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One-Loop Anomaly Mediated Scalar Masses and (g-2)_mu in Pure Gravity Mediation

We consider the effects of non-universalities among sfermion generations in models of Pure Gravity Mediation (PGM). In PGM models and in many models with strongly stabilized moduli, the gravitino mass may be O(100) TeV, whereas gaugino masses, generated through anomalies at 1-loop, remain relatively light O(1) TeV. In models with scalar mass universality, input scalar masses are generally very heavy (m_0 \simeq m_{3/2}) resulting in a mass spectrum resembling that in split supersymmetry. However, if one adopts a no-scale or partial no-scale structure for the Kähler manifold, sfermion masses may vanish at the tree level. It is usually assumed that the leading order anomaly mediated contribution to scalar masses appears at 2-loops. However, there are at least two possible sources for 1-loop scalar masses. These may arise if Pauli-Villars fields are introduced as messengers of supersymmetry breaking. We consider the consequences of a spectrum in which the scalar masses associated with the third generation are heavy (order m_{3/2}) with 1-loop scalar masses for the first two generations. A similar spectrum is expected to arise in GUT models based on E_7/SO(10) where the first two generations of scalars act as pseudo-Nambu-Goldstone bosons. Explicit breaking of this symmetry by the gauge couplings then generates one-loop masses for the first two generations. In particular, we show that it may be possible to reconcile the g_mu - 2 discrepancy with potentially observable scalars and gauginos at the LHC.