Relations between elementary particle masses
Relations between elementary particles masses are given using only known physical constants, without any arbitrary number.
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Publications and source records attributed to B. Tatischeff.
Relations between elementary particles masses are given using only known physical constants, without any arbitrary number.
This paper aims to give further evidence for the existence of low mass exotic baryons. Narrow structures in baryonic missing mass or baryonic invariant mass were observed during the last twelve years. Since their evidence is still under debate, various data, measured with incident hadrons, by different collaborations, are reanalyzed to bring evidence on these narrow exotic baryonic resonances excited in charge-exchange reactions. These structures are clearly exotic as there is no room for them in the $qqq$ configurations: their width is smaller than the widths of "classical" baryonic resonances, moreover some of the masses lie below the pion threshold mass.
New data are presented, concerning narrow exotic structures in mesons, baryons and dibaryons. The sequence of narrow baryons is quite well described starting from the sequence of narrow mesons. In the same way, the sequence of narrow dibaryons is rather well described starting from the sequence of narrow baryons. Lastly it is shown that the masses of these narrow hadronic structures lie on straight line Regge-like trajectories.
Recently, several papers discussed on the existence of a low mass new structure at a mass close to M=214.3 MeV. It was suggested that the $Σ^{+}$ disintegration: $Σ^{+}\to$pP$^{0}$, P$^{0}\toμ^{-}μ^{+}$ proceeds through an intermediate particle P$^{0}$ having such mass. The present work intends to look at other new or available data, in order to observe the eventual existence of small narrow peaks or shoulders in very low mesonic masses. Indeed narrow structures were already extracted from various data in dibaryons, baryons and mesons (at larger masses that those studied here).
Our previous paper, part I of the same study, shows the different experimental spectra used to conclude on the genuine existence of narrow, weakly excited mesonic structures, having masses below and a little above the pion (M=139.56 MeV) mass. This work \cite{previous} was instigated by the observation, in the $Σ^{+}$ disintegration: $Σ^{+}\to$pP$^{0}$, P$^{0}\toμ^{-}μ^{+}$ \cite{park}, of a narrow range of dimuon masses. The authors conclude on the existence of a neutral intermediate state P$_{0}$, with a mass M=214.3 MeV $\pm$ 0.5 MeV. We present here some attempts to understand the possible nature of the structures observed in part I.
Recently, several papers discussed the existence of a low mass leptonic structure. It was suggested that the $Σ^{+}$ disintegration: $Σ^{+}\to$pP$^{0}$, P$^{0}\toμ^{-}μ^{+}$ proceeds through an intermediate particle P$^{0}$ having a mass close to M$\approx$~214.3 MeV. The present work intends to look at other available data, in order to observe the eventual existence of a small peak or shoulder, at a mass close to M=214.3 MeV, which can strengthen the existence of a state produced by two leptons of opposite electric charge.
This paper aims to give further evidence for the existence of low mass exotic baryons. Narrow structures in baryonic missing mass or baryonic invariant mass were previously observed during the last ten years. Since their existence is sometimes questionable, the structure functions of one pion electroproduction cross sections, measured at JLAB, are studied to add informations on the possible existence of these narrow exotic baryonic resonances.
Two reactions, pp->ppX and pp->pπ^+X, are used to study the 1.47<M<1.68 GeV baryonic mass range. Three different final states are considered in the invariant masses: N^* or Δ^+, pπ^0, and pη. The last two channels are defined by software cuts applied to the missing mass of the first reaction. Several narrow structures are extracted with widths σ(Γ) varying between 3 and 9 MeV. Some structures are observed in one channel but not in others. Such nonobservation may be due either to the spectrometer momenta limits or to the physics (e.g. no such disintegration channel is allowed from the narrow state considered). We tentatively conclude that the broad Particle Data Group (PDG) baryonic resonances N(1520)D13, N(1535)S11, Delta(1600)P33, and N(1675)D15 are collective states built from several narrow and weakly excited resonances, each having a (much) smaller width than the one reported by PDG.
Although extracted from several experiments using hadronic probes \cite{bor1}, narrow baryonic structures have been sometimes met with disbelief. New signatures are presented, which appear from already published data, obtained with hadronic probes as well as with leptonic probes. The authors of these results did not take into account the possibility to associate the discontinuities of their spectra with the topic of narrow baryonic low mass structures. The stability of the observed narrow structure masses, represents a confirmation of their genuine existence.
Signals of two narrow structures at M=1747 MeV and 1772 MeV were observed in the invariant masses M_{pX} and M_{π^{+}X} of the pp->ppX and pp->pπ^{+}X reactions respectively. Many tests were made to see if these structures could have been produced by experimental artefacts. Their small widths and the stability of the extracted masses lead us to conclude that these structures are genuine and may correspond to new exotic baryons. Several attempts to identify them, including the possible "missing baryons" approach, are discussed.
Although narrow low mass baryonic structures, observed mainly in SPES3 (Saturne) data, were not confirmed in recent experiments using lepton probes, their existence is confirmed in other data, where hadronic probes were used.
Using mainly $\vec{p}$ p $\to$ p ${π^+}X$ and $\vec{p}$ p $\to$ p$_{f}$~p$_{s}$ X reactions, narrow baryonic structures were observed in the mass range 950$\le$ M $\le$ 1800 MeV.
The reaction p p $\to$ p ${π^+}X$ was studied at different incident energies around T$_{p}$=2 GeV. Narrow baryonic structures were observed in the missing mass M$_{X}$ and in the invariant mass M$_{pπ^{+}}$. The masses of these structures are: 1004, 1044, 1094, 1136, 1173, 1249, 1277, and 1384 MeV (and possibly 1339 MeV). Some of them were also observed at the same masses in the missing mass spectra of the d p $\to$ p p X reaction although with a weaker signature. Many checks were performed to make sure that these structures were not produced by experimental artifacts. Several narrow small amplitude peaks, were also extracted using already published photo-nucleon cross sections. The small widths of all these results, and the stability of the observed structures, regardless of the experiment, were used to conclude that they are genuine baryons which and not merely the consequence of dynamical rescatterings. These baryons cannot be associated with classical $q^{3}$ quark configurations. We associate them with two colored cluster quark configurations.
The total cross section of the p d -> p d eta reaction has been measured at two energies near threshold by detecting the final proton and deuteron in a magneti spectrometer. The values are somewhat larger than expected on the basis of two simple theoretical estimates.
The total cross section for omega production in the pp -> pp omega reaction has been measured at five c.m. excess energies from 3.8 to 30 MeV. The energy dependence is easily understood in terms of a strong proton-proton final state interaction combined with a smearing over the width of the state. The ratio of near-threshold phi and omega production is consistent with the predictions of a one-pion-exchange model and the degree of violation of the OZI rule is similar to that found in the pi-p -> n omega/phi reactions.
The polarized d d -> alpha X reaction at beam energies close to the eta threshold shows very strong structure in the missing mass corresponding to the ABC enhancement. The deuteron tensor analysing power A_yy, and the slope of the vector analysing power A_y with respect to angle, have been measured for this reaction around the forward direction. Both signals are small, and their variations with the alpha-particle momentum are in broad agreement with a theoretical model in which each pair of nucleons in the projectile and target deuterons undergoes pion production through the NN -> d pi reaction.
The total cross section of the pp -> pp eta' reaction has been measured at two energies near threshold by detecting the final protons in a magnetic spectrometer. The values obtained are about a factor of 70 less than for the corresponding eta production, in good agreement with the predictions of a one-pion-exchange model.
Double differential cross sections have been measured for pi+ and K+ emitted around midraidity in d+A and He+A collisions at a beam kinetic energy of 1.15 GeV/nucleon. The total pi+ yield increases by a factor of about 2 when using an alpha projectile instead of a deuteron whereas the K+ yield increases by a factor of about 4. According to transport calculations, the K+ enhancement depends both on the number of hadron-hadron collisions and on the energy available in those collisions: their center-of-mass energy increases with increasing number of projectile nucleons.