{'fraction_non_alphanumeric': 0.05727863931965983, 'fraction_numerical': 0.036101384025346, 'mean_word_length': 4.141448778396914, 'pattern_counts': {'":': 0, '<': 4, '<?xml version=': 0, '>': 2, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 21, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Correlating LHCb B_s^0 to \mu^+ \mu^- Results with the ATLAS-CMS Multijet Supersymmetry Search

We show that the No-Scale Flipped SU(5) construction is transparently consistent with recent LHCb results for B_s^0 to \mu^+ \mu^- decays, due primarily to suppression from the rather small value of tan\beta ~ 20 that is globally enforced across the model space. This fact should be interpreted in conjunction with the demonstrated evasion of mass limits from the ATLAS and CMS SUSY searches and the more important potential explanation of small observed excesses in the multijet data. The No-Scale Flipped SU(5) benchmark model that best fits these excesses has a gaugino mass scale of M_{1/2} = 708 GeV, which drives masses for the bino-dominated LSP m_\chi_1^0 = 143.4 GeV, light stop m_t1 = 786 GeV, gluino m_g = 952 GeV, and heavy squark m_uL = 1490 GeV. The corresponding total prediction for the rare B-decay of Br(B_s^0 to \mu^+ \mu^-) = 3.5 x 10^-9 suggests that the SUSY contribution may indeed be much smaller than that expected from the Standard Model in this framework, fitting quite comfortably within the very tightly constrained region remaining viable after the most recent LHCb measurements.


1
= 143.4 GeV, light stop m t 1 = 786 GeV, gluino m g = 952 GeV, and heavy squark m u L = 1490 GeV. The corresponding total prediction for the rare B-decay of Br(B 0 S → µ + µ − ) = 3.5 ×10 −9 suggests that the SUSY contribution may indeed be much smaller than that expected from the Standard Model in this framework, fitting quite comfortably within the very tightly constrained region remaining viable after the most recent LHCb measurements. Upon completion of several ATLAS and CMS 5 fb −1 supersymmetry (SUSY) searches of the total 2011 LHC data harvest [1][2][3][4][5][6], interesting correlations [7,8] began to emerge between event signatures registered by the collaborations and a high-energy model framework known as F -SU (5) (See Refs. [7][8][9][10][11][12][13][14][15][16][17] and all references therein), which combines the No-Scale Flipped SU (5) grand unified theory (GUT) with extra vector-like particles (flippons). Despite an absence of any conclusive signs of supersymmetry thus far at the LHC, we presented the case [7,8] that those studies with curious event excesses over the expected Standard Model (SM) background all implicate a consistent narrow swath of the F -SU (5) SUSY mass scale, subsequent to an embedding of the collaboration selection strategies into that construction. The largest significance in signal strength was observed in the ATLAS multijet realm [1, 2], permitting determination of prospective best fit SUSY masses for a bino-dominated LSP m χ 0 1 = 143.4 GeV, the light stop m t1 = 786 GeV, gluino m g = 952 GeV, and heavy squark m uL = 1490 GeV [7]. Intriguingly, the most meaningful signal strength within data reported by CMS also prevailed in the multijet domain [6]. Given that the F -SU (5) supersymmetric event landscape at the LHC is anticipated to be dominated by multijets [9,[11][12][13][14][15], the cumulative fidelity of the proffered explanation would be enhanced by the systematic preference of a budding phase of SUSY event production for the multijet search space.
These mounting correlations compel the undertaking of fresh consistency checks against recently improved B-decay constraints, specifically those from the flavour changing neutral current process B 0 S → µ + µ − [18], where the initial quark content is (s, b). We take the branching ratio from Refs. [19,20], which we write in the form (1) where f Bs is the B s decay constant, m B is the B meson mass, and τ B is the mean life. The factors C A , C ′ A are primarily determined by the Standard Model diagrams, whereas C S , C ′ S , C P , C ′ P include the SUSY loop contributions resulting from diagrams relating to particles such as, for example, the light stop, chargino, sneutrino, and Higgs bosons.
The LHCb has undertaken measurements of rare Bdecay processes with unprecedented precision, establishing an upper bound on the branching ratio of the B 0 S → µ + µ − process of Br(B 0 S → µ + µ − ) < 4.5(3.8) × 10 −9 at the 95% (90%) confidence level [21]. With well-defined predictions in the Standard Model of Br(B 0 S → µ + µ − ) = (3.2 ± 0.2) × 10 −9 [22,23], where the loop-level process employs a virtual W -boson to transmute the quark content and facilitate a tt → Z 0 fusion event, severe constraints may potentially be placed upon the viable pa-rameter spaces of any candidate SUSY framework [24]. In particular, the allowed SUSY contribution to these rare B-decays is in a state of rapid contraction following recent CMS [25] and LHCb [21] high-precision measurements. Simultaneously surviving the swiftly escalating ATLAS and CMS SUSY mass spectrum constraints while making only compulsorily insubstantial SUSY contributions to B 0 S → µ + µ − is truly becoming a fine needle to thread.
The vector-like flippon multiplets will contribute to the B rare decays to µ + µ − since they will contribute to the two axial-current operators O 10 and O ′ 10 from the mixings with the SM fermions [26]. Thus, the process B 0 s → µ + µ − will give strong constraints on the tree-level flavour changing neutral current effects [26]. Note that without flippon contributions, we have Br(B 0 s → µ + µ − ) = 3.5 × 10 −9 for the benchmark points of Ref. [7,16,17]. Thus, we must suppress the flippon contributions by some combined effect of i) the natural heaviness of the multiplets, around a few times the TeV scale, and ii) an assumption that the mixings between the flippons and the SM fermions are relatively small.
The F -SU (5) experimentally viable model space perimeter is shaped by application of the bare-minimal experimental constraints defined in Ref. [10], which is defined by simultaneous consistency with i) the dynamically established high-scale boundary conditions M 0 =A=B µ =0 of No-Scale Supergravity, ii) radiative electroweak symmetry breaking, iii) precision LEP constraints on the lightest CP-even Higgs boson m h [27,28] and other light SUSY chargino and neutralino mass content, iv) a top-quark mass 172.2 GeV ≤ m t ≤ 174.4 GeV, and v) a single, neutral supersymmetric cold dark-matter (CDM) candidate providing a relic density within the 7year WMAP limits 0.1088 ≤ Ω CDM ≤ 0.1158 [29]. These constraints represent those experiments that are regarded as exhibiting the greatest stability, with conclusions possessing the broadest acceptance. Moreover, we superpose on the model space derived out of the bare-minimal constraints upper and lower boundaries on the light Higgs boson mass of 124 ≤ m h ≤ 126 GeV, reflecting the recent 5σ over background discovery observed by ATLAS [30], CMS [31], and CDF/DØ [32]. The flippons fill an essential role in this context by coupling to the Higgs boson and naturally generating a 3-4 GeV upward shift [14] to m h , facilitating a physical Higgs boson mass in excellent conformity with the observations. The F -SU (5) model space remaining after implementation of the bare-minimal constraints plus the 124-126 GeV Higgs mass limits is illustrated in Figure (1) as a function of the gaugino mass M 1/2 and flippon mass M V , encompassing a narrow sliver confined to the region of 400 ≤ M 1/2 ≤ 900 GeV, 19.4 ≤ tanβ ≤ 23, and 950 ≤ M V ≤ 6000 GeV. The lowermost boundary at M 1/2 = 400 GeV is demanded by the LEP constraints, while the uppermost boundary at M 1/2 = 900 GeV is a consequence of a charged stau LSP exclusion around tanβ ≃ 23. The SUSY particle masses and B-decay branching ra-tios are calculated with MicrOMEGAs 2.1 [33], applying a proprietary modification of the SuSpect 2.34 [34] codebase to run the flippon-enhanced renormalization group equations (RGEs).
We inset into Figure (1) the multi-axis cumulative χ 2 fitting of Ref. [7], linked to the horizontal axis M 1/2 . Clearly illustrated is the well of the χ 2 at M 1/2 = 708 GeV, representing the best fit SUSY mass to those AT-LAS SUSY searches demonstrating a signal significance of S/ √ B + 1 > 2. The smoothly graded contours of color depict the value of Br(B 0 S → µ + µ − ). The rate for the SUSY contribution to B 0 S → µ + µ − is proportional to the sixth power of tanβ, and due to the fact that F -SU (5) globally enforces a relatively small value of 19.4 ≤ tanβ ≤ 23, the F -SU (5) model space within the median fit of the χ 2 well resides at Br(B 0 S → µ + µ − ) ≤ 3.6 × 10 −9 , with Br(B 0 S → µ + µ − ) = 3.5 ×10 −9 at M 1/2 = 708 GeV, both comfortably in accordance with the very tight LHCb constraint of Br(B 0 S → µ + µ − ) < 4.5 (3.8) ×10 −9 at the 95% (90%) confidence level. So indeed, it seems No-Scale F -SU (5) has successfully threaded the needle of ATLAS and CMS SUSY mass constraints in parallel with an exceptionally small SUSY contribution to B 0 S → µ + µ − , the combination deemed to be so intractable for the typical SUSY framework.
Conclusions-The LHC has amassed a total of 5 fb −1 of integrated luminosity at √ s = 7 TeV through the close of 2011. Consequently, the entire landscape of supersymmetric models has dwindled considerably, as the increasing SUSY mass limits have invalidated many prior contenders. For those few high-energy frameworks left standing, the unprecedented precision of the LHCb measurements of the B-decay process B 0 S → µ + µ − could have been the final blow. In spite of this dim outlook, we showed here that No-Scale F -SU (5), which has already demonstrated the capacity to evade the encroaching ATLAS and CMS SUSY mass constraints while perhaps moreover explaining the origin of small excesses in the 5 fb −1 multijet data observations, is in fact further bolstered by the new LHCb results. Due to the relatively small globally allowed range of 19.4 ≤ tan β ≤ 23, the F -SU (5) SUSY contribution to Br(B 0 S → µ + µ − ), which is proportional to the sixth power of tanβ, is much smaller than the effect expected within the Standard Model. Thus, a large value of Br(B 0 S → µ + µ − ) could have dealt a very damaging hit to F -SU (5). On the contrary, the now apparent insubstantial SUSY contribution measured at the LHCb is very consistent with that required in a No-Scale F -SU (5) universe. Indeed, we demonstrated that the SUSY mass spectrum of an LSP m χ 0 1 = 143.4 GeV, light stop m t1 = 786 GeV, gluino m g = 952 GeV, and heavy squark m uL = 1490 GeV, which can efficiently explain the ATLAS multijet data observation excesses, exhibits a B-decay of Br(B 0 S → µ + µ − ) = 3.5 ×10 −9 , well within the quite constrained LHCb result of Br(B 0 S → µ + µ − ) < 4.5 (3.8) ×10 −9 at the 95% (90%) confidence level. Whether nature is herself truly described by No-Scale F -SU (5) remains, for now, be-  [10] and Higgs boson mass calculations of Ref. [14] is illustrated by the narrow strip with the smoothly contoured color gradient. The gradient represents the total branching ratio (SM+SUSY) of the B-decay process B 0 S → µ + µ − , numerically scaled as displayed in the color bar legend. The inset diagram (with linked horizontal scale) is the multi-axis cumulative χ 2 fitting of Ref. [7], depicting the best SUSY mass fit and Standard Model limit of only those ATLAS and CMS SUSY searches exhibiting a signal significance of S/ √ B + 1 > 2. Shown is the best fit benchmark of Ref. [7] at M 1/2 = 708 GeV, with Br(B 0 S → µ + µ − ) = 3.5 × 10 −9 , consistent with the recent LHCb measurements of Br(B 0 S → µ + µ − ) < 4.5 (3.8) ×10 −9 at 95% (90%) confidence level.
yond our capacity to establish; however, it is becoming increasingly clear that her actions, spanning a broad and non-trivially correlated space of observations, conform remarkably well to the predictions that this model makes. This elegant evasion of myriad potential pitfalls, the rare B-decay limits being but one example among many, serves to highlight the sharp differences in phenomenology that exist between the F -SU (5) framework and the traditional CMSSM/mSUGRA constructions.