An isospin analysis of the reaction pN→NNπ from threshold to 2.90 GeV/c

We have performed an isospin analysis of single-pion production processes in antiproton-nucleon scattering from threshold to 2.90 GeV/c. Reactions used are $\text{p}\text{p}\text{→}\text{p}\text{p}\text{π}{}^0\text{,}\text{n}\text{p}\text{π}{}^{\mathrm{?}}\text{and}\text{p}\text{p}\text{→}\text{p}\text{p}\text{π}{}^{\mathrm{?}}$. Results show that σ₁, the total I=1 cross section, rises rapidly from threshold to reach a broad maximum around 2.5 GeV/c and σ₀, the I=0 cross section, rises from threshold and continues on a linearly rising trend at least up to 2.90 GeV/c. In the region of 2.9 GeV/c, σ₁ and σ₀ have comparable values, thus suggesting that considerable amount of $\text{I=}\text{1}\text{2}\text{N}\text{π}$ and $\text{N}\text{π}$ states is produced even in this low momentum region. We further determine that single pion production processes are not the source of the π₀ (2375,190) enhancement observed in the $\text{p}\text{p}$ and $\text{p}\text{d}$ total cross sections and may account for as much as 25±8% of the π₁ (2350,140) enhancement.     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

Inclusive π electroproduction in the deep inelastic region

Using 20.5 GeV electrons on protons, we measured inclusive π⁰'s (of transverse momentum, p_T, from 0 to 1.4 GeV/c) produced by virtual photons of energy, ν, from 4 to 16.5 GeV and four-momentum squared, q², from ?1.8 to ?8.5 (GeV/c)². Comparing with charged pion data, we find , supporting the quark model. Photon knockout of a quark is favored as the interpretation of these data because of scaling in z = E_π/ν and similarity in z-dependence of other pion production data. Consistent with this interpretation are the dependence of 〈p_T〉 on q², the azimuthal dependence, and fits to the constituent interchange model. We also observe a possible p_T^?4 dependence at large |q²| over a limited p_T range.     

Line reversal in baryon exchange reactions and the energy dependence of dip locations

An empirical investigation of $\text{p}\text{p}\text{→ππ}\text{and}\text{π}\text{p}\text{→π}\text{p}$ data provides evidence for a dynamical variable connected with the boundary of the physical region. Absence of a fixed u = ?0.2 dip in recent $\text{p}\text{p}\text{→π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ high-energy data disagrees with nucleon-exchange (N) line-reversal expectations from π⁺p→pπ⁺ backward scattering. We notice however that the π⁺p→pπ⁺ dip is not located at fixed u but remains with a surprising accuracy at a fixed distance u' = u ? u_min from the physical boundary. Conjecturing that dips associated with particle exchanges occur at fixed u', we predict that the N-exchange dip in $\text{p}\text{p}\text{→π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ will be considerably displaced at non-asymptotic energies. Our conjecture places the fixed u' = ?0.2 dip near $\text{u ? ?0.4}\text{in}\text{p}\text{p}\text{→π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ for momenta around 2 GeV/c. Folded $\text{p}\text{p}\text{→ ππ}$ distributions exhibit a dip structure at this location. These observations suggest that the failure of line reversal at low energies is due to direct-channel effects, since fixed u' dips occur naturally in geometrical and direct-channel models.     

Experimental results on J/ψ production by π±, K±, p and p incident on hydrogen at 39.5 GeV/c

J/ψ production at 40 GeV/c by π^±, K^±, p and $\text{p}$ incident on hydrogen has been studied and results compared with those obtained on tungsten in the same experiment. On hydrogen, J/ψ cross-section ratios relative to π^? have been measured to be (for $\text{x}{}_{\mathrm{<mtext>F</mtext>}}\text{> 0) σ(π}{}^{\mathrm{?}}\text{) : σ(π}{}^{\mathrm{+}}\text{) : σ(}\text{p}\text{) : σ(}\text{p}\text{) = 1 : (0.78 ± 0.09) : (0.83 ± 0.35) : (0.07 ± 0.04)}$. The suppression of the proton induced cross sections shows the importance of calence quark-antiquark fusiin J/ψ production at this energy (i.e. M_J²/_ψ/s=0.13).     

Search for non-strange exotic mesons produced via baryon exchange

Negative results on backward production, via baryon exchange, of exotic non-strange mesons are presented. The reactions π^?p→p_forwardX^?and π^?n→ p_forwardX^?? have been studied with a 12 GeV/cπ^? beam in the Omega spectrometer at CERN. No resonant peak in $\text{X}\text{→}\text{p}\text{p}\text{π}{}^{\mathrm{?}}\text{,}\text{p}\text{p}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{?}}\text{,}\text{p}\text{p}\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{,π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{?}}\text{π}{}^0$ has been seen. The upper limits obtained on cross sections for exotic meson production $\text{X}\text{→}\text{N}\text{N}\text{π,}\text{N}\text{N}\text{π, 4π}$ are lower than the ?^? backward production cross section in the π^?p→p?^? reaction; this result seems to contradict the predictions of the two-component duality model. Compared to already published experiments in the search for exotics produced via baryon exchange, the sensitivity of this experiment is increased by an order of magnitude.     

A note on the momentum distribution function for an electron gas

The one-electron momentum distribution function $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ for an electron gas is investigated by a diagrammatic analysis of perturbation theory. It is shown that $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ has the following exact asymptotic form for large k (k ? p_F; p_F, the Fermi momentum): $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉 =}\text{4}\text{9}\text{(}\text{αr}{}_{\mathrm{s}}\text{π}\text{)}{}^2\text{×(}\text{p}{}_{\mathrm{<mtext>F</mtext>}}{}^8\text{k}{}^8\text{) g?(0) + ?}$, where g?(0) is the zero-distance value of the spin-up-spin-down pair correlation function. The physical implications of the above asymptotic form are discussed.     

Inclusive K10(890) production in π−p interactions at 16 GeV/c

Inclusive $\text{K}{}^{10}$ production is studied in π^?p interactions at 16 GeV/c with x_? > 0.2. The $\text{K}{}^{10}$ is found to be pre-dominantly centrally produced with cross section $\text{σ(}\text{K}{}^{10}\text{) = (72 ± 12) μb}$ for x_? > 0.2 and compares closely to data on $\text{K}{}^{10}$ production in π⁺p interactions at the same energy.     

Inclusive K1±(892) production in pp and π+p interactions

A study is presented of the inclusive production cross sections of K^1±(892) vector mesons in pp interactions at 12 and 24 GeV/c and in π⁺p interactions at 16 GeV/c. The K^1± inclusive cross section is ～0.9 mb for both pp at 24 GeV/c and π⁺p interactions at 16 GeV/c. For pp interactions, $\text{σ(}\text{K}{}^{\mathrm{1+}}\text{)}$ and $\text{σ(}\text{K}{}^{\mathrm{1?}}\text{)}$ are seen to rise with energy, showing a threshold behaviour. In both pp and π⁺p interactions, $\text{σ(}\text{K}{}^{\mathrm{1+}}\text{)}$ largely exceeds $\text{σ(}\text{K}{}^{\mathrm{1?}}\text{)}$ at these energies and this excess is interpreted as K¹⁺ production by beam and target fragmentations. The decays of K^1±0 yield ～30% of the K⁰ observed in the final states. The p_T² dependence of both K¹⁺ and K^1? cross sections is described by an exponential with slope of ～3.3 (GeV/c)^?2. The longitudinal momentum spectra for K¹⁺ in 16 GeV/cπ⁺p and 24 GeV/c pp interactions are similar in shape in the target hemisphere. The K^1? spectra are similar over the whole kinematic region when viewed in the quark c.m.s. and point to a central production mechanism. Comparing K¹⁺ and ρ⁰ production, striking similarities are found.     

Search for 4n IN π− double charge exchange reactions with heavy nuclei

A search for the existence of the tetraneutron has been made using the double charge exchange reaction $\text{π}{}^{\mathrm{?}}\text{+}{}^{208}\text{Pb}\text{→}{}^4\text{n + π}{}^{\mathrm{+}}\text{+}$ residuals for ⁴n production and the capture process in the same target, ${}^{208}\text{Pb}\text{+}{}^4\text{n}\text{→}{}^{212}\text{Pb}\text{+ γ}$, for the ⁴n detection. No event has been found, giving an upper limit for the product of the production cross section σ_p, the detection cross section σ_d and the ⁴n lifetime τ. Assuming 10^?18 ≦ τ ≦ 10^?9 sec it follows that σ_pσ_dτ ≦ 2.5 × 10^?65cm⁴ sec with 90 % confidence, and for $\text{τ ≧ 10}{}^{\mathrm{?9}}\text{sec}\text{, σ}{}_{\mathrm{<mtext>p</mtext>}}\text{σ}{}_{\mathrm{<mtext>d</mtext>}}\text{≦ 2.5 × 10}{}^{\mathrm{?56}}\text{cm}{}^4$ with 90 % confidence. The magnitude of this value is comparable to the experimental limit of the ⁴He(π^?, π⁺)⁴n cross section.     

Lorentz contracted geometrical model

The model assumes that when two high energy particles collide each behaves as a geometrical object which has a Gaussian density and is spherically symmetric except for the Lorentz-contraction in the incident direction. Folding the two spatial distribution together we obtain the slope (b) of the elastic diffraction peak in terms of the c.m. velocities (β_i and β_j) and the sizes (A_i and A_j) of the two incident particles. These sizes are assumed to have the experimental s-dependence of σ_tot ∝ πA² for each reaction. The combined s-dependence of the σ_tot's and the β's gives the s-dependence of the elastic slope $\text{b}{}_{\mathrm{ij}}\text{(s) =}\text{1}\text{2}\text{(A}{}_{\mathrm{i}}{}^2\text{β}{}_{\mathrm{i}}{}^2\text{+ A}{}_{\mathrm{j}}{}^2\text{β}{}_{\mathrm{j}}{}^2\text{)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(s)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(∞)}$. This formula agrees with the experimental slope for p-p, $\text{p}$-p, K⁺-p, K^?-p and π^±-p elastic scattering from 3 to 1500 GeV/c, with only 3 parameters: A_π² = 6.1, A_K² = 3.3 and A_p² = 10.5 (GeV/c)^?2.     

Predissociation and Λ-doubling in the even-parity Rydberg states of the nitrogen molecule

Predissociations in the y¹Π_g and $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ Rydberg states of N₂ (configurations $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{4pσ}$ and $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{3pπ}$, respectively) and their likely causes, are discussed. Peaking of rotational intensity at unusually low J values, without sharp breaking off, is interpreted as due to case c^? or case cⁱ predissociation. Λ doubling in the y state, attributed to interactions with the $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state and with another, ¹Σ⁺, state of the same electron configuration as x, is analyzed. From this analysis the location of the (unobserved) ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state, here labeled x′, is obtained. It is concluded that the predissociation in the Π⁺ levels of the y state is an indirect one mediated by the interaction with x′ coupled with predissociation of x′ by a ${}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state dissociating to ${}^4\text{S +}{}^2\text{P}$ atoms: combined, however, with perturbation of the y state by the k¹Π_g Rydberg state (configuration $\text{3σ}{}_{\mathrm{g}}{}^{\mathrm{?1}}\text{4dπ}$), whose Π⁺ levels are completely predissociated.     

A t-channel isospin analysis of the chew-low plot for NN → N(Nπ) interactions at 5.7 GeV/c

A new approach to the t-channel isospin analysis of ZN → Z′(Nπ) reactions is presented. This approach, useful for $\text{Z = N,}\text{N}\text{, K}{}^{\mathrm{?}}$ when only five independent sets of data are availables, is used to analyse data of $\text{N}\text{N →}\text{N}\text{(Nπ)}$ reactions obtained in a $\text{p}\text{p →}\text{N}\text{N}\text{π}$ experiment at $\text{5.7}\text{GeV}\text{/c}\text{and a}\text{p}\text{d →}\text{N}\text{Nπp}{}_{\mathrm{s}}$ experiment at 5.5 GeV/c. the t behaviour of the different isospin exchange amplitudes, suggests their exchange mechanism production. The mass spectrum, M_πN, of the contributions produced by exchanged isospin I_ex = 1, shows enhancements corresponding to N(1490) N(1670) and Δ(1230) isobars, while the mass spectrum for I_ex = 0 presents only a large bump at ～1350 MeV commonly identified as N¹(1400).     

Multiplicity distributions and double-scattering effects in π−d interactions at 360 GeV/c

Double-scattering effects are studied in π^?d interactions at 360 GeV/c. The partial cross sections $\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(π}{}^{\mathrm{?}}\text{d}\text{), σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{p}\text{”)}\text{and}\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{n}\text{”)}$ are presented. The double-scattering probability per πd collision is found to be $\text{? = 0.15 ± 0.02}$. We have extracted the partial cross section X_N of the double-scattering plus interference contributions, and find that X_N obeys KNO scaling. The data are compared with various theoretical predictions.     

A study of the reaction pp → π− π+ at 10 GeV/c

The reaction $\text{p}\text{p}\text{→ π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ has been studied at 10.1 GeV/c in the ?t interval from 0.15 to 1.5 (GeV/c)². A line-reversal comparison with backward elastic scattering π⁺p → pπ⁺ shows good agreement for ?t > 0.3 (GeV/c)².     

Energies and orbital sizes for some Rydberg and valence states of the nitrogen molecule

Accurate SCF computations are reported on the Rydberg states of N₂ of electron configurations $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$, $\text{---1π}{}_{\mathrm{u}}{}^3\text{3σ}{}_{\mathrm{u}}$, and ---3σ_g2π_g, also on the valence states of the configuration $\text{---1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$. The Rydberg state calculations supplement those of Lefebvre-Brion and Moser. A comparison is made between the $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ states and the parallel set of states of the $\text{1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$ configuration. This comparison shows a sharp difference in the ¹Σ⁺ states of the two configurations, the ¹Σ⁺ state being very high in the latter but relatively low in the former configuration. Recknagel coefficients are given for the several states of the two configurations; as expected, these are much smaller for the $\text{1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ configuration. Also, the ¹Δ state is relatively lower for the latter configuration.     

The reaction pp→pπ−π+p at 25 and 40 GeV/c

The reaction $\text{p}\text{p}\text{→}\text{p}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}\text{p}$ has been studied at 25 and 40 GeV/c at the Serpukhov proton synchroton using the CERN-IHEP spectrometer. The differential cross section has been determined as a function of four-momentum transfer to the proton (0.05–0.30 (GeV/c)²) and $\text{p}\text{ππ}$ mass (up to 2.2 and 2.6 GeV/c²). At both energies there is a broad low-mass maximum with an enhancement at 1.6–1.8 GeV/c². The cross section in a given mass band falls rapidly with |t|, with an exponential slope that decreases with increasing mass. In both the background and the 1.7 GeV/c² peak there is a strong $\text{Δ}{}^{\mathrm{??}}\text{π}{}^{\mathrm{+}}$ component. Possible spin-parity (J^P) contributions to it are discussed. Throughout the range 1.5–2.2 GeV there is at least one state of $\text{J ?}\text{3}\text{2}$ and there is interference between states of opposite P, |ΔJ| ? 1. At the peak there is a $\text{J ?}\text{5}\text{2}$ component. There are striking parallels between this reaction and the boson reactions π^?p→π^?π^?π⁺p and K^? → K^?π^?π⁺p.     

Evidence for double dissociation in K-p interactions at 14.3 GeV/c

We have studied the reaction K^-p → K^-π⁺π^-π⁺π^-p at 14.3 GeV/c to search for evidence of the double dissociation process $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{QN}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1$. In the channel $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{K}{}^{10}\text{(890)}$π₁^-π₂^-Δ⁺⁺ (1236) there is evidence for simultaneous production of low-mass enhancements in the $\text{K}{}^{10}\text{π}{}_1{}^{\mathrm{-}}$ and Δ⁺⁺(1236)π₂^- subsystems which correspond to the $\text{Q}\text{→}\text{K}{}^1\text{(890)π}$ and $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1\text{→ Δπ}$ decay modes. In this particular final state the double fragmentation system is produced with a cross section of the order of a few microbarns. Our data are consistent with the factorizable pomeron exchange model of double diffractive dissociation.     

Inclusive strange particle production in π−p interactions at 6 GeV/c

The inclusive production of Λ, K_S⁰, Σ^±(1385) and $\text{K}{}^{\mathrm{1\pm }}\text{(892)}$ in π^?p interactions at 6 GeV/c has been studied. The observed cross sections are: σ(Λ)=0.94±0.06 mb, σ(K_S⁰)=0.98±0.06 mb, σ(Σ⁺(1385))=60±7 μb, σ(Σ^?(1385))=90±9 μb, $\text{σ(}\text{K}{}^{\mathrm{1+}}\text{(892))=216±28 μ}\text{b and}\text{σ(}\text{K}{}^{\mathrm{1?}}\text{(892))=41±8 μ}\text{b}$, respectively. The inclusive spectra of these particles are presented as functions of squared transverse momentum and Feynman scaling variable x. The polarization of Λ has also been investigated. It is found from a comparison with higher-energy data that the inclusive cross sections for Σ^±(1385) and the production ratios Σ^±(1385)/Λ in π^?p at 6 GeV/c have not reached the high-energy limiting values.