Natural Predictions for the Higgs Boson Mass and Supersymmetric Contributions to Rare Processes

0.42 MB·English

by  Tianjun Li

ACT-14-11, MIFPA-11-43
Natural Predictions for the Higgs Boson Mass
and Supersymmetric Contributions to Rare Processes
Tianjun Li,1,2 James A. Maxin,2 Dimitri V. Nanopoulos,2,3,4 and Joel W. Walker5
1Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics,
Chinese Academy of Sciences, Beijing 100190, P. R. China
2George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,
Texas A&M University, College Station, TX 77843, USA
3Astroparticle Physics Group, Houston Advanced Research Center (HARC), Mitchell Campus, Woodlands, TX 77381, USA
4Academy of Athens, Division of Natural Sciences,
28 Panepistimiou Avenue, Athens 10679, Greece
5Department of Physics, Sam Houston State University, Huntsville, TX 77341, USA
2 For John Ellis on the celebration of his 65th birthday...
1
0 In the context of No-Scale -SU(5), a model defined by the convergence of the -lipped SU(5)
F F
2 Grand Unified Theory, two pairs of hypothetical TeV scale vector-like supersymmetric multiplets
with origins in -theory, and the dynamically established boundary conditions of No-Scale Super-
n F
gravity, we predict that the lightest CP-even Higgs boson mass lies within the range of 119.0 GeV
a
J to 123.5 GeV, exclusive of the vector-like particle contribution to the mass. With reports by the
CMS,ATLAS,CDF,andDØCollaborations detailingenticingstatistical excessesinthevicinityof
6
120GeV insearches fortheStandardModel Higgsboson, allsigns pointtoanimminent discovery.
1
WhilebasicsupersymmetricconstructionssuchasmSUGRAandtheCMSSMhavealreadysuffered

overwhelmingreductionsinviableparameterizationduringtheLHC’sinitialyearofoperation,about
]
h 80%oftheoriginalNo-Scale -SU(5)modelspaceremainsviableafteranalysisofthefirst1.1fb−1
p of integrated luminosity. ThiFs model is moreover capable of handily explaining the small excesses
- recently reported in the CMS multijet supersymmetry search, and also features a highly favorable
p
“golden” subspace which may simultaneously account for the key rare process limits on the muon
e
anomalousmagneticmoment(g 2) andthebranchingratiooftheflavor-changingneutralcurrent
h µ
−
[ decay b sγ. In addition, the isolated mass parameter responsible for the global particle mass
normaliz→ation, the gaugino boundary mass M , is dynamically determined at a secondary local
1/2
2 minimization of the minimum of the Higgs potential Vmin, in a manner which is deeply consistent
v with all precision measurements at thephysical electroweak scale.
0
1 PACSnumbers: 11.10.Kk,11.25.Mj,11.25.-w,12.60.Jv
1
2
9. I. INTRODUCTION ofsupersymmetryhasthusfarbeendetectedbyCMS[5–
0 11]orATLAS[12–16],sothatonemaysuspecttheLHC’s
1 best initial chance to make a key discovery rests in all
The Large Hadron collider (LHC) has accumulated to
:1 date upto 2.3fb−1 ofdatafromproton-protoncollisions probability with the Higgs boson.
v
ata center-of-massbeam energyof√s = 7 TeV, already The anticipation for discovery of physics beyond the
i
X establishing firm constraints on the mass of the lightest SM at the LHC is fervent, heightening attention on the
CP-even Higgs boson. The CMS [1] and ATLAS [2, 3] task of ascertaining what particle physics models ex-
r
a Collaborations have uncovered appealing statistical ex- ist which can naturally accommodate, or even perhaps
cesses that hint of the properties of the Standard Model uniquely predict, a Higgs boson in the neighborhood
(SM) Higgs boson, though not yet approaching the five of 120 GeV. The foremost contender for an extension
standard deviations essential to claim a conclusive dis- to the SM is Supersymmetry (SUSY), a natural solu-
covery. CMS has reported a surplus of observed events tion to the gauge hierarchy problem. Supersymmet-
above the Standard Model background estimation near ric Grand Unified Theories (GUTs) with gravity medi-
120 GeV, positioned directly at a location where back- ated supersymmetry breaking, known in their simplest
ground competition against observation is particularly variations as minimal Supergravity (mSUGRA) and the
severe. Nevertheless, the extraordinarily rapid ramping Constrained Minimal Supersymmetric Standard Model
up of the LHC luminosity has allowed large quantities (CMSSM), have been exhaustively assessed against the
of new data to be sufficiently swiftly amassed that a first 1.1 fb−1 of integrated luminosity; an overwhelming
definitiveresolutiontothedualquestionsoftheexistence majorityoftheformerlyexperimentallyviableparameter
and mass of the Higgs boson could be imminent. More- space of these models has failed to survive this testing,
over,theseobservationsbeyondbackgroundexpectations and has now fallen out of favor. This fuels the ques-
are also in good agreement with newly established con- tion of whether there endure SUSY and/or superstring
straints from searches for the Higgs boson by the CDF post-StandardModelextensionsthatcancontinuetosuc-
and DØ Collaborations [4]. No equally suggestive signal cessfully counter the rapidlyadvancing constraintswhile
2
simultaneously providing a naturally derived Higgs bo- gauge interactions. In GUTs with gravity mediated su-
sonmass near120GeV, andwhile remaining potentially persymmetrybreaking,referredtoasminimalsupergrav-
visible to the early operation of the LHC. ity (mSUGRA), the supersymmetry breaking soft terms
An attractive candidate solution to this dilemma may can be parameterized by four universal parameters: the
be found in a class of models named No-Scale - gaugino mass M1/2, scalar mass M0, trilinear soft term
F
SU(5)[17–29]. Ithasbeendemonstratedthatamajority A, and the ratio of the low energy Higgs vacuum expec-
of the bare-minimally constrained [23] parameter space tationvalues (VEVs)tanβ, inadditiontothe signofthe
of No-Scale -SU(5),as defined by consistency with the Higgs bilinear mass term µ. The µ term and its bilinear
F
world average top-quark mass m , the dynamically es- soft term B are determined by the Z-boson mass M
t µ Z
tablished boundary conditions of No-Scale supergravity, andtanβ afterelectroweaksymmetrybreaking(EWSB).
radiative electroweak symmetry breaking, the centrally In the simplest No-Scale boundary conditions,
observed WMAP7 CDM relic density [30], and precision M =A=B =0, while M may be non-zero at the
0 µ 1/2
LEP constraints on the lightest CP-even Higgs boson unification scale, allowing for low energy supersymme-
m [31,32]andotherlightSUSYcharginoandneutralino try breaking. This scenario appears to come into its
h
mass content, remains viable even after careful compar- own only when implemented at a scale approaching the
ison against the first 1.1 fb−1 [27, 29] of LHC data. We Planck mass [50, 51]. Accordingly, MF, the point of the
shall show that exclusive of the vector-like particle con- second stage flipped SU(5) U(1) unification, tran-
X
×
tribution,the lightHiggsmassisstablypredictedwithin spires as a plausible candidate scale only when substan-
thisregiontotakeavaluebetween119.0-123.5GeV,con- tially decoupled from the primary GUT unification of
sistent with the surplus of observed events in the analy- SU(3) SU(2) at the scale M via a revision to the
C L 32
×
sespresentedbytheCMS,CDF,andDØCollaborations. renormalization group equations (RGE) from the extra
Significantly, the most promising subspace of this region -Theory vector multiplets [17, 18]. These interdepen-
F
includes secondary bounds on the flavor changing neu- denciesconspiretodiminishratherthanbroadenthelevel
tral current(b sγ) process,contributions to the muon of uncertainty in the model’s predicted phenomenology.
→
anomalous magnetic moment (g 2) , and the rare de- Utilizing the dynamically established boundary con-
µ
cay process B0 µ+µ−, all of w−hich cohere with spin- ditions of No-Scale Supergravity at the -SU(5) unifi-
s → F
independent σSI [33] and spin-dependent σSD [34] scat- cation scale MF, we have previously delineated the ex-
tering cross-section bounds on Weakly Interacting Mas- traordinarily constrained Golden Point [17] and afore-
siveParticles(WIMPs),inadditiontofreshlimitsestab- mentioned earliest derived incarnation of the Golden
lishedontheannihilationcross-section σv ofWIMPs Strip [18] which satisfied all current experimental con-
h iγγ
using gamma-rays derived from the Fermi Telescope ob- straints while additionally featuring an imminently ob-
servations [35][36]. This condensed subspace, an up- servable proton decay rate τ [52]. The most constric-
p
dating of our previously advertised “Golden Strip” [18], tive constraint imposed upon the viable model space is
offers a more focused prediction of the Higgs mass of the unification scale boundary on B =0. Furthermore,
µ
around 120-121 GeV. We emphasize that the prediction through application of a “Super No-Scale” condition for
of the Higgs in the vicinity of 120 GeV has been an ex- the dynamic stabilization of the stringy modulus related
ceedingly natural and robust prediction of No-Scale - to the M boundary gaugino mass [19, 20, 23, 28],
F 1/2
SU(5),stableacrossthe fullmodelspace,whichwe have this mass along with the ratio of the Higgs VEVs
consistentlyadvertisedoverthecourseofagrowingbody tanβ [19, 20, 23, 28] has been dynamically determined.
of work [17–29]. The recent embellishments to the ex- The complete collection of supersymmetry breaking
perimental support for this standing correlation furnish soft terms evolve from the single parameter M in
1/2
it with a greatly enhanced immediacy and interest. thesimplestNo-Scalesupergravity,andconsequentlythe
particle spectra are proportionally comparable up to an
overall rescaling on M , leaving the majority of the
1/2
II. THE -SU(5) MODEL “internal” physical properties invariant. This rescaling
F
capability on M is not generally expected in compet-
1/2
ing supersymmetrymodels,due to the presenceoflarger
The study launched here is built upon the framework
parameterizationfreedom, particularly with respect to a
of an explicit model, dubbed No-Scale -SU(5) [17–
F second independent boundary mass M for scalar fields.
29], uniting the -lipped SU(5) Grand Unified Theory 0
F Thisrescalingsymmetrycanbebrokentoaslightdegree
(GUT) [37–39] with two pairs of hypothetical TeV scale
by the vector-like mass parameter, although the depen-
vector-like supersymmetric multiplets with origins in -
F dence is rather weak.
theory [40–44] and the dynamically established bound-
aryconditions of No-ScaleSupergravity[45–49]. A more
completereviewofthismodelisavailableintheappendix
of Ref. [22]. III. PREDICTING THE HIGGS MASS
Supersymmetry is broken in the hidden sector in the
conventional framework, and then its breaking effects In the context of No-Scale supergravity, we require
are mediated to the observable sector throughgravityor M0=A=Bµ=0 at the unification scale MF, and permit
3
10000
-10 3.5 3.20
a ( 10 ) 3.10
-4
Br(b s ) ( 10 )
0 + - -9 3.00
8000 Br(Bs ) ( 10 ) 3.6
2.86
3.7
Region of the F-SU(5) parameter space
V) 6000 estimated to be excluded by the CMS 3.8
e Multijet Constraints
G 2.60
(V 3.9
M
4.0
4000 7
9
Golden Strip
2000 11
20
14
2.30
17
(M1/2,MV,mt,tan ) = (570,4000,173.2,21.5)
0
0 200 400 600 800 1000
M1/2 (GeV)
10000
mh lightest CP-even Higgs Boson Mass (GeV) 80014010500900
t1 Squark Mass (GeV) 1300
Gluino Mass (GeV)
uR Squark Mass (GeV)
8000 1200 1600
700
1100
600
Region of the F-SU(5) parameter space
V) 6000 estimated to be excluded by the CMS 1000
e Multijet Constraints 1200
G 500
(V 900 1100
M
800
4000 1000
123
900
118 122 Golden Strip
2000 800
119
700
120 600121
(M1/2,MV,mt,tan ) = (570,4000,173.2,21.5)
0
0 200 400 600 800 1000
M1/2 (GeV)
FIG.1: Thebare-minimallyconstrainedparameterspaceofNo-Scale -SU(5)isdepictedasafunctionofthegauginoboundary
F
mmaagssneMtic1/m2,otmheenvte(cgtor-2l)ike,amnadssthMeBV,0andµ+viµa−thperoscoelsisde,sdinasthheedu,papnedrdpolotttesdpaccoen,twouitrhltinheesm, tahsseg(rbad→ienstγs)i,nmGueoVnoafntohmeallioguhst
stop squarket1,gluino−ge,rµight-handedsu→psquarkueR,andlight Higgs massmh in thelower plotspace. WenotethattheHiggs
mass contours drawn here do not include any additional contributions from the vector-like particles. The region estimated to
be disfavored by the first inverse femtobarn of integrated LHC luminosity is marked out with the crosshatch pattern. The
vertical strip embossed in gold, referred to as the Golden Strip, represents an experimentally favored region consistent with
the bare-minimal experimental constraints of [23] and both the (b sγ) process and contributions to the muon anomalous
magnetic moment (g 2) . The Golden Strip also includes the B→0 µ+µ− decay, however this constraint is satisfied by
− µ s →
the entire viable model space. The expanded region adorned in silver imposes these identical constraints, though with a more
conservative estimate of ∆a =27.5 18.5 10−10. The labeled point is the benchmark of Table (I).
µ
± ×
4
distinctive inputs for the single parameter M1/2(MF) to We take µ > 0 as suggested by the results of (g 2)µ
−
translate under the RGEs to low scale outputs of B for the muon and execute a full scan of the model space
µ
and the Higgs mass squares M2 and M2 . This evo- throughinputfreedomofthegauginomassM ,vector-
Hu Hd 1/2
lution continues until the point of spontaneous break- like mass parameter M , and tanβ. The resultant so-
V
down of the electroweak symmetry at M2 +µ2=0, at lution space is then assessed against the bare-minimal
Hu
which scale minimization of the broken potential deter- constraint set introduced in Ref. [23]. To summarize
mines the physical low energy values of µ and tanβ. In from Ref. [23], the bare-minimal constraints are de-
practice, we implement this procedure by employing a fined by compatibility with the world average top quark
proprietarymodification of the SuSpect 2.34[53] code- mass m = 173.3 1.1 GeV [58], the prediction of a
t
±
base to run the RGEs within MicrOMEGAs 2.1 [54] to suitable candidate source of cold dark matter (CDM)
compute the supersymmetry and Higgs mass spectrum. relic density matching the upper and lower thresholds
In principle, the Bµ(MF)=0 condition fixes the value of 0.1088 ΩCDM 0.1158 set by the WMAP7 mea-
≤ ≤
tanβ atlowenergythroughrunningoftheRGEs,though surements [30], a rigid prohibition against a charged
this procedure is at odds with the current configuration lightest supersymmetric particle (LSP), conformity with
of the proprietary revised version of the SuSpect 2.34 the precision LEP constraints on the lightest CP-even
codebase. Thus, we equivalently isolate the Bµ(MF)=0 Higgs boson (mh 114 GeV [31, 32]) and other light
≥
solution set by instead allowing tanβ to float freely and SUSYchargino,stau,andneutralinomasscontent,anda
subsequently apply a self-consistency check. self-consistency specification on the dynamically evolved
For the gauge couplings, we consider two-loop RGE value of Bµ measured at the boundary scale MF. An
running, though we only consider one-loop RGE run- uncertainty of 1 GeV on Bµ = 0 is allowed, consistent
±
ning for the gaugino masses, µ term, supersymmetry withthe inducedvariationfromfluctuationofthestrong
breaking scalar masses, trilinear A-terms, and B term. coupling within its error bounds and the expected scale
µ
In -SU(5) models, the one-loop beta function b for of radiative electroweak (EW) corrections.
3
F
SU(3) is zero due to the vector-like particle contri- The cumulative result of the application of the bare-
C
bution [40], so the gaugino mass M is constant from minimalconstraintsshapes the parameterspace into the
3
the electroweak scale to the M32 scale [17]. In contrast, uniquely formed profile situated in the M1/2,MV plane
the two-loop gauge coupling RGE running and one-loop exhibited in Fig. (1), from a tapered light mass region
gauginomassRGErunningfortheSU(2) U(1) gauge withalowerboundoftanβ =19.4intoamoreexpansive
L Y
symmetry track eachother since the gauge×couplings for heavier regionthat ceases sharply with the chargedstau
SU(2) U(1) are weak; thus, the two loop effects are LSPexclusionaroundtanβ 23. The totalmodelspace
small.LF×or the cYalculation of the radiative corrections in beyondthehashedoverregio≃nillustratedinFig.(1)con-
the Higgssectorto determine the physicalHiggsmasses, sists of those points within the parameter space not ex-
weimplementthefullone-loopplusleadingtwo-loopcal- cluded by the CMS 1.1 fb−1 constraints, as derived in
culations. Ref. [27]. We demarcate the smooth light Higgs mass
m gradient in the lower plot space of Fig. (1) with the
To solve the “µ” problem for the vector-like parti- h
emphasizedboldcontourlines. TheregioninFig.(1)sur-
cle masses, we can consider the following mechanisms:
viving the CMS constraints assertively predicts a quite
(1) The Giudice-Masiero mechanism [55], where such a
narrow Higgs mass range of 119.0 to 123.5 GeV, linked
“µ” term is generated from high-dimensional operators;
toatopquarkmasswithin theworldaverage173.3 1.1
(2) There exist additional Standard Model singlets in F-
±
GeV. We note that this range of 119.0 to 123.5 GeV is
Theory models. The vector-like particles can couple to
exclusive of any contributions from the vector-like par-
these singlets and obtain their masses after these sin-
ticles, though we anticipate only a small upward shift
gletsacquireVEVs. Thisissimilartothesolutiontothe
in the Higgs mass for the region of the model space
“µ”probleminthenext-to-the-MinimalSupersymmetric
with M & 4 TeV, which includes the benchmark of
Standard Model (NMSSM). V
Table (I). Nonetheless, this span of Higgs masses thus
The vector-like particles can contribute to the Higgs
far agrees well with the excess of data events observed
boson masses if they couple to the Higgs fields. For sim-
by the CMS [1], CDF and DØ [4] Collaborations in the
plicity though, we assume here that such couplings are
vicinity of 120 GeV. Note also that the Higgs mass in
small. Regardless of this assumption however, our fa-
the entire model space is comfortably below the recently
vored benchmark point that we shall introduce in the
derived upper bounds of 145 GeV by CMS [1] and 146
next section and in Table (I) possesses an M of about
V GeV by ATLAS [2].
4 TeV, hence the contributions of the vector-like parti-
cles to the Higgs mass of the benchmark of Table (I) are
small even if their Yukawa couplings to the Higgs fields
IV. THE GOLDEN STRIP
are not small [56]. Though we assume negligible cou-
plings of the vector-like particles to the Higgs fields for
the entire model space here in this paper, we shall com- The Golden Strip is strictly defined by the mutual in-
pute the precise contributions ofthe vector-likeparticles tersection of the bare-minimalconstraints with the rare-
to the Higgs boson mass in a forthcoming analysis [57]. decay processes b sγ, B0 µ+µ−, and the muon
→ s →
5
anomalous magnetic moment, as depicted by the con-
TABLE I: Spectrum (in GeV) for M = 570 GeV, M =
densed vertical slice embossed with gold in both plot 1/2 V
4 TeV, m = 173.2 GeV, tanβ = 21.5. Here, Ω = 0.11 and
spaces of Fig. (1). For the experimental limits on the t χ
thelightest neutralino is 99.8% bino.
flavor changing neutral current process b sγ, we draw
on the two standard deviation limits B→r(b sγ) = χe01 115 χe±1 247 eeR 214 et1 623 ueR 1112 mh 120.5
3.52 0.66 10−4, where the theoretical a→nd exper- χe02 247 χe±2 925 eeL 602 et2 1039 ueL 1209 mA,H 1001
iment±al erro×rs are added in quadrature [59, 60]. We χe03 921 νee/µ 596 τe1 123 eb1 995 deR 1153 mH± 1004
l∆ikaew=ise27a.p5ply1t6h.5e tw1o0−s1t0an[6d1a]rfdordtehveiaatnioonmbaloouunsdmaraiegs- χe04 924 νeτ 581 τe2 590 eb2 1101 deL 1211 eg 783
µ
± ×
netic moment of the muon, (g 2) . Lastly, we use the
µ
1re.9ce×nt1ly0−p8ub[6li2s]hfeodruthpepeprrobcoeusns−dBos0f→Brµ(B+µs0−→. Tµh+eµ−m)or<e tisurteheofrNatoh-SercauleniFqu-SeUe(n5c)odwihnigchMfa(ceti1l)ita<tesMth(geis)d<extMer(itqey)
spacious vertical segment adorned in silver in Fig. (1)
of the SUSY particle mass hierarchy. This pattern of a
equally consists of all the above constraints, though
stoplightestsupersymmetric quark,followedby a gluino
adopting a more conservative estimate of the 2σ lower
which is likewise lighter than the remaining squarks, is
bound of ∆a 9.0 10−10. This shift is supported
µ stable across the full model space, and has not been ob-
≥ ×
byamorerecentexperimentwhichsuggestsadownward
served to be precisely replicated in any benchmark con-
shiftofthecentralvalue [63]. Moreover,weremarkthat
trol sample of the MSSM, and in particular not by any
our greater confidence between these two experimental
of the “Snowmass Points and Slopes” benchmarks [64].
metrics is with those referencing b sγ, and that since
This hierarchy allows No-Scale -SU(5) to bypass col-
→
the two key rare process constraints operate in overlap- F
lider limits on light squark masses much more adroitly
pingopposition,thesilverregionactuallycomescloserto
thanCMSSMconstructionswithcomparablylightLight-
the central value of this branching ratio. We note that
est Supersymmetric Particles (LSPs). It is moreover
the entire Gold and Silver Strips remainunblemished by
directly responsible for a smoking-gun signal of ultra-
the first 1.1 fb−1 of LHC data, representing optimum
high ( 9) jet multiplicity events, which is expected to
candidate regions for the discovery of supersymmetry. ≥
be prominently visible in LHC searches, given suitable
Additionally, notice that the Higgs mass in the Golden
data selection cuts [21, 22, 27]. The distinctive -SU(5)
Strip is right about 120 GeV, in accord with the over- F
sparticle mass hierarchyresponsible for a preponderance
all combined contributions of all individual Higgs decay
of the robust model characteristics summarized in this
channels observed by CMS above the Standard Model
work is graphically illustrated in the lower plot space of
expectations [1]. Fig. (1), where we demarcate the light stop et , gluino ge,
1
We select a benchmark from the Golden Strip repre- and ue squark mass contours.
R
sentingwhatwebelievetobethemostoptimumpointto
be assessed against experiment, as identified in Fig. (1)
by the model parameters, with the spectrum of super- TABLE II: Conformity with all the measured constraints for
symmetric masses given in Table (I). At the benchmark, the Table (I) benchmark point M = 570 GeV, M = 4
1/2 V
the isolated mass parameter responsible for the global TeV, mt = 173.2 GeV, tanβ = 21.5. Here MM is used to
particle mass normalization,namely the gauginobound- designate the minimum minimorumof ouruniverse.
ary mass M1/2=570 GeV, is dynamically determined at Constraint SU(5) Value
a secondary local minimization of the minimum of the F−
m >114 GeV 120.5 GeV
Higgs potential V [20, 23, 28] in a manner which is h
min
m =173.3 1.1 GeV 173.2 GeV
deeply consistent with all precisionmeasurements at the t ±
physicalelectroweakscale,andinparticular,theZ-boson Ωχe01 =0.1123±0.0035 0.1100
mass MZ itself [28]. Supplementing experimental con- Br(b sγ)=3.52 0.66 10−4 2.88 10−4
straints with the dynamical determination of this mini- ∆a→=27.5 16±.5 10×−10 11.5 ×10−10
µ
mum minimorum of our universe, this point fulfills the Br(B0 µ+µ±−) 1×.9 10−8 3.7×10−9
inclusivegroupofwell-establishedexperimentalandthe- s → ≤ × ×
τ 1.0 1034yr 5.1 1034yr
oretical constraints, as summarized in Table (II), merg- p ≥ × ×
σ <7 10−9pb 1.5 10−10pb
ing a bottom-up experimentally driven analysis with a SI × ×
theoretically motivated top-down approach. σSD <4.5 10−3pb 1 10−7pb
× ×
σv <10−26cm3/s 2 10−28cm3/s
h iγγ ×
M @M =91.187 0.001 GeV MM 572.2 GeV
1/2 Z ±
V. A SMOKING GUN SIGNAL
The mechanism of this distinctive signature may be
The intricate evasion of the full company of indepen- traced to a fact already noted, that the one-loop β-
dent experimental constraints cataloged in the body of functionb oftheSU(3) gaugesymmetryiszerodueto
3 C
Table (II) may appear serendipitous, but it is certainly the extra vector-like particle contributions [40]. The ef-
not accidental. The definitive phenomenological signa- fectonthe coloredgauginoisdirectinthe running down
6
from the high energy boundary, leading to the relation ultra-high jet cutting strategy in extracting a No-Scale
M /M α (M )/α (M ) (1) and precipitat- -SU(5) supersymmetry signal, we use the Discovery
3 1/2 3 Z 3 32
≃ ≃ O F
ing the conspicuously lightgluino mass assignment. The Index first presented in Ref. [25] and find that by im-
e
lightness of the stop squark t is likewise attributed to plementing upon the M =570 GeV benchmark point
1 1/2
the large mass splitting expected from the heaviness of of Table (I) the CMS post-processing cuts of Ref. [11],
the top quark, via its strong coupling to the Higgs. The thoughonlyretainingthoseeventswithninejetsormore,
vector-like particles, with a multiplet structure almost requires 8.5fb−1 of LHC data in order to achieve a five
uniquelymandatedbyavoidanceofaLandaupolewithin standard deviation discovery of supersymmetry. With 5
the -theorymodelbuilding [40–44]context, areinturn fb−1 currently in hand at the LHC as we close the year
neceFssaryinordertoachieveasubstantialseparationbe- 2011,andalsoconsideringprojectionsthat10fb−1 could
tween the initial gauge unification of SU(3) SU(2) be attained by the end of the year 2012, a five standard
C L
at M 1016 GeV, and the secondary unifi×cation of deviationdiscoveryofan -SU(5)supersymmetrysignal
32
SU(5) ≃U(1)X at MF 7 1017 GeV. This elevation usingthe CMSsearchstraFtegyof[11]iscertainlyachiev-
× ≃ ×
of the final GUT scale, which is possible only within able. However, a prerequisite of utmost importance for
the context of a model with a two-stage unification like the accessibility of such a discovery is that only those
Flipped SU(5),appearslikewiseto be necessaryinorder events with nine or more jets can be retained. For in-
to successfully implement the No-Scale boundary condi- stance,ifalleventswith6ormorejetsareretainedwhile
tions, and in particular,the vanishing of the Higgs bilin- maintaining the CMS post-processing cutting strategy
ear softterm B . We emphasize againthat this scenario of [11], then the discovery threshold for -SU(5) super-
µ
appearstocomesintoitsownonlywhenappliedatauni- symmetryelevatestoabout14fb−1. YetFevenmoregrave
ficationscaleapproachingthe Planckmass[50]. The dy- will be preserving all events with three jets or greater
namicsofNo-ScaleSupergravitymaythemselvesplayan while implementing the CMS cuts of [5], where in this
indispensable role in establishing the cosmological flat- extremely detrimental scenario a massive 100fb−1 of lu-
ness of our Universe, and possibly even in allowing for minosity at the LHC will be required for a five stan-
theshepherdingofavastmultitudeofsisteruniversesout darddeviation discoveryof an -SU(5) supersymmetric
F
of the primordial quantum “nothingness”, while main- signal. Therefore, we would implore the CMS and AT-
taining a zero balance of some suitably defined energy LAS Collaborations to not exclude the examination of
function. events with nine or more jets in the analysis of LHC
data; outside of this optimized search region, the super-
symmetrysignalofmodelslikeNo-Scale -SU(5)willbe
F
VI. LHC SEARCH STRATEGY strongly masked, and possibly undetectable. Given the
presently outlined phenomenological attributes that col-
lectively endorse No-Scale -SU(5)as a principalSUSY
In Fig. (2), we augment the analysis of Ref. [27] by F
GUT candidate, diligence in the investigation of its key
presenting the number of events generated in a Monte
experimental signature strikes us as rather advisable.
Carlo simulation of our M = 570 GeV benchmark
1/2 OursimulationwasperformedusingtheMadGraph[65,
point from Table (I) summed with the Standard Model
66] suite, including the standard MadEvent [67],
background statistics of Ref. [11]. We superimpose this
PYTHIA [68] and PGS4 [69] chain, with post-processing
-SU(5) plus Standard Model background signal onto
F performedby a customscriptCutLHCO[70] (availablefor
a reprinting of the CMS Preliminary Standard Model
download) which executes the desired cuts, and counts
backgroundstatisticsandobservedeventsfromRef.[11],
featuring 1.1 fb−1 of collision data and a √s = 7 TeV and compiles the associated net statistics. All 2-body
SUSY processes have been included in our simulation,
beam energy. We impose upon the -SU(5) signal a
F which follows in all regards the procedure detailed in
set of post-processing cuts designed to mimic those de-
Ref. [22]. The Monte Carlo is typically oversampled for
scribed in the CMS report. We emphasize that the
SUSY processes and scaled down to the requisite lumi-
-SU(5) benchmark is quite capable of accounting for
F nosity,whichcanhavetheeffectofsuppressingstatistical
theobservedeventexcesses,includingmostcompellingly
fluctuations.
at the nine jet count, while avoiding any conspicuous
overproduction. Although we do here attempt to con-
form with the -SU(5) CMS post-processing cuts pre-
sented in Ref. [F11], we maintain aggressive advocacy of VII. CONCLUSIONS
the ultra-high jet cutting strategy described extensively
in Refs. [21, 22, 25–27]. We believe that the discoveryof While the search for supersymmetry progressesat the
asupersymmetrysignalwillmostlikelymanifestitselfin LHC with no conclusive signal observed as of this date,
the data observations for nine or more jets; hence, a jet the questforthe Higgsbosonis rapidlyaccelerating. All
cuttingstrategyoptimizedforextractingsupersymmetry indications from the CMS, ATLAS, CDF, and DØ Col-
fromultra-highjeteventscouldprovetobemoreefficient laborations suggest that a statistically significant obser-
at the LHC by one order of magnitude [27]. vation of the Higgs boson in the vicinity of 120 GeV
Furthermore, to emphasize the significance of the could be on the near-term horizon, possibly by the end
7
FIG. 2: The CMS Preliminary 2011 signal and background statistics for 1.1 fb−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
-SU(5)modelspacebenchmarkofTable(I).Theplotcountseventsperjetmultiplicity,withnocutonαT. TheMonteCarlo
F
overlay consists of the -SU(5) supersymmetry signal plus the Standard Model background, thus permitting a direct visual
F
evaluation against theCMS observed data points.
of 2011. It is thus imperative that we begin to spotlight clude any contributions from the vector-like particles,
those supersymmetry models capable of engendering a we plan to return to this issue in the future to explic-
naturalpredictionforaHiggsbosonmassnear120GeV. itlycomputetheseadditionalcontributionsandaugment
We have focused on one such model here by the name of the mass limits as necessary. The benchmark selected
No-Scale -SU(5). for attention in the present work features particularly
F
heavy vector-like multiplets, so that we might for sim-
Applyingonlyasetofbare-minimalexperimentalcon-
plicity consider the contributionto the Higgs mass to be
straints, more than 80% of the resulting model space of
the -SU(5)remainsviable afterthe first1.1fb−1 oflu- suppressed. We thus anticipate that predictions for this
F region of the model space will remain stable when fu-
minosityattheLHC.Wefoundthatthisentiresurviving
ture attention is given to higher order effects, although
model space naturally generates a Higgs mass of 119.0-
that may not remain strictly true for smaller values of
123.5GeV,inaccordwiththeoverallcombinedcontribu-
M . Exposingacondensedsubspaceofthislargerregion
tions of all individual Higgs decay channels observed by V
where the bare-minimalconstraints intersect the thresh-
CMS above the expected Standard Model background.
olds of the b sγ, B0 µ+µ−, and muon anoma-
Though this 119.0-123.5 GeV mass range does not in- → s →
8
lous magnetic moment processes, we have uncoveredthe ranted enthusiasm throughout the high-energy physics
mostexperimentallyfavorableregion,dubbedtheGolden community, but we close with a brief suggestionof what
Strip, which continues untouchedby the rapidly advanc- the determination of a Higgs boson discovery around
ing LHC constraints, remaining wholly viable for super- 120 GeV might further disclose as to the structure of
symmetrydiscovery,while furtherindicatingaHiggsbo- a more fundamental theory at high energy scales. Given
son at about 120-121 GeV within this favored subspace. the recent radical curtailing of the dominant mSUGRA
Selecting a representative point from a location within and CMSSM model spaces,a Higgs boson near 120 GeV
the Golden Strip where the dynamical determination of mightbeinterpretedasaratherstronglysuggestivepiece
the secondary minimization of the minimum V of the of evidence to bolster the No-Scale -SU(5) framework
min
F
Higgs potential agrees to high-precision with precision in particular, and string theory in general.
measurements at the electroweak scale, we assessed this
benchmark for its ability to fit the CMS multijet data
points and elucidate any unexplained statistical excesses
in the first 1.1 fb−1 of LHC data reported by the CMS Acknowledgments
collaboration. The outcome was positive, with an inter-
esting surplus of events at nine jets perfectly explicable This research was supported in part by the DOE
within the realm of the No-Scale -SU(5)Golden Strip. grantDE-FG03-95-Er-40917(TLandDVN),bytheNat-
F
For those physicists and non-physicistsalike who have ural Science Foundation of China under grant numbers
been patiently awaiting a categorical discovery of the 10821504and11075194(TL),bytheMitchell-HeepChair
Higgs boson for decades, the time may be at hand, as inHighEnergyPhysics(JAM),andbytheSamHouston
anexceedinglyplausibleprospectofadiscoverynear120 StateUniversity2011EnhancementResearchGrantpro-
GeVloomslargeoverthe comingmonths. Certainly,the gram(JWW).WealsothankSamHoustonStateUniver-
first major discovery of the LHC era will generate war- sityforprovidinghighperformancecomputingresources.
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