Stau pairs from natural SUSY at high luminosity LHC

Natural supersymmetry (SUSY) with light higgsinos is perhaps the most plausible of all weak scale SUSY models while a variety of motivations point to (right) tau sleptons as the lightest of all the sleptons. We examine a SUSY model line with rather light right-staus embedded within natural SUSY. For light stau_1 of a few hundred GeV, then the decays stau_1 ->\tau\tchi_{1,2}^0 and \nu_\tau\tchi_1^- occur at comparable rates where the (higgsino-like) \tchi_1^\pm and \tchi_2^0 release only small visible energy: in this case, the expected \tau^+\tau^- +\eslt signature is diminished from usual expectations due to the presence of the nearly invisible decay mode \ttau_1 ->\nu_\tau\tchi_1^-. However, once m_{\ttau_1}>~m(bino), then decays to binos such as \ttau_1 ->\tau\tchi_3^0 open up where \tchi_3^0 decays to higgsinos plus W^\pm, Z^0 and h at comparable rates. For these heavier staus, then stau pair production gives rise to diboson+\eslt events which may contain 0, 1 or 2 additional hard \tau leptons. From these considerations, we examine the potential for future discovery of tau-slepton pair production at high-luminosity LHC. While we do not find a 5\sigma HL-LHC discovery reach for 3000 fb^{-1}, we do find a 95\% CL exclusion reach, ranging between m_{\ttau_1}:100-450 GeV for m_{\tchi_1^0}~ 100 GeV. This latter reach disappears for m_{\tchi_1^0}>~ 200 GeV.


Introduction
The search for weak scale supersymmetry (SUSY) [1] at hadron collider experiments often focusses on strongly interacting sparticles-the gluinos and squarks-since these have the largest production cross section for a given sparticle mass value.However, in many models the gluinos and squarks also have the largest mass values, while sleptons and electroweakinos (EWinos) are much lighter.Thus, for a given point in model parameter space, sleptons and EWino pair production may dominate the production cross sections by virtue of their smaller mass values.
In a previous work [2], we examined prospects for EWino pair production at luminosity upgrades of the CERN Large Hadron Collider (LHC) in the context of natural SUSY which is characterized by low values of electroweak finetuning measure ∆ EW ≲ 30 [3,4].The value of ∆ EW is a measure of practical naturalness [5]: that all independent contributions to an observable should be comparable to or less than its measured value.For the case of the Minimal Supersymmetric Standard Model, or MSSM, the weak scale (as typified by the Z-boson mass) is related to weak scale SUSY Lagrangian parameters as where m 2 H u,d are soft breaking squared masses of the Higgs doublets, tan β = v u /v d is the ratio of Higgs field vevs, µ is the SUSY conserving µ parameter 1 and the Σ u,d u,d terms contain over 40 1-loop and some 2-loop corrections to the scalar potential (explicit expressions are given in Ref's [4,7]).The measure ∆ EW is defined as ∆ EW ≡ |largest term on RHS of Eq.1|/(m 2 Z /2) so that no large unnatural finetunings are allowed in the derivation of m Z .A large negative value of A t which enters the expressions for Σ u u ( t1,2 ) leads to large cancellations (more naturalness) in both these terms [3] whilst lifting m h → 125 GeV [8].
Natural SUSY (natSUSY) models are considered more plausible than unnatural models in that they contain no implausible accidental tunings of unrelated terms in Eq. 1. Furthermore, it is now understood that natSUSY is the most likely expression of weak scale SUSY that ought to emerge from the string landscape [9][10][11].This arises since low ∆ EW ≲ 30 corresponds well with the anthropic Agrawal-Barr-Donoghue-Seckel (ABDS) [12,13] window of allowed weak scale values which give rise to complexity in the multiverse (atomic principle).For the case of fine-tuned models, then the available multiverse scan space shrinks to tiny volumes compared to natural models due to the finetuning which is required.
In the present work, we examine prospects for slepton (specifically, the lightest τ -slepton τ1 ) pair production at the high-luminosity upgrade of LHC (HL-LHC) in a natural SUSY context.We focus on lightest right-tau-sleptons for several reasons.
In models with high scale slepton universality (such as mSUGRA [14][15][16]/CMSSM [17] or NUHM2, NUHM3 or NUHM4 [18,19] models), the stau soft mass RGEs are given by where m2 L 3 is the third generation doublet slepton soft mass squared (giving rise to left-staus) and m 2 E 3 is the corresponding SU (2) L singlet slepton mass squared (giving rise to right-staus).Also, S = m 2 Hu − m 2 and t = log(Q).When running from high scales (e.g.Q = m GU T ) to Q = m weak , the SU (2) L gauge term in Eq. 3 drives m 2 L 3 to larger values than m 2 E 3 at the weak scale while the rather large τ -Yukawa coupling term containing 2f 2 τ in Eq. 4 drives the right-stau soft mass squared m 2 E 3 to smaller values than m 2 L 3 .For the natSUSY models considered here, usually S > 0 so this term also drives right-sleptons to smaller masses than left-sleptons at the weak scale.Thus, in models with intra-generation universality of scalar masses (which are motivated by SO (10) where all elements of each generation live in a single 16 − d spinor rep), we expect that right-stau masses are smaller than left-stau masses. 2  Also, on the theory side, the string landscape pulls soft breaking terms as large as possible until they over-contribute beyond the ABDS window to the weak scale.This effect tends to pull first/second generation sfermion masses to the tens-of-TeV values whilst third generation sfermions, which contribute proportional to their Yukawa couplings squared, only get pulled up to values of several TeV [23] at the high scale.
Furthermore, in orbifold compactifications on the minilandscape [24], first/second generation sfermions live near orbifold fixed points and "feel much less supersymmetry than third generation fields" [25] which instead live more in the bulk where they have large overlap with Higgs multiplets.Thus, third generation soft terms are more protected by SUSY and hence gain smaller soft masses than their first/second generation counterparts.
On the phenomenology side, light sleptons are preferred by the (g − 2) µ anomaly [26], and of all the sleptons, the right-staus are expected to be lightest.Also, light tau-sleptons with mass m τ1 ∼ m χ0 1 are required to thermally match the measured dark matter relic density in the so-called stau coannihilation region of SUSY model parameter space [27][28][29].
For these reasons, we examine prospects for detecting the lightest (right-) tau-sleptons, but within the context of natSUSY models.To this end, in Sec. 2, we develop a natural SUSY model line with low ∆ EW but with a variable right-stau soft mass.In Sec. 3, we present stau pair production cross sections which are expected at LHC14, and in Sec. 4, we compute expected τ1 branching fractions along our model line.Since we work within a natural SUSY context, then higgsinos are expected with mass ∼ µ ∼ 100 − 350 GeV [30,31].The presence of light higgsinos is expected to diminish the LHC reach for light staus compared to usual simplified models in that in the natSUSY case, a substantial branching fraction τ1 → ν τ χ− 1 where the χ± and the small m χ+ 1 − m χ0 1 mass gap leads to very low energy visible decay products.However, in the case where m τ1 > m(bino) ≫ m(higgsino), then the decay to binos rapidly dominates the stau decay rate leading to possibly new discovery signatures: diboson+τ τ + ̸E T .In Sec. 5, we evaluate the projected HL-LHC reach for stau pairs in natSUSY in the m τ1 vs. m χ0 1 plane.While we do not find a 5σ discovery reach for HL-LHC, we do find a 95%CL exclusion reach that extends from m τ1 ∼ 200 − 450 GeV for m χ0 1 ∼ 100 GeV.We conclude in Sec. 6.
In contrast, natural SUSY models with µ ∼ m Z contain three light higgsinos χ0 1,2 and χ± 1 .Since higgsinos annihilate and coannihilate at high rates in the early universe [44] they have no dark matter overproduction problem and hence no need for tuning the relic abundance into the stau coannihilation region and there is no reason to expect a situation with long-lived light staus.Instead, any light staus are expected to decay promptly to the three light higgsinos along with tau-leptons or tau-neutrinos (see upcoming Fig. 3 for branching fractions).
In Ref. [45], the ATLAS collaboration reported on a search for stau pair production using Run 2 data with 139 fb −1 at √ s = 13 TeV.The final state signature searched for was τ h τ h + ̸E T where τ h is a hadronically-decaying τ -jet.No signal was seen above SM backgrounds, and limits were placed in the m τ vs. m χ0 1 plane assuming 1. degenerate left-and right tau-sleptons and 2. just pair production of left tau-sleptons.
In both cases, a simplified model with the decay τ1 → τ χ0 1 at 100% branching fraction was assumed.In the former Case, with m χ0 1 ∼ 100 GeV, then m τL/R : 230 GeV − 350 GeV was excluded while for the second Case no limit ensues for m χ0 1 = 100 GeV although m τL : 150 GeV− 320 GeV can be excluded for m χ0 1 = 0.A similar search was reported on by CMS using Run 2 data with 138 fb −1 in Ref. [46].No excess was seen in the τ h τ h + ̸E T signal channel above SM background leading CMS in Case 1 to exclude m τL/R : 200 GeV − 380 GeV while in Case 2 m τL ∼ 280 GeV could be exluded for m χ0 1 = 100 GeV while m τL : 120 GeV − 350 GeV could be excluded for m χ0 1 = 0.The ATLAS Collaboration also performed a HL-LHC reach study in 2016 [47] for stau pair production with √ s = 14 TeV assuming 3000 fb −1 of integrated luminosity.This study examined the reach for Case 1 and 2 as above but also included reach results for just τR τR pair production (Case 3).For m χ0 1 = 100 GeV, they report a 95% CL exclusion reach in m τ up to 540 GeV in Case 3, 650 GeV in case 2 and 700 GeV in case 1.There was no 5σ discovery reach for any value of m τ in Case 3.An updated 2018 study by ATLAS was presented in Ref. [48].A similar study was performed by CMS in 2019 [49] where a 95% CL exclusion reach for HL-LHC in m τ up to 640 GeV was reported for Case 1 with m χ0 1 = 100 GeV.

A natural SUSY model line with light right-staus
We would like to embed light tau-sleptons within a natural SUSY model framework since it can be argued that SUSY models with low electroweak finetuning (with ∆ EW ≲ 30) are the most plausible of SUSY models in that the weak scale m weak ≃ m W,Z,h is of order ∼ 100 GeV because all MSSM contributions (some positive, some negative) in Eq. 1 are comparable (within a factor of several) to the m weak scale.Such models can be found for instance within the framework of non-universal Higgs models [18,19,50].Here, we will work within the NUHM4 model4 with parameters (where m 0 (i) refers to separate soft masses m 0 (1, 2, 3) for each generation, as is expected from general supergravity models where no known symmetry enforces generational mass universality [51][52][53]) and where it is common to trade the high scale soft terms m 2 Hu and m 2 H d for the more convenient weak scale parameters µ and m A : and where i = 1 − 3 is a generation index.In NUHM models, the required µ ∼ 100 − 350 GeV parameter can be dialed to fulfill one of the requirements of low ∆ EW in Eq. 1. Also, a large negative A 0 parameter lifts m h → 125 GeV [8,54] while reducing the top-squark loop corrections Σ u u ( t1,2 ) to Eq. 1 [3,4].This latter effect reconciles natural SUSY with the rather large measured value of m h and with m t ∼ 1 − 3 TeV (beyond present LHC top-squark mass bounds).
The benchmark point shown in Table 1 thus takes as parameter choices 1 is higgsino-like with a thermally-produced (TP) relic abundance of Ω T P χ h 2 ∼ 0.016.Since we would also like to be natural in the context of the strong CP problem, we invoke SUSY axions in the DFSZ model and expect the bulk of dark matter to be axions along with a smattering of higgsino-like WIMPs [55][56][57].
To embed light sleptons within natSUSY, we create a model line with variable third generation MSSM soft mass m E 3 .Then, dialing m E 3 down in value, we can generate light rightslepton masses as shown in Table 1, where we take m E 3 = 1.11TeV which then generates a light tau-slepton with mass m τ1 = 378 GeV.(We use ISAJET v7.91 [58] to generate the SUSY spectrum.)The lightest slepton eigenstate is given by [1] τ1 = cos θ τ τL − sin θ τ τR .The mixing angle θ τ = 89.9• listed in Table 1 shows that τ1 is dominantly τR .
A plot of m τ1 vs. m E 3 is shown in Fig. 1  m 2 E 3 tachyonic for small enough GUT scale values of m E 3 .(S = 0 in models such as CMSSM with universal scalar masses.)We find this same behavor occurs also in SOFTSUSY [60].Hence to obtain smaller values of m τ1 , we implement the weak-scale SUSY parameters from the BM point into the pMSSM solution embedded in ISASUSY [61], which doesn't include RG running and so allows lighter tau-sleptons as light as m τ1 ≃ m χ0 1 .
Figure 1: Plot of m τ1 vs. m E 3 along the light stau natural SUSY model line.

Stau pair production at LHC14
Pair production of light right-staus takes place via q q → γ * , Z * → τ1 τ1 X at the LHC.(Light left-staus can also be produced via q q′ → W * → τ1 ντ .)Next-to-leading order QCD corrections were computed in Ref. [62] and are included in PROSPINO [63] which we use for the total cross section computation.The total cross section in fb for production of tau-sleptons at LHC with √ s = 14 TeV is shown vs. m τ1 in Fig. 2. From the plot, we see that τ1 τ1 production occurs at σ > 1 fb for m τ1 ≲ 400 GeV.For HL-LHC with an assumed integrated luminosity of 3000 fb −1 , we would drop below the 30 total event level for m τ1 ≳ 850 GeV level.Thus, we would expect any sensitivity of HL-LHC to tau-slepton pair production to lie in the few hundred GeV region, based solely on total production cross section.

Right-stau branching fractions in natural SUSY
In this Section, we examine the expected light slepton branching fractions (BFs) within the context of natSUSY.The BFs of τ1 are computed using ISAJET 7.91.In Fig. 3, we plot the dominant BF (τ 1 ) vs. m τ1 along our τ1 natSUSY model line with rather light higgsinos.From the plot, we see that for m τ1 ≲ 550 GeV, then the decay τ1 → χ− 1 ν τ is actually dominant at ∼ 40%.Since this decay would be followed by χ− 1 → f f ′ χ0 1 , with m χ+ 1 just a few GeV heavier than m χ0 1 , then very soft visible energy will ensue and the decay mode is likely to be hardly visible in the LHC detector environment.
The next largest BF comes from τ1 → χ0 1 τ (blue curve) which occurs typically at the ∼ 35% level for m τ1 ≲ 550 GeV.For large enough τ1 − χ0 1 mass gap, then this mode can give rise to 2 is also mainly higgsino-like, but now can decay as χ0 2 → f f χ0 1 .Again, for small χ0 2 − χ0 1 mass gap, this decay will typically yield only soft visible energy unless the χ0 2 is somewhat boosted.The τ lepton may again be visible as a distinctive τ -jet.Thus, along the model line, and for m τ1 ≲ 550 GeV, we expect stau pair production to yield either one or two hard τ -jets plus missing energy, along with possibly soft visible debris from the quasidegenerate heavier higgsino decays.This is at odds with simplified model analyses, which usually assume 100% stau decay to hard visible τ -jets.
Of further note in Fig. 3 is that as m τ1 exceeds the bino mass, where χ0 3 is dominantly binolike, then new lucrative decay modes open up and rapidly dominate the τ1 branching fractions.For m τ1 ≳ 550 GeV, then τ1 → χ0 3 τ , but the bino χ0 3 → χ± 1 W ∓ at about 25% each, and also χ0 3 → χ0 1,2 Z and χ0 1 h at ∼ 22 − 25%.For this case, then stau pair production will yield final state events with two hard τ jets along with W W , W Z, W h, ZZ, Zh and hh.Such signatures would be very distinctive, but since the total production cross section tends to be rather low for such large values of m τ1 , it is unlikely that these would be easily visible at HL-LHC with √ s = 14 TeV.

Reach of HL-LHC for stau pairs in natural SUSY
In this Section, we examine the potential of HL-LHC (pp collisions at √ s = 14 TeV with 3000 fb −1 ) for probing τ + R τ − R pair production in the context of natural SUSY.

Event generation for signal and background
We use Isajet to first construct a SUSY Les Houches Accord (SLHA) file [64] for any natural SUSY parameter-space point and feed this into Pythia [65] to generate signal events.We also use Pythia to generate the various 2 → 2 background (BG) processes.For 2 → 3 background processes, we use Madgraph [66] coupled with Pythia.For our computation of SM backgrounds to the stau-pair signal, we include parton level production of t t, t tV , V +jets and V V production (here, V stands for W ± or Z).Specifically, we normalize the stau pair production cross sections to their NLO values obtained from Prospino.For the most important SM backgrounds, we normalize the cross sections to their values at the NLO level or better when available.The NNLO/NNLL t t cross section is normalized to 985.7 pb,5 the cross sections for t tV production are from Ref. [67], V + j cross sections are calculated using the K-factor from the ratio of NLO and LO cross sections from MadGraph with parton jets defined using the anti-k T algorithm with p T j > 25 GeV and ∆R = 0.4, and finally V V cross sections are normalized using the results in Ref. [68].We use the Delphes code [69] for detector simulation in our analysis.
Since our discovery channel contains backgrounds with high transverse momentum W and Z bosons decaying leptonically or hadronically, we focus on hard leptons and jets in the central part of the detector.With this in mind, we require isolated electrons and muons to satisfy, • p T (e) > 20 GeV, |η e | < 2.47, with P T Ratio < 0.1, and where P T Ratio is defined as the ratio of the transverse momentum (p ℓ T ) of the lepton to the scalar sum of the transverse momenta of all other particles in a ∆R = 0.3 cone around the lepton: We construct jets using an anti-k T jet algorithm and require, • p T (j) > 20 GeV with a cone size R ≤ 0.4 and |η(j)| < 4.5.
A jet is labeled as a b-jet if, in addition, it is tagged as a b-jet by Delphes.
For our signal search, we require additional triggers to select candidates events.A hadronic τ jet τ h satisfies 1. the requirement of a baseline jet, 2. |η j | < 2.4 and 3. be tagged as a τ -jet by Delphes 6

τ h τ h + ̸E T signal cuts
For this (dominant) signal channel, and after scrutinizing various signal and BG distributions, we require • At least two OS τ h which satisfy the SR τ h jet candidate requirement for signal search, p T (τ 1 ) > 115 GeV, and p T (τ 2 ) > 60 GeV for the two τ h selected as candidates.
After these cuts, we next plot the m T 2 distribution [71] for the τ h τ h + ̸ E T events for signal and SM BGs.

τ h ℓ+ ̸E T signal cuts
For this (subdominant) signal channel, after scrutinizing the signal and BG distributions, we require the following cuts: • At least one pair of OS lepton and τ h , p T (τ h ) > 165 GeV Then we require )) > 100 GeV, where ∆ϕ is the azimuthal angle between the ⃗ ̸E T and the closest lepton or jet with p T > 25 GeV, The resulting distributions in m T 2 are shown in Fig. 5 with color-coding as in Fig. 4. In this case, we find the signal histograms to be well below BG by at least an order of magnitude even in the most propitious bins.

Reach of HL-LHC for stau pair production
For each of the two signal channels from Subsec's 5.2 and 5.3, we examine the binned m T 2 distributions shown in Fig. 4-5.For exclusion of the stau-pair signal, we assume that the true distribution we would observe in an experiment would correspond to a background only distribution.Upper limits on m τ1 are then evaluated using a modified frequentist CL S method [72] with the profile likelihood ratio as the test statistic.The likelihood is built as a product of Poissonian terms for each of the bins in the distributions.A background systematic uncertainty is accounted for by introducing an independent nuisance parameter for each bin of each channel and the likelihood is modified by log-normal terms to account for these nuisance parameters, with uncertainty that we take to be 25%.Then, the largest value of m τ1 that can be excluded at 95%CL for a given assumed value of m χ0 1 is the exclusion limit.For discovery, we assume that the distribution one would observe in an experiment corresponds to signal-plus-background.We then test this against the background only distribution for each value of m τ1 .If the background only hypothesis can be rejected at at least the 5σ level, we deem that the HL-LHC would discover staus with a mass corresponding to that choice of m τ1 .For both the exclusion and discovery limits, we use the asymptotic expansion for obtaining the median significance [73]. 7 Our HL-LHC reach results are shown in Fig. 6a) in the m τ1 vs. m χ0 1 plane assuming the natSUSY benchmark scenario for the cse of no assumed systematic error.We vary µ in order to vary m χ0 1 .In our case of τ1 τ1 production within natSUSY, we do not find any discovery reach.However, the 95% CL exclusion curve is shown as the black dashed curve along with 1σ fluctuation limits shown as the yellow band. 8Unlike the ATLAS and CMS results, our m χ0 1 values only extend down to ∼ 100 GeV since LEP2 is expected to exclude higgsino-like charginos with mass m χ± 1 ≲ 100 GeV.For m χ0 1 ∼ 100 GeV, then we expect LHC experiments to be able to exclude m τ1 : 200 − 450 (400) GeV, assuming 0% (25%) systematic uncertainty.For lower values of m τ1 ≲ 200 GeV, then the final state τ s become too soft for our cuts, while for m τ1 ≳ 450 GeV, then the expected signal rates become too tiny for exclusion.We see that we do expect some exclusion for m χ0 1 values as high as ∼ 200 GeV; for higher m χ0 1 ∼ µ ≳ 200 GeV values, then most of the final-state energy goes into making to χ0 1 rest mass, and too little visible energy is left to distinguish a signal.For our exclusion plot, the above cuts were optimized for µ ∼ 200 GeV, so some small extension of this region may be gained if a lighter value of µ is assumed (but then one may begin to conflict with ATLAS/CMS bounds on µ from soft isolated dilepton plus jets plus ̸E T search results [74,75]).In frame Fig. 6b), we show how the reach is diminished if instead we include an assumed 25% systematic error.
Comparing our results to ATLAS and CMS, we find in the ATLAS (2018) Ref. [48] HL-LHC reach study that there also is no 5σ discovery reach for τR τR pairs, although there is a 95% CL exclusion region for m χ0 1 ≲ 100 GeV.This study includes some systematic errors plus an assumed pile-up that we have not included.This helps us to gain a larger exclusion region than ATLAS even though some of our staus decay invisibly.
Comparing with the CMS HL-LHC reach study, they do obtain a 5σ discovery reach even 7 We have checked that for every channel that we study there are at least ten (frequently significantly more) background events in the "sensitive regions" of the histograms in Fig. 4-5.This is large enough to justify the use of asymptotic formulae since for discovery (exclusion) we are concerned with fluctuations of the background (signal plus background). 8For Fig. 6a), the yellow band is purely statistical uncertainty.For Fig. 6b), the band includes the combined effects of statistical and systematic uncertainty.The reasons leading to larger (statistical) uncertainties for heavier mass scales of staus or neutralinos region are 1) Signal yield is small when m τ1 is large and 2) When the m χ0 1 is heavier, the mass difference between the stau and the χ0 1 becomes smaller such that the visible decay products become softer and thus the signal signatures are less distinguishable from the backgrounds.In both cases, the statistical uncertainty tends to be large which widens the uncertainty band.Such features are consistent with the reach contour from the current ATLAS search on direct stau production via τ h τ h + ̸E T .See e.g.Fig. 7 of [45].for m χ0 1 > 100 GeV.There reach should be better than our since they include both τL τ * L and τR τ * R production (but see the discussion below on this dangerous assumption).Meanwhile, their 95% CL exclusion limit ranges from m τ1 ∼ 100 − 650 GeV for m χ0 1 ∼ 100 GeV which is broader than our result although we include the invisible stau decay modes which are generic for natural SUSY, while they assume τ1 → τ χ0 1 at 100% branching fraction.

Summary and discussion
We have examined right-stau pair production at HL-LHC in the context of a natural SUSY model line wherein all independent contributions to the weak scale are comparable to m weak (thus, no weak scale finetuning is needed).This class of models can be considered as much more plausible than finetuned models which require accidentally large cancellations to obtain m W,Z,h ∼ 100 GeV.Furthermore, the right-staus are usually expected to be the lightest of the tau-sleptons.Thus, we embed light right staus within a natSUSY model line.
In such models, the four higgsino-like EWinos are the lightest of sparticles, so τ1 → χ− 1 ν τ (nearly invisible) at rates comparable to τ1 → χ0 1,2 τ .The latter decays lead to ditau + ̸ E T events at a reduced rate compared to the usual simplified models.The hadronic ditau+ ̸E T ends up being a more lucrative search channel than τ h ℓ+ ̸E T .By computing signal and SM BG in the m τ1 vs. m χ0 1 plane, we do not find any 5σ discovery regions at HL-LHC, but we do obtain a 95%CL exclusion reach.This region extends from m τ1 : 200−450 (400) GeV, assuming 0% (25%) systematic uncertainty, for m χ0 1 ∼ 100 GeV, but disappears entirely for m χ0 1 ≳ 200 GeV.The net reach is of course reduced by including an overall systematic error.These results illustrate the difficulty of finding light tau-sleptons at HL-LHC in a natSUSY context.

Comparison of stau pair searches in natural and unnatural SUSY
Most experimental search projections occur within simplified models which assume stau pair production (τ L τ * L and/or τR τ * R ) along with decay to a single light neutralino χ0 1 with BF (τ i → τ χ0 1 ) at 100%.Can one distinguish these presumably unnatural models (with decoupled higgsinos so that µ must be large) from our case of natSUSY which includes light higgsinos since |µ| ≲ 350 GeV?Most likely, the answer is yes.The natural case with light higgsinos will be accompanied by higgsino pair production signals [31] such as pp → χ0 1 χ0 2 and χ± 1 χ0 2 with χ0 2 → ℓ l χ0 1 .Higgsino pair production thus gives rise to soft opposite-sign dileptons + ̸E T which may be visible if the soft leptons recoil against a hard initial state jet radiation [76][77][78].In fact, there are some small excesses in both ATLAS [74] and CMS [75] Run 2 data in this channel.There is also a distinctive same-sign diboson signature in natSUSY which can occur from wino pair production followed by decay to lighter higgsinos [79,80].These higgsino related signatures would not occur for unnatural SUSY models.For a review of collider signals from natural SUSY, see e.g. the review [81].

The case of left-vs. right staus
The projected reach of ATLAS [48] and CMS [49] has been computed for stau pair production followed by 100% branching fraction τi → τ χ0 1 where i = L and/or R. Another question arises: can one tell whether one is producing τL τ * L from τR τ * R production, or indeed a mixture of both as is assumed in some experimental simplified model scenarios.One way may be to use the different decay energy distrbutions from left-versus right-tau lepton decays that arise from their parent τL or τR particles.
So far, we have argued that the lighter right-stau m τR ≪ m τL is more theoretically motivated, and so we have focussed on his case.In fact, the ATLAS and CMS studies assume certain simplified models which violate major theoretical constraints.Aside from assuming 100% stau branching fractions into a single mode τ χ0 1 , if one assumes a light left-stau τL , then necessarily it comes with a light tau-sneutrino.The weak scale mass relations are [11] so that most of the mass of τL and ντL comes from m 2 L 3 .This actually means that if you assume light left staus, one must also include pp → W * → τL ντL and ντL ν * τ L production where now the ντL also usually decays visibly.(Even if one assumes an invisible ντL → ν τ χ0 1 decay, the W * production channel will give rise to a large rate for mono-tau-jet+ ̸E T events which should be included in any search strategy.)The W * mediated production cross section dominates slepton pair production [82] and sneutrino pair production is comparable to stau-left pair production cross section.Thus, the total cross sections for left-slepton pair production will be much higher than typically assumed in simplified models, and the decay sigatures will be more complex, for a given value of m τL .We expect this much more complex, but more realistic, case of left-slepton pair production to be readily distinguishable from right stau pair production.At present, realistic analyses are lacking.

Figure 2 :
Figure 2: NLO cross sections (in fb) for pp → τ1 τ * 1 X production at a pp collider with √ s = 14 TeV versus m τ1 for the light τ1 natural SUSY model line of the text.

Figure 3 :
Figure 3: Branching fractions of τ1 from natural SUSY versus m τ1 for the light stau natural SUSY model line.
The results are shown in Fig. 4. The colored solid histograms show various SM backgrounds of which W W is dominant for m T 2 ≳ 100 GeV.Two signal BM points with various assumed m τ1 values are shown as dot-dashed histograms.From the plot, we see that the signal histogram for m τ1 = 400 GeV is comparable to the summed background for m T 2 ∼ 100 − 300 GeV while the m τ1 = 580 GeV signal distribution lies well below BG.For the m τ1 = 400 GeV BM point, we expect of order tens of signal events around m T 2 ∼ 100 − 200 GeV for 3000 fb −1 of integrated luminosity.

Figure 4 :
Figure 4: Distributions in m T 2 for τ h τ h + ̸ E T events from several right-stau pair production models and SM backgrounds at HL-LHC where we assume 3000 fb −1 of integrated luminosity.

Figure 5 :
Figure 5: Distributions in m T 2 for τ h ℓ ± + ̸ E T events from several right-stau pair production models and SM backgrounds at HL-LHC.

Figure 6 :
Figure 6: The 95% CL exclusion reach of HL-LHC for right-stau pair production events with a natSUSY setup.In frame a), we assume no systematic error whilst in frame b) we assume 25% systematic error.

Table 1 :
[58]the benchmark point but with variable m E 3 .The curve cuts off below m E 3 ≲ 1.1 TeV in that m 2 E 3 is driven to tachyonic values at an intermediate iteration in the SUSY RGE solution in ISASUGRA[59].The large S term (defined below Eq. 4) becomes large positive for non-universal Higgs models with m Hu ≫ m H d , which then drives Input parameters (TeV) and masses (GeV) for the light stau natural SUSY benchmark point from the NUHM2+E3 model with m t = 173.2GeVusingIsajet 7.91[58].