Low Momentum Particles Research Articles

Soft-particle spectra as a probe of interconnection effects in hadronic W

Cross-talk between the W^+ and W^- sources of hadron production at LEP2 offers a hope to learn about basic properties of QCD, but at the same time threatens high-precision measurements of the W boson mass. Directly visible effects are not expected to be large, however. It is, therefore, important to develop methods to measure the level of interconnection in the data --- `connectometers'. In this article we study one particular set of observables, namely the reduced rate of low-momentum particle production caused by reconnection. In realistic scenarios the expected signals are at the border of visibility, but not quite beyond reach. Special studies on kaons and protons, or with other subsets of the data, could provide supporting evidence. We also show how LEP1 Z$^0$ events could be used to define an alternative reference sample.

Soft-particle spectra as a probe of interconnection effects in hadronic W $^{+}$ W $^{-}$ events

Cross-talk between the ${\rm W}^+$ and ${\rm W}^-$ sources of hadron production at LEP2 offers a hope to learn about basic properties of QCD, but at the same time threatens high-precision measurements of the W boson mass. Directly visible effects are not expected to be large, however. It is, therefore, important to develop methods to measure the level of interconnection in the data –‘connectometers’. In this article we study one particular set of observables, namely the reduced rate of low-momentum particle production caused by reconnection. In realistic scenarios the expected signals are at the border of visibility, but not quite beyond reach. Special studies on kaons and protons, or with other subsets of the data, could provide supporting evidence. We also show how LEP1 ${\rm Z}^0$ events could be used to define an alternative reference sample.

Perturbative universality in soft particle production b

The spectrum of partons in a QCD jet becomes independent of the primary energy in the low momentum limit. This follows within the perturbative QCD from the colour coherence in soft gluon branching. Remarkably, the hadrons follow such behaviour closely, suggesting the parton hadron duality picture to be appropriate also for the low momentum particles. More generally, this scaling property holds for particles of low transverse and arbitrary longitudinal momentum, which explains an old experimental observation (“fan invariance”). Further tests of the perturbatively based picture for soft particle production are proposed for three-jet events in e+e− annihilation and di-jet production events in γp, γγ and \(p\bar p\) collisions. They are based upon the difference in the intensity of the soft radiation from primary \(q\bar q\) and gg antennae.

Supersymmetric electroweak baryogenesis, non-equilibrium field theory and quantum Boltzmann equations

The closed time path (CTP) formalism is a powerful Green function formulation to describe non-equilibrium phenomena in field theory and it leads to a complete non-equilibrium quantum kinetic theory. In this paper we make use of the CTP formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetrics of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources and tnserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest “memory” effects which are typical of the quantum transport theory and are not present in the classical approach. The slowdown of the relaxation processes may keep the system out of equilibrium for longer times and therefore enhance the final baryon asymmetry. We also stress that the classical approximation is not adequate to describe the quantum interference nature of CP violation and that a quantum approach should be adopted to compute the sources since they are most easily built up by the transmission of low momentum particles.

Perturbative universality in soft particle production b

The spectrum of partons in a QCD jet becomes independent of the primary energy in the low momentum limit. This follows within the perturbative QCD from the colour coherence in soft gluon branching. Remarkably, the hadrons follow such behaviour closely, suggesting the parton hadron duality picture to be appropriate also for the low momentum particles. More generally, this scaling property holds for particles of low transverse and arbitrary longitudinal momentum, which explains an old experimental observation (``fan invariance''). Further tests of the perturbatively based picture for soft particle production are proposed for three-jet events in e+e- annihilation and di-jet production events in gamma p, gamma-gamma and p\bar p collisions. They are based upon the difference in the intensity of the soft radiation from primary q\bar q and gg antennae.

Orbital resonances and chaos in a combined rf trap

The rf combined trap for confining a non-neutral plasma by a combination of rf fields and a uniform magnetic field is introduced. The particle motion is studied in such a trap in which the rf fields are given by the TM011 mode. The aim is to determine limits on a focus at the center for low angular momentum particles. Such a focus allows densities in excess of the local Brillouin limit. The motion is described in terms of an effective potential consisting of the ponderomotive potential Vpon(r,z) plus a radial potential mΩc2r2/8 due to the magnetic field Bz plus a centrifugal potential pθ2/2mr2. Near the origin r=0, z=0, the equations reduce to a pair of Mathieu equations for the r and z motions. For certain parameters the system is quasispherically symmetric, i.e. the effective ponderomotive frequencies Ωr, Ωz in r and z are equal. In this case the Brillouin limit for a uniform density plasma is shown to equal the usual cylindrical limit. Numerical integration of the ponderomotive equations is shown for parameters near those giving quasispherical symmetry. There is resonance for Ωr/Ωz=1, giving m=2, n=2 islands. The islands limit the size of the focus at the origin, even for pθ=0. For particles with large effective energy Eeff, there can also be chaos, depending on the elongation L/a of the rf cavity. It is found that the deleterious effect of islands and chaos on the focus is minimized by having the elongation L/a close to unity and having particles trapped deeply in the ponderomotive well.

QCD coherence and the soft limit of the particle spectrum

Perturbative QCD predicts an energy independent limit for the density of partons at small momenta in a jet which follows from the colour coherence in soft gluon production. The existing data on the charged and identified particle inclusive spectra in e + e − annihilation follow closely the perturbative prediction for partons which is in support of the local parton hadron duality picture also for low momentum particles. Further tests of this interpretation of the data are proposed.

From Sideward Flow to Nuclear Compressibility

The authors use the transport model (BUU) with different optical potentials, combining density and momentum dependence with strong or weak nuclear compressibility, to simulate heavy-ion collisions. Experiment by DIOGENE allows them to show that experimental sideward flow is close to their calculations using optical potential of soft momentum- and density-dependence (Potential I), as well as calculations using optical potential of stiff pure density-dependence (Potential II). On the other hand, the Plastic Ball experiment on sideward flow, mainly due to the instrumental rejection of low transverse momentum particles, allows the authors to tell the differences between Potential I and II, with calculations using Potential I being close to the experimental data. Combining the results above, they see that only potential I with soft nuclear compressibility can describe the experimental data. The uncertainty of NN cross section in the medium leads to the uncertainty in nuclear compressibility, they estimate that the nuclear compressibility K lies between 180 and 235 MeV.

Low p T intermittency in π + p and K + p collisions at 250 GeV/c

Density fluctuations are studied in rapidity, separately for low and intermediate transverse momentum particles. In our data, the effect of intermittency is increased when the analysis is restricted to low p T particles.

The ARGUS microvertex drift chamber

The ARGUS collaboration is currently building a new microvertex drift chamber (μVDC) as an upgrade of their detector. The μVDC is optimized for B-meson physics at DORIS energies. Important design features are minimal multiple scattering for low-momentum particles and three-dimensional reconstruction of decay vertices with equal resolutions in r- φ and r- z. Vertex resolutions of 15–25 μm are expected. Prototypes of the μVDC have been tested with different gas mixtures at various pressures. Spatial resolutions as small as 20 μm were obtained using CO 2/propane at 4 bar and DME at 1 bar. New readout electronics have been developed for the μVDC aiming at low thresholds for the TDC measurements. Employing a novel idea for noise and cross-talk suppression, which is based on a discrimination against short pulses, very low threshold settings are possible.

Some Hadron Calorimeter Properties Relevant to Storage Rings

At wide angles in a storage ring environment, a substantial part of the energy seen by a hadron calorimeter can be in the form of very low momentum particles such as jet fragments or resonance cascade decay products. Data are presented on the deviations from Gaussian resolution and linear response for such low momentum particles. The differing responses to incident e-, μ-, π+-, K+-, p and p̄ at momenta below 10 GeV/c are also compared.In addition, we discuss the significance of angle effects for a 4π calorimeter, and the problems of combining data from calorimeters with different physical characteristics. Experimental data are presented on the difference in hadron response between a fine grain ("electromagnetic") lead calorimeter and a coarser ("hadron") iron calorimeter, and on the dependence of the response on the energy sharing between the two calorimeters.

Predictions and measurements of mass spectra of the charged nucleonic component of cosmic rays at mountain altitude

A cosmic-ray mass spectrometer utilizing a superconducting magnet, digitized wire spark chambers, and time-of-flight scintillation counters has examined the mass spectrum of low-momentum charged particles at 2750-m altitude (747 g/cm/sup 2/). For the first time at mountain altitude, the deuteron spectrum has been clearly resolved. The proton results confirm earlier work. The data indicate the presence of a few /sup 4/He nuclei. Upper limits are given to fluxes of antiproton and hypothetical massive particles in the 5-to-10-GeV/c/sup 2/ range. The low-momentum deuteron spectrum, as well as the proton spectra at various atmospheric depths, can be well understood in terms of a cosmic-ray atmospheric cascade calculation. The deuterons are principally produced by N+N..-->..d+..pi.. and quasielastic nucleon scattering on n-p pairs within the nucleus. Calculations are also presented of the expected intensities of low-momentum antiprotons and hypothetical massive particles at mountain altitude.

Colour distribution in hadron-hadron scattering

In high p t quark-quark scattering a simple picture emerges for the colour distribution in the final state: the scattered quark of one of the incident hadrons forms a colour singlet with the spectators of the other hadron, i.e., the four fast coloured objects form two singlets. We assume that the decay of each colour single pair - apart from a trivial boost - is similar to that observed in deep inelastic lepton—hadron scattering. This picture leads to measurable anticorrelations for energy fluxes carried by low momentum particles. The predicted asymmetry is significant only in qq scattering, but not in q q , qg,… scattering, which leads to specific predictions.

Statistical mechanics of bosons with attractive interaction

In order to obtain meaningful results for a system of bosons interacting via a potential containing a long-ranged attraction, the coupling of low momentum particles with high momentum particles has to be taken into account. The method of thermal Green’s functions applied to this problem leads to involved graphical calculations even for temperatures close to the absolute zero. It is shown that the problem can be tackled much more simply and profitably by obtaining an effective hamiltonian for low momentum particles in a manner similar to that adopted in the recent renormalisation group approach to critical phenomena. The occurrence of anomalous pairings is avoided by performing suitable Bogolubov transformations. The procedure gives the quasiparticle spectrum besides yielding an explicit expression for the free energy in the low temperature limit. The results agree with those derived by Green’s function methods using partial summations.

Differential Production Cross Sections of Low-Momentum Particles from 12.3-BeV/cProtons on Beryllium and Copper

Measurements of the differential production cross sections of pions, kaons, protons, and antiprotons from 12.3-BeV/c protons incident upon copper and beryllium targets were made at the Zero-Gradient Synchrotron at Argonne National Laboratory. These measurements were taken at production angles between 0 and 11.2 deg and covered the momentum range 500-1030 MeV/c. The particles were detected by a time-of-flight technique, supplemented by \ifmmode \check{C}\else \v{C}\fi{}erenkov counters for kaons and antiprotons.

Particle Production at Large Angles by 30- and 33-Bev Protons Incident on Aluminum and Beryllium

A mass analysis has been made of the relatively low momentum particles emitted from Al and Be targets when struck by 30- and 33-Bev protons. Measurements were made at 90\ifmmode^\circ\else\textdegree\fi{}, 45\ifmmode^\circ\else\textdegree\fi{}, and 13\textonequarter{}\ifmmode^\circ\else\textdegree\fi{} relative to the direction of the Brookhaven AGS proton beam. Magnetic deflection and time-of-flight technique were used to determine the mass of the particles.

Fluctuations and Latitude Effect of Cosmic Rays at High Altitudes and Latitudes

Using a newly developed ionization chamber, which transmits its information by radio, simultaneous balloon flights were made from widely separated stations in the summer of 1951. Bismarck, North Dakota (geomagnetic latitude, ${\ensuremath{\lambda}}_{m}$, 56\ifmmode^\circ\else\textdegree\fi{}N) was used as a base station. Four flights were made from shipboard going north from Boston and five were made from Thule, Greenland (${\ensuremath{\lambda}}_{m}=88\ifmmode^\circ\else\textdegree\fi{}$N), simultaneous with those at Bismarck. In all, 28 successful flights were made by the two expeditions. In seeking to determine the geomagnetic effects on the low energy primaries, considerable information was gathered on the radiation that fluctuates from day to day. The following are the chief experimental findings together with some of the conclusions that may be drawn.(1) The fluctuations in the primary radiation at 90 000 feet were as much as 10 percent in a few days. (2) These were simultaneous (except as noted in the text) and very close to the same amount at the two stations. (3) The magnitude of the fluctuations at high altitudes was considerably larger than the geomagnetic effect between Bismarck and Thule. (4) The radiation that fluctuated contained both high (> 15 Bev/c) momentum and low (down to 1.5 Bev/c) momentum particles. (5) There was a good correlation between the fluctuations in the radiation at high altitudes and the fluctuations in the neutron and meson components at ground level. (6) The fact that no particles fluctuated at Thule that did not also fluctuate at Bismarck leads us to conclude that there are few, if any, low energy particles coming in at Thule that are not also present at Bismarck, otherwise they too would be expected to vary. (7) From the manner in which the fluctuating radiation is absorbed in the atmosphere, it is concluded that the fluctuations cannot be due to heavy primaries alone. Rather it appears that the particles that fluctuate are of the same nature as the other incoming particles but have somewhat less energy per particle. (8) Varying magnetic fields of the geomagnetic axially symmetrical type are discarded as being able to produce the kind of fluctuations observed. A more satisfactory mechanism appears to be varying electric fields. (9) There was a negative latitude effect in the total ionization at intermediate altitudes (30 000 to 50 000 feet) at high latitudes. This we attribute to the greater importance of $\ensuremath{\mu}$-meson decay in the warmer air of the stratosphere which exists at the more northerly latitudes. The temperature coefficient arrived at is -0.19 percent \ifmmode^\circ\else\textdegree\fi{}${\mathrm{C}}^{\ensuremath{-}1}$. (10) There was a positive latitude effect in the total ionization above 60 000 feet at high latitudes. Evidence is presented to show that this is not likely to be due either to atmospheric effects or to low energy particles admitted by the earth's magnetic field above 66\ifmmode^\circ\else\textdegree\fi{}N. We attribute this increase to the shadow effect of the earth. (11) The absence of particles with momenta in the range 1.5 to 0.6 Bev/Zc (0.8 to 0.14 Bev for protons), shown by (a) a lack of increase of ionization at very high altitudes between geomagnetic latitudes 58\ifmmode^\circ\else\textdegree\fi{} and 66\ifmmode^\circ\else\textdegree\fi{}N, (b) the absence of an increase of area under the ionization-depth curve at latitudes north of ${\ensuremath{\lambda}}_{m}=58\ifmmode^\circ\else\textdegree\fi{}$N, and (c) the absence of any particles that fluctuate at Thule that do not also fluctuate at Bismarck, indicates a cutoff of the primary particles. (12) This cutoff we attribute to a general solar magnetic field. The magnetic moment required is 0.65\ifmmode\times\else\texttimes\fi{}${10}^{34}$ gauss-${\mathrm{cm}}^{3}$ corresponding to a field at the solar equator of 19 gauss. (13) Any diurnal effect on cosmic rays due to such a magnetic moment would normally be hidden by the daily fluctuations of the primary particles.