Supersplit Supersymmetry and the 750 Gev Diphoton Excess
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Supersplit Supersymmetry and the 750 GeV Diphoton Excess Kyle Cranmer1 1Center for Cosmology and Particle Physics, Dept. of Physics, New York University, New York , NY 10003 (Dated: April 1, 2016) We examine the scenario of “supersplit supersymmetry” in light of the observed diphoton excess at 750 GeV. We discuss the difficulties of explaining tuning of the model with anthropic arguments alone and propose a new phenothropic principle. A brief statistical analysis of the model is conducted including the 2-dimensional look-elsewhere effect in two of the model parameters most relevant for LHC phenomenology. We find that the model is excluded by both ATLAS and CMS at the 2 − 3σ level; however, the excess can be accommodated by invoking the phenothropic selection mechanism with a small overall contribution to the tuning of the theory. I. INTRODUCTION SUSY Split SUSY Supersplit SUSY Mpl q,u˜ ˜ ,d,l,e˜ ˜ ˜, h˜ ,h˜ , g˜ The ATLAS and CMS collaborations have recently re- u d i h 2 ported an excess in the diphoton invariant mass spectrum at 750 GeV in both of the 8 and 13 TeV data sets [1, 2]. The possibility that this is the new physics holy grail we have been seeking has sent the theoretical community ˜ ˜ Mi q,u˜ ˜ ,d,l,e, h 2 into a frenzy [3]. We will refer to this putative particle with the Greek letter digamma ̥ [29]. Of course, the discovery\ of the Higgs boson at 125 GeV brought to the forefront the issue of naturalness and fine Mw q,u,d,l,e, h ,h , g q,u,d,l,e, h ,h˜ , h ˜ , q,u,d,l,e, h , g tuning [4, 5]. The arrival of the ̥ motivates reexami- u d i 1 u d 1 i g , g˜ nation of finely tuned theories. Let us briefly revisit the ˜ ˜ ˜ i i q,u˜ ˜ ,d,l,e˜ ˜, hu ,h d , g˜ i history and motivation of this paradigm. The realization that the broad string landscape may have an exponen- FIG. 1: Mass scales in the MSSM, split SUSY and supersplit tially large number of metastable vacua [6–8] supported SUSY. Taken from Ref. [12]. Weinberg’s anthropic argument for a solution to the cos- mological constant problem based upon a scan over many possible universes [9]. Agrawal et. al [10] and later The addition of the ̥ changes this picture and once Arkani-Hamed and Dimopoulos [11] argued that similar again pulls us back into the era in which the phenomeno- scanning may be relevant for weak scale physics. In “split logical consequences of additional fields must be studied. supersymmetry”, all but one scalar of the many scalars As was highlighted by Ref. [13] it is difficult to accommo- in the minimal supersymmetric standard model (MSSM) date additional scalars and address naturalness without are given very large masses. One linear combination of resorting to awkward mechanisms. On the other hand, the two scalar superpartners of the Higgsinos remains while the so-called “atomic principle” [10] has been used light and then acquires a vacuum expectation value (vev) as part of an anthropic argument for fine tuning of the which breaks electroweak symmetry and gives masses to weak scale, this does not carry over to the unexpected the weak gauge bosons. The fermion masses, which can ̥ resonance. Thus, we seek a new principle that can be protected by symmetries, remain small. address this additional source of tuning. Fox, et. al. [12] took the next logical extension by decoupling both Higgsinos and the gauginos in a model they call “supersplit supersymmetry”. The low energy II. THE PHENOTHROPIC PRINCIPLE effective theory consists of SU(3) SU(2) U(1) gauge fields and three generations of quarks× and leptons,× as well Already in Ref. [12], Fox, et. al. argued that the exis- as one scalar (whose mass is tuned to be light) which tence of fine tuning in nature dramatically increases the is responsible for electroweak symmetry breaking. The time scale over which fundamental physical laws are dis- Lagrangian for this model is simply covered. Since the rapid discovery of fundamental laws is 1 µν 1 µν 1 µν strongly correlated with the advance of technologies that = 2 Wµν W 2 Bµν B 2 Gµν G L −4g1 − 4g2 − 4gs might lead to the destruction of civilization, this should ∗ + ψ¯ (iγµD m )ψ + D hDµh V (h) (1) be taken into account in the Drake equation. In short, a f µ − f f µ − universe without fine-tuning, theoretical physics may not where f indexes the various fermions, and D is the ap- be possible. [30] propriate covariant derivative. The spectrum of split and Here we consider a variant of this idea. Instead of the supersplit supersymmetry are shown in Fig. 1. ill-defined notion of “theoretical physics”, we employ a 2 more quantitative measure, namely the number of pa- 100 pers submitted to the arXiv. Recently, a quantitative 9.6 model for the number of papers covering an unexpected 8.4 result was proposed [16]. In particular, the number of 80 papers as a function of time was derived from a com- 7.2 pounded Poisson process leading to a di-gamma function 60 6.0 Pl µN (T ) [31]. /M 4.8 ˜ Next we follow the logic of the anthropic principle, q 40 which can schematically be written using Bayes theorem M 3.6 as 2.4 20 p(universe us) p(us universe ) p(universe) . (2) 1.2 | ∝ | 0.0 |anthropic{z selection} 20 40 60 80 100 Mh /MPl We highlight the term p(us universe ) that is the mech- 2 anism for anthropic selection.| By analogy we introduce FIG. 2: Plot of q(Mh , Mq˜)= −2 ln λ(Mh , Mq˜). the phenothropic principle, which can schematically be 2 2 written p(excess papers) p(papers excess ) p(excess) . (3) is that the prior degree of belief in this unexpected res- | ∝ | onance is low, the risk associated to a false discovery is phenothropic| {z selection} high, and the time needed to collect enough data to make a more conclusive statement is short. The term p(papers excess ) is a new selection mechanism | Another issue that comes up in the statistical analy- addressed by Ref. [16], while p(excess) is the subject of sis of ̥ is that the data prefer a wide resonance. This more traditional statistical analysis and the following sec- leads to a look-elsewhere effect in both the mass and tion. width of the resonance. We briefly review the methodol- ogy used by ATLAS as described in a beautiful work by III. STATISTICAL CONSIDERATIONS Vitells and Gross [21]. In this formalism we have a likeli- hood function of the form L(µ,ν1,ν2) where µ is a signal strength parameter proportional to σ Br and ν1,ν2 are The ATLAS and CMS collaborations have quantified the unknown mass and width of the× new particle. Next the statistical significance of the excess in the mγγ spec- one performs the search by scanning over ν1 and ν2 and trum under a both spin-0 and spin-2 hypotheses. The calculating the test statistic [22] local significance for the 13 TeV data under the spin- 0 hypothesis stands at 3.9σ and 2.9σ, for ATLAS and maxθ L(µ =0,ν1,ν2,θ) q(ν1,ν2)= 2 log (4) CMS respectively. Of course, we do not know the mass of − maxµ,θ L(µ,ν1,ν2,θ) the resonance a priori, so one must correct for the look- elsewhere effect [17]. After this correction, the global The LEE correction in this case is based on significance for ATLAS is around 2σ and even less for 2 −u/2 CMS. While a heuristic approach would be to say that E[φ(Au)] = P (χ1 >u)+ e (N1 + √uN2) (5) one experiment tells you where too look, and the other provides the statistical evidence. This approach violates where Au is the ’excursion set above level u (eg. the set an obvious permutation symmetry and has been criti- of parameter points in (ν1,ν2) that have a q(ν1,ν2) >u), cized recently [18]. A more careful treatment would be φ(Au) is the Euler characteristic of the excursion set, to combine first and then correct for the look-elsewhere E[φ(Au)] is the expectation of the Euler characteristic 2 effect on the combination (see Ref. [19] for more details). of those excursion sets under the null, P (χ1 > u) is the While the objection to the heuristic approach is a good standard chi-square probability , and N1 and N2 are two one in principle, in this particular case it does not make coefficients that characterize the chi-square random field. a very large quantitative difference. Now we repeat, for the first time, this 2-d LEE correc- Perhaps more interesting is the issue of the 5σ discov- tion for a new physics model description of the ̥ excess. ery threshold. As discussed in Cousins’s tome on the Instead of scanning over the mass and width of a generic Jeffreys-Lindley Paradox (see the section on the mythol- spin-0 or spin-2 particle, we scan over two high-scale pa- ogy of 5σ) the arbitrary 5σ convention was adopted as rameters of the supersplit supersymmetry model. We an ad hoc way of protecting against the look-elsewhere perform this scan for many pairs of the model parame- effect [20]. To use 5σ threshold after correcting for the ters. Figure 2 shows the scan with respect to Mh2 and look-elsewhere effect is both arbitrary and breaking from Mq˜.