Lowering α s by flipping SU ( 5 )

We show that the prediction for αs(MZ) in flipped SU(5) is naturally lower than in minimal SU(5), and that the former can accommodate the full range of αs(MZ) presently allowed by experiment. Our computations include two-loop (δ2loop) and light (δlight) and heavy (δheavy) threshold effects. Unlike minimal SU(5), in flipped SU(5) the heavy threshold effects can naturally decrease the predicted value of αs(MZ). We also show that the value of the proton lifetime into the dominant channel p → e+π0 is within the observable range at SuperKamiokande, and should discriminate against minimal supersymmetric SU(5), where the dominant mode is p → ν̄K+. CERN-TH-95/260 DOE/ER/40717–17 CTP-TAMU-39/95 ACT-14/95 October 1995 One of the most impressive pieces of circumstantial evidence for Grand Unified Theories is the successful correlation they yield between αs(MZ) and sin 2 θW [1]. Historically, this was first phrased as a prediction of sin θW based on the measured value of αs, whose qualitative agreement with early electroweak data was impressive, particularly for supersymmetric GUTs [2]. The advent of precision electroweak data from LEP and elsewhere [3], and the measurement of the top-quark mass mt [4] has enabled sin θW to be determined with such accuracy that it is natural to turn the GUT correlation round the other way, and use it to predict αs(MZ), which is still not known with satisfactory precision [5]. The prediction of a minimal nonsupersymmetric SU(5) GUT is disastrously low, and debate centres on the the possibility of discriminating between different supersymmetric GUTs and/or obtaining indirect constraints on the scale of supersymmetry breaking. Progress on these questions is hampered by the persistent imprecision in the experimental value of αs(MZ), which is usually quoted as 0.118± 0.006. Most determinations lie within one standard deviation of this mean, but this consistency hides two schools of thought: one supported more strongly by high-energy determinations of αs which favour αs(MZ) ≥ 0.120 [3], and one favoured more strongly by low-energy determinations of αs which favour αs(MZ) ≤ 0.115 when evolved up to a higher scale [6]. It is not clear whether this apparent discrepancy is real, but it has led to various supersymmetric speculations, including the possibility that gluinos are sufficiently light to alter the evolution of αs between low energies and MZ [7], or that radiative corrections due to other light sparticles such as the chargino and top-squark reduce the value of αs(MZ) inferred from LEP data [8]. The minimal supersymmetric SU(5) prediction of αs(MZ) definitely lies on the upper side of the experimental range, and even above it, with values around 0.130 or higher being preferred [9, 10]. This preference should however be treated with caution, as the predicted value may be reduced by GUT threshold effects [11, 12] or by ‘slop’ induced by Planck-scale interactions [13]. One example of a supersymmetric GUT which makes a lower prediction for αs(MZ) is the Missing-Doublet Model (MDM) [14], in which the GUT threshold corrections are generally negative [15]. However, the MDM is quite cumbersome, containing several large Higgs representations that cannot easily be accommodated in a string framework [16]. By far the most economical realization of the missing-partner mechanism is that in flipped SU(5) [17], which needs only 10 and 10 representations of GUT Higgses and has been derived from string [18]. This model also provides another natural mechanism for reducing the prediction for αs(MZ), namely if the scale at which αs and the SU(2) electroweak coupling become equal is lower than the scale at which the SU(5) and U(1) couplings become equal [19]. In this paper we make a quantitative exploration of this possibility in the supersymmetric minimal flipped SU(5) GUT [17]. In addition to exploring the above-