Natural anomaly-mediation from the landscape with implications for LHC SUSY searches

Supersymmetric models with the anomaly-mediated SUSY breaking (AMSB) arose in two different settings: 1. extra-dimensional models where SUSY breaking occurred in a sequestered sector and 2. 4-d models with dynamical SUSY breaking in a hidden sector where scalars gain masses of order the gravitino mass m_{3/2} but with gauginos and trilinear soft terms of the AMSB form. Both have run into serious conflicts with 1. LHC sparticle and Higgs mass constraints, 2. constraints from wino-like WIMP dark matter searches and 3. bounds from naturalness. These conflicts may be avoided by introducing minor changes to the underlying phenomenological models consisting of non-universal bulk scalar Higgs masses and A-terms, providing a setting for {\it natural anomaly-mediation} (nAMSB). In nAMSB, the wino is still expected to be the lightest of the gauginos, but the higgsinos are expected to be the lightest electroweakinos (EWinos) in accord with naturalness. We examine what sort of spectra are expected to emerge when nAMSB arises from a string landscape setting. We explore the LHC phenomenology of nAMSB models via higgsino pair production and wino pair production. We characterize the dominant LHC signatures arising from the remaining patch of parameter space which should be fully testable at high-luminosity LHC via EWino pair production searches.


Introduction
Supersymmetric models [1] based on anomaly-mediated SUSY breaking (AMSB) arose from two different set-ups.

AMSB0: (GLMR)
The second, by Giudice et al. [2] (GLMR), which we label as AM SB0, was motivated by 4dimensional models where SUSY is broken dynamically in the hidden sector [3], and where SUSY breaking was communicated to the visible sector via gravity.The motivation here was that the SUSY breaking scale m hidden might be generated non-perturbatively via gaugino condensation and would then be exponentially-suppressed relative to the Planck scale via dimensional transmutation [4]: m hidden ∼ e −8π2 /g 2 m P , where m P is the reduced Planck scale.This would not only stabilize the weak scale (via SUSY), but also explain its exponential suppression from the Planck scale: m weak ∼ m sof t ∼ m 2 hidden /m P , where m hidden ∼ 10 11 GeV.Now in gravity mediation, gaugino masses arise via with f AB the gauge kinetic function depending on hidden sector fields S and where the F -term of S acquires a SUSY breaking value F S ; the gaugino masses arise as m λ ∼ (F S /m P ) ∼ m 3/2 ∼ m sof t ∼ m weak .However, if no hidden sector singlets are available as in (most) DSB models [5] 1 , then the gaugino masses are expected instead at the keV scale, which would be experimentally excluded.However, Ref. [2] found that the one-loop renormalization of the visible sector gauge couplings is given by [7] 1 4 where b 0 is the coefficient of the relevant gauge group beta-function and □ is the d'Alembertian operator.This leads to SUSY breaking gaugino masses via replacement of the UV cutoff Λ by the spurion superfield Λ exp(m 3/2 θ 2 ) leading to (loop-suppressed) gaugino masses [8] 2 For m 3/2 ∼ 100 TeV, then m λ ∼ 1 TeV as required to gain m weak ∼ m W,Z,h ∼ 100 GeV.
Similarly, the trilinear soft (A)-terms are not allowed at tree level if no singlets are available for a d 2 θ S m P ϕ i ϕ j ϕ k (4) coupling (where the ϕ i are generic visible sector superfields).The A-terms can also arise at oneloop level in AMSB and are proportional to derivatives of the anomalous dimensions.Scalar masses on the other hand arise from and are not protected by symmetries and so can be much larger, m 2 ϕ ∼ m 2 3/2 , and can gain their gravity-mediated form.This form of scalar mass generation suffers the usual SUSY flavor problem that is endemic to gravity-mediation.
The AMSB0 model thus yields a hierarchy of soft terms m ϕ ≫ m λ ∼ A as noted by Wells [13] in what he dubbed PeV-SUSY [14].This model also motivated realizations of split [15,16]-and minisplit [17] SUSY models.These later models eschew the notion of naturalness in hopes of a landscape solution to the naturalness problem, thus allowing for scalar masses in the range of 100-1000 TeV (for minisplit) and ranging up to m ϕ ∼ 10 9 TeV for split SUSY.Split SUSY predicts a light Higgs mass m h ∼ 130 − 160 GeV [18].The discovery of a SM-like Higgs boson with mass m h ∼ 125 GeV motivated a retreat to scalars in the range of minisplit models which allow for m h ∼ 125 GeV along with small A-terms.A value of m h ≃ 125 GeV can also be realized by TeV-scale top squarks but with near maximal stop mixing from large A-terms [19,20].
Since scalar masses arise as in gravity-mediation, this AM SB0 model may still be plagued by flavor problems, although these may be softened by the rather large values of scalar masses which are expected: a (partial) decoupling solution to the SUSY flavor problem [21].It also gave rise to unique phenomenological signatures [22] since in AMSB the wino rather than the bino was expected to be the lightest SUSY particle (LSP).

AMSB (RS)
Alternatively, in the Randall-Sundrum AMSB model [23] (AM SB), it was posited that SUSY breaking arose in a hidden sector sequestered from the visible sector in extra-dimensional spacetime.In such a set-up, the leading contribution to all soft SUSY breaking terms was from the superconformal anomaly, and suppressed by a loop factor from the gravitino mass m 3/2 .In this form of AMSB, a common value of scalar masses was expected thus avoiding the SUSY flavor problem which seems endemic to models of gravity-mediation.Also, since m sof t ≪ m 3/2 , the cosmological gravitino problem could be avoided since in the early universe thermally-produced gravitinos could decay before the onset of BBN [24].In both cases of AM SB and AM SB0, the thermally underproduced wino-like WIMPs could have their relic abundance non-thermally enhanced by either gravitino [25] or moduli-field decays [26,27].A drawback in the case of AM SB was that soft slepton masses were derived to be tachyonic thus leading to charge-breaking vacua in the scalar potential.Some extra contributions to scalar masses arising from fields propagating in the bulk of spacetime could be postulated to avoid this problem [23].

Further deliberations on AMSB
Some further notable theoretical explorations of AMSB soft terms include Gaillard et al. [28] where AMSB soft terms arose as quantum corrections under Pauli-Villars regularization of supergravity.In Anisimov et al. [29,30], brane world SUSY breaking (as in RS model) was examined, and it was found to be insufficient to guarantee the needed sequestering between hidden and observable sectors to generate dominant AMSB soft terms and flavor-conserving scalar masses.In Ref. [31], Luty presents pedagogical lectures on SUSY breaking leading up to and including AMSB.In Ref. [32], the connection of AMSB to dimensional transmutation is examined as a solution to the tachyonic slepton problem.In Ref. [33], Dine and Seiberg (DS) clarify the derivation of AMSB soft terms and relate them to the gaugino counterterm.In Ref. [34], de Alwis presents the derivation of AMSB soft terms and emphasizes their origin in work by Kaplunovsky and Louis [12] and DS, and shows there may be additional soft term contributions.This inspires his later development of the gaugino AMSB model [35].In Ref. [36], a clarifying derivation of AMSB soft terms is presented.In Ref. [37], Sanford and Shirman develop an arbitrary conformal compensator formalism which allows extrapolation between RS and DS derivations.In Ref. [38], anomaly mediation from IIB string theories is examined.In Ref. [39], the AMSB connection to gravitino mediation vs. Kähler mediation is examined.This work is extended to scalar masses in Ref. [40].In Ref. [41], Dine and Draper examine anomaly mediation in local effective theories.In Ref. [42], de Alwis examines the interplay of AMSB with spontaneous SUSY breaking.In Ref. [43], the connection between AMSB gaugino masses and the path integral measure is examined.
An alternative route to models with AMSB soft terms was developed by Luty and Sundrum [44], in models with strong hidden sector conformal dynamics.In these 4 − d models, strong hidden sector conformal dynamics leads to a suppression, or sequestering, of usual soft terms due to higher dimensional operators which mix the hidden and visible sectors.The suppression of gravity-mediated soft terms occurs between the messenger scale (taken here to be m P ) and some intermediate scale m int where conformal symmetry becomes broken.In such a case, the loop-suppressed AMSB soft terms may become dominant.In Ref. [45], the conformal suppression acts upon scalar masses and the Bµ term, but in Ref's [46,47] it is emphasized that conformal sequestering may also act on the gaugino sector.

Status of minimal phenomenological AMSB model (mAMSB)
A minimal phenomenological AMSB model (mAMSB) was proposed in Ref's [48] and [49] with parameter space where m 0 was an added universal bulk scalar mass and the gravitino mass m 3/2 set the scale for the AMSB soft terms m AM SB ∼ c(g 2 /16π 2 )m 3/2 with c a calculable constant of order unity and g is a gauge group coupling constant.The bulk scalar mass is generic to the AM SB0 set-up and phenomenologically required to gain positive slepton squared masses in AM SB.Various studies for mAMSB at LHC appeared in Ref's [50,51,52,53,54].At present, both these set-ups within the mAMSB model seem phenomenologically disfavored and perhaps even ruled out.The first problem is that in mAMSB the SUSY conserving µ parameter is typically fine-tuned to large values compared to the measured value of the weak scale m weak ∼ m W,Z,h ∼ 100 GeV, thus violating [55] even the most conservative measure of naturalness ∆ EW [56,57], where ∆ EW is defined as the largest value on the right-hand-side (RHS) of the scalar potential minimization condition divided by m 2 Z /2.The second problem is that the small values of mAMSB A-terms typically lead to too small a value of m h ≪ 125 GeV unless third-generation soft scalar masses lie in the 10-100 TeV range [58,59] thus also violating naturalness [55] via the radiative corrections Σ u u ( t1,2 ), leading again to a large value for the electroweak fine-tuning measure ∆ EW .A third problem is that wino-only dark matter [26] now seems excluded by a combination of direct and indirect WIMP search experiments [60,61,62].This latter exclusion may be circumvented in cases of mixed axion-wino dark matter (two DM particles) wherein the relic wino abundance forms only a small portion of the total DM abundance [63].This latter scenario posits a PQ axion which also solves the finetuning problem of the θ parameter in the QCD sector.

Natural anomaly-mediated SUSY breaking (nAMSB)
In Ref. [64], two minor changes to the mAMSB model were suggested to circumvent its undesirable phenomenological properties. 3First, separate bulk masses for m Hu ̸ = m H d ̸ = m 0 were applied to scalar masses which then allowed for a small µ parameter in accord with naturalness (a unified mass m 0 just for matter scalars is highly motivated by the fact that the matter superfields are unified within the 16-dimensional spinor rep of SO (10)).Second, bulk contributions to trilinear soft terms A 0 were advocated which then allowed for large stop mixing which in turn uplifts the Higgs mass m h →∼ 125 GeV [65] without requiring the stop sector to lie in the unnatural multi-TeV range or beyond.These two adjustments allowed for EW naturalness and for m h ∼ 125 GeV.Models with these attributes were denoted as natural AMSB (nAMSB): where we also allow for possible non-universal bulk contributions to the different generations i = 1 − 3. It is convenient to then trade the high scale parameters m 2 Hu and m 2 H d for weak scale parameters µ and m A using the scalar potential minimization conditions [66,67].
Like mAMSB, the nAMSB model has winos as the lightest of the gauginos.Unlike mAMSB, the nAMSB model (usually) has higgsinos as the lightest EWinos, in accord with naturalness.By requiring the natural axionic solution to the strong CP problem, one then expects mixed axion plus higgsino-like WIMP dark matter [68,69], and one can circumvent the constraints on wino-only dark matter [62].

nAMSB from the landscape
The advent of the string theory landscape [70,71] led to some major changes in SUSY models with AMSB soft terms.First, it was found that flux compactification [72] of type IIB string models on Calabi-Yao orientifolds led to enormous numbers of string vacuum states (10 500 is a prominently quoted number [73,74] although much larger numbers have also been found in F -theory compactifications [75]).Such large numbers of vacuum possibilities allow for Weinberg's [76] anthropic solution to the cosmological constant (CC) problem and "explains" the finetuning of Λ CC to a part in 10 120 .Then, if the CC is finetuned by anthropics, might one also allow for the little hierarchy m weak ≪ m sof t to also be finetuned?In split SUSY, electroweak naturalness is eschewed while WIMP dark matter and gauge coupling unification are retained [13,15,77].A possible model framework for split SUSY would then be charged SUSY breaking [16,14], wherein tree level gaugino masses (and A-terms) are forbidden by some symmetry (perhaps R-symmetry?) while scalar masses are allowed as heavy as one likes.Values of m scalar ∼ 10 9 GeV were entertained, leading to a signature of long-lived gluinos.The heavy scalars also allowed for a decoupling solution to the SUSY flavor and CP problems [21].
In split SUSY, one expects light Higgs masses in the m h ∼ 130 − 160 GeV range [18,78], in contrast to the 2012 Higgs discovery with m h ≃ 125 GeV.To accommodate the measured Higgs mass, scalar masses were dialed down to the 10 3 TeV range.These minisplit models [17,79] then allowed for m h ∼ 125 GeV while still potentially allowing for a decoupling solution to the SUSY flavor and CP problems.
However, only recently has the occurrence frequency of highly finetuned SUSY models been examined in an actual landscape context.In Ref. [80], a toy model of the landscape was developed, and it was shown that EW natural models should be more likely than finetuned models to emerge from a generic landscape construction.In retrospect, the reason is rather simple.In Agrawal et al. [81] (ABDS), it was found that within a multiverse wherein each pocket universe would have a different value for its weak scale, then only complex nuclei, and hence complex atoms (which seem necessary for life as we know it) would arise if the pocket universe value of the weak scale were within a factor of a few of its measured value in our universe (OU): 0.5m OU weak ≲ m P U weak ≲ 5m OU weak .We call this range of m P U weak the ABDS window.Now in models where all contributions to the weak scale (to the RHS of Eq. 7) are natural (in that they lie within the ABDS window), then the remaining parameter selection (typically either µ(weak) or m Hu (weak)) will also have a wide range of possibilities, all lying within the ABDS window, to gain an ultimate value for m weak within the ABDS window.On the other hand, if any contribution to m weak is far beyond m weak , then finetuning is needed and only a tiny portion of parameter space will lead to m weak ∼ 100 GeV.This scheme was then used in Ref. [82] to compute relative probabilities P µ for different natural and finetuned SUSY models (and the SM) to emerge from the landscape.For instance, from Ref. [82], it was found that for a radiative natural SUSY model, where all contributions to the weak scale lie within the ABDS window, a relative probability P µ ∼ 1.4 was computed whilst the SM, valid up to the reduced Planck mass m P , had P µ ∼ 10 −26 .Also, split SUSY-with scalar masses at 10 6 TeV-had P µ ∼ 10 −11 .Other models such as CMSSM [83], PeV-SUSY [14], spread SUSY [84], minisplit [17], high-scale SUSY [85] and G 2 M SSM [86] were also examined and found to have tiny values of P µ .Thus, while the emergence of EW fine-tuned models is logically possible from the landscape, their liklihood is highly suppressed compared to natural models: natural SUSY models are much more plausible as a low energy effective field theory (LE-EFT) realization of the string landscape.
With the above considerations in mind, in this paper we first wish to explore in Sec. 2 the expectations for Higgs boson and sparticle masses from the nAMSB model with sequestered sector SUSY breaking-as might be expected from SUSY brane-world models, and as char-acterized by the presence of bulk A-terms (A 0 ̸ = 0 but also including AMSB A-terms).The nAMSB0 model with A 0 = 0 has been shown in Fig. 2 of Ref. [64] to allow for naturalness (∆ EW ≲ 30) but only if m h ≲ 123 GeV.With the string landscape in mind, we expect the various bulk soft terms and m 3/2 to be distributed as a power-law draw to large values in the multiverse as suggested by Douglas [87].By combining the draw to large soft terms with the requirement of a weak scale within the ABDS window, then the putative distribution of Higgs and sparticle masses from the landscape may be derived in the context of those string models which reduce to a nAMSB low energy effective theory.Generically, under charged SUSY breaking with gravity-mediated scalar masses, we expect non-universality within different GUT multiplets and different generations, so we adopt independent masses m 0 (i), (i = 1−3 a generation index), along with m Hu ̸ = m H d .Motivated by the fact that all members of each generation fill out a complete 16-d spinor of SO (10), we maintain universality within each generation (as emphasized by Nilles et al. [88]).One issue is that the bulk trilinear soft terms A 0 are expected to be forbidden under charged SUSY breaking [14].These results show the difficulty of deriving m h ∼ 125 GeV in such models without bulk A-terms.Thus, our ultimate parameter space is We then restrict ourselves to a set of string landscape vacua with the MSSM as the low energy EFT, but where gauginos gain AMSB masses, but the remaining soft terms scan within the multiverse and include bulk terms.(While soft terms are expected to be correlated within our universe, they may scan within the multiverse [89].)With this setup in mind, the remainder of this paper is organized as follows.In Sec. 2, we assume a simple n = +1 power-law draw on soft terms in the landscape, and plot out probability functions for the various expected Higgs and sparticle masses for nAM SB with A 0 ̸ = 0.These models can be natural whilst also respecting m h ∼ 125 GeV.In Sec. 3, we present several AM SB benchmark points and model lines.In Sec. 4, we present sparticle production cross sections expected from nAMSB along our given model line.Here, we find that typically higgsino and wino pair production is dominant over the entire range of m 3/2 values.In Sec. 5, we discuss the wino decays in nAMSB for the dominantly produced sparticles.In Sec's 6, we discuss the main signal channels expected for LHC searches for nAMSB.Given the AMSB weak scale gaugino mass ratio M 1 : M 2 : M 3 ∼ 3 : 1 : 8, it is possible that strong new limits on gaugino pair production from LHC could exclude nAM SB up to and perhaps even beyond its naturalness limit.However, there remains a low mass window with m(wino) ≳ m(higgsino) which is still allowed due to the semi-compressed spectrum of the EWinos.After implementing present LHC constraints on nAMSB parameter space, in Sec.7 we discuss the most favorable avenues for future SUSY searches within the nAMSB framework: via higgsino and wino pair production.Our summary and conclusions follow in Sec. 8.

Sparticle and Higgs masses in nAM SB from the landscape
Here, we scan over parameters with a landscape-motivated m 1 sof t (linear) draw to large soft terms [87,90]: In accord with naturalness, we fix µ = 250 GeV.In lieu of requiring the pocket-universe value of m P U Z to lie within the ABDS window, we instead invoke ∆ EW < 30 to avoid finetuning from terms beyond the ABDS window: the finetuned solutions are much more rare compared to nonfinetuned (natural) solutions because in the finetuned case the scan parameter space rapidly shrinks to a tiny interval [80,82].For the present case, we restrict the landscape to those vacuum solutions which lead to the nAMSB model as the low energy effective field theory, but where the contributions to the soft breaking terms scan over this restricted portion of the multiverse.
Our first results are shown in Fig. 1 for the nAMSB0 model where A 0 is fixed at zero.In this case, we see that the probability distribution peaks at m h ∼ 120 GeV and falls sharply with increasing m h .While some probability still exists for m h ∼ 125 GeV, we henceforth move beyond nAMSB0 to the nAMSB model with A 0 ̸ = 0 where prospects for generating a Higgs mass m h in accord with LHC data are much better.
Our first results for nAMSB are shown in Fig. 2. In frame a), we show the differential probability distribution dP/dm h vs. m h , where P is the probability normalized to unity.The red histogram shows the full probability distribution while the blue-dashed histogram shows the same distribution after LHC sparticle mass limits (discussed in Sec. 6) are imposed.We see that dP/dm h has only small values for m h ≲ 123 GeV, but then peaks sharply in the range m h ∼ 125 − 127 GeV.This is in accord with similar results in models with unified gaugino masses [90] or mirage-mediated gaugino masses [91]: basically, the soft terms m 0 (1, 2), m 0 (3), A 0 , m A and m 3/2 are selected to be as large as possible subject to the condition that the derived value of m P U Z lies within the ABDS window.This pulls the stop soft terms m 0 (3) large into the ∼ 5 TeV range (but not too large) and also the bulk term A 0 to large-nearly maximalmixing values, but not so large as to lead to CCB minima of the scalar potential (CCB or no-EWSB minima must be vetoed as not leading to a livable universe as we know it).These conditions pull m h up to the vicinity of ∼ 125 GeV.We also show in frame b) the distribution in pseudoscalar Higgs mass m A , where m A contributes directly to the weak scale through Eq. 7 since for m Here, we see that m A reaches peak probability around ∼ 2.5 TeV, somewhat beyond the reach of HL-LHC [92].Maximally, m A can extend up to ∼ 6 TeV before overcontributing to the weak scale.
In Fig. 3, we show the probability for selected nAMSB model input parameters.In frame a), the distribution dP/dm 3/2 rises to a broad peak between m 3/2 : 100 − 250 TeV and cuts off sharply around 300 TeV.The upper cutoff on m 3/2 occurs because as m 3/2 → 300 TeV, then m g is pulled beyond 5 − 6 TeV.In this case, the coupled RGEs pull stop masses so high that Σ u u ( t1,2 ) start contributing too much to the weak scale.In frame b), we show the distribution in first/second generation sfermion soft mass m 0 (1, 2).Here, the distribution rises steadily to the scan upper limit since first/second generation sfermion contributions to the weak scale Σ u u ( f1,2 ) are proportional to the corresponding fermion Yukawa coupling.This pull to multi-TeV values of first/second generation squarks and sleptons provides a landscape amelioration of the SUSY flavor and CP problems [93].We also show as a black-dashed histogram the results from a special run with increased upper scan limit of m 0 (1, 2) < 50 TeV.In this case, the distribution peaks at m 0 (1, 2) ∼ 15 − 30 TeV before getting damped by the anthropic condition that m P U Z lies within the ABDS window.In frame c), we show the distribution in third generation soft term m 0 (3).In this case, the distribution peaks at ∼ 5 TeV albeit with a distribution extending between 2 − 10 TeV.The reason for the upper cutoff is usually that the Σ u u ( t1,2 ) contribution to the weak scale becomes too large.Finally, in frame d), we show the distribution in the ratio A 0 /m 0 (3).This distribution shows the prediction of large bulk A-terms which actually suppress the contributions of Σ u u ( t1,2 ) to the weak scale [56].But if A 0 gets too big, then one is pulled into CCB vacua [94] which fail the anthropic criteria.
In Fig. 4, we show the n = +1 landscape probability distribution predictions for various sparticle masses.In frame a), we show the distribution in gluino mass m g.The distribution begins around m g ∼ 2 TeV and peaks at m g ∼ 3 − 4.5 TeV.This "stringy natural" [95] distribution can explain why it was likely that LHC would not discover weak scale SUSY via gluino pair production at Run 2, and why gluino pair searches may even elude HL-LHC searches [96].The light stop mass distribution is shown in frame b), and predicts m t1 ∼ 1 − 2.5 TeV which is mostly within range of HL-LHC [97].In frame c), we show the distribution in m χ± 2 which is approximately the wino mass.Here, the bulk of the probability distribution lies between M 2 ∼ 300 − 700 GeV, making wino pair production an inviting target for LHC searches.In Fig. 4d), we show the distribution in mass difference of the two lightest neutralinos: m χ0 2 −m χ0 1 .This mass gap is relevant for the reaction pp → χ0  2 where χ0 2 → f f χ0 1 and thus provides a kinematic upper bound for the m(f f ) invariant mass.From the distribution, the mass gap peaks between 10-15 GeV with a tail extending out to 40 GeV (and even beyond).

AM SB benchmark points and model lines
In this Section, we compile three AMSB model benchmark points using the Isajet 7.91 code [98] for sparticle and Higgs mass spectra.The 7.91 version includes several fixes which give better convergence in the nAMSB model than previous versions.
3.1 mAM SB, nAM SB0 and nAM SB benchmark points

mAM SB benchmark
In Table 1, we list three AMSB model benchmark points from three different AMSB models, but with similar underlying parameters which are convenient for comparison.In Column 2, we list sparticle and Higgs masses for the usual minimal AMSB model [48,49] where universal bulk scalar contributions m 2 0 were added to all AMSB scalar soft masses but no bulk A 0 terms were included.We take m 3/2 = 125 TeV and tan β = 10 with m 0 = 5 TeV.The µ term is finetuned to a value µ = 1719 GeV to ensure m Z = 91.2GeV, so the model will be highly finetuned with ∆ EW = 711 (as listed).The gluino mass m g = 2.73 TeV so that gluinos are safely beyond LHC Run 2 search limits which require m g ≳ 2.3 TeV (in simplified models).The light Higgs mass m h = 120.3GeV: too light compared to its measured value (and so this BM point is ruled out).The LSP is wino-like with mass m χ0 1 = 366 GeV while χ0 2 is binolike and the χ0 and χ± 2 are higgsinolike with mass ∼ µ.The top-squark is not very mixed with m t1 = 3.43 TeV, safely above LHC stop search limits.With a wino-like LSP, the thermally-produced relic abundance Ω T P χ h 2 = 0.009, underabundant by a factor ∼ 13.Thus, non-thermal wino production mechanisms would need to be active to fulfill the relic abundance with pure wino dark matter, which would then be ruled out by indirect WIMP detection experiments, where winos could annihilate strongly in dwarf galaxies, thus yielding high energy gamma rays in violation of limits [62] from Fermi-LAT and HESS.Alternatively, a tiny abundance of wino DM could be allowed if some other particle such as axions constituted the bulk of dark matter [63].

nAM SB0 benchmark
Benchmark point nAMSB0 shows the expected sparticle and Higgs mass spectra from the generalized AMSB model inspired by DSB where hidden sector singlets are not allowed.This leads to allowed-but non-universal-scalar masses whilst gaugino masses and A-terms are suppressed and thus assume their loop-suppressed AMSB form.Thus, for nAMSB0 we adopt the parameter space Eq. 9 but with A 0 = 0. We adopt a natural value of µ = 250 GeV with m A = 2 TeV and also allow for higher first/second generation scalar masses as expected from the landscape, with m 0 (1, 2) = 10 TeV whilst m 0 (3) = 5 TeV as in the mAMSB benchmark point.
For nAMSB0, the natural value of µ = 250 GeV implies light higgsinos so that while winos are still the lightest gauginos, the higgsinos are the lightest EWinos, and thus the expected phenomenology markedly changes from mAMSB.The small value of µ also makes the nAMSB0 model much more natural than mAMSB, where ∆ EW has dropped to 60.The dominant contributions to ∆ EW come now from Σ u u ( t1,2 ).But the model is still somewhat unnatural since the largest contribution to the RHS of Eq. 7 is still ∼ 500 GeV, outside the ABDS window [81] and thus in need of finetuning.Another problem is the light Higgs mass m h = 120.7 GeV.Both of these issues arise from the rather small AMSB0 value for the trilinear soft terms.

nAM SB benchmark
In the fourth column of Table 1, we list the nAMSB benchmark point which could arise from the sequestered SUSY breaking scenario of RS [23], where in addition to bulk scalar masses, bulk A-terms are also expected.Here, we use the same parameters as in nAMSB0 except now also allow A 0 = 6 TeV.The large trilinear soft term leads to large stop mixing which feeds into the m h value (which is maximal for stop mixing parameter x t ∼ √ 6m t) so that now the value of m h is lifted to 125 GeV in accord with LHC measurements.Also, the large positive A-term leads to cancellations in both of Σ u u ( t1 ) and Σ u u ( t2 ) leading to increased naturalness where now ∆ EW = 15.For the nAMSB0 benchmark, the more-mixed lighter stop mass has dropped to just m t1 ∼ 1.5 TeV, within striking distance of HL-LHC [97].

Corresponding AMSB model lines
In this Subsection, we elevate each of the AMSB benchmark points to AMSB model lines where we keep the auxiliary parameters fixed as before but now allow the fundamental AMSB parameter m 3/2 to vary.We compute the AMSB model line spectra using Isasugra.
In Fig. 5, we first show the naturalness measure ∆ EW for each model line.For the mAMSB model line, we see that ∆ EW starts at ∼ 100 for low m 3/2 ∼ 50 TeV, and then steadily increases to ∆ EW ∼ 10 4 for m 3/2 ∼ 500 TeV.As for the mAMSB BM point, the dominant contribution to ∆ EW comes from the (finetuned) µ parameter.This model line thus seems highly implausible for all m 3/2 values based on naturalness.We also show the nAMSB0 model line as the orange curve.Here, ∆ EW ranges from 50 − 200 as m 3/2 varies over 50 − 500 TeV.While more natural than mAMSB, it still lies outside the ABDS window which is typified by ∆ EW ≲ 30.The blue curve shows the nAMSB model line.In this case, ∆ EW ranges from ∼ 15 − 150.The line ∆ EW = 30 is shown by the dashed red curve.Here, we see the model line starts becoming unnatural for m 3/2 ≳ 265 TeV.
In Fig. 6, we show the computed value of m h along the three model lines.The LHC measured window is between m h : 123 − 127 allowing for a ±2 GeV theory error in the computed value of m h .We see that the mAMSB model line enters the allowed region of m h only for m 3/2 ≳ 400 TeV while the nAMSB0 model line enters the allowed m h range for m 3/2 ≳ 300 TeV.Both model lines are highly unnatural for such large m 3/2 values.However, the nAMSB model line is within the m h = 125 ± 2 GeV band for m 3/2 : 50 − 280 TeV, consistent with its natural allowed range (thanks to the presence of bulk A 0 terms).
In Fig. 7, we show various sparticle masses for the nAMSB model line vs. m 3/2 .The dark and light blue and lavendar lines show the various higgsino-like EWinos which are typically of order m(higgsinos) ∼ µ ∼ 250 GeV.Next heaviest are the wino-like EWinos χ0 3 and χ± 2 , shown as green and orange curves.These masses vary from m(winos) : 300 − 2000 GeV over the range of m 3/2 shown, and are, as we shall see, subject to present and future LHC EWino searches.
The black curve shows the gluino mass m g : 1.2 − 10 TeV.We also show the LHC lower

LHC production cross sections
In this Section, we pivot to prospects for LHC searches for SUSY within the context of the nAMSB model.First, we adopt the computer code PROSPINO [99] to compute the NLO production cross sections for various pp → SU SY reactions, given input from the Isajet SUSY Les Houches Accord (SLHA) file [100].Our first results are shown in Fig. 8     t * 1 cross section is also relatively flat, this time reflecting that m t1 hardly changes with increasing m 3/2 (from Fig. 7).The pp → gg cross section is falling rapidly with increasing m 3/2 , reflecting that the gluino mass is directly proportional to m 3/2 .From the plot, we thus expect most of the reach of LHC for the nAMSB model will come from EWino pair production rather than from gluino or stop pair production.
There are many subreactions that contribute to the summed EWino pair production cross sections.Each subreaction leads to different final states and thus different SUSY search strategies.In Fig. 9a), we show the several chargino-chargino pair production reactions vs. m 3/2 .The upper blue curve denotes χ+ 1 where the light charginos are mainly higgsino-like (except for some substantial mixing at low m 3/2 where the wino soft term M 2 ∼ µ).Given the small m χ+ 1 − m χ0 1 mass gap, where much of the reaction energy goes into the invisible LSP mass and energy, this reaction is likely to be largely invisible at LHC.The orange curve denotes charged wino pair production: χ+ 2 χ− 2 .Given its modest size and the branching fractions from Sec. 5, it can be very promising for LHC searches.The third reaction, mixed higgsino-wino χ± 1 χ∓ 2 production, occurs at much lower rates.
In Fig. 9b), we show the ten neutralino pair production reactions σ(pp → χ0 i χ0 j ).By far, the dominant neutralino pair production reaction is pp → χ0  2 .This reaction takes place dominantly via s-channel Z * exchange involving the coupling W ij of Eq. 8.101 of Ref. [101].The signs of the neutralino mixing elements add constructively in this case leading to a large higgsino pair production reaction that leads to promising LHC signature in the soft opposite- sign dilepton plus jets plus ̸ E T channel [102,103] (OSDLJMET).This cross section is flat with increasing m 3/2 since µ is not a soft term and not expected to directly scan in the landscape, but instead is by whatever solution to the SUSY µ problem attains [104].The next largest neutralino pair production cross section is pp → χ0  3 : wino-higgsino production, which again has a constructive sign interference along with large mixing terms.Other neutralino pair production reactions are subdominant and typically decreasing with increasing m 3/2 .
In Fig. 9c), we show χ0   1 can contribute to the OS-DLJMET signature mentioned above.The corresponding reactions with negative charginos are comparable to these reactions but somewhat suppressed since they occur mainly via s-channel W * production and LHC is a pp collider which favors positively charged W bosons.The remaining higgsino-wino production reactions fall with increasing m 3/2 and are subdominant.
In Fig. 9d), we show the χ0 4 are all subdominant and may not be so relevant for LHC SUSY searches.

Sparticle decay modes
In this Section, we wish to comment on some relevant sparticle branching fractions leading to favorable final state search signatures for LHC.It is evident from the preceeding Section that EWino pair production is the dominant sparticle production mechanism at LHC14.The reaction pp → χ0 1 χ0 2 (neutral higgsino pair production) is dominant, where χ0 2 → f f χ0 1 and where the f are SM fermions.For the case of nAMSB, the mass gap m χ0 2 − m χ0 1 can range up to 50-60 GeV when winos are light, leading to substantial wino-higgsino mixing for lower values of m 3/2 ∼ 100 TeV.The lucrative leptonic branching fraction χ0 2 → ℓ + ℓ − χ0 1 occurs typically at the 2% level due to competition with other decay modes such as χ0 2 → χ± 1 f f ′ .The other lucrative production mode from the previous Section is wino pair production pp → χ0 3 χ± 2 .To assess the expected final states from this reaction, we plot in Fig. 10 the major wino decay branching fractions along the nAMSB model line.In frame a), we plot the BF ( χ+ 2 ) values vs. m 3/2 while in frame b) we plot the BF ( χ0 3 ) values.From frame a), the region with m 3/2 ≲ 90 TeV is already excluded by LHC gg searches (albeit in the context of simplified models).Below 90 TeV, there is actually a level-crossing: since µ is fixed at 250 GeV, a low enough value of m 3/2 leads to m(wino) < m(higgsino) and an increased m χ+ 2 − m χ+ 1 mass gap (see Fig. 7) so that χ+ 2 → χ+ 1 h is allowed.Then, as m 3/2 increases, the mass gap drops (due to wino-higgsino degeneracy) and the χ+ 2 → χ+ 1 h mode becomes kinematically closed.As m 3/2 increases beyond ∼ 100 TeV, then χ+ 2 becomes wino-like, and the mass gap enlarges so that the decay χ+ 2 → χ+ 1 h becomes allowed again.As m 3/2 increases further, then all four decay modes χ+ 2 → χ0 1 W + , χ0 2 W + , χ+ 1 Z and χ+ 1 h asymptote to ∼ 25%.Thus, we expect the charged wino to decay to higgsino plus W , Z or h in a ratio ∼ 2 : 1 : 1.Since the higgsinos may be quasi-visible (depending on decay mode and mass gap), then we get wino decay to W , Z or h +quasi-visible higgsinos as a final state.
In Fig. 10b), we show the neutral wino χ0 3 branching fractions along the nAMSB model  1 h are allowed and can occur at the ∼ 20% level while decays to χ∓ 1 W ± asymptote to ∼ 50%.The remaining branching fraction goes to mixing-suppressed modes.Thus, for wino pair production, we expect a final state of V V + M ET , V h + M ET and hh + M ET where M ET stands for missing transverse energy and V stands for the vector bosons W and Z.The M ET may not really be entirely missing since it may include 3-body decay products of the heavier higgsinos.

LHC excluded regions
Certain regions of nAMSB model parameter space seem already excluded by existing LHC13 search limits from Run 2 with ∼ 139 fb −1 of integrated luminosity.

LHC constraint from gluino pair searches
In the case of gluino pair production, for the bulk of LHC-allowed nAMSB parameter space, we expect g → t t * 1 followed by further t1 cascade decays.The approximate ATLAS and CMS simplified model limits for gg production followed by decay to third generation particles should Figure 12: Allowed/excluded regions of m(wino) vs. m(higgsino) plane from ATLAS analysis of EWino pair production followed by decay to W, Z, h with decay to boosted dijets.

LHC constraint from EWino pair production followed by decay to boosted dijets
A recent ATLAS study [109] reports searching for EWino pair production followed by two-body decays to W , Z or h.These heavy SM objects are assumed to decay hadronically to boosted dijet/fat-jet states which are then identified.A similar study by CMS was also made [110], but with smaller parameter space exclusion regions.The simplified model limits presented in Fig. 14c) of Ref. [109] should roughly apply to our case for wino-pair production pp → χ± 2 χ0 3 as shown in Fig. 9d) followed by decays to vector bosons and Higgs bosons as shown in Fig. 10.The digitized ATLAS exclusion curve is shown in Fig. 12 in the m(wino) vs. m(higgsino) plane.Our nAMSB model line with µ = 250 GeV is denoted by the horizontal dashed line.From the plot, we would expect that the range m(wino) : 625 − 1000 GeV would be ruled out, corresponding to a range of m 3/2 : 200 − 350 TeV.For model lines with larger or smaller values of µ, the exclusion region changes accordingly in Fig. 12.

LHC constraints from SModelS/CheckMATE2 analysis
To test for further limits on nAMSB parameter space, we employ two recent recasting softwares: SModelS [111,112,113] and CheckMATE2 (CM2) [114,115] to study the impact of the current searches on nAMSB parameter space.SModelS is a popular tool for interpreting simplifiedmodel results from the LHC.It decomposes Beyond the Standard Model (BSM) collider signatures presenting a Z 2 -like symmetry into Simplified Model Spectrum (SMS) topologies and compares the BSM predictions for the LHC in a model independent framework with the relevant experimental constraints.The main variable for comparison of a BSM theory to the LHC experimental searches is the r-ratio which is defined as the ratio of the expected σ × BR for a specific final state to the corresponding upper limit on the σ ×BR×ϵ (where ϵ is the acceptance efficiency provided by the experimental paper).CheckMATE2 is a reinterpretation software for interpreting LHC results for all BSM models.It is based on recasting the full experimental analyses using events after full Monte Carlo simulation, hadronization and detector smearing of the final state objects and implementing the cuts as in the experimental analyses.It provides the r value defined as the ratio of the expected number of events from the signal, after implementing all cuts, to the 95%CL upper limit from the experimental result.In both cases, for a BSM model to be allowed by current constraints, one requires r < 1.
The wino-higgsino mass gap, quantified by ∆m 31 = m χ 0 3 − m χ 0 1 , increases with m 3/2 as seen in Fig. 13.Fig. 14 shows the variation of the highest r value obtained from SModelS and CheckMATE2 for the √ s = 13 TeV results from LHC.The highest r-value defined as the ratio of the signal over the 95%CL upper limit from the signal region is plotted against m 3/2 .The red dotted lines denote the constraints from the ATLAS search of boosted hadronically decaying bosons + ̸ E T [109] while the black dotted line denote the bound from the gluino searches implying m 3/2 ≥ 90 TeV as discussed in Section 6.2 and 6.1 respectively.
For the constraints from the CheckMATE2 CMS results (blue), we observe the tightest constraints arise from the multi-lepton (2/3) + ̸ E T searches [116] for m 3/2 ∼ 150 TeV with rvalue ∼ 0.15 and it falls off on either side of the peak.This is due to other searches gaining more importance such as searches for ≥ 4ℓ+ ̸ E T for larger mass-gaps between the wino-like and higgsino-like neutralino.From the CheckMATE2 ATLAS result (green), the r-value decreases with increasing m 3/2 from r = 0.25 arising from the hadronic searches of squarks and gluinos [117].
From SModelS (red), the most stringent constraint occurs at m 3/2 < 100 TeV from searches of three leptons + ̸ E T [118].For m 3/2 = 100 − 250 TeV range, the most stringent constraints arise from the boosted hadronically decaying diboson + ̸ E T searches the multi-lepton searches involving two or three leptons+ ̸ E T [119,118] are the most sensitive searches near the peak at m 3/2 ∼ 225 TeV.For higher m 3/2 = 250 − 400 TeV, the dominant constraints arise from the multi-lepton searches and sub dominant constraints arise from the boosted hadronically decaying dibosons + ̸ E T .As m 3/2 increases, the multijet + ̸ E T [120] searches start constraining the parameter space dominantly.However, the r-value always remains less than 1: thus, the remaining allowed range of m 3/2 ∼ 90 − 200 TeV appears to be presently allowed.

LHC-allowed nAMSB parameter space
Our final allowed nAMSB model line parameter space is shown in Fig. 15.The left gray shaded region is excluded by LHC gluino search limits while the central gray shaded region is excluded by the ATLAS limits on EWino pair production followed by decay to two boosted dijet final states.The naturalness limit is denoted by the vertical dashed line within the central excluded band: the region to the right is unnatural, and thus highly unlikely (but not impossible) to emerge from the landscape.The unshaded region extends from m 3/2 : 90 − 200 TeV and is thus the presently allowed parameter space.For convenience, we display again the sparticle masses along our nAMSB model line.The remaining SUSY particle spectrum for m 3/2 ∼ 90 − 200 TeV should provide a target for future LHC searches seeking to discover or to rule out natural AMSB.
7 Prospects for nAMSB at Run3 and Hi-Lumi LHC searches In models with light higgsinos, as in natural SUSY, a compelling LHC search reaction [121] is pp → χ0 1 χ0 2 followed by χ0 2 → ℓ + ℓ − χ0 1 , where the dilepton pair is energetically rather soft since its invariant mass a kinematically bounded by m χ0 2 − m χ0 1 .By triggering on hard initial state QCD radiation [102,103], then such soft dilepton + ̸ E T events can be searched for at LHC. Prospects for soft dileptons, jets + ̸ E T events (soft OSDLJMET) at LHC have been presented   in the higgsino discovery plane [122] and in Ref. [123] where new angular cuts were proposed to aid in discovery.Recent search results from CMS [119] and ATLAS [124] have been presented.The soft OSDJMET signal is a particularly compelling signal for SUSY in the nAMSB model in light of the large pp → χ0 1 χ0 2 cross section from Fig. 9b).A distinguishing feature of the nAMSB model compared to models with gaugino mass unification or mirage mediation is the relatively larger ∆m 21 ≡ m χ0 2 − m χ0 1 mass gap ranging from ∼ 15 − 60 GeV for nAMSB as shown in Fig. 16 (due to the larger wino-higgsino mixing from light winos).Current searches from CMS and ATLAS probe a maximal µ value of ∼ 200 GeV for mass gaps ∆m 21 ∼ 10 GeV.Future ATLAS and CMS probes at HL-LHC with 3000 fb −1 can probe to µ ∼ 300 GeV [125] and the improved angular cuts may allow HL-LHC to probe as high as µ ∼ 325 GeV [123].It should be noted that both ATLAS and CMS seem to have a 2σ excess in this channel at present with 139 fb −1 of integrated luminosity.In nAMSB with a larger m χ+ 1 − m χ0 1 mass gap, soft trilepton plus jet+ ̸ E T signatures should also be available from χ±  The rather light winos expected from the allowed parameter-space window in Fig. 15 provide an inviting target for LHC wino pair production searches.In the case of pp → χ± 2 χ0 3 production, then the relevant signatures occur in the V V + ̸ E T , V h+ ̸ E T and hh+ ̸ E T channels, where V = W or Z.While the strong ATLAS limits from boosted V or H → jj already exclude m 3/2 : 200−350 TeV, a search for non-boosted multijets+ ̸ E T may be warranted for electroweakproduced wino pairs.These searches may be augmented by searching for the presence of h → b b and V → leptons in the signal events.New targeted analyses using Run 2 data or forthcoming Run 3 data may even be able to close this allowed window (or else discover nAMSB SUSY!).Certainly the allowed window in nAMSB parameter space can be closed by analysis of HL-LHC data.

Same-sign diboson signature
The other lucrative search channel for wino pair production followed by decay to light higgsinos is the same-sign diboson channel (SSdB) [126], where pp → χ± 2 χ0 3 will be followed by χ± 2 → W ± χ0 1,2 and χ0 3 → W ± χ∓ 1 .These production and decay modes lead equally to W + W − + ̸ E T and W ± W ± + ̸ E T final states where the former has large SM backgrounds from W W and t t production whilst SM backgrounds for the latter SSdB signature are far smaller [126,127,128].This relatively jet-free (only jets from initial state QCD radiation) signature is distinct from the usual same-sign dilepton signature arising from gluino and squark pair production which should be accompanied by many hard final state jets.
The reach of HL-LHC for the natural SUSY SSdB signature has been computed in Ref. [128] where peak signal cross sections after cuts reach the 0.03 fb level compared to total SM backgrounds of 0.005 fb.Whereas the present reach of LHC with 139 fb −1 is minimal at present (for the harder, high luminosity cuts advocated in Ref. [128]), the low wino mass m(wino) ∼ 300 − 600 GeV region should be accessible to LHC Run 3 and HL-LHC data sets in the 300-3000 fb −1 regime.Alternatively, a fresh analysis by the experimental groups using softer cuts for the low wino mass region is clearly warranted.So far, it seems no dedicated analysis of the SSdB signature from natural SUSY has been undertaken.Another SUSY search channel for the nAMSB model is via light top squark pair production pp → t1 t * 1 followed by t1 → b χ+ 1 at ∼ 50% and t1 → t χ0 1,2 each at ∼ 25%.The reach of HL-LHC for light top-squarks with these decay modes has been recently evaluated [97].The 5σ discovery reach of HL-LHC with 3000 fb −1 was found to extend to m t1 ∼ 1.7 TeV while the 95% CL reach extended to m t1 ∼ 2 TeV.These sorts of search limits, performed within the NUHM2 model, are expected to pertain also to stop pair production within the nAMSB model.

Summary and conclusions
Supersymmetric models with anomaly-mediated SUSY breaking are well-motivated in several different SUSY breaking scenarios.In charged SUSY breaking (AMSB0), gauginos and A-terms have suppressed gravity-mediated masses but can gain dominant AMSB masses whilst scalar masses assume their usual gravity-mediated form.In the RS AMSB model with sequestered SUSY breaking, then gaugino masses, A-terms and scalar masses all have the AMSB form, leading to negative squared slepton masses.Further bulk scalar mass contributions are required for a viable model.The phenomenology of mAMSB models is characterized by a wino LSP, and wino-like WIMP dark matter.The minimal phenomenological version of these models seems to be triply ruled out by 1. the difficulty to generate m h ∼ 125 GeV unless huge, unnatural third generation bulk scalar masses are included, 2. the presence of wino-like WIMP dark matter which seems excluded by direct-and indirect-dark matter detection limits and 3. the large, unnatural value of µ-and hence large ∆ EW -that such models possess, even for weak-scale soft terms.Rather minor tweaks to the mAMSB model, already suggested in the original work of RS [23], ameliorate these problems: non-universal bulk scalar Higgs masses and bulk A-terms.While AMSB0 with non-universal scalar masses still seems ruled out (due to A 0 ∼ 0 and hence too low m h values), the natural AMSB model is both natural and can accommodate m h ∼ 125 GeV.In nAMSB, while the wino is still the lightest gaugino, the higgsinos are instead the lightest EWinos.The dark matter issues can be resolved by postulating mixed axion-higgsinolike WIMP dark matter which is mainly coposed of axions [68].
In this work, we investigated in some detail LHC constraints on natural AMSB models.LHC gluino mass limits already require a gravitino mass m 3/2 ≳ 90 TeV.The presence of relatively light winos with mass m(wino) ∼ 300 − 800 GeV implies the model is susceptible to ATLAS/CMS searches for two boosted dijets + ̸ E T .Recent ATLAS results seem to rule out m 3/2 ∼ 200 − 350 TeV, whereas naturalness (∆ EW ≲ 30) requires m 3/2 ≲ 265 TeV.The combined constraints leave an open lower mass window of m 3/2 ∼ 90−200 TeV.This lower mass window may soon be excluded (or else nAMSB may be discovered!) by a combination of 1. soft OS dilepton plus jet+ ̸ E T (OSDLJMET) searches which arise from higgsino pair production, 2. non-boosted hadronically decaying wino pair production searches and 3. jet-free same-sign diboson searches which are a characteristic signature of wino pair production followed by wino decay to W +higgsino.Some excess above SM background in the OSDLJMET channel already seems to be present in both ATLAS and CMS data [124,119].

Figure 1 :
Figure 1: Plot of dP/dm h from an n = 1 landscape scan in the nAMSB0 model where A 0 = 0.

Figure 2 :
Figure 2: Plot of a) dP/dm h and b) dP/dm A , from an n = 1 landscape scan in the nAMSB model.The red histogram shows the full probability distribution while the blue-dashed histogram shows the remaining distribution after LHC sparticle mass limits are imposed.

Figure 4 :
Figure 4: Plot of a) dP/dm g, b) dP/dm t1 , c) dP/dm χ± 2 and d) dP/d(m χ0 2 − m χ0 1 ) from an n = 1 landscape scan in the nAMSB model.The red histogram shows the full probability distribution while the blue-dashed histogram shows the remaining distribution after LHC sparticle mass limits are imposed.

Figure 5 :
Figure 5: Plot of ∆ EW vs. m 3/2 along the AMSB model lines.The region below the dashed line ∆ EW < 30 is regarded as natural.
where we show cross sections for pp → gg, t1 t * 1 and (summed) EWino pair production vs. m 3/2 along the nAMSB model line.At the top of the plot, we see EWino pair production is dominant and relatively flat vs. m 3/2 since it is dominated by higgsino pair production and µ is fixed at 250 GeV.The EWino cross section are divided up into summed χ0

Figure 6 :
Figure 6: Plot of m h vs. m 3/2 along the AMSB model lines.The light Higgs mass is constrained by LHC measurements to lie between the dashed lines, given some theory error on the calculation of m h .

Figure 13 :
Figure 13: Variation of ∆m 31 = m χ 0 3 − m χ 0 1 vs. m 3/2 .The region left of the black-dashed curve is excluded by LHC13 gluino pair searches and the region to the right of the blue-dashed line is unnatural with ∆ EW ≳ 30.

Figure 14 :
Figure 14: Plot of r from SModelS and CheckMate2 vs. m 3/2 along the nAMSB model line.

Figure 15 :
Figure 15: Allowed/excluded regions of our nAMSB model-line along with various sparticle masses.

Table 1 :
Input parameters and masses in GeV units for the mAMSB, nAMSB0 and nAMSB natural generalized anomaly mediation SUSY benchmark points with m t = 173.2GeV using Isajet 7.91.