Aspects of the same-sign diboson signature from wino pair production with light higgsinos at the high luminosity LHC
Howard Baer, Vernon Barger, James S. Gainer, Michael Savoy, Dibyashree Sengupta, Xerxes Tata
UUH-511-1285-17
Aspects of the same-sign diboson signaturefrom wino pair production with light higgsinosat the high luminosity LHC
Howard Baer ∗ , Vernon Barger † , James S. Gainer ‡ ,Michael Savoy § , Dibyashree Sengupta ¶ , and Xerxes Tata (cid:107) Dept. of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA Dept. of Physics, University of Wisconsin, Madison, WI 53706, USA Dept. of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USA
Abstract
Naturalness arguments applied to simple supersymmetric (SUSY) theories require aset of light higgsinos with mass ∼ | µ | not too far from m h . These models have an invertedelectroweakino spectrum with | µ | (cid:28) M which leads to a rather clean, hadronically quiet,same-sign diboson (SSdB) signature at hadron colliders arising from neutral-plus-chargedwino pair production. We improve and expand our earlier studies of this signature fordiscovering SUSY in natural SUSY models by (i) including backgrounds which were notpreviously considered and which turn out to be significant, (ii) devising more efficient cutsto successfully contend with these larger backgrounds and determining the discovery reachand exclusion ranges for winos with these cuts, emphasizing projections for the updatedintegrated luminosity target for HL-LHC of 3 ab − , and (iii) emphasizing the utility of thischannel for natural models without gaugino mass unification. We display the kinematiccharacteristics of the relatively jet-free same sign dilepton+ (cid:54) E T events (from leptonic decaysof both W s) and find that these are only weakly sensitive to the parent wino mass. Wealso examine the charge asymmetry in these events and show that its measurement canbe used to check the consistency of the wino origin of the signal. Finally, we show that– because the wino branching fractions in natural SUSY are essentially independent ofdetails of the underlying model – a determination of the rate for clean, same-sign dileptonevents yields a better than 10% determination of the wino mass over the entire mass rangewhere experiments at the HL-LHC can discover the wino signal. ∗ Email: [email protected] † Email: [email protected] ‡ Email: [email protected] § Email: [email protected] ¶ Email: [email protected] (cid:107)
Email: [email protected] a r X i v : . [ h e p - ph ] O c t Introduction
The search for supersymmetry in Run 2 of LHC with √ s = 13 TeV and ∼
36 fb − of datahas resulted in mass limits of m ˜ g > ∼ m ˜ t > ∼ . unnaturalness ; if true, such considerations could undermine the entire raison d’etre for weakscale supersymmetry [3]. It should, however, be stressed that conclusions from naturalnessregarding upper bounds on sparticle masses [4, 5] (limits on stop masses are the most widelydiscussed) do not apply if the model parameters– often assumed to be independent– turn outto be correlated[6, 7, 8].Quantitative measures of naturalness generally derive from calculations of the fine-tuning ofthe weak scale, typically represented by the Z boson mass, which is related to other weak-scaleSUSY parameters via the MSSM scalar potential minimization condition, m Z m H d + Σ dd − ( m H u + Σ uu ) tan β tan β − − µ ∼ − m H u − µ − Σ uu (˜ t , ) . (1)where m H u,d are soft SUSY breaking Higgs mass parameters, µ is the superpotential Higgs/higgsino mass term, tan β ≡ v u /v d is the ratio of Higgs field vacuum expectation values (vevs),and the Σ uu and Σ dd terms include a variety of radiative corrections (expressions for these canbe found in the Appendix of Ref. [9]). Recently, several of us have suggested using electroweaknaturalness as a conservative criterion [9, 10] to determine whether a SUSY model spectrum isunnatural. The electroweak naturalness measure is defined as∆ EW = max | each term on the RHS of Eq . | / ( m Z / . (2)Naturalness, then, is the requirement that ∆ EW is relatively small. Conservatively, requiring∆ EW <
30 implies: • | µ | ∼ −
300 GeV (the closer to m Z the better); • m H u is radiatively driven from large high scale values to small negative values ( ∼ − (100 − GeV ) at the weak scale; • the magnitude of Σ uu is also bounded by about (300 GeV) . This is possible even if stopmasses – though bounded above – are in the multi-TeV range, and gluinos are as heavyas 5-6 TeV [11] (depending on the details of the model). These conditions are met in a class of “Radiatively-driven Natural SUSY models” (RNS) [9]. Inthese SUSY models with low ∆ EW , the largest of the radiative corrections typically come fromthe top-squark sector contributions to Σ uu and are minimized for highly mixed TeV scale topsquarks, a condition which also lifts the Higgs mass, m h , into the vicinity of its measured value ∼
125 GeV [9, 10]. We emphasize, however, that as Eq. (1) holds in general in the MSSM, the The limit on the gluino mass arises because radiative corrections from gluino loops raise the stop mass, andas a result Σ uu (˜ t ) becomes too large [12]. | µ | , and concomitantly light higgsinos, applies whether or not one uses Eq. (2) to define fine-tuning.We advocate using ∆ EW for discussions of naturalness. It yields a conservative measureof fine-tuning because it allows for the possibility that model parameters, frequently regardedas independent, might turn out to be correlated once the SUSY breaking mechanism is un-derstood. Ignoring this may lead to an over-estimate of the UV sensitivity of m Z and causeus to prematurely discard perfectly viable models. We also mention that the commonly usedBarbieri-Giudice measure [4, 15] of fine-tuning reduces to ∆ EW once appropriate correlationsbetween model parameters are properly implemented [6, 7]. That the use of ∆ EW to assessnaturalness is indeed conservative is brought home by explicit examples [7] where the evaluationof ∆ BG with parameter correlations ignored yields ∆ BG >
300 ∆ EW .While naturalness favors a small superpotential µ parameter, LHC results seem to favorrather heavy gauginos, at least in models with gaugino mass unification (where gaugino massesare related by M = M = M ≡ m / at the energy scale Q = m GUT (cid:39) × GeV). Insuch models, renormalization group evolution of gaugino masses typically leads to weak scalegaugino masses in the ratio M : M : M ∼ M ( weak ) > ∼ M , > ∼
600 GeV, and M > ∼ not a prerequisitefor naturalness [16], and also that direct limits from electroweak gaugino searches at the LHCshould be regarded as independent of those from gluino searches. Indeed searches for wino pairproduction [17] in simplified models where the charged wino decays via (cid:102) W ± → W ± + the lightestsupersymmetric particle (LSP), and the neutral wino decays via (cid:102) W → Z +LSP lead to lowerbounds ∼
500 GeV for an LSP mass of about 200 GeV. Interestingly, the strongest boundarises from the dilepton-plus-jet channel rather than the clean but rate-suppressed trileptonchannel. One might naively expect that as long as the higgsinos are essentially invisible thesebounds will continue to apply. However, these bounds weaken considerably in natural SUSYmodels once the expected branching fractions (see below) for wino decays to light higgsinos areincorporated, and there is essentially no bound if higgsinos are heavier than about 150 GeVbut still significantly lighter than the winos. The inversion of the gaugino-higgsino mass pattern expected in natural supersymmetry hasimportant implications not only for SUSY collider searches but also for dark matter expec-tations. Since the lightest SUSY particle is expected to be a higgsino-like neutralino, it isthermally underproduced as dark matter. Naturalness in the QCD sector seems to requireintroduction of an axion [18] which may be expected to constitute the remainder of the darkmatter [19]. While the axion and its cousins are well-motivated, we recognize that there aremany other possibilities that could lead to the observed dark matter, including out of equilib- Here, we are implicitly assuming that the superpotential parameter, µ , is the dominant source of thehiggsino mass. A soft SUSY-breaking contribution to the higgsino mass is possible if there are no additionalgauge singlets that couple to higgsinos [13]. In extended frameworks with additional TeV scale fields it istheoretically possible to decouple the higgsino mass from the Higgs boson mass parameter that enters intoEq. (1) [14]. While this is strictly speaking true only for the analysis using chargino-neutralino production alone, innatural SUSY chargino pair production also makes a (subdominant) contribution to the
W Z channel. Theupper limits on winos of natural SUSY will nonetheless be significantly reduced from those in Ref.[17]. M is phenomenologically constrained to be > ∼ | µ | is not hierarchically larger than M Z ,then it is reasonable to explore LHC prospects for SUSY scenarios with, | µ | < M , M < M , (3)where the heavier (wino-like) charginos and neutralinos decay to the light higgsinos via (cid:102) W ± → (cid:101) Z , + W ± , (cid:102) W ± → (cid:102) W ± + Z, h and (cid:101) Z → (cid:101) Z , + Z, h , (cid:101) Z → (cid:102) W ± + W ∓ . Although electroweak higgsino pair production processes pp → (cid:101) Z i (cid:101) Z j , (cid:102) W (cid:101) Z i ( i, j = 1 ,
2) havea large rate for higgsino masses ∼ −
300 GeV, it is difficult to detect these above SMbackgrounds unless electroweak gauginos are fortuitously also much lighter than required bynaturalness [16]. However, for the generic situation with | M , | (cid:29) | µ | , the higgsino spectraare very compressed, resulting in only relatively soft visible decay products from (cid:102) W , (cid:101) Z decaysand modest missing transverse energy. One strategy for searching for light higgsinos at theLHC focuses on higgsino pair production in association with a hard jet from initial state QCDradiation which also serves as a trigger. Detailed studies show that although it may be possibleto obtain a “signal statistical significance of 5 σ ” above backgrounds after hard cuts, the S/B ratio is just ∼ S/B ratio can be greatly improved by requiring an additional low invariant mass, sameflavor, opposite sign soft dilepton pair from (cid:101) Z → (cid:101) Z (cid:96) + (cid:96) − in these hard monojet events. It hasbeen shown that higgsinos up to 200-220 GeV would be detectable at the 5 σ level at LHC14,assuming an integrated luminosity of 1 ab − [21]. Note though that this search will not coverthe entire space of SUSY models with ∆ EW <
30 even at the high luminosity LHC.There are several ways to search for superpartners in natural SUSY models. Old favoriteslike gluino pair production [24] and top-squark pair production [25] remain as important searchchannels, although now cascade decay events may contain occasional low mass dilepton pairsarising from (cid:101) Z → (cid:101) Z (cid:96) + (cid:96) − decay [26, 27]. We have already mentioned the search for softdileptons in events triggered by a hard monojet (or monophoton). Indeed, the first limitsfrom such a search have been presented by the CMS collaboration in the m (cid:101) Z vs. m (cid:101) Z − m (cid:101) Z plane [28].Yet another distinctive signature for SUSY with light higgsinos (which is the topic of thispaper) arises from wino pair production [26, 29] via the Feynman diagram shown in Fig. 1: pp → (cid:102) W ± (cid:101) Z followed by (cid:102) W ± → W ± (cid:101) Z , and (cid:101) Z → W ± (cid:102) W ∓ decays. Half of the time, thedaughter W s will have the same sign, leading to distinctive same sign di-boson (SSdB) plus (cid:54) E T events with no additional jet activity other than from QCD radiation. The subsequent leptonicdecays of the W s lead to clean same-sign dilepton + (cid:54) E T events for which the SM backgrounds In denoting the wino-like neutralino by (cid:101) Z we have implicitly assumed that the wino is heavier than thebino. This is not really a limitation to the analysis because the bino-like state couples rather weakly and so isphenomenologically relatively less important, as long as it is not the LSP. The detection of pair production of light higgsinos at e + e − colliders with √ s > m ( higgsino ) should alsobe straightforward [22, 23], at least for higgsino mass gaps larger than 10 GeV. t ¯ t , W Z , and t ¯ tW production (though t ¯ tZ and inclusive W ± W ± production from qq → q (cid:48) q (cid:48) W ± W ± processes are also mentioned). After a set of cutsto help distinguish the natural SUSY SSdB signal from SM backgrounds, it was found thatthe background dominantly arose from t ¯ tW production, and the LHC14 reach was obtained inthe two-extra-parameter non-universal Higgs (NUHM2) [31] model . It was emphasized thatin models with gaugino mass unification (such as the NUHM2 model), the SUSY reach via theSSdB channel would (for integrated luminosities larger than ∼
100 fb − ) exceed the reach viagluino pair production because the winos are only a third as light as gluinos. This assumes thatgluinos decay democratically to all generations. In natural SUSY, where gluinos preferentiallydecay to the third generation, it has been shown that b -tagging [32] could be used to furtherenhance the gluino reach [24] in the (cid:54) E T channel. In Ref. [33], it was emphasized that fornatural SUSY models with gaugino mass unification, the pp → (cid:101) Z (cid:101) Z j reaction followed by (cid:101) Z → (cid:96) + (cid:96) − (cid:101) Z decay, combined with the SSdB channel, would cover the majority of naturalSUSY parameter space with ∆ EW <
30 at the high luminosity LHC. This conclusion no longerobtains in string-motivated models such as natural generalized mirage mediation [34] or theminilandscape [35] where the compressed spectrum of gauginos may allow for both wino andgluino masses beyond HL-LHC reach even while maintaining naturalness.In the current paper, we revisit the SSdB signature from wino pair production in SUSYmodels with light higgsinos, making a number of important improvements. First, we expandupon earlier calculations by explicitly including several additional SM background processes: Since the NUHM2 model allows the soft terms m H u and m H d to be traded for weak scale inputs µ and m A , it is easy to generate natural SUSY models by inputting low values of | µ | ∼ −
300 GeV.
W W jj production, (2) t ¯ tZ production, (3) t ¯ tt ¯ t production and (4) W W W production. Second, we focus on the updated integrated luminosity target for the HL-LHC, namely 3000fb − = 3 ab − . Third, we emphasize that the SSdB signature from wino pair production offersan independent discovery channel for natural SUSY models, whether gaugino masses are unifiedor not. For instance, in anomaly-mediated SUSY breaking (AMSB) models, the gaugino massesare expected to occur in the weak scale ratio of M : M : M ∼ . −
7. For natural AMSBwith | µ | (cid:28) M , it could be that gluino masses are well above LHC reach while wino masses arequite light: M > ∼
300 GeV. In such a case, the SSdB signature might be a robust discoverychannel even if gluinos are too heavy to be detected. Since we do not assume gaugino massunification, we present results in terms of the physical wino mass rather than e.g. in terms of m / .In addition to presenting projections for the 5 σ reaches for the discovery of winos in thischannel for various values of the wino mass m (cid:102) W and the values of m (cid:102) W that can be expected tobe excluded at 95% confidence level, we also analyze the prospects for wino mass measurement.We point out that using rate information, we can measure the wino mass at better than the 10%level over its entire discovery range. We show that if there is an excess in the clean SS dileptonsample, a determination of the charge asymmetry would provide an important consistencycheck. We also examine various kinematic distributions that may reveal characteristic featuresof the SSdB events. We find that although these distributions in themselves are not stronglysensitive to the wino mass, they may still be useful in a multivariate approach for extracting M .We discuss our calculation of wino pair production, along with the expected wino decaypatterns in natural SUSY and describe our simulation of signal and background processes inSec. 2. The analysis cuts that we suggest for optimizing the SSdB signal at the HL-LHC aredescribed in Sec. 3. In Sec. 4 we show our projections of the discovery and exclusion reach forwinos in the SSdB channel, while various characteristics of signal events are discussed in Sec. 5.In Sec. 6, we examine the precision with which the wino mass may be extracted from the SSdBsignal rate. Our conclusions are presented in Sec. 7. Since the SSdB signature from pair production of winos is the subject of this study, we beginby showing in Fig. 2 the leading order (LO) and next-to-leading order (NLO) production crosssections for various wino pair production processes– as solid and dashed curves respectively.These cross sections are calculated for the √ s = 14 TeV LHC using the Prospino computercode [39] and are plotted with respect to the charged wino mass, m (cid:102) W . Since we will also be In addition, our current calculations adopt
MadGraph [36] and
Pythia [37] for signal/background cal-culations and
Delphes [38] for our LHC detector simulation. While it is not obvious that
Delphes / PYTHIA is an improvement over our previous use of the
Isajet detector simulation, the relative consistency of ournew results with our previous results (when direct comparisons can be made) does provide a check on possiblesystematic errors. √ s = 14 TeV.interested in examining the lepton charge asymmetry, we also show separately the cross sectionsfor pp → (cid:102) W +2 (cid:101) Z (red curves) and for pp → (cid:102) W − (cid:101) Z (green curves).Note that the (cid:102) W +2 (cid:101) Z cross section typically exceeds the cross section for (cid:102) W − (cid:101) Z by a factor ∼ −
4. This charge asymmetry in production cross section arises from the preponderanceof valence u quarks in the proton versus valence d quarks and increases with m (cid:102) W due tothe growing importance of valence quark over sea quark annihilation as the sampled partonfractional momentum, x F , increases. This results in a preponderance of ++ over −− dileptonevents as we shall see below.The charged wino pair production cross section pp → (cid:102) W +2 (cid:102) W − (blue curves) lies in betweenthe (cid:102) W +2 (cid:101) Z and (cid:102) W − (cid:101) Z curves. The black curves denote the cross sections for the summed winopair production channels, which vary from the tens of fb level for m (cid:102) W ∼
600 GeV to ∼ − fb for m (cid:102) W ∼ . The (cid:102) W and (cid:101) Z branching fractions are calculated using Isajet (cid:102) W +2 → (cid:101) Z , W + , (cid:102) W +1 Z and (cid:102) W +1 h decays each rapidly asymptote to ∼
25% for heavywinos with only small branching fractions to the bino-like (cid:101) Z . Likewise, the branching fractionsfor (cid:101) Z → (cid:102) W +1 W − , (cid:102) W − W + , (cid:101) Z , Z and (cid:101) Z , h are also each ∼
25% for | µ | (cid:28) | M | .These simple decay patterns can be analytically understood in the limit that the (cid:102) W and (cid:101) Z , are mostly higgsino-like, and (cid:102) W and one of (cid:101) Z or (cid:101) Z is mostly a wino (with the otherneutralino being dominantly a bino). As already mentioned, the bino-like neutralino couples tothe wino only via its small higgsino component, so decays to it are dynamically suppressed evenif they are kinematically allowed. In natural SUSY, we are interested in the case µ (cid:28) M , and6edium to large tan β values, typically with tan β > | M /µ | . In this case, it is straightforwardto check that the chargino mixing angle γ L ∼ − γ R µM (we use the notation of Ref. [41]) so that γ L can be ignored compared to γ R . The small gaugino components of the higgsino-like statesand the higgsino components of the wino-like states can be evaluated to lowest order in thegaugino-higgsino mixing angles, and the relevant couplings and partial widths for the variousdecays obtained from the expressions in Appendix B of Ref. [41]. We then findΓ( (cid:102) W → (cid:101) Z W ) (cid:39) Γ( (cid:102) W → (cid:101) Z W ) (cid:39) Γ( (cid:102) W → (cid:102) W Z ) (cid:39) Γ( (cid:102) W → (cid:102) W h ) (cid:39) g π m (cid:102) W , (4)Γ( (cid:101) Z → (cid:102) W − W + ) (cid:39) Γ( (cid:101) Z → (cid:102) W +1 W − ) (cid:39) Γ( (cid:101) Z → (cid:101) Z , Z ) (cid:39) Γ( (cid:101) Z → (cid:101) Z , h ) (cid:39) g π m (cid:101) Z , (5)where, to illustrate our point, we have retained only the largest mass terms in the expressionsfor the partial widths. This is a good approximation when higgsinos are much lighter than thewinos. In our numerical calculation, we retain the full expressions, of course. In the last of theseequations we have assumed that (cid:101) Z is the wino-like state. Also, the neutral wino decay widthsto Z or h are the summed widths to both higgsino-like states. If other decay modes of the wino( e.g. , to the bino, to sfermions, or to the heavy Higgs bosons) are kinematically or dynamicallysuppressed, we obtain the approximately equal branching fractions of 25% mentioned above.We have checked by a numerical scan that when | µ | = 150 −
300 GeV, as favored by naturalness,the branching ratios for these modes are well within the 0.23-0.27 range if the wino is heavierthan 500 GeV and the bino is not quasi-degenerate with the wino.Combining decay channels, we find that typically ∼ / (cid:102) W ± (cid:101) Z production events lead tofinal states with same-sign dibosons W + W + or W − W − . To identify SSdB events, we requireleptonic decays of the final state W s to e or µ which reduces our overall branching fraction to ∼ × − . Thus, although the wino pair production cross sections may be as large as 10 fb,the combined signal channel branching fractions lead to relatively small signal rates. Therefore,the SSdB signal channel really becomes the signal of choice only for the very high integratedluminosities projected to be accumulated at the high-luminosity LHC. To make specific predictions for the expected SSdB signal rate, we will adopt a natural SUSYmodel line using the two-extra-parameter non-universal Higgs model NUHM2 [31]. This modelallows for direct input of a low µ parameter as required by naturalness. The model line weadopt is adapted from Ref. [26] and has m = 5 TeV, A = − β = 10, m A = 1 . µ = 150 GeV. We will allow the unified gaugino mass parameter m / to vary from 700to 1375 GeV which corresponds to m ˜ g ∼ . − . m (cid:102) W ∼ − m h is ∼
125 GeV along the entire model line, while ∆ EW is ∼ −
30, corresponding to The reader may wonder why the decay rates to Higgs bosons which go via the unsuppressed wino-higgsino-Higgs boson coupling are comparable to the decay rates to vector bosons which can only occur via small mixingangles. The reason is that this suppression is compensated by the enhancement of the amplitude for decays tolongitudinal W or Z bosons by a factor m (cid:102) W , (cid:101) Z /M W,Z , an example of the Goldstone boson equivalence theorem.
70% - 3% EW fine-tuning. Although the NUHM2 model assumes a unification of gaugino massparameters, this is unimportant for the analysis of the wino signal that we are focussing upon,in the sense that essentially identical results would be obtained in any model with the samevalue of the wino mass M . While there may be some sensitivity to the bino mass parameter,we remind the reader that the bino-like state couples to the wino-vector boson system onlyvia its small higgsino components, so any decays into this state typically have small branchingfractions.In Table 1, we show a listing of various sparticle masses and observables associated with ourmodel line for the benchmark model with m / = 800 GeV, labeled as Point B . Within theNUHM2 framework, the model point with the 692 GeV wino state (cid:102) W has m ˜ g ≈ ∼
35 fb − ).Though the details of most of the SUSY spectrum are unimportant for our present purposes, wenote that our sample case (indeed the entire model line) has very heavy first/second generationsfermions, with stops and gluinos in between these and the EW gauginos, while higgsinos arevery light. This qualitative pattern is a generic feature of natural SUSY models. We emphasizethat while our benchmark model line is in a model with gauge coupling unification, this willhave very little (if any) effect on any conclusions we draw about the prospects for discovery,exclusion, or mass measurement of the parent wino. In other words, for the purposes of analysisof the wino signal alone, we can disregard the LHC gluino limit and model cases with lighterwinos that may arise in natural models without gaugino mass unification using m / as asurrogate for the wino mass, M . In order to assess prospects for observability of the signal, we must have a good understandingof various SM backgrounds that could also lead to the clean same sign dilepton plus (cid:54) E T signature. We have considered backgrounds from t ¯ t , W Z , t ¯ tW , t ¯ tZ , t ¯ tt ¯ t , W W W , and W ± W ± jj production processes in the SM. Top pair production yields (non-instrumental) backgroundsonly if a secondary lepton from top decay is accidently isolated. We use LO event generationfrom MadGraph in our simulation of both signals and backgrounds, but rescale the LO totalcross sections to be in accordance with NLO values found in the literature.Specifically, we use 953.6 pb as the total NLO cross section for t ¯ t , following Ref. [42].Ref. [43] gives us a K factor of 1 .
27 for four-top production. We use 1 .
88 as the K factor forassociated
W Z production following Ref. [44] and 1 .
24 for the K factor for t ¯ tW productionfollowing Ref. [45] . We obtain the K factor 1 .
39 for t ¯ tZ from Ref. [46]; Ref. [47] gives usa K factor of 1 .
04 for
W W jj . Finally, for the W W W process we use the cross sections in We refer to this as
Point B because we consider three signal benchmark points, labeled A, B, and C, inorder of increasing wino mass. While in Ref. [44], K factors differ slightly for W + Z and W − Z , and in Ref. [45] the K factors differ slightlyfor t ¯ tW + and t ¯ tW − , these are very close (1 .
86 and 1 .
92 respectively for W + Z and W − Z and 1 .
22 and 1 .
27 for t ¯ tW + and t ¯ tW − respectively), especially when compared with likely theory errors, so we use 1 .
88 (1 .
24) as theK factor for both
W Z ( t ¯ tW ) processes. This is the value in Ref. [47] for the two-jet inclusive cross section with factorization and renormalizationscales set to 150 GeV. If we were to further restrict to one-jet and zero-jet bins (see our analysis cuts, below),the K factor would move closer to 1; we have chosen the larger K factor to be conservative.
Point B m m / A -8000tan β µ m A m ˜ g m ˜ u L m ˜ u R m ˜ e R m ˜ t m ˜ t m ˜ b m ˜ b m ˜ τ m ˜ τ m ˜ ν τ m (cid:102) W m (cid:102) W m (cid:101) Z m (cid:101) Z m (cid:101) Z m (cid:101) Z m h std (cid:101) Z h BF ( b → sγ ) × . BF ( B s → µ + µ − ) × . σ SI ( (cid:101) Z , p ) (pb) 4 . × − σ SD ( (cid:101) Z p ) (pb) 1 . × − (cid:104) σv (cid:105)| v → (cm /sec) 2 . × − ∆ EW Point B with m t = 173 . m / = 800 GeV.9ef. [48]. In our analyses we use a common K factor of 2 .
45 for both
W W W processes, whichis not appreciably different than the W + W + W − K factor of 2 .
38 or the W + W − W − K factorof 2 .
59. We note that these are K factors for inclusive
W W W production; if one imposes a jetveto the K factor is significantly reduced (to 1 .
29 for the combined
W W W
K factor). Whilewe do impose a jet multiplicity cut of n jet ≤
1, we choose to be conservative and use the largervalue for the K factor in our calculation of the background.These K factors and NLO cross sections for the underlying fundamental SM processes areshown in columns 2 and 3 of Table 2, together with the corresponding information for thesignal benchmark
Point B . These are, of course, the raw production cross sections for thevarious final states; various branching fractions and detection efficiencies have to be folded into obtain the signal and background cross sections. We see that even the various 2 → → To simulate SSdB signal events, we first generate the SUSY spectrum as a Les Houches Ac-cord (LHA) file using
Isajet
MadGraph/MadEvent
Pythia
Delphes E T ( jet ) >
50 GeV and pseudorapidity | η ( jet ) | < . / √ E ⊕ . / √ E ⊕
3% for | η | < . / √ E ⊕
5% for | η | > .
6, where ⊕ denotes combination in quadrature.3. The jet energy scale correction is turned off.4. The anti- k T jet algorithm [49] is utilized, but using R = 0 . R = 0 .
5. (Jet finding in Delphes is implemented via
FastJet [50].) One motivationfor choosing R = 0 . b -taggingefficiencies [51].5. We performed jet flavor association using our own module which implements the “ghosthadron” procedure [52] which allows the assignment of decayed hadrons to jets in anunambiguous manner. We use this module to aid in b -tagging, specifically in determiningwhether jets contain B hadrons. When a jet contains a B hadron in which the b quarkwill decay at the next step of the decay, then if this B hadron lies within | η | < . E T >
15 GeV, we identify this b -jet as a “truth b -jet”. We b -tag truth b -jets with | η | < . b -tag jets which are not truth b -jets with | η | < . /X where X = 150 for E T <
100 GeV, X = 50 for E T >
250 GeV10nd X is found from a linear interpolation for 100 GeV < E T <
250 GeV . We havechecked [24] that our b -jet tagging algorithm yields good agreement with the b -taggingefficiencies and mistag rates in Ref. [51]; specifically it gives results intermediate betweenthe CMS “medium” and “tight” b -tagging algorithms.6. “Tau tagging”, i.e. , identifying objects as taus, is not used.7. The lepton isolation modules were modified to allow us to adopt the isolation criterionthat the sum of E T of physics objects in a cone with ∆ R < . . E T ( (cid:96) )), where E T ( (cid:96) ) is the transverse energy of the lepton.( Delphes E T or a fraction of the lepton E T .) We begin by imposing the selection cuts, listed below, that were suggested in Ref’s. [29, 26] toenhance same sign dilepton events originating in wino production over those coming from SMprocesses. • Exactly two isolated same-sign leptons with p T ( (cid:96) ) >
20 GeV and p T ( (cid:96) ) >
10 GeV. ( (cid:96) denotes the higher p T lepton, while (cid:96) is the lower p T lepton.) • n ( b − jets) = 0 • (cid:54) E T >
200 GeV, and • m minT >
175 GeV,where m minT = min [ m T ( (cid:96) , (cid:54) E T , m T ( (cid:96) , (cid:54) E T )]. We denote these initial cuts as cut set C1 .The cross sections after these cuts– after folding in various branching fractions and detectionefficiencies– for the Point B signal benchmark point and from various SM processes (in ab)are listed in column 4 of Table 2. The combined same-sign dilepton cut, large (cid:54) E T cut, and b -jet veto serve to severely reduce the t ¯ t background. Indeed, after these cuts, the analysisof Ref. [26, 29] found the dominant background to come from t ¯ t and W Z production. Any t ¯ t background events which survive these cuts will likely have one lepton arising from real W → (cid:96)ν decay with the other lepton arising from a semi-leptonic b decay, which will hence be soft. Insuch a case, at least to the extent that the (cid:54) E T dominantly arises from the leptonic decay of asingle W , the transverse mass, m T ( (cid:96), ν (cid:96) ), is mostly bounded by m W (up to small contaminationfrom off-shell W s, (cid:54) E T smearing, and any additional (cid:54) E T from leptonic decays of the B -hadron).Thus, the further requirement of m minT (cid:29) m W should serve to greatly reduce the t ¯ t and also W Z backgrounds. Here, in accord with Refs. [26, 29], we require m minT >
175 GeV; afterimposing this cut we are indeed left with no t ¯ t or W Z backgrounds in our samples. Among The parameters for this b -tagging procedure are based on ATLAS studies of b -tagging efficiencies andrejection factors in t ¯ tH and W H production processes [53]. t ¯ tW production, which we find to be a factor of two larger than inRef. [26]. Unlike the earlier studies, we also find sizable contributions from t ¯ tZ production aswell as from W W W production and W ± W ± jj production. Summing these sources, we find atotal background cross section after C1 cuts of 34 ab in contrast to just 6 ab after the samecuts in Ref. [26]. The cross section for the signal at the benchmark Point B is 29 ab, or alittle under 5 σ statistical significance for an integrated luminosity of 1 ab − , and over 8 . σ significance with 3 ab − . The cut set C1 was suggested in Ref. [26, 29] to determine the reach of LHC14 in the SSdBchannel for 100-1000 fb − . Since one of our goals is to project the maximum reach of theHL-LHC for SUSY in the SSdB channel, we attempt to further optimize our cuts.We begin by noting that the various background processes in Table 2 with significant crosssections after C1 cuts are all expected to contain additional hard jets, while jet activity in thesignal process arises only from initial state QCD radiation (and very soft jets from decay ofthe heavier higgsinos). We thus anticipate that jet multiplicity will be a useful discriminatingvariable. With this motivation we show the expected jet multiplicity, n ( j ), from signal andbackground events after the C1 cuts in Fig. 3. From the solid (red) signal histogram, wesee that signal events indeed mainly have n ( j ) = 0 or 1. In contrast, background events, thesum of which is shown by the shaded histogram, generally have n ( j ) ≥
2. Thus, we apply theadditional cut, • n ( j ) ≤ C1 and n ( j ) ≤ t ¯ tW and W W W production pro-cesses. To further reduce these, we examined several other kinematic distributions including (cid:54) E T , m T ( (cid:96) (cid:96) , (cid:54) E T ) (the dilepton-plus- (cid:54) E T cluster transverse mass) [54], m minT and m T [55]. Themost useful of these turned out to be the (cid:54) E T distribution shown in Fig. 4. From this figure, wesee that in the (cid:54) E T = 200 −
250 GeV bin, the summed background exceeds the signal for
PointB , while in higher (cid:54) E T bins, signal clearly emerges above background. However, care must betaken since our signal rate is already rather small. We elect to make one final cut • (cid:54) E T >
250 GeV,and label this set of cuts ( C1 cuts plus n ( j ) ≤
1, plus (cid:54) E T >
250 GeV) as the cut set C2 .We show the expected p T distributions of the leptons after the C2 cuts in Fig. 5 for threesignal benchmark points along the model line, as well as for the summed SM background. Thepoints have m (cid:102) W = 530 GeV ( Point A ), 692 GeV (
Point B , already introduced above), and886 GeV (
Point C ). We see that the distributions are qualitatively similar, and while the
S/B ratio may be slightly improved by requiring harder cuts on the leptons, this would only be atthe cost of reducing an already rate-limited signal. We choose, therefore, not to impose anyfurther cuts. In this vein, the scalar sum of jet E T or the ratio of this to the scalar sum of leptonic E T may prove to beeven more robust and equally discriminating variables. n ( j ), for SSdB events from the Point B signal bench-mark point and various SM backgrounds after C1 cuts.process K − factor σ (NLO) (ab) C1 C1 + n jet ≤ C2 SUSY (
Point B ) 1.25 1 . · t ¯ t . · W Z . · t ¯ tW . · t ¯ tZ . · t ¯ tt ¯ t . · W W W . · W W jj . · . · ab before any cuts, after C1 cuts,after C1 cuts plus a jet veto, and after C2 at LHC14. Also shown is the K -factor that we use.13igure 4: Distribution of (cid:54) E T for the signal benchmark Point B and various SM backgroundsin SSdB production after C1 cuts plus the n ( j ) ≤ p T ( (cid:96) ) (left frame) and p T ( (cid:96) ) (right frame ) for the Point A , PointB , and
Point C benchmarks, which are points along our NUHM2 model line with m (cid:102) W = 530,692 and 886 GeV, respectively, together with the total SM background after C2 cuts.14he total background after these cuts is shown in the last column of Table 2. We see thatalmost half this background comes from SM W W W production. We remind the reader of ourdiscussion in Sec. 2.4, where we mentioned that we have used K W W W = 2 . i.e , the valueobtained for inclusive W W W production, instead of the much smaller value K W W W = 1 . W W W production with a jet veto. It is very possible that we may have over-estimated this background, but we choose to err on the conservative side in our assessment ofthe discovery prospects of the HL-LHC, the subject of the next section.
In Fig. 6, we show the total same sign dilepton signal rate after our final analysis cuts, C2 ,as a function of the wino mass, m (cid:102) W , (solid blue curve) along with the total SM background(denoted by the dotted red line). We also compute the reach for 5 σ discovery and 95% CLexclusion for the HL-LHC (using Poisson statistics) with a data sample of 3 ab − . We findthat the 5 σ discovery reach extends to m (cid:102) W ∼
860 GeV, while the 95% CL exclusion reachextends to m (cid:102) W ∼ M (cid:29) | µ | , as expected in natural SUSY. In models with gauginomass unification, the 5 σ (95% CL) reach in m (cid:102) W correspond to a reach (exclusion) in termsof the unified gaugino mass m / of ∼ m ˜ g , these correspond to m ˜ g ∼ σ − HL-LHC for direct gluino pair production of m ˜ g ∼ C2 cuts,the discovery reach of the LHC extends to 500 GeV (720 GeV) for an integrated luminosity of300 fb − (1 ab − ), while the corresponding 95%CL exclusion extends to 780 GeV (980 GeV).It is worth keeping in mind that especially for the 300 fb − case, somewhat softer analysiscuts [26, 29] may be better suited for optimizing the LHC reach.The key mass relation for the SSdB signature is that | µ | (cid:28) M . It is therefore interestingto explore our discovery reach beyond our benchmark assumption of | µ | = 150 GeV. In Fig. 7,we denote the (3 ab − ) HL-LHC (5 σ ) discovery reach in the µ - M plane by the green solid linein the vicinity of m (cid:102) W (cid:39) −
900 GeV. As expected the reach is only weakly sensitive to thehiggsino mass. The red diagonal line in Fig. 7 shows where µ = m (cid:102) W . Above this line the SSdBsignature arises from higgsino pair production and subsequent decays to winos; but it wouldhave a much smaller rate because (1) the higgsino cross section is smaller than the wino crosssection, and (2) dilution of the signal from higgsino decays to binos (if these are accessible).Below the blue diagonal line in Fig. 7 denotes the region where (cid:102) W → (cid:101) Z , + W or (cid:101) Z → (cid:102) W + W decays can occur, leading the the SSdB final state, with on-shell W s. Close to this line and fornot-too-large m (cid:102) W , though, the same sign dilepton events would not necessarily be clean as thelarge wino-higgsino mixings would lead to sizeable mass gaps and concomitant harder debrisfrom the decay of the lighter inos. As µ increases, the model becomes increasingly unnatural,with a value µ >
350 (indicated by a magenta dashed line) corresponding to electroweak fine-tuning measure ∆ EW >
30. The natural SUSY region is the region below this horizontal line.15igure 6: Cross section for SSdB production after C2 cuts versus m ( wino ) at the LHC with √ s = 14 TeV. We show the 5 σ and 95% CL reach assuming a HL-LHC integrated luminosityof 3 ab − . 16igure 7: Discovery reach in the SSdB channel at the HL-LHC in the m (cid:102) W vs. µ plane.17 SSdB SUSY event characteristics
We have already illustrated the (cid:54) E T and lepton transverse momentum distributions after all cutsin Fig. 4 and Fig. 5, respectively. We saw that while the (cid:54) E T distribution from signal emergesfrom the background for (cid:54) E T >
250 GeV, this distribution is typically backed up against thecut. Although the distribution may harden somewhat with increasing wino mass, we saw thatthe observability of the signal becomes rate limited by the time we reach m (cid:102) W = 860 GeV, sowino events would typically have (cid:54) E T ∼ −
500 GeV. The lepton p T distributions peak at200-250 GeV for the hard lepton and 50-100 GeV for the second lepton, independent of thewino mass. This should not be very surprising because the leptons are produced at the end of acascade decay chain, so the p T (cid:96) distributions are only altered by the changes in the boost of thedaughter W bosons which share the parent wino energy with the (nearly invisible) higgsinos.To further characterize the nature of the SSdB events from SUSY, and to see if we cangain some sensitivity to the wino mass from the kinematic properties of these events, we haveexamined several kinematic variables: A eff , m minT (which entered the C1 cuts), its sibling m maxT , m T , m CT and m (cid:96)(cid:96) , where A eff = (cid:54) E T + n ( j ) (cid:88) i p T ( j i ) + p T ( (cid:96) ) + p T ( (cid:96) ) , and m CT is the cluster transverse mass given by m CT = m CT = (cid:18) (cid:54) E T + (cid:113) (cid:126)p T (cid:96)(cid:96) + m (cid:96)(cid:96) (cid:19) − ( (cid:126) (cid:54) E T + (cid:126)p T (cid:96)(cid:96) ) . In Fig. 8, we show the normalized distributions of m minT (because it enters our analysis cuts)together with those of A eff , m CT , and m maxT , the larger of the transverse masses of the leptonand (cid:54) E T . These are the distributions whose shapes show the most sensitivity to the wino massfor the three benchmark SUSY cases introduced above. We see that even for these three caseswith a fairly wide separation of wino masses, the shapes of the distributions are qualitativelyquite similar, with perhaps the m maxT distribution showing the greatest sensitivity to the parentwino mass. As we noted in the discussion of Fig. 5, the wino mass has a relatively small effecton the kinematics of signal events, affecting only the boost of the W bosons. While these (quitecorrelated) distributions show some differences, especially in the tails of the distributions whichcorrespond to relatively low numbers of signal events, we will see below that because the signalrate can be predicted with good precision, the event rate for the SSdB signal offers a muchbetter handle on the wino mass. We stress, though, that the kinematic properties of theseevents are nonetheless useful for validating the signal origin, and could potentially serve asingredients in an artificial neural network stew.The charge asymmetry A = n (++) − n ( −− ) n (++) + n ( −− )of clean same sign dilepton events (which, of course, includes both signal and background events)provides yet another handle for validating the wino origin of any signal. We show a fit to the18igure 8: Distributions of m minT (top left), A eff (top right), m CT (bottom left) and m maxT (bottom right) from the SUSY SSdB signal plus SM backgrounds after C2 cuts for the threebenchmark cases Point A , Point B , and
Point C introduced earlier in the text. We havenormalized these distributions to all have the same area.19igure 9: Same-sign dilepton charge asymmetry from signal-plus-background vs. m (cid:102) W fromSUSY same-sign diboson production after C2 cuts versus m (cid:102) W at LHC with √ s = 14 TeV.The statistical error with which the charge asymmetry can be determined is ∼ ± . m (cid:102) W < ∼
800 GeV.expected A values (our simulated sample had considerable statistical fluctuations) for signal-plus-background events versus m (cid:102) W in Fig. 9, together with the expected background value.The charge asymmetry arises because there are more up-type than down-type valence quarksin a proton. The importance of valence quark collisions for wino pair production processesincreases with wino mass, so we expect the asymmetry to also increase with m (cid:102) W . This isindeed borne out in the figure where we see that the expected asymmetry ranges from 0.2for m (cid:102) W as low as ∼
300 GeV to 0.4 for m (cid:102) W ∼ Unfortunately, the measuredcharge asymmetry does not provide as good of a wino mass determination as one might naivelysuppose from looking at the figure. The reason is that because of the relatively low total eventrate, even with 3 ab − , the statistical error on its measurement is ∼ ± . m (cid:102) W <
800 GeV,which corresponds to a wino mass uncertainty of ∼
300 GeV. We nevertheless stress that adetermination of the charge asymmetry provides a consistency check of wino origin of the SSdBsignal if m (cid:102) W can be extracted from the total event rate. An examination of this extraction isthe subject of the next section. The asymmetry of the background is even larger because the W ± W ± jj component of the background,though subdominant, has contributions from collisions of two valence quarks. Measurement of the wino mass in the SSdB channel
We saw that while experiments at the HL-LHC would be able to discover winos with masses upto 860 GeV and to exclude these out to 1100 GeV if no excess is seen, the determination of itsmass from the kinematic properties of the signal event proved rather difficult. We traced thisto the fact that the leptons were produced only at the end of a cascade so that the sensitivityto the mass of the parent winos is correspondingly reduced.In principle, it should also be possible to determine the wino mass from the rate with whichthe signal events are produced. This is particularly true in this case because the cross sectionfor wino production can be rather precisely computed for the case of natural SUSY (for whichthe heavier inos are expected to be nearly pure gauginos) and depends on just the wino mass.We also saw in Sec. 2.2 that, at least for m (cid:102) W >
500 GeV, the natural SUSY branching fractionfor wino decays to W is 0 . ± .
02 with conservative error bars. The determination of theSSdB signal rate after C2 cuts shown in Fig. 6 thus provides a plausible mass measurementstrategy, because, to a good approximation, the observed number of events depends only onthe wino mass.For example, for our assumed benchmark point, Point B , and using C2 cuts, with 3 ab − we expect a total of 63 ± ± ≈ C2 cuts (as in Fig. 6) corresponds to a measurement of m (cid:102) W ∼ ±
35 GeV, which representsa better than 5% measurement of the wino mass.This precision is possible when we consider statistical errors alone. There is also a systematicerror arising from the theory uncertainty on the cross section, uncertainties on the wino decaybranching ratios, uncertainties on the efficiencies for events passing cuts, uncertainties on thereconstruction efficiencies, etc. Since the current uncertainty ( ∼
10% in the production crosssection) mostly arises from the uncertainties in the parton distributions which will undoubtedlybe well-measured by the time this analysis is done, and the lepton detection efficiencies will alsobe well understood, we expect the main systematic will arise from the squared wino branchingfraction, which as we have already noted is < ∼ ∼ Point B increases to ≈
50 GeV. Even if thetotal systematic error on the cross section is 30%, then the combined statistical and systematicerror on the mass is ≈
70 GeV, which is about a 10% measurement of the wino mass. If ourbackground is underestimated by a factor of two, our measurement of the wino mass will bebiased by ≈
70 GeV toward lower values; if it is over-estimated by a factor of two, then ourmeasurement will be biased by ≈
35 GeV toward higher values.We can still make a good mass measurement for large values of the wino mass; for instance,the purely statistical error on the mass measurement is still only ≈
10% for a 1 TeV wino(although there is no 5 σ signal). However for these larger mass values with their correspond- As we have already noted, the observation of a signal in the clean, same sign dilepton channel alreadypoints to light higgsinos and much heavier EW gauginos. Additional circumstantial evidence for light higgsinoscould, for instance, come from the observation of monojet plus soft dilepton events, which must be present atobservable rates if m (cid:101) Z − m (cid:101) Z > ∼
10 GeV and higgsinos are not much heavier than 220-240 GeV. − of data. Ourpoint is that better than 10% determination of the wino mass will be possible if the SSdB signalfrom natural SUSY is detected at the HL-LHC In this paper we have re-visited and explored aspects of the SSdB signature, which is a powerfulchannel for discovering natural SUSY models with | µ | (cid:28) M , especially if M is larger than inunified models. This signature arises from wino pair production, pp → (cid:102) W (cid:101) Z , followed by winodecays to W bosons plus quasi-visible higgsinos. Thus, the signal consists of (cid:96) ± (cid:96) (cid:48)± + (cid:54) E T eventswhich are distinct from same-sign dilepton events from gluino/squark production in that theyare relatively free of hard jet activity. We emphasize that the SSdB search channel offers a probeof natural SUSY – indeed of all SUSY models with light higgsinos – that is independent of anysignals from gluino pair or top-squark pair production. The SSdB channel is especially usefulbecause (i) SM backgrounds for such a signature are tiny and (ii) this type of signature is notexpected in many previously studied “unnatural” SUSY models, such as mSUGRA/CMSSM,where the opposite mass hierarchy, M < | µ | , and M < M is expected.We have evaluated several new background contributions to the SSdB signature including W W jj production, 4 t production, and 3 W production. We find these new background reactionscan be suppressed beyond the previously examined C1 cuts by an additional jet veto n ( jets ) ≤ (cid:54) E T cut at a modest cost to the signal. The surviving signal rate should beobservable at HL-LHC with 3 ab − of integrated luminosity over a large range of wino mases.After our C2 analysis cuts, the HL-LHC 5 σ reach (95%CL exclusion) extends out to m (cid:102) W = 860GeV (1080 GeV). We show that a determination of the clean same sign dilepton event rate allowsa better than 10% measurement of the wino mass over the entire range of masses for whichexperiments at the HL-LHC will be able to discover a wino in this channel. A measurementof the like-sign dilepton lepton charge asymmetry will test the consistency of the wino originof the signal. If gluinos are also discovered at the HL-LHC, experiments will be able to probewhether or not gaugino masses arise from a common mass at Q (cid:39) M GUT at the 10% level [24].We encourage continued experimental scrutiny of the clean same sign dilepton + (cid:54) E T channelas the integrated luminosity at the LHC goes beyond ∼
100 fb − . Acknowledgments
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