Induced gravity and Planck zeros

Physics

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Scientific paper

Starting with an asymptotically free gauge theory with dynamical symmetry breaking and a mass hierarchy, we investigate the Adler-Zee formula for the induced gravitational constant. We study the two-point function ψ(q2), constructed with the trace of the energy-momentum tensor. First, we show that if the zeros of ψ are at a mass scale significantly below the leading scale, then Gind-1=O(mzero2) making it impossible to get a realistic Gind from the Adler-Zee formula with low-mass zeros. Next we use the Jensen formula to derive a sum rule for |mzero|. The analysis of this sum rule coupled with the result above leads to a dilemma with only one reasonable resolution. To get a realistic Gind from the Adler-Zee formula, ψ(q2) must have a pair of complex-conjugate zeros at q2=M02+/-2iγM0, where M0 is large and of the maximal scale and γM0<<1. The presence of this zero essentially determines Gind-1. It gives a lower bound, which with our previously derived general upper bound gives [π24(ln10)288]CψM02<=(16πG)-1<=[5π2288]CψM02, where Cψ is the anomaly coefficient, a number easily determined by low-order perturbation theory for any group.

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