Annihilation Diagrams Research Articles

Low-energy proton-antiproton scattering in the non-relativistic 3P 0 quark model

We are investigating low-energy proton-antiproton-scattering cross sections in the framework of a potential model. The nucleon-antinucleon interaction is assumed to have two parts. The short-range annihilation part is derived from a non-relativistic quark model where nucleon-antinucleon transitions involving two- and three-meson final states are taken into account. The underlying quark dynamics is ruled by annihilation diagrams, where quark-antiquark pairs are created or destroyed with vacuum quantum numbers ( 3P 0 in LS-coupling). The long- and medium-ranged elastic interaction is taken from a G-parity-transformed one-boson-exchange model for the nucleon-nucleon interaction. We present models, employing differing one-boson-exchange parts, as defined by the Bonn and the Paris potentials. We compare the results for the total, elastic, annihilation, charge-exchange and differential cross sections with the experimental data. We encounter an old shortcoming of microscopic models — albeit in a somewhat improved form: their inability to fully understand the total flux into the annihilation channels. We show that the annihilation cross section strongly depends on the elastic interaction.

Annihilation diagrams in two-body nonleptonic decays of charmed mesons.

In the pole-dominance model for the two-body nonleptonic decays of charmed mesons [ital D][r arrow][ital PV] and [ital D][r arrow][ital VV], it is shown that the contributions of the intermediate pseudoscalar and the axial-vector meson poles cancel each other in the annihilation diagrams in the chiral limit. In the same limit, the annihilation diagrams for the [ital D][r arrow][ital PP] decays vanish independently.

Comparison of 20 exclusive reactions at large t.

We report a study of 20 exclusive reactions measured at the AGS at 5.9 GeV/c incident momentum, 90\ifmmode^\circ\else\textdegree\fi{} center of mass. This experiment confirms the strong quark flow dependence of two-body hadron-hadron scattering at large angle. At 9.9 GeV/c an upper limit had been set for the ratio of cross sections for $\frac{(\overline{p}p\ensuremath{\rightarrow}\overline{p}p)}{(pp\ensuremath{\rightarrow}pp)}$ at 90\ifmmode^\circ\else\textdegree\fi{} c.m., with the ratio less than 4%. The present experiment was performed at lower energy to gain sensitivity, but was still within the fixed angle scaling region. A ratio $R(\frac{\overline{p}p}{pp)}\ensuremath{\approx}\frac{1}{40}$ was measured at 5.9 GeV/c, 90\ifmmode^\circ\else\textdegree\fi{} c.m. in comparison to a ratio near 1.7 for small angle scattering. In addition, many other reactions were measured, often for the first time at 90\ifmmode^\circ\else\textdegree\fi{} c.m. in the scaling region, using beams of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, ${K}^{\ifmmode\pm\else\textpm\fi{}}$, $p$, and $\overline{p}$ on a hydrogen target. There are similar large differences in cross sections for other reactions: $R(\frac{{K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\Sigma}}^{\ensuremath{-}}}{{K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\Sigma}}^{+}})\ensuremath{\approx}\frac{1}{12}$, for example. The relative magnitudes of the different cross sections are consistent with the dominance of quark interchange in these 90\ifmmode^\circ\else\textdegree\fi{} reactions, and indicate that pure gluon exchange and quark-antiquark annihilation diagrams are much less important. The angular dependence of several elastic cross sections and the energy dependence at a fixed angle of many of the reactions are also presented.

NONLEPTONIC DECAYS OF CHARMED MESONS INTO TWO PSEUDOSCALAR MESONS

We investigate the nonleptonic decay of charmed meson into two pseudoscalar mesons using the vector-dominance model, and compare the results with those obtained from the factorization model. In particular, we discuss the role of the annihilation diagrams in the two models.

Do [formula omitted]p annihilations at rest choose the Eightfold way?

Dynamical selection rules observed in p p annihilation at rest are linked to relations between SU(3) invariant amplitudes. The ϱπ puzzle, the K K suppression in P wave, and the unexplained production rates of πa 2 (1320) are shown to be manifestions of one SU(3) amplitude ratio. The dynamical selection rules observed in the production of strange mesons lead to symmetries in SU(3) amplitudes. We conjecture that these symmetries reflect the underlying quark-gluon dynamic. It is shown that the contribution of annihilation diagrams to important annihilation channels like ϱ 0 π 0 or ηω is small or vanishes. Hence rearrangement must play an important role. The use of SU(3) relations in the context of N N interactions has been critized since the small rate for strangeness production seems to imply very large SU(3) breaking effects. The weakness of this argument is pointed out.

Single weak boson production at TeV e +e − colliders

We present exact tree level matrix elements for all the single weak boson production processes to order e 3 in very high energy e +e − collisions; e +e − → e ± v (−) c W ∓, e +e − Z, v c v c Z and γγZ. The electron mass is kept finite so that the differential and total cross sections are accurate up to terms of order m e 2/ s. The weak boson distributions are compared with those obtained by the equivalent photon/electron approximation (EPA), which works reasonably well at high vector boson transverse momenta but fails at small transverse momenta for the processes e +e −→ e +e −Z and γγZ. A simple modification of the EPA formulae is found to give a reasonable overall description of the distributions for all the single weak boson production processes. Electron helicity-flip amplitudes are found to contribute at the percent level at most, which can be reproduced accurately by a novel collinear approximation with equivalent real photon or electron distributions in an electron. Interference effects between the annihilation and non-annihilation diagrams are found to be significant only below the weak boson pair production threshold. Also explained is a straightforward method to incorporate the leptonic and parton level hadronic decays of the weak bosons into the production amplitudes.

Interference effects in Kη and Kη′ decay modes of heavy mesons. Clues to understanding weak transitions and CP violation

Interference between amplitudes producing η and η′ mesons via their strange and nonstrange components give relative suppression factors of an order of magnitude in certain diagrams and can be used to identify penguin contributions to B→Kη and B→Kη′ decays as well as annihilation diagram contributions to corresponding D decays. Similar suppression factors also arise in D 0→π 0η and D 0→π 0η′ decays and in charmonium decays to K +K −η and K +K −η′.

The decay K +→ π+X in SU(2) × U(1) × U′(1) gauge theories

In the framework of SU(2) × U(1) × U′(1) gauge models we investigate the decay K +→ π + + X, where X is the light gauge boson corresponding to the U′(1) group. Contributions of the annihilation and spectator diagrams are taken into account. We discuss possibilities of the experimental observation of the X-bosons in the decays K +→ π + + X. It is shown that if the X boson is the carrier of a new long-range interaction (“the fifth force”), then the width of the process K +→ π + X is extremely small.

Precocious asymptotia and a universal description of hadron total cross sections for [formula omitted

The value reported (N.A. Amos et al., Phys. Rev. Lett. 63 (1989) 2784) forσ tot ( pp ) at s =1.8 TeV of 78.3±5.9 mb is less than two standard deviations from the value of 87.5 mb predicted in 1974 by a four-parameter “two-component pomeron” model (Nucl. Phys. B 214 (1983) 136) based on universality of meson-nucleon and baryon-nucleon scattering with all parameters fixed at that time by analysis of data below P lab =200 GeV c . This success in extrapolating so well from mesons to baryons and over two orders of magnitude in s without any adhustment of parameters suggests a possible universal approach to asymptopia which warrants further investigations, both theoretical and by experimental measurements of meson-nucleon total cross sections in the 500 GeV c range. The high energy fit is explainable if asymptotic hadron-nucleon scattering is universal and the dominant non-asymptotic contributions arise from simple quark annihilation and exchange diagrams. Then an asymptotic formula for σ tot is obtained by fitting low energy data in meson-nucleon channels like γp which have no contribution from these nonasymptotic diagrams and whose smooth monotonically increasing behavior for 2⩽P lab ⩽200 GeV c suggest early asymptopia.

Extended state model and group approach to new polynomials

The extended Kauffman state model is presented by introducing the annihilation diagrams. This new state model enables the authors to establish a connection between the Akutsu-Wadati type polynomials (1987) and the group approach of Witten (1988).

Something, but not much follows from the quark line rule in nucleon-antinucleon annihilations

Validity and consequences of the quark line rule (QLR) in nucleon (N)— antinucleon (¯N) annihilations into two or three mesons at LEAR energies are investigated. Recent data on proton-antiproton annihilation into anη orη′ together with additional non-strange pseudoscalar or vector meson (s) is used to successfully test the rule. We find that for present data any pseudoscalar meson mixing angle ΦPS restricted to −260<ΦPS<−2.20 is approximately consistent with the QLR. Since the assumptions leading to this test are valid in any present-day quark model of nucleon-antinucleon annihilation, improvement of the data will be of utmost importance. If proven valid, the QLR can be used to test if quark-antiquark annihilation dominates over quark exchange inN¯N → mesons at LEAR energies or vice versa. Previously proposed tests of the quark line diagrams (annihilation or rearrangement) describing the quark flavor flux under either of these assumptions are worked out. We investigate without a definite conclusion if dominance of annihilation over rearrangement is consistent with present data onp¯p → π0 π0,ηη, π0ρ0, π0ω, ηρ0,ηω, ρ0ρ0,ωω. As a main consequence, dominance of annihilation predicts without any ambiguity equality of the proton-antiproton annihilation cross sections σ(ωω) and σ(ρ0ρ0). Further consequences of dominance of either annihilation or rearrangement diagrams for proton-antiproton annihilation into two or three mesons are also worked out. We compare the predictions of the models we discuss to the sparse present data. It is emphasized that our predictions only exploit the quark flavor flux within the quark line diagrams that are assumed to dominate. They thus are independent of gluon contributions to these diagrams.

Annihilation contributions in a Wilson-loop formalism.

The neglected annihilation contributions in the Wilson-loop formalism of Eichten and Feinberg are defined and calculated. An annihilation time scale is introduced to discriminate the glueball contributions from true annihilation contributions to isoscalar-pseudoscalar-meson states. In this formalism it is found that there is no mixing between two quarkonium states with different quark masses through the annihilation diagram. In a fixed state the annihilation contributions oscillate as functions of the annihilation time scale, and so provide a possible mechanism to shift the mass of \ensuremath{\eta} upward instead of downward as in the QED case.

Minimal total cross section fore + e −→W + W −

The total cross section with the most general form for the gauge boson vertices is given at tree level for the processe + e −→W + W −. Each vertex is parametrized with 7 couplings and the minimum of the total cross section is studied in a wide energy range. Although there are large cancellations between the neutrino exchange diagram and the photon andZ annihilation diagrams, it is surprisingly not possible to get significantly below the standard model cross section for any value of the parameters.

Proton-antiproton annihilation in the quark model

The non-relativistic Quark Model is used to describe the proton-antiproton annihilation and scattering. We investigate which of the diagrams is dominant in the annihilation into three and two mesons. A very sensitive test for the dominance of the different rearrangement and annihilation diagrams is the annihilation into p-wave mesons. Different mechanisms for the annihilation/creation of a quark-antiquark pair are studied. The data clearly prefer the non-perturbative annihilation/ creation into or out of the vacuum ( 3P 0) compared to the annihilation/ creation into a gluon ( 3S 1). For the initial proton-antiproton state, we include the coupling to the delta and antidelta degrees of freedom. For the distortion of the initial state we use one of the one-meson exchange Bonn potentials applying G parity. The imaginary part is calculated from the annihilation into two and three mesons. A comparison with the data shows clearly that the non perturbative annihilation diagrams into two and three mesons are the dominant ones. This is also consistent with the observation that the non-perturbative annihilation of a quark-antiquark pair into the vacuum is stronger than the perturbative annihilation or creation into or out of a gluon. The agreement with the branching ratios of the proton-antiproton decay into mesons and the description of the proton-antiproton scattering and charge exchange cross sections is good.

Hyperfine structure of toponium due to Z0

Using the electroweak theory of Weinberg and Salam in conjunction with the Bethe-Salpeter formalism, the authors calculate the contribution of the Z0, both the exchange and annihilation diagrams, to the hyperfine structure of toponium. As a function of the Higgs mass, they also calculate the contribution of a single Higgs boson to the hyperfine structure. Furthermore, they examine both the electromagnetic and strong contribution to the hyperfine structure.

PSEUDOSCALAR QUARK ANNIHILATION DIAGRAM AND THE U(1) η0 MASS

We present a self-consistent second order gluon annihilation diagram calculation for the U(1) singlet η0 mass based on a once-subtracted dispersion relation. A value in the same range as the one obtained by particle mixing considerations is obtained.

Positronium versus the mirror universe

A mirror universe of fermions and forces isomorphic to but distinct from those we see couples directly to our universe only by gravity. Particles at any mass scale enjoying both normal and shadow forces forge an electromagnetic link (by radiative corrections) between the two universes such that mirror particles display conventional electric charges 10 −3–10 −5 e. This produces mixing between triplet positronium and its analogous mirror state through a one-photon annihilation diagram. Consequent effects are contrary to experiment. The possible existence of such a mirror universe is thereby excluded.

Spontaneous breakdown and the scalar nonet

In the context of the QCD quark model and on the basis of dynamical Bethe-Salpeter ladder graphs, we suggest that (i) the existence of the scalar q-barq hadron multiplet, like the pseudoscalar q-barq multiplet, is a direct consequence of dynamical spontaneous breakdown of chiral symmetry with a chiral-limiting nonstrange mass scale of m/sub sigmaNS//sup CL/ = 2m/sub dyn/ roughly-equal630 MeV, (ii) the lifting of the nonstrange sigma-delta degeneracy is expected from the s-wave quark-gluon annihilation diagram, and (iii) the observed sigma-S* mixing follows from the existence of the p-wave scalar quark-annihilation diagram. The resulting predicted 0q-barq nonet is then sigma(750 MeV), kappa(800), S*(980), and delta(985), in agreement with data for the resonant masses, the mixing angle, and also decay widths except for the kappa(800).

Nucleon-Antinucleon Optical Potential

A model has been constructed for nucleon-antinucleon annihilation which is of short range but is state (energy, spin, isospin, ...) dependent as dictated by the calculation of annihilation diagrams. This model fulfills general theoretical requirements and, at the same time, provides a good fit of the presently available pp-bar experimental data; better than the existing models which are state independent but effectively long ranged. The present results contradict the generally accepted claim that fitting the pp-bar data requires an effective long-ranged annihilation potential.

Central and diffractive components of charm production

To $\mathrm{O}({{\ensuremath{\alpha}}_{s}}^{2})$ in perturbative QCD one can identify two separate components in the production of heavy flavors such as charm: central $q\overline{q}\ensuremath{\rightarrow}c\overline{c}$, $\mathrm{gg}\ensuremath{\rightarrow}c\overline{c}$ and diffractive $\mathrm{qc}\ensuremath{\rightarrow}\mathrm{qc}$, $\mathrm{gc}\ensuremath{\rightarrow}\mathrm{gc}$. For diffractive production, QCD evolution is the source of charm quarks inside the colliding hadrons. With an estimated 0.5% charm momentum fraction at ${Q}^{2}\ensuremath{\simeq}4{{m}_{c}}^{2}$ from QCD evolution, a hard $x$ distribution of charm, and a resolution cutoff on gluonexchange contributions, the diffractive component reproduces the ${\ensuremath{\Lambda}}_{c}^{+}$ and $D$ cross sections observed at intermediate to large longitudinal $x$, both at Fermilab and at CERN ISR energies. The diffractive component also contributes to charm production near ${x}_{L}=0$. This explains the failures of previous analyses, based on annihilation diagrams alone, to account for the observed charm cross sections in the central region. Estimates are made of cross sections and ${x}_{L}$ dependences of $b$- and $t$-quark production up to $\stackrel{-}{\mathrm{pp}}$ collider energies.