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Register a new userReview and Update of the Compactified M/string Theory Prediction of the Higgs Boson Mass and Properties
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The August 2011 Higgs mass prediction was based on an ongoing six year project studying M-theory compactified on a manifold of G2 holonomy, with significant contributions from Jing Shao, Eric Kuflik, and others, and particularly co-led by Bobby Acharya and Piyush Kumar. The M-theory results include: stabilization of all moduli in a de Sitter vacuum; gauge coupling unification; derivation of TeV scale physics (solving the hierarchy problem); the derivation that generically scalar masses are equal to the gravitino mass which is larger than about 30 TeV; derivation of the Higgs mechanism via radiative electroweak symmetry breaking; absence of the flavor and CP problems, and the accommodation of string axions. tan beta and the mu parameter are part of the theory and are approximately calculated; as a result, the little hierarchy problem is greatly reduced. This paper summarizes the results relevant to the Higgs mass prediction. A recent review describes the program more broadly. Some of the results such as the scalar masses being equal to the gravitino mass and larger than about 30 TeV, derived early in the program, hold generically for compactified string theories as well as for compactified M-theory, while some other results may or may not. If the world is described by M-theory compactified on a G2 manifold and has a Higgs mechanism (so it could be our world) then the Higgs mass was predicted to be 126 +/- 2 GeV before the measurement. The derivation has some assumptions not related to the Higgs mass, but involves no free parameters.
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Recently it has been recognized that in compactified string/M-theories that satisfy cosmological constraints, it is possible to derive some robust and generic predictions for particle physics and cosmology with very mild assumptions. When the matter and gauge content below the compactification scale is that of the MSSM, it is possible to make precise predictions. In this case, we predict that there will be a single Standard Model-like Higgs boson with a calculable mass 105 GeV $lesssim M_h lesssim$ 129 GeV depending on tan beta (the ratio of the Higgs vevs in the MSSM). For tan beta > 7, the prediction is : 122 GeV $lesssim M_h lesssim$ 129 GeV.
We study a realistic top-down M-theory compactification with low-scale effective Supersymmetry, consistent with phenomenological constraints. A combination of top-down and generic phenomenological constraints fix the spectrum. The gluino mass is predicted to be about 1.5 TeV. Three and only three superpartner channels, $tilde{g} tilde{g}$, $chi_2^0 chi_1^pm$ and $chi_1^+ chi_1^-$ (where $chi_2^0, chi_1^pm$ are Wino-like), are expected to be observable at LHC-14. We also investigate the prospects of finding heavy squarks and Higgsinos at future colliders. Gluino-stop-top, gluino-sbottom-bottom associated production and first generation squark associated production should be observable at a 100 TeV collider, along with direct production of heavy Higgsinos. Within this framework the discovery of a single sparticle is sufficient to determine uniquely the SUSY spectrum, yielding a number of concrete testable predictions for LHC-14 and future colliders, and determination of $M_{3/2}$ and thereby other fundamental quantities.
We consider multi-Higgs-doublet models which, for symmetry reasons, have a universal Higgs-Yukawa (HY) coupling, $g$. This is identified with the top quark $g=g_tapprox 1$. The models are concordant with the quasi-infrared fixed point, and the top quark mass is correctly predicted with a compositeness scale (Landau pole) at $M_{planck}$, with sensitivity to heavier Higgs states. The observed Higgs boson is a $bar{t}t$ composite, and a first sequential Higgs doublet, $H_b$, with $gapprox g_tapprox 1$ coupled to $bar{b}_R(t,b)_L$ is predicted at a mass $3.0 lesssim M_b lesssim 5.5$ TeV and accessible to LHC and its upgrades. This would explain the mass of the $b-$quark, and the tachyonic SM Higgs boson mass$^2$. The flavor texture problem is no longer associated with the HY couplings, but rather is determined by the inverted multi-Higgs boson mass spectrum, e.g., the lightest fermions are associated with heaviest Higgs bosons and vice versa. The theory is no less technically natural than the standard model. The discovery of $H_b$ at the LHC would confirm the general compositeness idea of Higgs bosons and anticipate additional states potentially accessible to the $100$ TeV $pp$ machine.
Predictions for the scale of SUSY breaking from the string landscape go back at least a decade to the work of Denef and Douglas on the statistics of flux vacua. The assumption that an assortment of SUSY breaking F and D terms are present in the hidden sector, and their values are uniformly distributed in the landscape of D=4, N=1 effective supergravity models, leads to the expectation that the landscape pulls towards large values of soft terms favored by a power law behavior P(m(soft))~ m(soft)^n. On the other hand, similar to Weinbergs prediction of the cosmological constant, one can assume an anthropic selection of weak scales not too far from the measured value characterized by m(W,Z,h)~ 100 GeV. Working within a fertile patch of gravity-mediated low energy effective theories where the superpotential mu term is << m(3/2), as occurs in models such as radiative breaking of Peccei-Quinn symmetry, this biases statistical distributions on the landscape by a cutoff on the parameter Delta(EW), which measures fine-tuning in the m(Z)-mu mass relation. The combined effect of statistical and anthropic pulls turns out to favor low energy phenomenology that is more or less agnostic to UV physics. While a uniform selection n=0 of soft terms produces too low a value for m(h), taking n=1 or 2 produce most probabilistically m(h)~125 GeV for negative trilinear terms. For n>=1, there is a pull towards split generations with m(squarks,sleptons)(1,2)~10-30 TeV whilst m(t1)~ 1-2 TeV. The most probable gluino mass comes in at ~ 3-4 TeV--apparently beyond the reach of HL-LHC (although the required quasi-degenerate higgsinos should still be within reach). We comment on consequences for SUSY collider and dark matter searches.
In this paper, we establish a fully string-theoretic framework for calculating one-loop Higgs masses directly from first principles in perturbative closed string theories. Our framework makes no assumptions other than worldsheet modular invariance and is therefore applicable to all closed strings, regardless of the specific string construction utilized. This framework can also be employed even when spacetime supersymmetry is broken (and even when this breaking occurs at the Planck scale), and can be utilized for all scalar Higgs fields, regardless of the particular gauge symmetries they break. This therefore includes the Higgs field responsible for electroweak symmetry breaking in the Standard Model. Notably, using our framework, we demonstrate that a gravitational modular anomaly generically relates the Higgs mass to the one-loop cosmological constant, thereby yielding a string-theoretic connection between the two fundamental quantities which are known to suffer from hierarchy problems in the absence of spacetime supersymmetry. We also discuss a number of crucial issues involving the use and interpretation of regulators in UV/IR-mixed theories such as string theory, and the manner in which one can extract an EFT description from such theories. Finally, we analyze the running of the Higgs mass within such an EFT description, and uncover the existence of a dual IR region which emerges at high energies as the consequence of an intriguing scale-inversion duality symmetry. We also identify a generic stringy effective potential for the Higgs fields in such theories. Our results can therefore serve as the launching point for a rigorous investigation of gauge hierarchy problems in string theory.
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