Testing No-Scale Supergravity with the Fermi Space Telescope LAT
Tianjun Li, James A. Maxin, Dimitri V. Nanopoulos, Joel W. Walker
aa r X i v : . [ h e p - ph ] F e b ACT-9-13, MIFPA-13-30
Testing No-Scale Supergravity with the Fermi Space Telescope LAT
Tianjun Li,
1, 2
James A. Maxin, Dimitri V. Nanopoulos,
2, 4, 5 and Joel W. Walker State Key Laboratory of Theoretical Physics and Kavli Institute for Theoretical Physics China (KITPC),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 Department of Physics and Astronomy, Ball State University, Muncie, IN 47306 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, USA
We describe a methodology for testing No-Scale Supergravity by the LAT instrument onboardthe Fermi Space Telescope via observation of gamma ray emissions from lightest supersymmetric(SUSY) neutralino annihilations. For our test vehicle we engage the framework of the supersym-metric grand unified model No-Scale Flipped SU (5) with extra vector-like flippon multiplets derivedfrom F-Theory, known as F - SU (5). We show that through compression of the light stau and lightbino neutralino mass difference, where internal bremsstrahlung (IB) photons give a dominant con-tribution, the photon yield from annihilation of SUSY dark matter can be elevated to a number ofevents potentially observable by the Fermi-LAT in the coming years. Likewise, the increased yieldin No-Scale F - SU (5) may also have rendered the existing observation of a 133 GeV monochromaticgamma ray line visible, if additional data should exclude systematic or statistical explanations. Thequestion of intensity aside, No-Scale F - SU (5) can indeed provide a natural weakly interacting mas-sive particle (WIMP) candidate with a mass in the correct range to yield γγ and γZ emission linesat m χ ∼
133 GeV and m χ ∼
145 GeV, respectively. Additionally, we elucidate the emerging empir-ical connection between recent Planck satellite data and No-Scale Supergravity cosmological modelswhich mimic the Starobinsky model of inflation. Together, these experiments furnish rich alternateavenues for testing No-Scale F - SU (5), and similarly structured models, the results of which maylend independent credence to observations made at the LHC. PACS numbers: 11.10.Kk, 11.25.Mj, 11.25.-w, 12.60.Jv
I. INTRODUCTION
Supersymmetry (SUSY) provides an elegant solutionto naturally resolve the gauge hierarchy problem withinthe Standard Model (SM), and presuming R parity con-servation, the lightest supersymmetric particle (LSP)neutralino serves as a viable cold dark matter (CDM)candidate [1, 2]. The empirical search for a weakly in-teracting massive particle (WIMP) currently evolves onmultiple fronts. For instance, the Large Hadron Collider(LHC) at CERN sifts through trillions of proton-protoncollisions for a rare glimpse of an anomalous missingtransverse energy component of hypothetical supersym-metric interactions, where the SUSY LSP escapes thedetector without direct observation as a consequence ofits neutral U (1) EM charge and status as an SU (3) C sin-glet. Sharing an equivalent objective, the XENON [3],CDMS [4], and LUX [5] experiments parse through statis-tics gathered from ionization and scintillation of inertgases and semiconductors to potentially uncover directobservation of elastic collisions of a WIMP within thescintillating material. Likewise, the Fermi Space Tele-scope [6] strives toward this goal through latent obser-vation of photon decay relics from WIMP annihilations.Status of observability for this latter conjectural phenom-ena, primarily within the context of a well defined modelnamed No-Scale F - SU (5), presides as the motivating in- tent of this work; this approach offers a viable link be-tween SUSY bino dark matter and a recently observedmarginal sharp line spectra, and perhaps more perti-nently, crafts a roadmap for future discovery of bino darkmatter utilizing current and forthcoming sky-scanningsurveys.The annihilation of WIMPS within inner galactic re-gions can be prospective sources of gamma ray emissionsthat compete with the astrophysical background. SUSYLSP neutralinos can annihilate directly to gamma raysmono-energetically, yielding a (quasi-) monochromaticenergy spectrum via annihilation processes e χ e χ → γγ ( E γ = m χ ), e χ e χ → γZ , and e χ e χ → γh . These pro-cesses occur at 1-loop, since WIMPS cannot directlycouple to the photons, thereby suppressing the cross-section of thermally produced dark matter. Internalbremsstrahlung (IB) photons can also produce sharpspectral features with annihilation into charged particlesvia e χ e χ → f f γ , with the benefit that IB processes occurat tree level, thus providing a larger annihilation rate forbino neutralinos and amplifying observability.In 2012, a tentative 130 GeV monochromatic gammaray line was observed [7, 8] in the Fermi-LAT all skysurveys, exhibiting a local signal significance of 4.3–4.6 σ (3.1–3.3 σ global). Post reprocessing of the data by theFermi Collaboration, the budding signal shifted closer to133 GeV with a diminished local signal significance of3.3 σ (global 1.6 σ ) [9], somewhat dampening the enthusi-asm for a prospective indirect discovery of dark matter.Additionally, a deviation at this same E γ ∼
133 GeV hasbeen observed by the LAT instrument in a control sampleof gamma rays from the Earth’s limb, elevating the like-lihood that the reported effects are systematic in origin.Therefore, the jury remains out on the validity of the sig-nal, and a conclusive judgment may not be pronouncedfor as much as two additional years, pending additionaldata acquisition and analysis. Yet, this tentative obser-vation highlights the importance of a model dependentanalysis of the Fermi-LAT’s reach into the supersymmet-ric parameter space. Due to the small bino annihilationcross-section of h σv i γγ ∼ − cm / sec, in comparisonto the best fit of the deviation in the Fermi-LAT data of h σv i γγ ∼ − cm / sec [7, 8], the supersymmetric ori-gins of the 130 GeV monochromatic gamma ray signalwere quickly dismissed [10]. Minus the presence of anextraordinarily large boost factor ( BF ) of BF ∼ γγ emission at 133 GeV and γZ emission at ∼
145 GeV canbe naturally explained [11] in the supersymmetric grandunified theory (GUT) model No-Scale flipped SU (5) withextra vector-like matter multiplets called “ flippons ” [11–34], the model referred to as F - SU (5). When consid-ering a dominant contribution from the IB final states,the No-Scale F - SU (5) upper 2 σ limit on the WIMP massfor the observed monochromatic gamma ray line is about M / ∼ e χ e χ → τ + τ − final state, where the latest up-per limit on the annihilation cross-section from obser-vation of cosmic rays is h σv i ττ . × − cm / sec [36],though parallel studies suggest the current limit couldbe as low as h σv i ττ . × − − − cm / sec [37].However, the SUSY mass M / ∼
775 GeV in No-Scale F - SU (5) has an annihilation cross-section of h σv i ττ =6 . × − cm / sec, placing the necessarily required largeboost factor of BF ∼ ∼ − × [seeTable II]) larger than the gamma gamma flux, the IBcross section is roughly 20 times larger than the gammagamma cross section. Therefore, the No-Scale F - SU (5)IB cross section is on the order of 5 × − cm / sec.Thus, the corresponding boost factor that is needed toexplain the 133 GeV Fermi-LAT gamma ray line in thisscenario is substantively smaller, on the order of 50 to100. If one allows that the dark matter density, whichenters into the pairwise interaction as a square, is sevento ten times larger than what is traditionally used in thedark matter subhalo, this mechanism can explain the ob-served gamma ray line.Regardless of whether the existing marginal 133 GeVgamma ray line eventually is shown to be a system-atic or statistical effect, upcoming data from the FermiSpace Telescope (or future projects including Gamma-400, DAMPE and HERD) may provide exclusive insightsinto the SUSY parameter space in the No-Scale F - SU (5)model. A central task confronted by this document isclassification of the gamma ray signatures associable with F - SU (5), and quantification of their detection prospectsacross the model space, especially in the context of anadditional six years of data collection by the Fermi-LATinstrument. Given the reality (failing upward revisionsin estimates of the dark matter density profile) that thepresent generation gamma telescope will not achieve thesensitivity required to observe bino dark matter at an-nihilation cross-sections of h σv i γγ ∼ − cm / sec, wehighlight a phenomenologically viable scenario where theprobability of uncovering an observable indirect detectionsignature is somewhat more appreciable; in particular,we shall consider increasing the photon yield from anni-hilation via compression of the lightest slepton and LSPneutralino mass difference to near degeneracy, therebyestablishing upward pressure on the annihilation rate,which can further elevate the advantage of the alreadydominant tree level IB effects over monochromatic looplevel dark matter annihilation. This methodology can bequite naturally accommodated in No-Scale F - SU (5) withno effect on the spectrum calculations and experimen-tal constraints established in the model space [33]. Theone unavoidable consequence of such a maneuver mani-fests itself in a suppressed bino neutralino relic densityfor M / . M / in No-Scale F - SU (5), a naturally occur-ring linear compression in the light stau and LSP massdifference counteracts this bino relic density suppres-sion in F - SU (5) [33] ( i.e. elevation in the annihilationrate induced by mass degeneracy is counteracted by sim-ple mass suppression), eventually generating the Planckmeasured CDM relic density Ω h = 0 . ± . M / ∼ M ( e χ , e τ ) ≃ F - SU (5) framework suggested here asa vehicle for interpreting Fermi-LAT observations hasalready been well developed. The model is basedupon the tripodal foundations of the dynamically estab-lished boundary conditions of No-Scale Supergravity, theFlipped SU (5) Grand Unified Theory (GUT), and thepair of TeV-scale hypothetical flippon vector-like super-multiplets [11–34] derived within local F-theory modelbuilding. The convergence of these features has beenshown to naturally resolve many longstanding theoreticalissues, whilst comparing positively with real world exper-imental observation. Moreover, a recent analysis [40–42]suggests that a cosmological model based upon the No-Scale supergravity sector yields compatibility with thePlanck satellite measurements. With convenient super-potential parameter choices, the new cosmological modelcompatible with Planck data is a No-Scale supergravityrealization of the Starobinsky model of inflation [43–45].This prospective empirical evidence of the existence ofa ubiquitous No-Scale supergravity sector amplifies ourmotivation for implementing No-Scale F - SU (5) as a re-alistic framework appropriate for evaluation against for-merly recorded and forthcoming Fermi-LAT gamma rayemission statistics.The structure of this paper is as follows. First we pro-vide a brief review of the No-Scale F - SU (5) model, andthen elaborate the interesting empirical correlation be-tween recent Planck satellite data and cosmological mod-els based upon No-Scale Supergravity that realize infla-tion in the Starobinsky mode. Next we shall presentmore detailed aspects of the IB effects on the annihila-tion rate and, finally, we present some benchmark mod-els with SUSY spectra linked to neutralino annihilationcross-sections testable by the Fermi Space Telescope inthe upcoming years, as well as benchmarks consistentwith a No-Scale F - SU (5) explanation of the observed133 GeV monochromatic gamma ray line. II. THE NO-SCALE F - SU (5) MODEL
Mass degeneracy of the superpartners has not beenobserved, indicating that SUSY breaking occurs near theTEV scale. Supergravity models are GUTs with gravitymediated supersymmetry breaking, where we can fullycharacterize the supersymmetry breaking soft terms bya limited set of universal parameters: universal gauginomass M / , universal scalar mass M , Higgsino mixing µ -parameter, Higgs bilinear B µ -parameter, and univer-sal trilinear coupling A . The B µ and | µ | parameters are then determined at low energy through minimization ofthe Higgs potential triggering radiative electroweak sym-metry breaking (REWSB), with the sign of µ remainingundetermined. Equivalently, we can trade B µ at low en-ergy for the low energy ratio of the Higgs vacuum ex-pectation values (VEVs) tan β . Subsequently remainingare the high-energy boundary conditions M / , M , B µ , A , and the low energy boundary condition tan β , plusthe undetermined sign of µ , which we always take to besgn( µ ) >
0, as suggested by the results of ( g µ − / M / undeterminedat the minimum of the scalar potential; iii) the quantityStr M is zero at the minimum. Large one-loop correc-tions would force M / to be either identically zero or ofthe Planck scale if the third condition were violated. Aminimal K¨ahler potential that meets the first two condi-tions is [46, 47] K = − T + T − X i Φ i Φ i ) , (1)where T is a modulus field and Φ i are matter fields, whichparameterize the non-compact SU ( N, /SU ( N ) × U (1)coset space. The third condition can always be satis-fied in principle and is model dependent [48]. From theK¨ahler potential in Eq. (1) we automatically attain theNo-Scale boundary condition M = A = B µ = 0, while M / is allowed to be non-zero and hence evolve natu-rally, and in fact, is necessary for SUSY breaking. More-over, the high-energy boundary condition B µ = 0 in prin-ciple determines tan β at low energy. The gravitino mass M / is determined by the equation d ( V EW ) min /dM / =0 due to the fact that the minimum of the electroweak(EW) Higgs potential ( V EW ) min depends on M / , andconsequently, the supersymmetry breaking scale is de-termined dynamically. We are thus left with a natural one - parameter model, with the sole degree of freedombeing the gaugino mass M / . As a deep fundamentalcorrelation to string theory, No-scale supergravity canbe realized in the compactification of the weakly coupledheterotic string theory [49], as well as the compactifica-tion of M-theory on S /Z at the leading order [50].Precise string-scale gauge coupling unification whilealso evading the Landau pole problem can be real-ized by supplementing the standard F -lipped SU (5) × U (1) X [51–54] SUSY field content with the followingTeV-scale vector-like multiplets (flippons) [55] (cid:16) XF ( , ) ≡ ( XQ, XD c , XN c ) , XF ( , − ) (cid:17) , (cid:0) Xl ( , − ) , Xl ( , ) ≡ XE c (cid:1) , (2)where XQ , XD c , XE c , XN c have the same quan-tum numbers as the quark doublet, the right-handeddown-type quark, charged lepton, and neutrino, respec-tively. Models of this nature can be realized in F -ree F -ermionic string constructions [56] and F -theory modelbuilding [57, 58], and have been appropriately designated F - SU (5) [57].The split-unification framework of F - SU (5) [51–54]provides for fundamental GUT scale Higgs represen-tations (not adjoints), natural doublet-triplet splitting,suppression of dimension-five proton decay [54, 59], and atwo-step see-saw mechanism for neutrino masses [60, 61].Adjustments to the one-loop gauge β -function coeffi-cients b i induced by inclusion of the vector-like flipponmultiplets generate the required flattening of the SU (3)Renormalization Group Equation (RGE) running ( b =0) [12], which manifests as a wide separation betweenthe primary SU (3) C × SU (2) L unification near 10 GeVand the secondary SU (5) × U (1) X unification near thePlanck mass. The corresponding baseline extension forlogarithmic running of the No-Scale boundary conditions,especially that of B µ = 0, permits ample scale for natu-ral dynamic evolution into phenomenologically favorablevalues consistent with experiment at the EW scale. The SU (3) C gaugino mass scale flattening generates a stablecharacteristic mass texture of M ( e t ) < M ( e g ) < M ( e q ),engendering a light stop and gluino that are lighter thanall other squarks [12].The No-Scale F - SU (5) model space satisfies a minimalset of necessary constraints from theory and phenomenol-ogy [18, 33]. The constraints are: i) consistency with thedynamically established boundary conditions of No-Scalesupergravity (most significantly the strict enforcement ofa vanishing B µ parameter at the ultimate flipped SU (5)GUT unification near M Pl , imposed as | B µ ( M F ) | ≤ h = 0 . ± . m t = 173 . ± . m h = 125 . ± . m h ∼
125 GeV, while also preservinga testably light SUSY spectrum that does not reintro-duce the gauge hierarchy problem via very heavy scalarsthat SUSY was originally intended to solve in the firstplace. A two-dimensional parameterization in the vector-like flippon super-multiplet mass scale M V and the uni-versal gaugino boundary mass scale M / is excised froma larger four-dimensional hyper-volume that also includesthe top quark mass m t and the ratio tan β . The en-during model space after application of these minimalconstraints is capable of maintaining the delicate bal-ance needed to realize the two conditions B µ = 0 andΩ h = 0 . ± . F - SU (5) model space after di-rect application of the constraints noted above consistsof a diagonal wedge ( cf. Ref. [33]) in the ( M / , M V )space, the width of which at small M / and small M V isbounded by the LEP constraints and by the CDM con-straints and the transition to a charged stau LSP at large M / and large M V . Conversely, the upper limit at large M V and the lower limit at small M V are constrained bythe central experimental range on the top quark mass.The intersection of all constraints yields a net experi-mentally viable model space extending from M / ≃ M / ≃ M V ≃ M V ≃
180 TeV.
III. NO-SCALE SUPERGRAVITY INFLATION
The elegantly minimalistic formalism of No-Scale Su-pergravity [46, 47, 64–66] allows for a deep fundamentalcorrelation to string theory in the infrared limit, the nat-ural inclusion of general coordinate invariance (generalrelativity), a supersymmetry breaking mechanism thatpreserves a vanishing cosmological constant at tree level(facilitating the observed longevity and cosmological flat-ness of our Universe [46]), natural suppression of CP vio-lation and flavor-changing neutral currents, dynamic sta-bilization of the compactified spacetime by minimizationof the loop-corrected scalar potential, and a powerful con-traction in parameterization freedom.Recently, an added phenomenological boost has beengiven to No-Scale Supergravities by detailed measure-ment of the Cosmic Microwave Background (CMB) per-turbations (the structural seeds of galactic superclusterformation residually imprinted upon the faint afterglowof the big bang) from the Planck [67] satellite. Manyimportant features predicted qualitatively by the cosmo-logical inflationary paradigm have been borne out, for in-stance, there are no significant signs of non-Gaussian fluc-tuations or hints of non-trivial topological features suchas cosmic strings. Additionally, these observations veri-fied a highly statistically significant tilt n s ≃ . ± . r < .
08 of tensor (directional) to scalar (isotropic)perturbations. These measurements, particularly of n s ,place many leading models of cosmic inflation in jeop-ardy (cf. Fig. 1 of Ref. [67]), although a curious sce-nario suggested by Starobinsky [43] in 1980 is known [44]to match the data effortlessly. This model is a ratherad-hoc modification of Einstein’s description of gravity,which combines a quadratic power of the Ricci scalar withthe standard linear term. At face value, this ( R + R )model is rather difficult to take seriously, but there issubstantial enthusiasm for the observation by John El-lis, Keith Olive and one of the authors (D.V.N), thatthis esoteric model is in fact conformally equivalent toNo-Scale supergravity with an SU (2 , /SU (2) × U (1)K¨ahler potential [40–42], which is a subcase of Eq. (1).To be specific, the algebraic equations of motion corre-sponding to an auxiliary scalar field Φ with a quadraticpotential that couples to a conventional Einstein termmay be freely substituted back into the action, resultingin the phenomenologically favorable quadratic power ofthe scalar curvature [68, 69]. In short, inflation in our F - SU (5) No-Scale SU ( N,
1) framework can be realizednaturally and is consistent with the Planck results.
IV. TESTING NO-SCALE F - SU (5) WITHFERMI-LAT
The monochromatic line signals are not the only mech-anism capable of generating gammas visible to the Fermi-LAT instrument. In fact, dark matter annihilation intotwo Standard Model particles with a radiated photon, aprocess known as internal bremsstrahlung, can also givesharp spectral features in the ray spectrum close to thedark matter mass [70]. The photon can arise from thefinal state radiation (FSR) or virtual charged particle ra-diation/virtual IB (VIB). Thus, the IB photons will bethe total contributions from both FSR and VIB.It is well known that the annihilation cross section ofthe LSP neutralinos into a pair of light SM fermions isstrongly suppressed by a factor m f /m χ due to the he-licity properties of a highly non-relativistic pair of Ma-jorana neutralinos. However, such suppression can beevaded if the fermion final states contain an additionalphoton f ¯ f γ , particularly when the photon is emittedfrom virtual sfermions with a mass close to the LSP neu-tralino. Therefore, the IB effects may explain the 133GeV Fermi-LAT gamma ray line [71, 72], or may predicta higher energy (for example 200 GeV) gamma ray linein No-Scale F - SU (5). Furthermore, the EW or stronggauge boson IBs have considerably larger rates due tothe larger gauge coupling constants. Recently, a com-plete calculation of the leading EW corrections to theLSP neutralino annihilations for various final states [73]shows that such corrections may significantly enhance theannihilation rates. Although those processes do not gen-erate the pronounced spectral features in gamma rayslike the corresponding electromagnetic (EM) corrections,the integrated photon yield may be enhanced up to twoorders of magnitude compared to the tree level results,which may also be probed by the ongoing Fermi SpaceTelescope experiment. As such, we have ample motiva-tion to study those regions of the viable parameter spacewith small mass differences between the LSP neutralinoand light stau.Our mission here then is to augment the SUSY neu-tralino annihilation rates to enhance detection opportu-nity for a nearly pure bino LSP ( >
99% bino). Throughnear degeneracy amongst the lightest slepton and lightbino masses, we can certainly increase the annihilationrate and boost IB effects to a dominant contribution,albeit with downward pressure on the bino relic den- sity. For a SUSY bino, this requires a compressed∆ M ( e χ , e τ ) ≃ − M ( e χ , e τ ) ≃ − F - SU (5) quite natu-rally via slight shifts of the low energy boundary condi-tion tan β . The resultant minor increase in tan β doeslead to marginally enhanced light stau mixing effects inthe stau sector, slightly lowering the light stau mass.Satisfaction of the CDM relic density in a traditionalthermal manner leads to an intrinsic escalation in thebaseline value of this parameter, from tan β ≃ . β ≃
25 for a corresponding upward escalation in thegaugino mass from M / ≃
400 to M / ≃ β required to squeeze the light stau mass and LSP to neardegeneracy recedes with an inflating SUSY mass scale.The positive deviation in tan β , with possibly small shiftsin the gaugino mass M / and flippon mass M V , are allthat are required to achieve the 0–2 GeV delta betweenthe light stau mass and the LSP in the large unprobed re-gion of the parameter space. In particular, no variationof the top quark mass m t (within its experimental un-certainty) is necessary. As a result, the SUSY spectrumundergoes only a negligible transition, and thus the richphenomenology (setting aside the relic density constraint,which must now be satisfied through non-thermal mech-anisms) prevails wholly preserved. Indeed, the wedge ofmodel space remains relatively static and persists in theform of Ref. [33], the lone exception being small shifts inthe tan β contours and indiscernible shifts in M / and M V .From this perspective, the No-Scale F - SU (5) SUSYspectra corresponding to the wedge of viable model spaceprovided in Ref. [33], duly suppressing the light staumass, are potentially testable by the Fermi Space Tele-scope or a future gamma ray telescope; moreover, the twovariations in determination of the light stau mass maybe observationally distinguished. Crucially, experimen-tal results from both the LHC and the LAT can be con-nected to the same SUSY spectrum, providing the typeof cross-correlation testing which may play a significantrole in substantiating any SUSY GUT model. In partic-ular, probing of a specific ( e χ , e t , e g, e q ) point in the SUSYparameter space may potentially be achieved via dualexperimental methodologies. This is possible since theNo-Scale F - SU (5) SUSY spectrum exhibits the ratherspecial attribute of leading order en masse proportion-ality to only M / . Specifically, the internal physics of F - SU (5) are predominantly invariant under a numeri-cal rescaling of only M / . Consequently, each sparti-cle within the SUSY spectrum can be multiplicativelyadjusted by an identical trivial rescaling of only M / ,though the linear slope relationship between M / andeach sparticle can vary. From a practical point of view,this property of No-Scale F - SU (5) permits the SUSYspectrum to be approximately determined from only agiven value of M / , or alternatively, from only a given -14 -14 -14 -14 -13 -13 -13 M = 775 GeV, M( ) = 161 GeV, M = 7.87 GeV, h = 0.1220 M = 774 GeV, M( ) = 160 GeV, M = 1.95 GeV, h = 0.0363 M = 774 GeV, M( ) = 160 GeV, M = 0.06 GeV, h = 0.0197 M = 990 GeV, M( ) = 214 GeV, M = 6.43 GeV, h = 0.1200 M = 990 GeV, M( ) = 213 GeV, M = 2.06 GeV, h = 0.0562 M = 1000 GeV, M( ) = 216 GeV, M = 0.21 GeV, h = 0.0363 M = 1200 GeV, M( ) = 276 GeV, M = 4.54 GeV, h = 0.1220 M = 1200 GeV, M( ) = 276 GeV, M = 2.07 GeV, h = 0.0838 M = 1200 GeV, M( ) = 276 GeV, M = 0.08 GeV, h = 0.0557 M = 1500 GeV, M( ) = 349 GeV, M = 2.06 GeV, h = 0.1220 M = 1500 GeV, M( ) = 349 GeV, M = 0.07 GeV, h = 0.0863 I B pho t on s / ann i h il a t i on E [GeV] I B ( pho t on s c m - s e c - G e V - ) E [GeV]
FIG. 1: No-Scale F - SU (5) Electromagnetic IB spectrum, given in terms of photons per annihilation (top frame) and differentialflux (bottom frame), as a function of energy. All curves represent the benchmarks given in Tables I-II. The thin curves (lower)in both frames satisfy the Planck satellite CDM relic density measurements Ω h = 0 . ± . M ( e χ , e τ ) ≃ M ( e χ , e τ ) ≃ M / = 774 −
775 GeV benchmarks are consistent with the previouslyobserved 133 GeV monochromatic gamma ray line. The ∆ M value given in the plot legend refers to the lightest neutralino andlight stau mass difference. All IB photon counts and fluxes are calculated with DarkSUSY 5.1.1 . For the local dark matter relicdensity, we use the value ρ = 0 . . All differential fluxes are in units of photons cm − sec − GeV − and all massesare in GeV. The Ω h shown in the plot legend is the thermal neutralino relic density calculated with MicrOMEGAs 2.4 . Forthose benchmarks with Ω h < . ± . TABLE I: Ten No-Scale F - SU (5) benchmarks, with points that can satisfy the Planck satellite relic density measurements,points with ∆ M ( e χ , e τ ) ≃ M ( e χ , e τ ) ≃ M / , flipponmass M V , tan β , top quark mass m t , relic density Ω h , EM ff , γγ , and γZ annihilation cross-sections, SUSY masses, andlight Higgs boson mass m h . All benchmark LSP compositions are greater than 99% bino. The Ω h shown is the thermalneutralino density calculated with MicrOMEGAs 2.4 . For those benchmarks with Ω h < . ± . MicrOMEGAs 2.4 and
DarkSUSY 5.1.1 calculations. The total h σv i ff annihilation cross-section is composed of h σv i ff = h σv i τ + τ − + h σv i tt + h σv i bb . The ∆ M value refers to the lightest bino neutralino and light stau mass difference. Thelight Higgs boson mass includes both the tree level+1-loop+2-loop+3-loop+4-loop and flippon contributions. All masses arein GeV and all cross-sections in cm / sec. M / M V tan β m t Ω h h σv i ff h σv i γγ h σv i γZ m χ m e τ ∆ M m χ ,χ ± m e t m e g m e u R m h
775 4800 22 . . .
122 68 . × − . × − . × −
161 169 7 .
87 342 861 1047 1475 124 . . . .
036 77 . × − . × − . × −
160 162 1 .
95 341 860 1046 1473 124 . . . .
020 81 . × − . × − . × −
160 160 0 .
06 341 860 1046 1473 124 . . . .
120 45 . × − . × − . × −
214 220 6 .
43 449 1104 1328 1824 125 . . . .
056 47 . × − . × − . × −
213 216 2 .
06 449 1104 1328 1824 125 . . . .
036 46 . × − . × − . × −
216 216 0 .
21 454 1116 1341 1841 125 . ,
830 24 . . .
122 20 . × − . × − . × −
276 281 4 .
54 572 1335 1633 2102 124 . ,
830 24 . . .
084 20 . × − . × − . × −
276 279 2 .
07 572 1335 1634 2102 124 . ,
830 24 . . .
056 21 . × − . × − . × −
276 277 0 .
08 572 1335 1634 2102 124 . ,
636 24 . . .
122 8 . × − . × − . × −
349 351 2 .
06 717 1661 2009 2602 126 . ,
636 24 . . .
086 8 . × − . × − . × −
349 349 0 .
07 717 1661 2009 2602 126 . F - SU (5) benchmarks of Table I, with the IB photon flux Φ IB from e χ e χ → ffγ events, the photonflux Φ γγ from e χ e χ → γγ events, and the photon flux Φ γZ from e χ e χ → γZ events. The IB flux has been integrated across energyrelative to the differential flux plotted in Figure 1. All fluxes are also integrated over the solid line-of-sight angle from the centerof our galaxy, taking a detector acceptance of 2.5 steradians corresponding to the LAT instrument’s 20% sky field of view, andare in units of photons cm − sec − . All fluxes are calculated with DarkSUSY 5.1.1
The γγ flux includes the factor of 2 for thetwo photons. For the local dark matter relic density, we use the value ρ = 0 . , with the spherically symmetric NFWhalo profile. The column entry Φ IB / Φ γγ is indicative of the increase in the magnitude of the IB flux over the gamma pair flux,and the adjacent column Φ γγ / Φ γZ likewise compares the gamma pair flux to that of the photon plus Z-boson. The final twocolumns provide the gamma radiation energy in GeV at the IB spectrum peak and its relation to the LSP mass in GeV. M / M V tan β m t Φ IB Φ γγ Φ γZ Φ IB / Φ γγ Φ γγ / Φ γZ IB Peak m χ
775 4800 22 .
53 174 . . × − . × − . × − . . .
95 174 . . × − . × − . × − . . .
08 174 . . × − . × − . × − . . .
34 174 . . × − . × − . × − . . .
61 174 . . × − . × − . × − . . .
73 174 . . × − . × − . × − . . ,
830 24 .
26 173 . . × − . × − . × − . . ,
830 24 .
41 173 . . × − . × − . × − . . ,
830 24 .
53 173 . . × − . × − . × − . . ,
636 24 .
67 174 . . × − . × − . × − . . ,
636 24 .
77 174 . . × − . × − . × − . . value of any other sparticle mass, exhibiting the prag-matic predictive elegance of the model.The final ingredient of our strategy involves derivationof a suitable set of benchmarks for comparison to ex-periment. We present ten benchmarks in Table I, withgaugino mass M / , flippon mass M V , tan β , top quarkmass m t , relic density Ω h , EM f f , γγ , and γZ annihi-lation cross-sections, SUSY masses, and light Higgs bo-son mass. All benchmark LSP compositions are greaterthan 99% bino. The points have been extracted froma broad numerical scan, utilizing MicrOMEGAs 2.1 [74]to compute SUSY mass spectra and a proprietary mod-ification of the
SuSpect 2.34 [75] codebase to run theflippon enhanced RGEs. To be consistent with previ-ous No-Scale F - SU (5) parameter space analyses [18, 33],we show in Table I the thermal relic density as com-puted by the updated routines in MicrOMEGAs 2.4 [76].Serving as a secondary verification, we further computethe thermal relic density with
DarkSUSY 5.1.1 [77, 78],reading as input an SLHA [79, 80] mass file generatedfrom the flippon enhanced RGEs in our proprietary ver-sion of the
SuSpect 2.34 [75] codebase, finding only asmall variation in the respective relic density computa-tions. The annihilation cross-sections h σv i ff , h σv i γγ ,and h σv i γZ are calculated with both MicrOMEGAs 2.4 and
DarkSUSY 5.1.1 , where we show the average of thetwo calculations in Table I. The total h σv i ff annihila-tion cross-section includes the only three non-negligiblecontributions in No-Scale F - SU (5) for a nearly pureSUSY bino: h σv i ff = h σv i τ + τ − + h σv i tt + h σv i bb . The∆ M value in Table I refers specifically to the light neu-tralino and light stau mass difference, which we arecompressing to increase the annihilation rate and IB ef-fects. The light Higgs boson mass m h in Table I includesboth the tree level+1-loop+2-loop+3-loop+4-loop con-tributions and the additional vector-like flippon contri-bution [33].Expected photon flux rates are listed in Table II forthe annihilation channels e χ e χ → f f γ , e χ e χ → γγ , and e χ e χ → γZ , for the same ten No-Scale F - SU (5) bench-marks of Table I. For the local dark matter relic density,we use the value ρ = 0 . , adopting the spher-ically symmetric NFW dark matter halo profile. Thesquare of the dark matter density is integrated along theline of sight for each orientation within an angular de-tector acceptance of 2.5 steradians (sr) about the galac-tic center. This value is selected in correspondence withthe LAT instrument’s field of view, which encompassesabout 20% of the sky at any given moment. Results arenot overly sensitive to this parameter, given a value suf-ficiently wide to encapsulate the region of primary den-sity. Since the IB scenario represents a continuum of ra-diation frequencies, the differential fluxes plotted in thelower panel of Figure 1 are integrated across energy toyield consistent units of photon counts per square cen-timeter per second in Table II. All fluxes are computedwith DarkSUSY 5.1.1 . The γγ flux includes the factorof 2 for the two photons. The ratio Φ IB / Φ γγ in Table II represents the magnitude of the integrated IB flux rela-tive to the γγ line flux, which provides an advantage ofabout 10 across the full model space. Likewise, the col-umn Φ γγ / Φ γZ . reports the ratio of monochromatic fluxrates for a gamma pair relative to a gamma plus Z-boson,which similarly yields an advantage of one magnitude or-der across the model space.It is evident from Figure 1 that compressing the lightbino neutralino and light stau does indeed enhance theEM IB effects for the benchmarks of Table I. The curvesin the top frame of Figure 1 depict the number of IBphotons per annihilation resulting from annihilation intocharged particles. The bottom frame illustrates the IBflux Φ IB energy spectrum for the same ten benchmarks.The thin curves (lower) in both frames represent a regionof the No-Scale F - SU (5) model space where the thermalLSP relic density can satisfy the Planck satellite CDMmeasurements Ω h = 0 . ± . DarkSUSY 5.1.1 , as are the IB fluxes. Clearly, theEM IB photon count, and hence the flux, increases forsmaller ∆ M , an effect we presume will be enhanced whenalso including the EW contributions [73]. We leave thenumerical results of the EW IB photon yield and addi-tional flux for a future work [81]. At this juncture, weare content with a projection that the photon counts andfluxes in Figure 1 could be amplified via the additionalEW IB contributions [73].Our scale for the benchmarks in Tables I-II and Fig-ure 1 begins at M / = 775 GeV, which is in the vicinityof the scale threshold that may be considered firmly ex-cluded from the No-Scale F - SU (5) model space by theLHC SUSY search, as based upon a Monte Carlo eventanalysis [32]. We select sufficient points to provide thor-ough coverage of the entire viable model space. We directattention to the region of the parameter space exempli-fied by the M / = 774 −
775 GeV benchmarks of Ta-bles I-II as that consistent with an upper 2 σ limit on theWIMP mass that can explain the previously observed133 GeV monochromatic gamma ray line. ComparingFigure 1 with Table II, it is apparent that compressionof the ∆ M ( e χ , e τ ) mass gap substantially strengthens theIB signal in the narrowly peaked spectral range close tothe LSP mass, whereas the advantage in integrated pho-ton flux is less pronounced; this is relevant given higherexperimental sensitivity to signals that more closely ap-proximate a line spike. V. SUMMARY OF EXPERIMENTALPROSPECTS
In this final section, we attempt to make a quantitative,if in some regards na¨ıve, assessment of the experimen-tal prospects of the various F - SU (5) model benchmarkspreviously described. The primary metric for assessmentwill be the integrated photon flux, i.e. the area undereach differential flux curve displayed in the lower elementof Figure 1, in units of photons cm − sec − , as reportedin Table II. Since both background (following a power lawwith spectral index −
2) and the internal bremsstrahlungsignal accrue in linear proportion with time, the S/ √ B signal to background discriminant may be expected toscale as the square root of time. Based upon four yearsof data collection in whole-sky survey mode (achievinga full 4 π steradian coverage once per two earth orbits),the Fermi collaboration has established sensitivity at fivestandard deviations to gamma flux rates above about3 − × − cm − sec − for line sources positioned athigh galactic latitudes [82]; the sensitivity is diminishedby about half an order of magnitude in the highly activegalactic center. Taking an active Fermi mission lifetimeof ten years, one sees that the data doubling advantagehas already been largely depleted in the existing results,although the remaining multiple of 2.5 in integrated timemay yet garner an improvement of around 1.6 deviationsin sensitivity; in other words, any potential discovery ap-parent by the end of the Fermi mission should already beshowing evidence above three standard deviations. Like-wise, the expected end of mission line sensitivity may beprojected at about 2 × − cm − sec − .The root- t scaling is actually a bit pessimistic for sig-nals approximating a line width, and better sensitivityis possible. Additionally, the Fermi instrument has be-gun a transition toward more targeted observation of thegalactic center for the remainder of its mission, whichmay garner an additional factor of about two in sensi-tivity, admitting however that baseline sensitivities arelower in this region. Likewise, substantial improvementsin understanding of the detector and relevant analysistechniques are poised to reduce background contamina-tion and improve overall instrument sensitivity [83]; welikewise assign a factor of about two to processing up-grades of this type, which are retroactive to already col-lected data. Holding backgrounds constant, a furtherreduction in the signal flux by a factor around 3 / × − cm − sec − on any potentially vis-ible gamma flux. Given continuum dispersion of the IBgamma signal, it is somewhat over optimistic to applysensitivities extrapolated from line-signal searches, andthis deficiency becomes more pronounced at higher massscales with widening and flattening of the signal profile,as is visible in Figure 1. Nevertheless, it is important torecognize that any IB gamma signal may be compoundedwith line signals from loop order neutralino annihilationto gamma pairs and/or gamma Z, in the same basic spec-tral range, although potentially substantially suppressed,as indicated in Table II. Without an appreciable boostfactor O (50–100) in the computed annihilation rate, the F - SU (5) IB gamma flux, while more favorable for de- tection than the flux associated with mono-energetic linesources, may remain obscured by background processesto the LAT instrument. However, if there is any valid-ity to the existing 130 GeV signal, then it becomes quitelikely that some undiagnosed boost factor is actually inplay. Plausible sources of this upward shift in the fluxinclude underestimation of the local dark matter den-sity (or corrections to the assumption of a smooth profiledistribution), and internal bremsstrahlung contributionsfrom EW or strong gauge bosons.As a closing note, we draw attention to the increasein the thermally produced bino relic density in Table Ifor those points with ∆ M ( e χ , e τ ) ≃ − M / is lifted; this is due primarily tothe incrementally larger LSP mass, and a correspond-ing slow increase in the value of tan β , which tracks theelevation in M / , automatically enhancing the light staumixing for larger SUSY mass scales. Interestingly, the vi-able No-Scale F - SU (5) parameter space terminates near M / ∼ M / ∼ M / ∼ VI. CONCLUSIONS
We presented here a methodology for testing No-ScaleSupergravity with the FERMI satellite’s Large Area Tele-scope, and similar future gamma ray telescopes. For ourtesting vehicle, we chose the supersymmetric grand uni-fied model No-Scale Flipped SU (5) with extra vector-like flippon multiplets derived from F-Theory, dubbed F - SU (5). Building upon ample extant phenomenologicalmotivation for No-Scale F - SU (5), we discussed the po-tentially significant empirical support recently providedto cosmological models of inflation based upon No-ScaleSupergravity by intrinsic Starobinsky-like conformancewith the Planck measurements, for a suitable choice ofsuperpotential parameters. Given this impetus, we dis-cussed how compressing the light stau and LSP mass dif-ference can increase the internal bremsstrahlung effectsand thus enhance the photon count from annihilation toelevate detection probabilities, albeit with a reduced binorelic density. We additionally explained how the Planck0satellite observed relic density can nevertheless be gen-erated through a non-thermal mechanism. For concreteexamples, we gave several benchmark points with lightstau and LSP mass differences of 0–2 GeV, achieved byslight upward shifts in the low energy boundary condi-tion tan β , in conjunction with negligible variations in thegaugino mass M / and flippon mass M V ; these modifi-cations leave the SUSY spectrum, aside from the lightstau mass, unchanged, preserving the rich phenomenol-ogy (modulo appeal to non-thermal mechanisms of relicdensity generation) that is currently being probed bythe LHC and several other Beyond the Standard Model(BSM) experiments. While the IB mechanism emerges asa more favorable context for observing a gamma ray sig-nal generated consistently with the F - SU (5) model than monochromatic sources, a clear signal in the present gen-eration instrument still requires a boost of order O (50–100) in the expected rate of flux. Acknowledgments
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