Initial Meson Research Articles

Cross sections for inelastic K+ϕ scattering* *Supported by the National Natural Science Foundation of China (11175111)

In the first Born approximation, we study the reactions , , , and with quark-antiquark annihilation and creation. Transition amplitudes are derived with the development in the spherical harmonics of the relative-motion wave functions of two initial mesons and two final mesons so that parity is conserved and the total angular momentum of the final mesons equals that of the initial mesons. Unpolarized cross sections are calculated from the transition amplitudes that also contain mesonic quark-antiquark relative-motion wave functions and transition potentials for quark-antiquark annihilation and creation. The notable temperature dependence of the cross sections is shown. The cross sections for , , and may be of the millibarn scale, whereas the cross section for is small.

Meson production from kink-meson scattering

In a ($1+1$)-dimensional scalar quantum field theory, we calculate the leading-order probability of meson multiplication, which is the inelastic scattering process: $\mathrm{kink}+\text{meson}$ $\ensuremath{\rightarrow}$ kink $+2$ mesons. We also calculate the differential probability with respect to the final meson momenta and the probability that one or two of the final mesons recoils back towards the source. In the ultrarelativistic limit of the initial meson, the total probability tends to a constant, which we calculate analytically in the ${\ensuremath{\phi}}^{4}$ model. At this order the meson sector conserves energy on its own, while the incoming meson applies a positive pressure to the kink. This is in contrast with the situation in classical field theory, where Romanczukiewicz and collaborators have shown that, in the presence of a reflectionless kink, only meson fusion is allowed, resulting in a negative radiation pressure on the kink.

Entanglement generation in(1+1)DQED scattering processes

We study real-time meson-meson scattering processes in $(1+1)$-dimensional QED by means of Tensor Networks. We prepare initial meson wave packets with given momentum and position introducing an approximation based on the free fermions model. Then, we compute the dynamics of two initially separated colliding mesons, observing a rich phenomenology as the interaction strength and the initial states are varied in the weak and intermediate coupling regimes. Finally, we consider elastic collisions and measure some scattering amplitudes as well as the entanglement generated by the process. Remarkably, we identify two different regimes for the asymptotic entanglement between the outgoing mesons: it is perturbatively small below a threshold coupling, past which its growth as a function of the coupling abruptly accelerates.

Cross sections for 2-to-1 meson\u2013meson scattering

We study the processes K{bar{K}} rightarrow phi , pi D rightarrow D^*, pi {bar{D}} rightarrow {bar{D}}^*, and the production of psi (3770), psi (4040), psi (4160), and psi (4415) mesons in collisions of charmed mesons or charmed strange mesons. The process of 2-to-1 meson–meson scattering involves a quark and an antiquark from the two initial mesons annihilating into a gluon and subsequently the gluon being absorbed by the spectator quark or antiquark. Transition amplitudes for the scattering process derive from the transition potential in conjunction with mesonic quark–antiquark wave functions and the relative-motion wave function of the two initial mesons. We derive these transition amplitudes in the partial wave expansion of the relative-motion wave function of the two initial mesons so that parity and total-angular-momentum conservation are maintained. We calculate flavor and spin matrix elements in accordance with the transition potential and unpolarized cross sections for the reactions using the transition amplitudes. Cross sections for the production of psi (4040), psi (4160), and psi (4415) relate to nodes in their radial wave functions. We suggest the production of psi (4040), psi (4160), and psi (4415) as probes of hadronic matter that results from the quark–gluon plasma created in ultrarelativistic heavy-ion collisions.

Cross sections for inelastic 2-to-2 meson-meson scattering in hadronic matter * * National Natural Science Foundation of China (11175111)

With quark-antiquark annihilation and creation in the first Born approximation, we study the reactions: , , , , , , , , , , , and . Unpolarized cross sections for the reactions are obtained from transition amplitudes that are composed of mesonic quark-antiquark relative-motion wave functions and the transition potential for quark-antiquark annihilation and creation. Using a quark-antiquark potential that is equivalent to the transition potential, we prove that the total spin of the two final mesons may not be equal to the total spin of the two initial mesons. Based on flavor matrix elements, cross sections for some isospin channels of reactions can be obtained from other isospin channels of the reactions. Remarkable temperature dependence of the cross sections was observed.

Cross sections for inelastic meson-meson scattering

We study two kinds of inelastic meson-meson scattering. The first kind is inelastic 2-to-2 meson-meson scattering that is governed by quark interchange as well as quark-antiquark annihilation and creation. Cross-section formulas are provided to get unpolarized cross sections for $\pi K \to \rho K^\ast$ for $I=1/2$, $\pi K^\ast \to \rho K$ for $I=1/2$, $\pi K^\ast \to \rho K^\ast$ for $I=1/2$, and $\rho K \to \rho K^\ast$ for $I=1/2$. Near threshold, quark interchange dominates the reactions near the critical temperature. The second kind is 2-to-1 meson-meson scattering with the process that a quark in an initial meson and an antiquark in another initial meson annihilate into a gluon and subsequently the gluon is absorbed by the other antiquark or quark. The transition potential for the process is derived. Four Feynman diagrams at tree level contribute to the 2-to-1 meson-meson scattering. Starting from the $S$-matrix element, the isospin-averaged unpolarized cross section with transition amplitudes is derived. The cross sections for $\pi \pi \to \rho$ and $\pi K \to K^*$ decrease with increasing temperature.

Two-body strong decay of Z(3930) as the χ c2(2P) state

The new particle Z(3930) found by the Belle and BaBar Collaborations through the $\gamma\gamma\rightarrow D\bar D$ process is identified to be the $\chi_{c2}(2P)$ state. Since the mass of this particle is above the $D\bar D^{(\ast)}$ threshold, the OZI-allowed two-body strong decays are the main decay modes. In this paper, these strong decay modes are studied with two methods. One is the instantaneous Bethe-Salpeter method within Mandelstam formalism. The other is the combination of the $^3P_0$ model and the former formalism. The total decay widths are 26.3 and 27.3 MeV for the methods with or without the $^3P_0$ vertex, respectively. The ratio of $\Gamma_{D\bar D}$ over $\Gamma_{D\bar D^\ast}$ which changes along with the mass of the initial meson is also presented.

Role of quark-interchange processes in evolution of mesonic matter

We divide the cross section for a meson-meson reaction into three parts. The first part is for the quark-interchange process, the second for quark-antiquark annihilation processes and the third for resonant processes. Master rate equations are established to yield time dependence of fugacities of pions, rhos, kaons and vetor kaons. The equations include cross sections for inelastic scattering of pions, rhos, kaons and vector kaons. Cross sections for quark-interchange-induced reactions, that were obtained in a potential model, are parametrized for convenient use. The number densities of pion and rho (kaon and vector kaon) are altered by quark-interchange processes in equal magnitudes but opposite signs. The master rate equations combined with the hydrodynamic equations for longitudinal and transverse expansion are solved with many sets of initial meson fugacities. Quark-interchange processes are shown to be important in the contribution of the inelastic meson-meson scattering to evolution of mesonic matter.

Temperature-dependent cross sections for meson–meson nonresonant reactions in hadronic matter

We present a potential of which the short-distance part is given by one gluon exchange plus perturbative one- and two-loop corrections and of which the large-distance part exhibits a temperature-dependent constant value. The Schrödinger equation with this temperature-dependent potential yields a temperature dependence of the mesonic quark–antiquark relative-motion wave function and of meson masses. The temperature dependence of the potential, the wave function and the meson masses brings about temperature dependence of cross sections for the nonresonant reactions π π → ρ ρ for I = 2 , K K → K * K * for I = 1 , K K * → K * K * for I = 1 , π K → ρ K * for I = 3 / 2 , π K * → ρ K * for I = 3 / 2 , ρ K → ρ K * for I = 3 / 2 and π K * → ρ K for I = 3 / 2 . As the temperature increases, the rise or fall of peak cross sections is determined by the increased radii of initial mesons, the loosened bound states of final mesons, and the total-mass difference of the initial and final mesons. The temperature-dependent cross sections and meson masses are parametrized.

Strong two-body decays of light mesons

In this paper, we present results on strong two-body decay widths of light $q\bar q$ mesons calculated in a covariant quark model. The model is based on the Bethe-Salpeter equation in its instantaneous approximation and has already been used for computing the complete meson mass spectrum and many electroweak decay observables. Our approach relies on the use of a phenomenological confinement potential with an appropriate spinorial Dirac structure and 't Hooft's instanton--induced interaction as a residual force for pseudoscalar and scalar mesons. The transition matrix element for the decay of one initial meson into two final mesons is evaluated in lowest order by considering conventional decays via quark loops as well as Zweig rule violating instanton--induced decays generated by the six--quark vertex of 't Hooft's interaction; the latter mechanism only contributes if all mesons in the decay have zero total angular momentum. We show that the interference of both decay mechanisms plays an important role in the description of the partial widths of scalar and pseudoscalar mesons.

Right-handed currents in rare exclusive decays

The effects of possible right-handed weak hadronic currents in rare exclusive semileptonic decays B -> (K, K*) nu bar{nu} are investigated using a lattice-constrained dispersion quark model for the calculation of the relevant mesonic form factors. The results obtained for the branching ratios and the missing energy spectra are presented and the sensitivity of various observables to long-distance physics is investigated. It is shown that the asymmetry of transversely polarized K*(T) mesons as well as the K / K*(T) production ratio are only slightly sensitive to long-distance contributions and mostly governed by the relative strength and phase of right-handed currents. In particular, within the Standard Model the production of right-handed K*(T) mesons turns out to be largely suppressed with respect to left-handed ones, thanks to the smallness of the final to initial meson mass ratio. Therefore, the measurement of produced right-handed K*(T) mesons in rare B -> K* nu bar{nu} decays offers a very interesting tool to investigate right-handed weak hadronic currents.

Pion and eta photoproduction in nuclei

We calculate the quasifree photoproduction of pions and eta mesons on nuclei from12C to208Pb. Assuming that for the quasifree process the cross sections forπ/η photoproduction on a nucleon in medium are — besides a lowering due to Pauli blocking — identical to those on a free nucleon, we use these as an input. The produced mesons or resonances then propagate through the nucleus where they can undergo several scattering and absorption processes. This final state interaction, which leads to a lowering of the initial meson yield up to 70%, we simulate in a coupled channel Boltzmann-Uehling-Uhlenbeck transport model. It allows us to study in detail the influence of Fermi motion, Pauli blocking and of the additional decay channels for nucleon resonances in medium on the photoproduction cross section. The calculated total and differential cross sections are compared to experimental data and the influence of the different medium effects on the cross sections is discussed in detail.

Primary populations in mesonic hydrogen atoms

Cross sections for the formation of mesonic hydrogen have been calculated in the Born approximation with the complete perturbation operator and its dipole part. The dependence of the cross section on the initial meson energy and final state quantum number has been studied. Primary populations of mesonic atom levels have been calculated taking the competition between the moderation and the atomic capture of mesons into account. The population distribution over n extends deep into the range of large n. The Cnl distributions have maxima at intermediate values of l=l0 (dependent upon the meson mass) and fall off abruptly when l>l0. The primary alignment of the angular momentum of the mesonic atom is close to the limiting value corresponding to the zero-order projection of the angular momentum.

Quark Model for Meson-Baryon Processes

An SU(3)-invariant model of the elastic quark (Q) meason (pseudoscalar) scattering amplitude is proposed in the spirit of an impulse approximation, for the description of meson-baryon scattering and production processes involving both the positive- and negative-parity baryons looked upon as 3Q composites. The mesons are looked upon as elementary particles, rather than QQ¯ composites. The positive-parity baryons are assumed to belong to the 56 representation of SU(6), and the negative parity ones to the (70,3) representation of SU(6)⊗O(3). The results for the scattering and production amplitudes are expressed in the form of sum rules connecting physically interesting processes. We obtain several sum rules for the elastic scattering amplitudes which agree with the Johnson-Treiman and Lipkin relations. For production processes within the 56 of baryons, some of our results, which do not agree with SU(6) or SU(6) W , are at least not disfavored by experiment compared with the latter. A number of relations among amplitudes connecting production of negative-parity baryonic states are also obtained, but these cannot be tested experimentally at this stage. A slight variant of the model, in which the initial meson is replaced by a spurion octet, reproduces in a natural way all the known sum rules for nonleptonic decays of ∑, Λ, and Ξ. For the Ω - decay to Ξπ and Ξ * π systems, the predictions of the model are, however, different from those of SU(6) or of partially conserved axial-vector current with equal-time commutators.

X-Ray Deficiency in Mesonic Atoms

We present an analysis of $\ensuremath{\pi}$-mesonic atoms, based upon cascade calculations taking into account the known processes of radiation, Auger transitions, and nuclear absorption. This analysis, together with the previous one on $\ensuremath{\mu}$-mesonic atoms, is intended to provide a deeper insight into the unsolved problem of the deficiency of x rays in mesonic atoms. It is shown that the $\ensuremath{\pi}$-mesonic $L$ x-ray yields (for $Z\ensuremath{\le}20$) are quite insensitive to the strength of nuclear absorption and depend only upon the chosen initial meson population of the higher levels. Similarly, the ratios of basic (${K}_{\ensuremath{\alpha}}$, ${L}_{\ensuremath{\alpha}}$, etc.) to higher x-ray yields, both for $\ensuremath{\mu}$ and $\ensuremath{\pi}$ mesons, depend strongly on the initial distribution. The best agreement between the calculations and experiment was obtained for a "modified statistical" initial population of the form $(2l+1){e}^{\mathrm{al}}$, with $a=0.2$, in the $n=14$ level. From the existing experimental data on $\ensuremath{\pi}$-mesonic $K$ x rays, the mean life of the $\ensuremath{\pi}$ meson in nuclear matter was deduced: ${\ensuremath{\tau}}_{c}=2.75\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}$ sec. Within the framework of the present theory we are still unable to account for the x ray deficiency in the light atoms. However, it is shown that the quantum loss as a function of energy is different for $\ensuremath{\pi}$- and $\ensuremath{\mu}$-mesonic atoms, and therefore it is very probably due to a real physical effect. Furthermore, by comparing our predicted Auger electron yields with the experimental data, we can rule out any hypothetical simple Auger process in which the full energy of the "missing" quantum is given to a single electron.

On the μ-mesonic atoms

In an attempt to get a deeper insight into the problem of the « missing X-rays » in the capture ofμ-mesons in the light elements, a complete cascade calculation of theμ-meson transitions in the mesonic atom was conducted. The results indicate again that the calculatedK X-ray yields belowZ=6 and theL X-ray yields belowZ=14 are much above the experimental values. As was noted before by other authors, the deficiency of X-rays increases linearly with decreasing quantum energy between about 90 keV and 20 keV. The experimental yields agree with the calculations above 90 keV, and are lower than the calculated values, by a factor of about 5, at 20 keV. Good agreement between the calculations and experiment is obtained, however, for the (approximately energy-independent) ratios of the higher to basic X-ray yields, provided that a proper choice of the initial meson distribution is made. A comparison between the calculated Auger electron yields and the experimental results forμ−-capture in nuclear emulsions seems to indicate that the « mixed » Auger-radiative transitions introduced by Ruderman are indeed effective (apparently close to 100%) in the de-excitation of the metastable 2s level in CNO. If this mixed transitions play the same role also in the lightest elements (Li, Be, B), the problem of the « missing » X-rays becomes more serious than before. The expected Auger electron spectrum forμ−-capture in the heavy elements (AgBr) of nuclear emulsion has also been calculated.

Meson NucleonS scattering and crossing theorem

It is noticed that the low energyS wave calculations of meson nucleon scattering cannot be very satisfactory if they do not obey the « crossing theorem ». It may be interesting to modify the iteration treatments in order to satisfy the symmetry requirements. For this purpose the series of scattering processes considered is completed by a new series in which the initial meson and the final meson are exchanged. In this way, we generalize Levy’s covariant treatment ofS wave scattering. The result of the calculation is deeply modified by the introduction of these new processes. It is not possible to get a quantitative agreement with experiment. The signs of the phase shifts, however, are correct near G2/4π = 15. The approximations used in solving the integral equations are discussed by comparison with other calculations.

Radiation Accompanying Meson Creation

Electromagnetic radiation is expected to accompany the creation of charged mesons in nucleon-nucleon collisions. The amount and character of this radiation is calculated for mesons of spin 0, $\frac{1}{2}\ensuremath{\hbar}$, and $\ensuremath{\hbar}$, in each case with normal magnetic moment. The ratio of radiated energy to initial meson energy increases logarithmically for high meson energy in the first two cases, and is of the order of 1 percent for the highest energies of interest in cosmic radiation. For vector (spin $\ensuremath{\hbar}$) mesons, this ratio is $(\frac{11\ensuremath{\alpha}}{4860\ensuremath{\pi}}){(\frac{E}{m{c}^{2}})}^{4}$ in the relativistic region, where $\ensuremath{\alpha}$ is the fine-structure constant, and $m$ and $E$ are the rest mass and the initial energy of the meson in the coordinate system in which the center of mass of the colliding nucleons is at rest. This is so large at high energies that the assumption that $\ensuremath{\pi}$-mesons have spin $\ensuremath{\hbar}$ would, with a plausible theory of the multiplicity of meson production, account for the observation of soft radiation in conjunction with energetic nuclear events.