Factorizable dual model of pions
Abstract
A new dual-resonance model of mesons is constructed through the use of creation and annihilation operators having simple anticommutation properties as well as harmonic-oscillator type operators of the conventional model. This model has the following virtues not shared by the conventional one: (i) The leading trajectory (ϱ-f 0) does not make a particle when it passes through zero. (ii) A π-trajectory lies one-half unit below the ϱ-trajectory. (iii) Trajectories with abnormal-parity couplings to pions, such as ω-A 2 and η', also occur. (iv) The gp, ϱ, f 0, ω, A 2 and η' are all forced to have the proper G-parity and isospin. (v) The amplitudes for ππ→ ππ and ππ→ πω are precisely the ones that have been suggested previously. (vi) The model contains neither embarrassing unobserved low-mass states nor an excessive number of high-mass states. (vii) All the physical states that we have checked have positive norms. To be fair, we should also list some shortcomings of our model: (a) Trajectories with normal-parity couplings occur one-half unit too high. Thus, for example, α ϱ(0) = 1 and α π(0) = {1}/{2}, so that the π is a tachyon and the ϱ massless. On the other hand, the abnormal-parity trajectories are nicely located. For example, α ω(0) = {1}/{2}and α η'(0) = -1 . (b) A straightforward generalization to SU(3) is unsatisfactory because of the non-degeneracy of the ϱ and ω. These features of the model clearly indicate that it is not accurately describing the real world. Perhaps its most important property is that it contains a gauge algebra larger than the Virasoro algebra of the conventional model. We believe that an understanding of this algebra may prove to be very important in the construction of more realistic models.
- Publication:
-
Nuclear Physics B
- Pub Date:
- August 1971
- DOI:
- 10.1016/0550-3213(71)90448-2
- Bibcode:
- 1971NuPhB..31...86N