Natural Predictions for the Higgs Boson Mass and Supersymmetric Contributions to Rare Processes
Tianjun Li, James A. Maxin, Dimitri V. Nanopoulos, Joel W. Walker
aa r X i v : . [ h e p - ph ] J a n ACT-14-11, MIFPA-11-43
Natural Predictions for the Higgs Boson Massand Supersymmetric Contributions to Rare Processes
Tianjun Li,
1, 2
James A. Maxin, Dimitri V. Nanopoulos,
2, 3, 4 and Joel W. Walker Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics,Chinese Academy of Sciences, Beijing 100190, P. R. China George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A & M University, College Station, TX 77843, USA Astroparticle Physics Group, Houston Advanced Research Center (HARC), Mitchell Campus, Woodlands, TX 77381, USA Academy of Athens, Division of Natural Sciences,28 Panepistimiou Avenue, Athens 10679, Greece Department of Physics, Sam Houston State University, Huntsville, TX 77341, USAFor John Ellis on the celebration of his 65th birthday...
In the context of No-Scale F - SU (5), a model defined by the convergence of the F -lipped SU (5)Grand Unified Theory, two pairs of hypothetical TeV scale vector-like supersymmetric multipletswith origins in F -theory, and the dynamically established boundary conditions of No-Scale Super-gravity, we predict that the lightest CP-even Higgs boson mass lies within the range of 119.0 GeVto 123.5 GeV, exclusive of the vector-like particle contribution to the mass. With reports by theCMS, ATLAS, CDF, and DØ Collaborations detailing enticing statistical excesses in the vicinity of120 GeV in searches for the Standard Model Higgs boson, all signs point to an imminent discovery.While basic supersymmetric constructions such as mSUGRA and the CMSSM have already sufferedoverwhelming reductions in viable parameterization during the LHC’s initial year of operation, about80% of the original No-Scale F - SU (5) model space remains viable after analysis of the first 1.1 fb − of integrated luminosity. This model is moreover capable of handily explaining the small excessesrecently reported in the CMS multijet supersymmetry search, and also features a highly favorable“golden” subspace which may simultaneously account for the key rare process limits on the muonanomalous magnetic moment ( g − µ and the branching ratio of the flavor-changing neutral currentdecay b → sγ . In addition, the isolated mass parameter responsible for the global particle massnormalization, the gaugino boundary mass M / , is dynamically determined at a secondary localminimization of the minimum of the Higgs potential V min , in a manner which is deeply consistentwith all precision measurements at the physical electroweak scale. PACS numbers: 11.10.Kk, 11.25.Mj, 11.25.-w, 12.60.Jv
I. INTRODUCTION
The Large Hadron collider (LHC) has accumulated todate up to 2.3 fb − of data from proton-proton collisionsat a center-of-mass beam energy of √ s = 7 TeV, alreadyestablishing firm constraints on the mass of the lightestCP-even Higgs boson. The CMS [1] and ATLAS [2, 3]Collaborations have uncovered appealing statistical ex-cesses that hint of the properties of the Standard Model(SM) Higgs boson, though not yet approaching the fivestandard deviations essential to claim a conclusive dis-covery. CMS has reported a surplus of observed eventsabove the Standard Model background estimation near120 GeV, positioned directly at a location where back-ground competition against observation is particularlysevere. Nevertheless, the extraordinarily rapid rampingup of the LHC luminosity has allowed large quantitiesof new data to be sufficiently swiftly amassed that adefinitive resolution to the dual questions of the existenceand mass of the Higgs boson could be imminent. More-over, these observations beyond background expectationsare also in good agreement with newly established con-straints from searches for the Higgs boson by the CDFand DØ Collaborations [4]. No equally suggestive signal of supersymmetry has thus far been detected by CMS [5–11] or ATLAS [12–16], so that one may suspect the LHC’sbest initial chance to make a key discovery rests in allprobability with the Higgs boson.The anticipation for discovery of physics beyond theSM at the LHC is fervent, heightening attention on thetask of ascertaining what particle physics models ex-ist which can naturally accommodate, or even perhapsuniquely predict, a Higgs boson in the neighborhoodof 120 GeV. The foremost contender for an extensionto the SM is Supersymmetry (SUSY), a natural solu-tion to the gauge hierarchy problem. Supersymmet-ric Grand Unified Theories (GUTs) with gravity medi-ated supersymmetry breaking, known in their simplestvariations as minimal Supergravity (mSUGRA) and theConstrained Minimal Supersymmetric Standard Model(CMSSM), have been exhaustively assessed against thefirst 1.1 fb − of integrated luminosity; an overwhelmingmajority of the formerly experimentally viable parameterspace of these models has failed to survive this testing,and has now fallen out of favor. This fuels the ques-tion of whether there endure SUSY and/or superstringpost-Standard Model extensions that can continue to suc-cessfully counter the rapidly advancing constraints whilesimultaneously providing a naturally derived Higgs bo-son mass near 120 GeV, and while remaining potentiallyvisible to the early operation of the LHC.An attractive candidate solution to this dilemma maybe found in a class of models named No-Scale F - SU (5) [17–29]. It has been demonstrated that a majorityof the bare-minimally constrained [23] parameter spaceof No-Scale F - SU (5), as defined by consistency with theworld average top-quark mass m t , the dynamically es-tablished boundary conditions of No-Scale supergravity,radiative electroweak symmetry breaking, the centrallyobserved WMAP7 CDM relic density [30], and precisionLEP constraints on the lightest CP-even Higgs boson m h [31, 32] and other light SUSY chargino and neutralinomass content, remains viable even after careful compar-ison against the first 1.1 fb − [27, 29] of LHC data. Weshall show that exclusive of the vector-like particle con-tribution, the light Higgs mass is stably predicted withinthis region to take a value between 119.0-123.5 GeV, con-sistent with the surplus of observed events in the analy-ses presented by the CMS, CDF, and DØ Collaborations.Significantly, the most promising subspace of this regionincludes secondary bounds on the flavor changing neu-tral current ( b → sγ ) process, contributions to the muonanomalous magnetic moment ( g − µ , and the rare de-cay process B s → µ + µ − , all of which cohere with spin-independent σ SI [33] and spin-dependent σ SD [34] scat-tering cross-section bounds on Weakly Interacting Mas-sive Particles (WIMPs), in addition to fresh limits estab-lished on the annihilation cross-section h σv i γγ of WIMPsusing gamma-rays derived from the Fermi Telescope ob-servations [35][36]. This condensed subspace, an up-dating of our previously advertised “Golden Strip” [18],offers a more focused prediction of the Higgs mass ofaround 120-121 GeV. We emphasize that the predictionof the Higgs in the vicinity of 120 GeV has been an ex-ceedingly natural and robust prediction of No-Scale F - SU (5), stable across the full model space, which we haveconsistently advertised over the course of a growing bodyof work [17–29]. The recent embellishments to the ex-perimental support for this standing correlation furnishit with a greatly enhanced immediacy and interest. II. THE F - SU (5) MODEL
The study launched here is built upon the frameworkof an explicit model, dubbed No-Scale F - SU (5) [17–29], uniting the F -lipped SU (5) Grand Unified Theory(GUT) [37–39] with two pairs of hypothetical TeV scalevector-like supersymmetric multiplets with origins in F -theory [40–44] and the dynamically established bound-ary conditions of No-Scale Supergravity [45–49]. A morecomplete review of this model is available in the appendixof Ref. [22].Supersymmetry is broken in the hidden sector in theconventional framework, and then its breaking effectsare mediated to the observable sector through gravity or gauge interactions. In GUTs with gravity mediated su-persymmetry breaking, referred to as minimal supergrav-ity (mSUGRA), the supersymmetry breaking soft termscan be parameterized by four universal parameters: thegaugino mass M / , scalar mass M , trilinear soft termA, and the ratio of the low energy Higgs vacuum expec-tation values (VEVs) tan β , in addition to the sign of theHiggs bilinear mass term µ . The µ term and its bilinearsoft term B µ are determined by the Z-boson mass M Z and tan β after electroweak symmetry breaking (EWSB).In the simplest No-Scale boundary conditions, M =A= B µ =0, while M / may be non-zero at theunification scale, allowing for low energy supersymme-try breaking. This scenario appears to come into itsown only when implemented at a scale approaching thePlanck mass [50, 51]. Accordingly, M F , the point of thesecond stage flipped SU (5) × U (1) X unification, tran-spires as a plausible candidate scale only when substan-tially decoupled from the primary GUT unification of SU (3) C × SU (2) L at the scale M via a revision to therenormalization group equations (RGE) from the extra F -Theory vector multiplets [17, 18]. These interdepen-dencies conspire to diminish rather than broaden the levelof uncertainty in the model’s predicted phenomenology.Utilizing the dynamically established boundary con-ditions of No-Scale Supergravity at the F - SU (5) unifi-cation scale M F , we have previously delineated the ex-traordinarily constrained Golden Point [17] and afore-mentioned earliest derived incarnation of the GoldenStrip [18] which satisfied all current experimental con-straints while additionally featuring an imminently ob-servable proton decay rate τ p [52]. The most constric-tive constraint imposed upon the viable model space isthe unification scale boundary on B µ =0. Furthermore,through application of a “Super No-Scale” condition forthe dynamic stabilization of the stringy modulus relatedto the M / boundary gaugino mass [19, 20, 23, 28],this mass along with the ratio of the Higgs VEVstan β [19, 20, 23, 28] has been dynamically determined.The complete collection of supersymmetry breakingsoft terms evolve from the single parameter M / inthe simplest No-Scale supergravity, and consequently theparticle spectra are proportionally comparable up to anoverall rescaling on M / , leaving the majority of the“internal” physical properties invariant. This rescalingcapability on M / is not generally expected in compet-ing supersymmetry models, due to the presence of largerparameterization freedom, particularly with respect to asecond independent boundary mass M for scalar fields.This rescaling symmetry can be broken to a slight degreeby the vector-like mass parameter, although the depen-dence is rather weak. III. PREDICTING THE HIGGS MASS
In the context of No-Scale supergravity, we require M =A= B µ =0 at the unification scale M F , and permit a ( 10 -10 ) Br(b s ) ( 10 -4 ) Br(B + - ) ( 10 -9 ) Region of the F-SU(5) parameter spaceestimated to be excluded by the CMS Multijet Constraints 3.53.73.83.94.0 3.00 3.203.102.862.602.30 7911141720 M V ( G e V ) M (GeV) Golden Strip (M ,M V ,m t ,tan ) = (570,4000,173.2,21.5)
122 123121120
700 900800700600500 120011001000900800600 160015001400130012001000900 m h lightest CP-even Higgs Boson Mass (GeV) t Squark Mass (GeV) Gluino Mass (GeV) u R Squark Mass (GeV)Region of the F-SU(5) parameter spaceestimated to be excluded by the CMS Multijet Constraints M V ( G e V ) M (GeV) (M ,M V ,m t ,tan ) = (570,4000,173.2,21.5) Golden Strip
FIG. 1: The bare-minimally constrained parameter space of No-Scale F - SU (5) is depicted as a function of the gaugino boundarymass M / , the vector-like mass M V , and via the solid, dashed, and dotted contour lines, the ( b → sγ ), muon anomalousmagnetic moment ( g − µ , and the B s → µ + µ − processes in the upper plot space, with the mass gradients in GeV of the lightstop squark e t , gluino e g , right-handed up squark e u R , and light Higgs mass m h in the lower plot space. We note that the Higgsmass contours drawn here do not include any additional contributions from the vector-like particles. The region estimated tobe disfavored by the first inverse femtobarn of integrated LHC luminosity is marked out with the crosshatch pattern. Thevertical strip embossed in gold, referred to as the Golden Strip, represents an experimentally favored region consistent withthe bare-minimal experimental constraints of [23] and both the ( b → sγ ) process and contributions to the muon anomalousmagnetic moment ( g − µ . The Golden Strip also includes the B s → µ + µ − decay, however this constraint is satisfied bythe entire viable model space. The expanded region adorned in silver imposes these identical constraints, though with a moreconservative estimate of ∆ a µ = 27 . ± . × − . The labeled point is the benchmark of Table (I). distinctive inputs for the single parameter M / ( M F ) totranslate under the RGEs to low scale outputs of B µ and the Higgs mass squares M H u and M H d . This evo-lution continues until the point of spontaneous break-down of the electroweak symmetry at M H u + µ =0, atwhich scale minimization of the broken potential deter-mines the physical low energy values of µ and tan β . Inpractice, we implement this procedure by employing aproprietary modification of the SuSpect 2.34 [53] code-base to run the RGEs within
MicrOMEGAs 2.1 [54] tocompute the supersymmetry and Higgs mass spectrum.In principle, the B µ ( M F )=0 condition fixes the value oftan β at low energy through running of the RGEs, thoughthis procedure is at odds with the current configurationof the proprietary revised version of the SuSpect 2.34 codebase. Thus, we equivalently isolate the B µ ( M F )=0solution set by instead allowing tan β to float freely andsubsequently apply a self-consistency check.For the gauge couplings, we consider two-loop RGErunning, though we only consider one-loop RGE run-ning for the gaugino masses, µ term, supersymmetrybreaking scalar masses, trilinear A-terms, and B µ term.In F - SU (5) models, the one-loop beta function b for SU (3) C is zero due to the vector-like particle contri-bution [40], so the gaugino mass M is constant fromthe electroweak scale to the M scale [17]. In contrast,the two-loop gauge coupling RGE running and one-loopgaugino mass RGE running for the SU (2) L × U (1) Y gaugesymmetry track each other since the gauge couplings for SU (2) L × U (1) Y are weak; thus, the two loop effects aresmall. For the calculation of the radiative corrections inthe Higgs sector to determine the physical Higgs masses,we implement the full one-loop plus leading two-loop cal-culations.To solve the “ µ ” problem for the vector-like parti-cle masses, we can consider the following mechanisms:(1) The Giudice-Masiero mechanism [55], where such a“ µ ” term is generated from high-dimensional operators;(2) There exist additional Standard Model singlets in F-Theory models. The vector-like particles can couple tothese singlets and obtain their masses after these sin-glets acquire VEVs. This is similar to the solution to the“ µ ” problem in the next-to-the-Minimal SupersymmetricStandard Model (NMSSM).The vector-like particles can contribute to the Higgsboson masses if they couple to the Higgs fields. For sim-plicity though, we assume here that such couplings aresmall. Regardless of this assumption however, our fa-vored benchmark point that we shall introduce in thenext section and in Table (I) possesses an M V of about4 TeV, hence the contributions of the vector-like parti-cles to the Higgs mass of the benchmark of Table (I) aresmall even if their Yukawa couplings to the Higgs fieldsare not small [56]. Though we assume negligible cou-plings of the vector-like particles to the Higgs fields forthe entire model space here in this paper, we shall com-pute the precise contributions of the vector-like particlesto the Higgs boson mass in a forthcoming analysis [57]. We take µ > g − µ for the muon and execute a full scan of the model spacethrough input freedom of the gaugino mass M / , vector-like mass parameter M V , and tan β . The resultant so-lution space is then assessed against the bare-minimalconstraint set introduced in Ref. [23]. To summarizefrom Ref. [23], the bare-minimal constraints are de-fined by compatibility with the world average top quarkmass m t = 173 . ± . . ≤ Ω CDM ≤ . m h ≥
114 GeV [31, 32]) and other lightSUSY chargino, stau, and neutralino mass content, and aself-consistency specification on the dynamically evolvedvalue of B µ measured at the boundary scale M F . Anuncertainty of ± B µ = 0 is allowed, consistentwith the induced variation from fluctuation of the strongcoupling within its error bounds and the expected scaleof radiative electroweak (EW) corrections.The cumulative result of the application of the bare-minimal constraints shapes the parameter space into theuniquely formed profile situated in the M / , M V planeexhibited in Fig. (1), from a tapered light mass regionwith a lower bound of tan β = 19.4 into a more expansiveheavier region that ceases sharply with the charged stauLSP exclusion around tan β ≃
23. The total model spacebeyond the hashed over region illustrated in Fig. (1) con-sists of those points within the parameter space not ex-cluded by the CMS 1.1 fb − constraints, as derived inRef. [27]. We demarcate the smooth light Higgs mass m h gradient in the lower plot space of Fig. (1) with theemphasized bold contour lines. The region in Fig. (1) sur-viving the CMS constraints assertively predicts a quitenarrow Higgs mass range of 119.0 to 123.5 GeV, linkedto a top quark mass within the world average 173.3 ± M V & IV. THE GOLDEN STRIP
The Golden Strip is strictly defined by the mutual in-tersection of the bare-minimal constraints with the rare-decay processes b → sγ , B s → µ + µ − , and the muonanomalous magnetic moment, as depicted by the con-densed vertical slice embossed with gold in both plotspaces of Fig. (1). For the experimental limits on theflavor changing neutral current process b → sγ , we drawon the two standard deviation limits Br ( b → sγ ) =3 . ± . × − , where the theoretical and exper-imental errors are added in quadrature [59, 60]. Welikewise apply the two standard deviation boundaries∆ a µ = 27 . ± . × − [61] for the anomalous mag-netic moment of the muon, ( g − µ . Lastly, we use therecently published upper bound of Br ( B s → µ + µ − ) < . × − [62] for the process B s → µ + µ − . The morespacious vertical segment adorned in silver in Fig. (1)equally consists of all the above constraints, thoughadopting a more conservative estimate of the 2 σ lowerbound of ∆ a µ ≥ . × − . This shift is supportedby a more recent experiment which suggests a downwardshift of the central value [63]. Moreover, we remark thatour greater confidence between these two experimentalmetrics is with those referencing b → sγ , and that sincethe two key rare process constraints operate in overlap-ping opposition, the silver region actually comes closer tothe central value of this branching ratio. We note thatthe entire Gold and Silver Strips remain unblemished bythe first 1.1 fb − of LHC data, representing optimumcandidate regions for the discovery of supersymmetry.Additionally, notice that the Higgs mass in the GoldenStrip is right about 120 GeV, in accord with the over-all combined contributions of all individual Higgs decaychannels observed by CMS above the Standard Modelexpectations [1].We select a benchmark from the Golden Strip repre-senting what we believe to be the most optimum point tobe assessed against experiment, as identified in Fig. (1)by the model parameters, with the spectrum of super-symmetric masses given in Table (I). At the benchmark,the isolated mass parameter responsible for the globalparticle mass normalization, namely the gaugino bound-ary mass M / =570 GeV, is dynamically determined ata secondary local minimization of the minimum of theHiggs potential V min [20, 23, 28] in a manner which isdeeply consistent with all precision measurements at thephysical electroweak scale, and in particular, the Z-bosonmass M Z itself [28]. Supplementing experimental con-straints with the dynamical determination of this mini-mum minimorum of our universe, this point fulfills theinclusive group of well-established experimental and the-oretical constraints, as summarized in Table (II), merg-ing a bottom-up experimentally driven analysis with atheoretically motivated top-down approach. V. A SMOKING GUN SIGNAL
The intricate evasion of the full company of indepen-dent experimental constraints cataloged in the body ofTable (II) may appear serendipitous, but it is certainlynot accidental. The definitive phenomenological signa-
TABLE I: Spectrum (in GeV) for M / = 570 GeV, M V =4 TeV, m t = 173.2 GeV, tan β = 21.5. Here, Ω χ = 0.11 andthe lightest neutralino is 99.8% bino. e χ e χ ± e e R e t e u R m h . e χ e χ ± e e L e t e u L m A,H e χ e ν e/µ e τ e b e d R m H ± e χ e ν τ e τ e b e d L e g ture of No-Scale F - SU (5) which facilitates this dexterityis the rather unique encoding M ( e t ) < M ( e g ) < M ( e q )of the SUSY particle mass hierarchy. This pattern of astop lightest supersymmetric quark, followed by a gluinowhich is likewise lighter than the remaining squarks, isstable across the full model space, and has not been ob-served to be precisely replicated in any benchmark con-trol sample of the MSSM, and in particular not by anyof the “Snowmass Points and Slopes” benchmarks [64].This hierarchy allows No-Scale F - SU (5) to bypass col-lider limits on light squark masses much more adroitlythan CMSSM constructions with comparably light Light-est Supersymmetric Particles (LSPs). It is moreoverdirectly responsible for a smoking-gun signal of ultra-high ( ≥
9) jet multiplicity events, which is expected tobe prominently visible in LHC searches, given suitabledata selection cuts [21, 22, 27]. The distinctive F - SU (5)sparticle mass hierarchy responsible for a preponderanceof the robust model characteristics summarized in thiswork is graphically illustrated in the lower plot space ofFig. (1), where we demarcate the light stop e t , gluino e g ,and e u R squark mass contours. TABLE II: Conformity with all the measured constraints forthe Table (I) benchmark point M / = 570 GeV, M V = 4TeV, m t = 173.2 GeV, tan β = 21.5. Here MM is used todesignate the minimum minimorum of our universe.Constraint F− SU(5) Value m h >
114 GeV 120 . m t = 173 . ± . . e χ = 0 . ± . . Br ( b → sγ ) = 3 . ± . × − . × − ∆ a µ = 27 . ± . × − . × − Br ( B s → µ + µ − ) ≤ . × − . × − τ p ≥ . × yr 5 . × yr σ SI < × − pb 1 . × − pb σ SD < . × − pb 1 × − pb h σv i γγ < − cm / s 2 × − cm / s M / @ M Z = 91 . ± .
001 GeV MM 572 . The mechanism of this distinctive signature may betraced to a fact already noted, that the one-loop β -function b of the SU (3) C gauge symmetry is zero due tothe extra vector-like particle contributions [40]. The ef-fect on the colored gaugino is direct in the running downfrom the high energy boundary, leading to the relation M /M / ≃ α ( M Z ) /α ( M ) ≃ O (1) and precipitat-ing the conspicuously light gluino mass assignment. Thelightness of the stop squark e t is likewise attributed tothe large mass splitting expected from the heaviness ofthe top quark, via its strong coupling to the Higgs. Thevector-like particles, with a multiplet structure almostuniquely mandated by avoidance of a Landau pole withinthe F -theory model building [40–44] context, are in turnnecessary in order to achieve a substantial separation be-tween the initial gauge unification of SU (3) C × SU (2) L at M ≃ GeV, and the secondary unification of SU (5) × U (1) X at M F ≃ × GeV. This elevationof the final GUT scale, which is possible only withinthe context of a model with a two-stage unification likeFlipped SU (5), appears likewise to be necessary in orderto successfully implement the No-Scale boundary condi-tions, and in particular, the vanishing of the Higgs bilin-ear soft term B µ . We emphasize again that this scenarioappears to comes into its own only when applied at a uni-fication scale approaching the Planck mass [50]. The dy-namics of No-Scale Supergravity may themselves play anindispensable role in establishing the cosmological flat-ness of our Universe, and possibly even in allowing forthe shepherding of a vast multitude of sister universes outof the primordial quantum “nothingness”, while main-taining a zero balance of some suitably defined energyfunction. VI. LHC SEARCH STRATEGY
In Fig. (2), we augment the analysis of Ref. [27] bypresenting the number of events generated in a MonteCarlo simulation of our M / = 570 GeV benchmarkpoint from Table (I) summed with the Standard Modelbackground statistics of Ref. [11]. We superimpose this F - SU (5) plus Standard Model background signal ontoa reprinting of the CMS Preliminary Standard Modelbackground statistics and observed events from Ref. [11],featuring 1.1 fb − of collision data and a √ s = 7 TeVbeam energy. We impose upon the F - SU (5) signal aset of post-processing cuts designed to mimic those de-scribed in the CMS report. We emphasize that the F - SU (5) benchmark is quite capable of accounting forthe observed event excesses, including most compellinglyat the nine jet count, while avoiding any conspicuousoverproduction. Although we do here attempt to con-form with the F - SU (5) CMS post-processing cuts pre-sented in Ref. [11], we maintain aggressive advocacy ofthe ultra-high jet cutting strategy described extensivelyin Refs. [21, 22, 25–27]. We believe that the discovery ofa supersymmetry signal will most likely manifest itself inthe data observations for nine or more jets; hence, a jetcutting strategy optimized for extracting supersymmetryfrom ultra-high jet events could prove to be more efficientat the LHC by one order of magnitude [27].Furthermore, to emphasize the significance of the ultra-high jet cutting strategy in extracting a No-Scale F - SU (5) supersymmetry signal, we use the DiscoveryIndex first presented in Ref. [25] and find that by im-plementing upon the M / =570 GeV benchmark pointof Table (I) the CMS post-processing cuts of Ref. [11],though only retaining those events with nine jets or more,requires 8.5 f b − of LHC data in order to achieve a fivestandard deviation discovery of supersymmetry. With 5 f b − currently in hand at the LHC as we close the year2011, and also considering projections that 10 f b − couldbe attained by the end of the year 2012, a five standarddeviation discovery of an F - SU (5) supersymmetry signalusing the CMS search strategy of [11] is certainly achiev-able. However, a prerequisite of utmost importance forthe accessibility of such a discovery is that only thoseevents with nine or more jets can be retained. For in-stance, if all events with 6 or more jets are retained whilemaintaining the CMS post-processing cutting strategyof [11], then the discovery threshold for F - SU (5) super-symmetry elevates to about 14 f b − . Yet even more gravewill be preserving all events with three jets or greaterwhile implementing the CMS cuts of [5], where in thisextremely detrimental scenario a massive 100 f b − of lu-minosity at the LHC will be required for a five stan-dard deviation discovery of an F - SU (5) supersymmetricsignal. Therefore, we would implore the CMS and AT-LAS Collaborations to not exclude the examination ofevents with nine or more jets in the analysis of LHCdata; outside of this optimized search region, the super-symmetry signal of models like No-Scale F - SU (5) will bestrongly masked, and possibly undetectable. Given thepresently outlined phenomenological attributes that col-lectively endorse No-Scale F - SU (5) as a principal SUSYGUT candidate, diligence in the investigation of its keyexperimental signature strikes us as rather advisable.Our simulation was performed using the MadGraph [65,66] suite, including the standard
MadEvent [67],
PYTHIA [68] and
PGS4 [69] chain, with post-processingperformed by a custom script
CutLHCO [70] (available fordownload) which executes the desired cuts, and countsand compiles the associated net statistics. All 2-bodySUSY processes have been included in our simulation,which follows in all regards the procedure detailed inRef. [22]. The Monte Carlo is typically oversampled forSUSY processes and scaled down to the requisite lumi-nosity, which can have the effect of suppressing statisticalfluctuations.
VII. CONCLUSIONS
While the search for supersymmetry progresses at theLHC with no conclusive signal observed as of this date,the quest for the Higgs boson is rapidly accelerating. Allindications from the CMS, ATLAS, CDF, and DØ Col-laborations suggest that a statistically significant obser-vation of the Higgs boson in the vicinity of 120 GeVcould be on the near-term horizon, possibly by the end
FIG. 2: The CMS Preliminary 2011 signal and background statistics for 1 . − of integrated luminosity at √ s = 7 TeV,as presented in [11], are reprinted with an overlay consisting of a Monte Carlo collider-detector simulation of the No-Scale F - SU (5) model space benchmark of Table (I). The plot counts events per jet multiplicity, with no cut on α T . The Monte Carlooverlay consists of the F - SU (5) supersymmetry signal plus the Standard Model background, thus permitting a direct visualevaluation against the CMS observed data points. of 2011. It is thus imperative that we begin to spotlightthose supersymmetry models capable of engendering anatural prediction for a Higgs boson mass near 120 GeV.We have focused on one such model here by the name ofNo-Scale F - SU (5).Applying only a set of bare-minimal experimental con-straints, more than 80% of the resulting model space ofthe F - SU (5) remains viable after the first 1.1 fb − of lu-minosity at the LHC. We found that this entire survivingmodel space naturally generates a Higgs mass of 119.0-123.5 GeV, in accord with the overall combined contribu-tions of all individual Higgs decay channels observed byCMS above the expected Standard Model background.Though this 119.0-123.5 GeV mass range does not in- clude any contributions from the vector-like particles,we plan to return to this issue in the future to explic-itly compute these additional contributions and augmentthe mass limits as necessary. The benchmark selectedfor attention in the present work features particularlyheavy vector-like multiplets, so that we might for sim-plicity consider the contribution to the Higgs mass to besuppressed. We thus anticipate that predictions for thisregion of the model space will remain stable when fu-ture attention is given to higher order effects, althoughthat may not remain strictly true for smaller values of M V . Exposing a condensed subspace of this larger regionwhere the bare-minimal constraints intersect the thresh-olds of the b → sγ , B s → µ + µ − , and muon anoma-lous magnetic moment processes, we have uncovered themost experimentally favorable region, dubbed the GoldenStrip, which continues untouched by the rapidly advanc-ing LHC constraints, remaining wholly viable for super-symmetry discovery, while further indicating a Higgs bo-son at about 120-121 GeV within this favored subspace.Selecting a representative point from a location withinthe Golden Strip where the dynamical determination ofthe secondary minimization of the minimum V min of theHiggs potential agrees to high-precision with precisionmeasurements at the electroweak scale, we assessed thisbenchmark for its ability to fit the CMS multijet datapoints and elucidate any unexplained statistical excessesin the first 1.1 fb − of LHC data reported by the CMScollaboration. The outcome was positive, with an inter-esting surplus of events at nine jets perfectly explicablewithin the realm of the No-Scale F - SU (5) Golden Strip.For those physicists and non-physicists alike who havebeen patiently awaiting a categorical discovery of theHiggs boson for decades, the time may be at hand, asan exceedingly plausible prospect of a discovery near 120GeV looms large over the coming months. Certainly, thefirst major discovery of the LHC era will generate war- ranted enthusiasm throughout the high-energy physicscommunity, but we close with a brief suggestion of whatthe determination of a Higgs boson discovery around120 GeV might further disclose as to the structure ofa more fundamental theory at high energy scales. Giventhe recent radical curtailing of the dominant mSUGRAand CMSSM model spaces, a Higgs boson near 120 GeVmight be interpreted as a rather strongly suggestive pieceof evidence to bolster the No-Scale F - SU (5) frameworkin particular, and string theory in general. Acknowledgments
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