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Register a new userLittle hierarchies solve the little fine-tuning problem: a case study in supersymmetry with heavy guinos
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Radiative corrections with new heavy particles coupling to Higgs doublets destabilize the electroweak scale and require an ad-hoc counterterm cancelling the large loop contribution. If the mass scale m1 of these new particles in in the TeV range, this feature constitutes the little fine-tuning problem. We consider the case that the new-physics spectrum has a little hierarchy with two particle mass scales m1, m2 and m2 = O(10 m1) and no tree-level couplings of the heavier particles to Higgs doublets. As a concrete example we study the (next-to-)minimal supersymmetric standard model ((N)MSSM) for the case that the gluino mass M3 is significantly larger than the stop mass parameters m_{L,R} and show that the usual one-loop fine-tuning analysis breaks down. If m_{L,R} is defined in the dimensional-reduction (DR-bar) or any other fundamental scheme, corrections enhanced by powers of M3^2/m_{L,R}^2 occur in all higher loop orders. After resumming these terms we find the fine-tuning measure substantially improved compared to the usual analyses with M3 <~ m_{L,R}. In our hierarchical scenario the stop self-energies grow like M3^2, so that the stop masses m_{L,R}^{OS} in the on-shell (OS) scheme are naturally much larger than their DR-bar counterparts m_{L,R}^{DR-bar}. This feature permits a novel solution to the little fine-tuning problem: DR-bar stop masses are close to the electroweak scale, but radiative corrections involving the heavy gluino push the OS masses, which are probed in collider searches, above their experimental lower limits. As a byproduct, we clarify which renormalization scheme must be used for squark masses in loop corrections to low-energy quantities such as the B-B-bar mixing amplitude.
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In supersymmetric models with scalar sequestering, superconformal strong dynamics in the hidden sector suppresses the low-energy couplings of mass dimension two, compared to the squares of the dimension one parameters. Taking into account restrictions on the anomalous dimensions in superconformal theories, I point out that the interplay between the hidden and visible sector renormalizations gives rise to quasi-fixed point running for the supersymmetric Standard Model squared mass parameters, rather than driving them to 0. The extent to which this dynamics can ameliorate the little hierarchy problem in supersymmetry is studied. Models of this type in which the gaugino masses do not unify are arguably more natural, and are certainly more likely to be accessible, eventually, to the Large Hadron Collider.
We point out that in theories where the gravitino mass, $M_{3/2}$, is in the range (10-50)TeV, with soft-breaking scalar masses and trilinear couplings of the same order, there exists a robust region of parameter space where the conditions for electroweak symmetry breaking (EWSB) are satisfied without large imposed cancellations. Compactified string/M-theory with stabilized moduli that satisfy cosmological constraints generically require a gravitino mass greater than about 30 TeV and provide the natural explanation for this phenomenon. We find that even though scalar masses and trilinear couplings (and the soft-breaking $B$ parameter) are of order (10-50)TeV, the Higgs vev takes its expected value and the $mu$ parameter is naturally of order a TeV. The mechanism provides a natural solution to the cosmological moduli and gravitino problems with EWSB.
We show that all the parameters which destabilize the weak scale can be taken around the weak scale in the MSSM without conflicting with the SM Higgs mass bound set by LEP experiment. The essential point is that if the lightest CP-even Higgs h in the MSSM has only a small coupling to Z boson, g_{ZZh}, LEP cannot generate the Higgs sufficiently. In the scenario, the SM Higgs mass bound constrains the mass of the heaviest CP-even Higgs H which has the SM like g_{ZZH} coupling. However, it is easier to make the heaviest Higgs heavy by the effect of off-diagonal elements of the mass matrix of the CP-even Higgs because the larger eigenvalue of 2 times 2 matrix becomes larger by introducing off-diagonal elements. Thus, the smaller stop masses can be consistent with the LEP constraints. Moreover, the two excesses observed at LEP Higgs search can naturally be explained as the signals of the MSSM Higgs h and H in this scenario. One of the most interesting results in the scenario is that all the Higgs in the MSSM have the weak scale masses. For example, the charged Higgs mass should be around 130 GeV. This looks inconsistent with the lower bound obtained by the b --> s gamma process as m_{H^pm}>350GeV. However, we show that the amplitude induced by the charged Higgs can naturally be compensated by that of the chargino if we take the mass parameters by which the little hierarchy problem can be solved. The point is that the both amplitudes have the same order of magnitudes when all the fields in the both loops have the same order of masses.
A semantic equivalence assessment is defined as a task that assesses semantic equivalence in a sentence pair by binary judgment (i.e., paraphrase identification) or grading (i.e., semantic textual similarity measurement). It constitutes a set of tasks crucial for research on natural language understanding. Recently, BERT realized a breakthrough in sentence representation learning (Devlin et al., 2019), which is broadly transferable to various NLP tasks. While BERTs performance improves by increasing its model size, the required computational power is an obstacle preventing practical applications from adopting the technology. Herein, we propose to inject phrasal paraphrase relations into BERT in order to generate suitable representations for semantic equivalence assessment instead of increasing the model size. Experiments on standard natural language understanding tasks confirm that our method effectively improves a smaller BERT model while maintaining the model size. The generated model exhibits superior performance compared to a larger BERT model on semantic equivalence assessment tasks. Furthermore, it achieves larger performance gains on tasks with limited training datasets for fine-tuning, which is a property desirable for transfer learning.
We explore a new class of natural models which ensure the one-loop divergences in the Higgs mass are cancelled. The top-partners that cancel the top loop are new gauge bosons, and the symmetry relation that ensures the cancellation arises at an infrared fixed point. Such a cancellation mechanism can, a la Little Higgs models, push the scale of new physics that completely solves the hierarchy problem up to 5-10 TeV. When embedded in a supersymmetric model, the stop and gaugino masses provide the cutoffs for the loops, and the mechanism ensures a cancellation between the stop and gaugino mass dependence of the Higgs mass parameter.
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