Finite-Energy Sum Rules and Their Application toπNCharge Exchange

Abstract

We derive and discuss the finite-energy sum rules, which form consistency conditions imposed by analyticity on the Regge analysis of a scattering amplitude. Their finite form makes them particularly useful in practical applications. We discuss the various applications, emphasizing a new kind of bootstrap predicting the Regge parameters from low-energy data alone. We apply our methods to xiV charge exchange and are able to derive many interesting features of the high-energy amplitudes at various t. In particular, we establish the existence of zeros of the amplitudes and of additional p poles. On the basis of the finiteenergy sum rules and the analysis of the irN amplitudes, we present theoretical and experimental evidence that double counting is involved in the interference model, which adds direct-channel resonances to the exchanged Regge terms.

Gauge-String Dualities and some Applications

“…However, the pseudo-scalar mode we found breaks this symmetry: from the form of the perturbations (9.1) we see that δF (3) is even under the interchange of (θ1, φ1) with (θ2, φ2), while F (3) is odd; similarly δF (5) is odd while F (5) is even. Therefore, the scalar mode must also break the I symmetry because in the field theory it breaks the symmetry between expectation values of |A| and of |B|.…”

“…Empirical evidence for a string-like structure of hadrons comes from arranging mesons and baryons into approximately linear Regge trajectories. Studies of πN scattering prompted Dolen, Horn and Schmid [5] to make a duality conjecture stating that the sum over s-channel exchanges equals the sum over t-channel ones. This posed the problem of finding the analytic form of such dual amplitudes.…”

“…For τ ≫ 1 we may introduce another radial coordinate r defined by 5) and in terms of this coordinate we find ds 2 6 → dr 2 + r 2 ds 2 T 1,1 . The basis one-forms g i in terms of which this metric is diagonal are defined by…”

Boson-fermion confusion: the string path to supersymmetry

“…String Theory stems from the Dual Resonance Model, formulated to satisfy Dolen-Horn-Schmid duality [5], according to which, in pion-nucleon scattering, the averaged s-channel fermionic resonances were related to the t-channel boson exchanges. As such it implied a relation between bosons and fermions, although early workers seem to have put aside spin as an inessential complication.…”

Minimal Regge model for meson-baryon scattering: duality, SU(3) and phase-modified absorptive cuts

“…We can write equation 3 In the general case T-(s, z) does not vanish as z goes to infinity, but rather T-(s, z) = where N(s) is an integer and e is |z|+ * some positive value. In this case we must write a subtracted dispersion relation and the projection of the partial wave amplitude becomes…”