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Register a new userA Fresh Look at Gauge Coupling Unification
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Dimitri Bourilkov
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The apparent unification of gauge couplings around 10^16 GeV is one of the strong arguments in favor of Supersymmetric extensions of the Standard Model (SM). In this contribution a new analysis, using the latest experimental data, is performed. The strong coupling alpha_s emerges as the key factor for evaluating the results of the fits, as the experimental and theoretical uncertainties in its measurements are substantially higher than for the electromagnetic and weak couplings. The present analysis pays special attention to numerical and statistical details. The results, combined with the current limits on the supersymmetric particle masses, favor a value for the SUSY scale <~ 150 GeV and for alpha_s = 0.118-0.119.
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The apparent unification of gauge couplings around 10^16 GeV is one of the strong arguments in favor of Supersymmetric extensions of the Standard Model (SM). In this contribution two new analyses of the gauge coupling running, the latter using in contrast to previous studies not data at the Z peak but at LEP2 energies, are presented. The generic SUSY scale in the more precise novel approach is 93 < M_SUSY < 183 GeV, easily within LHC, and possibly even within Tevatron reach.
We investigate gauge coupling unification at 2-loops for theories with 5 extra vectorlike SU(5) fundamentals added to the MSSM. This is a borderline case where unification is only predicted in certain regions of parameter space. We establish a lower bound on the scale for the masses of the extra flavors, as a function of the sparticle masses. Models far outside of the bound do not predict unification at all (but may be compatible with unification), and models outside but near the boundary cannot reliably claim to predict it with an accuracy comparable to the MSSM prediction. Models inside the boundary can work just as well as the MSSM.
We make a detailed study of the unification of gauge couplings in the MSSM with large extra dimensions. We find some scenarios where unification can be achieved (with the strong coupling constant at the Z mass within one standard deviation of the experimental value) with both the compactification scale and the SUSY breaking scale in the few TeV range. No enlargement of the gauge group or particle content is needed. One particularly interesting scenario is when the SUSY breaking scale is larger than the compactification scale, but both are small enough to be probed at the CERN LHC. Unification in two scales scenarios is also investigated and found to give results within the LHC.
We discuss the hot hand paradox within the framework of the backward Kolmogorov equation. We use this approach to understand the apparently paradoxical features of the statistics of fixed-length sequences of heads and tails upon repeated fair coin flips. In particular, we compute the average waiting time for the appearance of specific sequences. For sequences of length 2, the average time until the appearance of the sequence HH (heads-heads) equals 6, while the waiting time for the sequence HT (heads-tails) equals 4. These results require a few simple calculational steps by the Kolmogorov approach. We also give complete results for sequences of lengths 3, 4, and 5; the extension to longer sequences is straightforward (albeit more tedious). Finally, we compute the waiting times $T_{nrm H}$ for an arbitrary length sequences of all heads and $T_{nrm(HT)}$ for the sequence of alternating heads and tails. For large $n$, $T_{2nrm H}sim 3 T_{nrm(HT)}$.
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