I desire to give thank you lot Luboš for suggesting that I explicate the compactified M-theory predictions of the superpartner masses, especially for the gluino that should travel seen at LHC inwards Run II. I’ll include the before Higgs boson majority too decay branching ratio predictions equally well. I’ll exclusively give references to a few papers that allow the reader to consider to a greater extent than details of derivations too of calculated numbers, plus a few of the master papers that established the basic compactification, normally only alongside arXiv numbers so the interested reader tin hold off at them too line the literature, because this is a brusque explanation exclusively focused on the LHC predictions. I apologize to others who could travel referenced. Before a few years agone it was non possible to exercise compactified string/M-theories to predict superpartner masses. All “predictions” were based on naturalness arguments, too turned out to travel wrong.String/M-theories must travel formulated inwards 10 or xi dimensions to give a consistent quantum theories of gravity. In lodge to examine their predictions for our 4D world, they apparently must travel projected onto 4D, a procedure called “compactification”. Compactified string/M-theories exhibit gravity, plus many properties that characterize the Standard Model of particle physics. These include Yang-Mills gauge theories of forces (such equally \(SU(3)_{\rm color} \times SU(2)_{\rm electroweak}\times U(1)\)); chiral quarks too leptons (so parity violation); supersymmetry derived, non assumed; softly broken supersymmetry; hierarchical quark masses; families; moduli; too more. Thus they are attractive candidates for exploring theories extending the Standard Model.
At the nowadays fourth dimension which string/M-theory is compactified (Heterotic or Type II or M-theory etc), too to what matter-gauge groups, is non however determined past times derivations or principles. Following a trunk of piece of work done inwards the 1995-2004 era [1,2,3,4,5,6,7], my collaborators too I receive got pursued compactifying M-theory. The 11D M-theory is compactified on a 7D manifold of \(G_2\) holonomy, so seven curled upwardly minor dimensions too 3 large infinite ones. We assume appropriate \(G_2\) manifolds be – at that topographic point has been a lot of progress via mathematical study of such manifolds inwards recent years, including workshops. For M-theory it is known that gauge affair arises from singular 3-cycles inwards the 7D manifold [3], too chiral fermions from conical singularities on the 7D manifold [4]. Following Witten [5], nosotros assume compactification to an \(SU(5)\)-MSSM. Other alternatives tin travel studied later. Having inwards heed the destination of finding \({\rm TeV}\) physics arising from a Planck-scale compactification, too knowing that fluxes (the generalization of electromagnetic fields to extra dimensional worlds) receive got dimensions too so naturally Pb to physics nigh the Planck scale but non nigh a \({\rm TeV}\), nosotros compactify inwards a fluxless sector. With the LHC information coming nosotros focused on moduli stabilization, supersymmetry breaking too electroweak symmetry breaking.
In lodge to calculate inwards the compactified theory, nosotros demand the superpotential, the Kähler potential too the gauge kinetic function. To larn the features characteristic of the theory, nosotros receive got the generic Kähler potential too gauge kinetic function. The moduli superpotential is a total of non-perturbative damage because the complex moduli receive got an axion imaginary component division too it has a shift symmetry [8,9,10]. We produce most of the calculations alongside 2 superpotential terms, since that is sufficient to guarantee that supergravity approximations piece of work well, too nosotros tin divulge semi-analytic results. When it matters nosotros cheque alongside numerical piece of work for to a greater extent than damage inwards the superpotential. The signs of the superpotential damage are determined past times axion stabilization [8,9,10]. We exercise the known generic Kähler potential [6] too gauge kinetic business office [7]. By using the generic theory nosotros divulge the natural predictions of such a theory, alongside no costless parameters. This is really of import – if i introduces extra damage past times hand, order inwards the Kähler potential, predictivity is lost.
In add-on to the higher upwardly assumptions nosotros assume the lack of a solution to the cosmological constant work does non halt us from making reasonable predictions. Solving the CC problems would non assist us larn the gluino or Higgs boson mass, too non solving the CC problems does non preclude us from calculating the gluino or Higgs boson mass. Eventually this volition receive got to travel checked.
We showed that the M-theory compactification stabilized all moduli too gave a unique de Sitter vacuum for a given manifold, simultaneously breaking supersymmetry. Moduli vevs too masses are calculable. We calculate the supersymmetry soft-breaking Lagrangian at the compactification scale. Then nosotros receive got the 4D softly broken supergravity quantum land theory, too tin calculate all the predictions of the fully known parameter-free soft-breaking Lagrangian. The theory has many solutions alongside electroweak symmetry breaking.
We equally good demand to receive got the \(\mu\) parameter inwards the theory. That is done next the method of Witten [5] who pointed out a generic discrete symmetry inwards the compactified M-theory that implied \(\mu=0\). We recognized that stabilizing the moduli broke that symmetry, so \(\mu\approx 0\). Since \(\mu\) would vanish if either supersymmetry were unbroken or moduli non stabilized, its value should travel proportional to typical moduli vevs (which nosotros calculated to travel nearly \(1/10\) or \(1/20\) of the Planck scale) times the gravitino mass, so \(\mu\approx 3\TeV\). Combining this alongside the electroweak symmetry breaking weather condition gives \(\tan\beta\approx 5\).
The resulting model (let’s telephone phone it a model fifty-fifty though it is a existent theory too has no adjustable parameters, since nosotros made the assumptions nearly compactifying to the \(SU(5)\)-MSSM, using the generic Kähler potential too gauge kinetic function, too estimating \(\mu\)) has a publish of additional achievements. The lightest modulus tin generate both the affair asymmetry too the nighttime affair when it decays, too thus their ratio. The moduli dominate the loose energy density of the universe shortly after the terminate of inflation, so at that topographic point is a non-thermal cosmological history. Axions are stabilized too at that topographic point is a solution to the strong CP problem. There are no flavour or CPV problems, too EDMs are predicted to travel small, below electrical flow limits, since the soft-breaking Lagrangian at the high scale is existent at tree level, too the RGE running is known [14]. I get upwardly these aspects to illustrate that the model is broadly relevant, non exclusively to LHC predictions.
The soft-breaking Lagrangian contains the damage for the Higgs potential, \(M_{H,u}\) too \(M_{H,d}\) at the high scale. At the high scale all the scalars are nearly equal to the gravitino mass, nearly \(40\TeV\) (see below). All the damage needed for the RGE running are equally good calculated, so they tin travel run downward to the \({\rm TeV}\) scale. \(M_{H,u}\) runs rapidly, downward to nearly a \({\rm TeV}\) at the \({\rm TeV}\) scale. One tin examine all the solutions alongside electroweak symmetry breaking, too finds they all receive got the shape of the well-known 2 Higgs doublet “decoupling sector”, alongside i low-cal Higgs too other physical Higgs bosons whose majority is nearly equal to the gravitino mass. For the decoupling sector the Higgs decay branching ratios are equal to the Standard Model ones except for minor loop corrections, mainly the chargino loop. The low-cal Higgs majority is calculated past times the “match too run” technique, using the latest 2 too iii loop contributions for heavy scalars, etc., too the low-cal Higgs majority for all solutions is \(126.4\GeV\). This was done before the LHC information (arXiv:1112.1059 too reports at before meetings), though that doesn’t affair since the calculation does non depend on anything that changes alongside time. The RGE calculation has been confirmed past times others.
The value of the gravitino majority follows from gaugino condensation too the associated dimensional transmutation. The M-theory hidden sectors generically receive got gauge groups (and associated matter) of diverse ranks. Those alongside the largest gauge groups volition run downward fastest, too their gauge coupling volition acquire large, leading to condensates, analogous to how QCD forms the hadron spectrum but at a much higher loose energy scale. This scale, telephone phone it \(\Lambda\), is typically calculated to travel nearly \(10^{14}\GeV\). The superpotential \(W\) has dimensions of majority cubed, so \(W\sim\Lambda^3\). The gravitino majority is \[
M_{3/2}=\frac{e^{K/2}W}{M_{pl}^2}\approx\left(\frac{\Lambda}{M_{pl}}\right)^3\cdot \frac{M_{pl}}{V_3}
\] since \(e^{K/2}\sim 1/V_3\). The constituent \((\Lambda/M_{pl})^3\) takes us from the Planck scale downward a constituent \(10^{-12}\), too including the calculable book constituent gives \(M_{3/2}\approx 50\TeV\). This lawsuit is generic too robust for the compactified M-theory. It predicts that scalars (squarks, sleptons, \(M_{H,u}\), \(M_{H,d}\)) are of lodge \(50\TeV\) at the high scale, before RGE running.
The suppression of the gaugino masses from the gravitino scale to the \({\rm TeV}\) scale is completely full general (Acharya et al, hep-th/0606262; Phys.Rev.Lett 97(2006)191601). The supergravity facial expression for the gaugino masses, \(M_{1/2}\), is a total of damage each given past times an F-term times the derivative of the visible sector gauge kinetic business office alongside honor to each F-term. The visible sector gauge kinetic business office does non depend on the chiral fermion F-terms, so the associated derivative vanishes, too \(M_{1/2}\) is proportional to the moduli F term generated past times gaugino condensation inwards the hidden sector 3-cycles. The ratio of the gaugino condensate F-term to the chiral fermion F-term is to a greater extent than or less the ratio of volumes, \(V_3/V_7\), of lodge 1/40, for appropriate dimensionless units. \(V_7\) determines the gravitino majority but non \(M_{1/2}\). Let’s in conclusion plow to the gaugino masses. The reader should sympathise immediately that the prediction is non only a “little higher upwardly the limits”, but follows from a generic, robust calculation. Semi-quantitatively, the gluino majority is \([(\Lambda/M_{pl})^3/V_7]M_{pl}\).
Then the gaugino masses alongside the suppression described higher upwardly are generically nearly \(1\TeV\). Detailed calculation, using the Higgs boson majority to pivot downward the gravitino majority to a greater extent than exactly (giving \(M_{3/2}=35\TeV\)) too then predicts the gluino majority to travel nearly \(1.5\TeV\), the wino majority \(614\GeV\), too the LSP bino nearly \(450\GeV\) [12]. These iii states tin travel observed at LHC Run II but none of the other superpartners should travel seen inwards Run II (also an of import prediction). The higgsinos too squarks tin travel seen at an \(\sim 100\TeV\) collider via squark-gluino associated production [12,13].
The LHC gluino production cross department is \(10\)-\(15\,{\rm fb}\) [12]. Note that for squarks too gluinos having equal masses the squark telephone commutation contribution to gluino production is significant, so the park cross department claimed for gluino production is larger than our prediction when squarks are heavy. Simplified searches using larger cross sections volition overestimate limits. Surprisingly, experimental groups too many phenomenologists receive got reported highly model theme limits much larger than the right ones for the compactified M-theory equally if those limits were general. The wino dyad production cross department is equally good of lodge \(15\,{\rm fb}\). The wino has nearly 100% branching ratio to bino + higgs, which is helpful for detection. Gluinos decay via the park virtual squarks nearly 45% into commence too minute theater unit of measurement quarks, 55% into 3rd theater unit of measurement quarks, so simplified searches volition overestimate limits. Branching ratios too signals are explained inwards [12]. The LHC t-tbar cross department is nearly \(4500\,{\rm fb}\), so it gives the primary background (diboson production gives the adjacent worse background). Background study should of course of study travel done past times experimenters, for realistic branching ratios to non travel misleading. We guess that to consider a \(3\sigma\) signal for a \(1.5\TeV\) gluino volition receive got over \(40\,{\rm fb}^{-1}\) integrated luminosity at LHC, so mayhap it tin travel seen past times or during autumn 2016 if the luminosity accumulates sufficiently rapidly.
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