideuterons to π^? is (5 ± 1) × 10^?5. The deuteron to antideuteron ratio is 3.7 ± 1.2. No new stable particle has been amongst 0.7 × 10⁸ charged particles entering our detector.     

A comparison of direct photon, π0 in pp and pp interactions at the CERN ISR

We have measured the production of direct photons, π⁰'s, and η's in p$\text{p}$ and pp collisions at √s=53 GeV in the range 2≈p_T≈6 GeV/c for the central rapidity region |y| 0.4. No statistically significant difference between pp? and pp interactions is observed.     

K−p and pp elastic scattering at 10.1 GeV/c

The differential cross sections for K^?p and $\text{p}$p elastic scattering have been measured over the range of four-momentum transfer squared 0.18<?t<3.3 (GeV/c)². The K^?p data decrease smoothly as a function of ?t, whereas, the $\text{p}\text{p}$ data shows a break at ?t = 0.6 (GeV/c)² followed by a fast drop to ?t ? 1.6 (GeV/c)² where the differential cross section levels off and stays constant out to ?t = 3 (GeV/c)².     

The charge exchange pp → nn at 5.0 and 7.76 GeV/c near the forward direction

The differential cross section for the charge exchange $\text{p}\text{p}\text{→}\text{n}\text{n}$ has been measured with high statistics at 7.76 GeV/c and at 5.0 GeV/c. The 7.76 GeV/c data show a very narrow [Δt ? 0.01 (GeV/c)²] forward peak superposed on a slow exponential fall-off.     

On triviality of the :expλϕ:4 quantum field theory in a finite volume

The ?dν(λ):expλ?:_n (without counterterms) quantum field theory is considered. Here ν(·) is a finite positive measure.Let n ? 3, or n = 2 and supp$\text{ν ∩ [?}\text{8π}\text{,}\text{8π}\text{] = ?}$. Under these conditions the theory ?dν(λ):expλ?:_n (without counterterms)converges to the free-field theory when the cut- offs are removed.     

The resistance jump in the pure type-I superconductors tin,indium and lead

It is shown that for tin, indium and lead samples of sufficiently high purity, sufficiently large diameter (2–3mm), and sufficiently close to the critical temperature (ΔT<0.15K), there exists a common value close to $\text{2}\text{3}$(0.64?R(i_c)/R_n ? 0.69) of the resistance jump at the transition from the superconducting to the intermediate state.     

Results from the first physics run of PHENIX at RHIC

First results from measurements of Au?Au collisions at $\sqrt {s_{NN} } = 130$ GeV, performed with the PHENIX experiment during the initial physics run of Brookhaven National Laboratory’s Relativistic Heavy Ion Collider in summer 2000, are summarized. Global characterization of the collisions was obtained from charged-particle multiplicity and transverse energy densities. At mid-rapidity, dN _ch /dν and dE _T /dν rise steadily with the event centrality, while the ratio <E _T >/<N _ch > remains constant. Transverse momentum spectra of charged particles up to 5 GeV/c yield a suppression of high-momentum particles in the most central events when compared to a simple scaling of binary nucleon-nucleon collisions. The scaling matches with peripheral collisions. Transverse momentum spectra of identified neutral pions from 1 to 4 GeV/c in peripheral collisions show consistency with point-like scaling with the average number of binary collisions. Yields in central collisions are significantly suppressed. Transverse momentum spectra of identified charged hadrons up to 3.5 GeV/c were measured in minimum bias events. The mass and centrality dependencies of inverse slope parameters and mean transverse momenta were determined. Inclusive spectra of electrons were measured for momenta from a few hundred MeV/c to 4 GeV/c. Inclusive photon spectra from a few hundred MeV/c to 3 GeV/c were obtained from conversion pair measurements.     

Off-shell NN annihilation studied in π+p interactions at 8 and 16 GeV/c

Interactions in which the baryon is emitted forwards in the c.m.s. are studied in 8 and 16 GeV/cπ⁺p collisions. These interactions are interpreted as representing baryon exchange. The properties of such off-shell $\text{N}$N annihilation events are studied. It is found that the multiplicity distribution of the multi-pion system as a function of the effective mass for events with |u_pp| < 1 GeV² is the same as for real $\text{N}\text{N}$ annihilations.