arXiv subjects
Publications and source records attributed to Göran Fäldt.
In two earlier papers it was demonstrated that Lorentzian and Galilean symmetries could both be useful in the analysis of the annihilation reaction $e^+ e^- \to γΛ(\rightarrow pπ^-) \barΛ(\rightarrow \bar{p}π^+)$. It was also demonstrated that any pair of hyperon form factors would be acceptable, but that the $\{G_E, G_M\}$ pair would probably be the simplest one to handle.
We have previously investigated joint $Λ\barΛ$ decay in the reaction $e^+ e^- \rightarrow γΛ(\rightarrow pπ^-) \barΛ(\rightarrow \bar{p}π^+)$. The cross-section-distribution functions encountered were relativistically covariant and expressed in terms of scalar products of the four-momentum vectors of the particles involved. In the present, sequel investigation, we show that by working with three-momentum scalars instead results could possibly become more transparant.
We investigate roads for evaluating model-independent cross-section distributions for the sequential hyperon decay $Σ^0\rightarrowΛγ;Λ\rightarrow pπ^- $ and its corresponding antihyperon decay. The hyperons are produced in the reaction $e^+e^-\rightarrow J/ψ\rightarrow Σ^0\barΣ^0$. Cross-section distributions are calculated using the folding technique.
We report on a study of the sequential hyperon decay $Σ^0\rightarrowΛγ;Λ\rightarrow pπ^- $ and its corresponding anti-hyperon decay. We derive a multi-dimentional and model-independent formalism for the case when the hyperons are produced in the reaction $e^+e^-\rightarrowΣ^0\barΣ^0$. Cross-section distributions are calculated using the folding technique. We also study sequential decays of single-tagged hyperons.
Using the helicity formalism of Jacob and Wick we derive spin density matrices of baryon antibaryon pairs produced in $e^+e^-$ annihilation. We consider the production of pairs with spins $1/2+\overline{1/2}$, $1/2+\overline{3/2}$ (+c.c.) and $3/2+\overline{3/2}$. We provide modular expressions to include chains of weak hadronic two-body decays of the produced hyperons. The expressions are suitable for the analysis of high statistics data from $J/ψ$ and $ψ(2S)$ decays at $e^+e^-$ colliders, by fits to the fully differential angular distributions of the measured particles. We illustrate the method by examples, such as the inclusive measurement of the $e^+e^-\toψ(2S)\toΩ^-\barΩ^+$ process where one decay chain $Ω^-\toΛK^-$ followed by $Λ\to pπ^-$ is considered. Finally we show that the inclusive angular distributions can be used to test spin assignment of the produced baryons.
We investigate production and decay of the $Λ_c^+ $ hyperon. The production considered is through the $e^+e^-$ annihilation channel, $e^+e^-\rightarrowΛ_c^+ \barΛ_c^-$, with summation over the $\barΛ_c^- $ anti-hyperon spin directions. It is in this situation that the $Λ_c^+ $ decay chain is identified. Two kinds of sequential decays are studied. The first one is the doubly weak decay $B_1\rightarrow B_2 M_2$, followed by $B_2 \rightarrow B_3 M_3$. The other one is the mixed weak-electromagnetic decay $B_1\rightarrow B_2 M_2$, followed by $B_2 \rightarrow B_3 γ$. In both schemes $B$ denotes baryons and $M$ mesons. We should also mention that the initial state of the $Λ_c^+ $ hyperon is polarized.
Cross-section distributions are calculated for the reaction $e^+ e^- \rightarrow J/ψ\rightarrow \barΛ(\rightarrow \bar{p}π^+) Λ(\rightarrow pπ^-)$, and related annihilation reactions mediated by vector mesons. The hyperon-decay distributions depend on a number of structure functions that are bilinear in the, possibly complex, psionic form factors $G_M^ψ$ and $G_E^ψ$ of the Lambda hyperon. The relative size and relative phase of these form factors can be uniquely determined from the unpolarized joint-decay distributions of the Lambda and anti-Lambda hyperons. Also the decay-asymmetry parameters of Lambda and anti-Lambda hyperons can be determined.
Cross-section, vector-polarization, and tensor-polarization distributions are calculated for the reactions $e^+ e^- \rightarrow \bar{p}p$ and $e^+ e^- \rightarrow \barΛ Λ$. Each reaction requires six characteristic functions that are bilinear in the, possibly complex, electromagnetic form factors, denoted $G_E(P^2)$ and $G_M(P^2)$, of $p$ and $Λ$. For the hyperon reaction also the joint-decay distributions of $Λ$ and $\barΛ$ are calculated. Their knowledge allow a complete determination of the hyperon electromagnetic form factors, without measuring hyperon spins. We explain how this is done in practice. For some tensor-polarization components our results are in conflict with previously repeatedly published distributions.
We investigate the joint $Λ\barΛ$ decay in the reaction $e^+ e^- \rightarrow γΛ(\rightarrow pπ^-) \barΛ(\rightarrow \bar{p}π^+)$. This reaction may provide information on the electromagnetic form factors of the Lambda baryon, in the time-like region. We present a conventional diagram-based calculation where production and decay steps are coherent and summations over final-state proton and anti-proton spins are performed. The resulting cross-section distribution is explictly covariant as it is expressed in scalar products of the four-momentum vectors of the participating particles. We compare this calculation with that of the folding method which we extend and make explicitly covariant. In the folding method production and decay distributions, not amplitudes, are folded together. Of particular importance is then a correct counting of the number of possible intermediate-hyperon-spin states.
Pion-nucleus bremsstrahlung offers a possibility of measuring the structure functions of pion-Compton scattering from a study of the small-momentum-transfer region where the bremsstrahlung reaction is dominated by the single-photon-exchange mechanism. The corresponding cross-section distribution is characterized by a sharp peak at small momentum transfers. But there is also a hadronic contribution which is smooth and constitutes an undesired background. In this communication the modification of the single-photon exchange amplitude by multiple-Coulomb scattering is investigated as well as the Coulomb-nuclear interference term.
Pseudoscalar mesons can be produced and studied in high-energy electron-nucleus scattering. We review and extend our previous analysis of meson production in the nuclear Coulomb field. The $P\rightarrow γγ$ decay rates are most directly determined for mesons produced in the double-Coulomb region where both photons are nearly real, and provided the background-hadronic contribution remains small. The larger the mass of the meson the higher the electron energy needed to assure such a condition.
Experimental studies of meson production through two-photon fusion in inelastic electron-nucleus scattering is now under way. A high-energy photon radiated by the incident electron is fused with a soft photon radiated by the nucleus. The process takes place in the small-angle-Coulomb region of nuclear scattering. We expound the theory for this production process as well as its interference with coherent-radiative-meson production. In particular, we investigate the distortion of the electron wave function due to multiple-Coulomb scattering.
The coherent-nuclear reaction a + A -> a* + A is in the small-angle region dominated by the one-photon-exchange mechanism, often referred to as the Primakoff effect. In this region information about the electromagnetic decay a* -> a + gamma can be obtained. Well-known examples are the two-photon decays of the pi- and eta-mesons. Also decays of charged hadrons can be studied. For charged hadrons the one-photon-exchange amplitude comes with a Coulomb-phase factor and a Coulomb-form factor, which depend on the ratio between transverse- and logitudinal-momentum transfers, the latter being fixed. At the peak of the cross-section distribution, where the two momentum transfers are equal, the form factor could cut down the cross-section value by as much as 40 %. Consequently, a determination of a radiative-decay rate that relies on the peak value becomes sensitive to a proper treatment of the Coulomb-form factor.
The pion-polarizability functions are structure functions of pion-Compton scattering. They can be assessed in high-energy pion-nucleus bremsstrahlung reactions, $π^- +A\toπ^- +γ+A$. We present numerical expectations for pion-nucleus bremsstrahlung cross sections in the Coulomb region, i.e. the small-angle region where the nuclear scattering is dominated by the Coulomb interaction. We investigate the prospects of measuring the polarizability functions for pion-Compton c.m. energies from threshold up to 1 GeV. A meson-exchange model is used for the pion-Compton amplitude.
Hard high-energy pion-nucleus bremsstrahlung, $π^- +A\toπ^- +γ+A$, is studied in the Coulomb region, i.e. the small-angle region where the nuclear scattering is dominated by the Coulomb interaction. Special attention is focussed on the possibility of measuring the pion polarizability in such reactions. We study the sensitivity to the structure of the underlying the pion-Compton amplitude through a model with $σ$, $ρ$, and a_1 exchanges. It is found that the effective energy in the virtual pion-Compton scattering is often so large that the threshold approximation does not apply.
A model for high-energy, small-angle pion-nucleus bremsstrahlung, $ π^- +A\toπ^- +γ+A$,is developed within the Glauber diffraction theory. Special attention is focussed on the possibility of measuring the pion polarisability in such reactions. That is the case under the Coulomb peak provided the bremsstrahlung photon carries practically all the energy of the incident pion. Only radiation from external legs is considered.
CP violation leads to a difference between the parameters $g^+$ and $g^-$ describing the energy distributions of the charged pions produced in the $K^+ \toπ^0 π^0 π^+$ and $K^- \to π^0π^0 π^-$ decays. We study the difference $(g^+ - g^-)$ as a function of the relative contributions from the QCD-penguin and the electroweak-penguin diagrams. We find that the combination of these contributions in $(g^+ - g^-)$ is very similar to the corresponding one defining the parameter $ε'$ in the $K_L \to 2π$ decays. This observation allows a determination of the value of $(g^+ - g^-)$, using data on $ε'$.
We evaluate, in the high-energy limit, $s\gg|t|\gg m^2\ggλ^2$, the sum of amplitudes corresponding to a class of Feynman diagrams describing two-loop virtual photonic corrections to Bhabha scattering. The diagrams considered are box and crossed box diagrams with a vacuum polarization insertion in one of the photon lines.