Supersymmetric models accompanied by certain anomaly-free discrete <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math> symmetries <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="double-struck">Z</mi><mi>n</mi><mi>R</mi></msubsup></math> are attractive in that 1. the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math> symmetry (which can arise from compactified string theory as a remnant of the broken 10-d Lorentz symmetry) forbids unwanted superpotential terms while allowing for the generation of an accidental, approximate global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>P</mi><mi>Q</mi></mrow></msub></math> symmetry needed to solve the strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem and 2. they provide a raison d’etre for an otherwise ad-hoc <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-parity conservation. We augment the minimal supersymmetric Standard Model (MSSM) by two additional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="double-struck">Z</mi><mi>n</mi><mi>R</mi></msubsup></math>- and Peccei-Quinn (PQ)-charged fields <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi></math> wherein supersymmetry (SUSY) breaking at an intermediate scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mtext>hidden</mtext></msub></math> leads to PQ breaking at a scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mi>a</mi></msub><mo>∼</mo><msup><mn>10</mn><mn>11</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> leading to a SUSY Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion. The same SUSY breaking can trigger <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-parity breaking via higher-dimensional operators leading to tiny <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-violating couplings of order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msub><mi>f</mi><mi>a</mi></msub><mo>/</mo><msub><mi>m</mi><mi>P</mi></msub><msup><mo stretchy="false">)</mo><mi>N</mi></msup></math> so that both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>P</mi><mi>Q</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math> parity emerge as accidental, approximate symmetries. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="double-struck">Z</mi><mn>4</mn><mi>R</mi></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="double-struck">Z</mi><mn>8</mn><mi>R</mi></msubsup></math>, we find only an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>1</mn></math> suppression. Then the lightest SUSY particle (LSP) of the MSSM becomes unstable with a lifetime of order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo>−</mo><msup><mn>10</mn><mn>1</mn></msup></math> s so the LSPs all decay away before the present epoch. That leaves a universe with all axion cold dark matter and no weakly interacting massive particles (WIMPs) in accord with recent LZ(2024) WIMP search results.

United States

Howard Baer

Vernon Barger

Italy

Dibyashree Sengupta

Kairui Zhang

All axion dark matter from supersymmetric models

Hidden sector supersymmetry (SUSY) breaking where charged hidden sector fields obtain SUSY breaking vacuum expectation values once seemed common in dynamical SUSY breaking (DSB). In such a case, scalars can obtain large masses but gauginos and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math>-terms gain loop-suppressed anomaly-mediated contributions which may be smaller by factors of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><mn>16</mn><msup><mi>π</mi><mn>2</mn></msup><mo>∼</mo><mn>1</mn><mo>/</mo><mn>160</mn></math>. This situation leads to models such as PeV or minisplit supersymmetry with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>scalars</mi></mrow></msub><mo>∼</mo><mn>160</mn><msub><mrow><mi>m</mi></mrow><mrow><mi>gaugino</mi></mrow></msub></mrow></math>. In order to generate a light Higgs mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>h</mi></msub><mo>≃</mo><mn>125</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, the scalar mass terms are required in the 10–100 TeV range, leading to large, unnatural contributions to the weak scale. Alternatively, in gravity mediation with singlet hidden sector fields, then <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>scalars</mi></mrow></msub><mo>∼</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>gauginos</mi></mrow></msub><mo>∼</mo><mi>A</mi></mrow></math>-terms and the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math>-terms lift <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>h</mi></msub><mo stretchy="false">→</mo><mn>125</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> even for natural values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><msub><mover accent="true"><mi>t</mi><mo stretchy="false">˜</mo></mover><mn>1</mn></msub></msub><mo>∼</mo><mn>1</mn><mi>–</mi><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>. Requiring naturalness, which seems probabilistically preferred by the string landscape, then the measured Higgs mass seems to favor singlets in the hidden sector, which can be common in metastable and retrofitted DSB models.

Jessica Bolich

Implications of Higgs mass for hidden sector SUSY breaking

The string landscape statistical draw to large scalar soft masses leads to a mixed quasidegeneracy/decoupling solution to the supersymmetry (SUSY) flavor and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problems where first/second generation matter scalars lie in the 20–40 TeV range. With increasing first/second generation scalars, SUSY models actually become more natural due to two-loop renormalization group (RG) effects that suppress the corresponding third generation soft masses. This can also lead to substantial parameter space regions that are forbidden by the presence of charge and/or color breaking minima of the scalar potential. We outline the allowed SUSY parameter space for the gravity-mediated three extra-parameter-nonuniversal Higgs model NUHM3. The natural regions with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>h</mi></msub><mo>∼</mo><mn>125</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Δ</mi><mrow><mi>EW</mi></mrow></msub><mo>≲</mo><mn>30</mn></math> and decoupled first/second generation scalar are characterized by rather heavy gluinos and EW gauginos, but with rather small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> and top squarks not far beyond LHC Run 2 limits. This scenario also explains why SUSY has so far eluded discovery at LHC in that the parameter space with small scalar and gaugino masses is all excluded by the presence of charge and/or color breaking minima.

Living dangerously with decoupled first and second generation scalars: SUSY prospects at the LHC

While the minimal anomaly-mediated SUSY breaking model (mAMSB) seems ruled out by constraints on Higgs mass, naturalness and wino dark matter, a slightly generalized version dubbed natural AMSB (nAMSB) remains both viable and compelling. Like mAMSB, nAMSB features winos as the lightest gauginos, but unlike mAMSB, nAMSB allows a small <math><mi>μ</mi></math> parameter so that Higgsinos are the lightest of electroweakinos (EWinos). nAMSB spectra depend on the input value of gravitino mass <math><msub><mi>m</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math>, where the lower range of <math><msub><mi>m</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math> is excluded by LHC gluino pair searches while a higher <math><msub><mi>m</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math> band is excluded by LHC limits on wino pair production followed by boosted hadronic wino decays. A remaining intermediate gap in <math><msub><mi>m</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math> values remains allowed by present LHC searches, but appears to be completely explorable by high luminosity upgrades of LHC (HL-LHC). We explore a variety of compelling discovery channels that may allow one to close the intermediate gap in <math><msub><mi>m</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math> values: (1) same-sign <math><mrow><mi>diboson</mi><mo>+</mo><msub><mrow><mrow><mi>E</mi></mrow></mrow><mrow><mi>T</mi></mrow></msub></mrow></math> (SSdB) production arising from wino pair production, leading to same-sign dileptons plus missing <math><msub><mi>E</mi><mi>T</mi></msub></math>, (2) trilepton production arising from wino pair production and (3) soft dilepton plus jet events from Higgsino pair production, (4) top-squark pair production. From our signal-to-background analysis along a nAMSB model line, we expect HL-LHC to either discover or rule out the nAMSB model with <math><mn>3000</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of integrated luminosity.

Juhi Dutta

Minding the gap: Testing natural anomaly-mediated SUSY breaking 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 <math><msub><mover><mi>τ</mi><mo>˜</mo></mover><mn>1</mn></msub></math> of a few hundred GeV, the decays <math><msub><mover><mi>τ</mi><mo>˜</mo></mover><mn>1</mn></msub><mo>→</mo><mi>τ</mi><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow><mn>0</mn></msubsup></math> and <math><msub><mi>ν</mi><mi>τ</mi></msub><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mo>−</mo></msubsup></math> occur at comparable rates where the (Higgsino-like) <math><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mo>±</mo></msubsup></math> and <math><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mn>2</mn><mn>0</mn></msubsup></math> release only small visible energy: in this case, the expected <math><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup><mo>+</mo><msub><mi>E</mi><mi>T</mi></msub></math> signature is diminished from the usual expectations due to the presence of the nearly invisible decay mode <math><msub><mover><mi>τ</mi><mo>˜</mo></mover><mn>1</mn></msub><mo>→</mo><msub><mi>ν</mi><mi>τ</mi></msub><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mo>−</mo></msubsup></math>. However, once <math><msub><mi>m</mi><msub><mover><mi>τ</mi><mo>˜</mo></mover><mn>1</mn></msub></msub><mo>≳</mo><mi>m</mi><mo>(</mo><mi>b</mi><mi>i</mi><mi>n</mi><mi>o</mi><mo>)</mo></math>, decays to binos such as <math><msub><mover><mi>τ</mi><mo>˜</mo></mover><mn>1</mn></msub><mo>→</mo><mi>τ</mi><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mn>3</mn><mn>0</mn></msubsup></math> open up where <math><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mn>3</mn><mn>0</mn></msubsup></math> decays to Higgsinos plus <math><msup><mi>W</mi><mo>±</mo></msup></math>, <math><msup><mi>Z</mi><mn>0</mn></msup></math>, and <math><mi>h</mi></math> at comparable rates. For these heavier staus, the stau pair production gives rise to <math><mrow><mtext>diboson</mtext><mo>+</mo><msub><mrow><mrow><mi>E</mi></mrow></mrow><mrow><mi>T</mi></mrow></msub></mrow></math> events, which may contain 0, 1, or 2 additional hard <math><mi>τ</mi></math> leptons. From these considerations, we examine the potential for future discovery of tau-slepton pair production at a high-luminosity LHC. While we do not find a <math><mn>5</mn><mi>σ</mi></math> HL-LHC discovery reach for <math><mn>3000</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, we do find a 95% CL exclusion reach, ranging between <math><msub><mi>m</mi><msub><mover><mi>τ</mi><mo>˜</mo></mover><mn>1</mn></msub></msub><mo>:</mo><mtext> </mtext><mtext> </mtext><mn>100</mn><mi>–</mi><mn>450</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> for <math><msub><mi>m</mi><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mn>0</mn></msubsup></msub><mo>∼</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. This latter reach disappears for <math><msub><mi>m</mi><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mn>0</mn></msubsup></msub><mo>≳</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.

Stau pairs from natural SUSY at high luminosity LHC

Supersymmetric models with a strongly interacting superconformal hidden sector (HS) may drive soft supersymmetry (SUSY) breaking scalar masses, bilinear soft term <math><mrow><mi>B</mi><mi>μ</mi></mrow></math> and Higgs combinations <math><mrow><msubsup><mrow><mi>m</mi></mrow><mrow><msub><mrow><mi>H</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>d</mi></mrow></msub></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msup><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> to small values at some intermediate scale, leading to unique sparticle mass spectra along with possibly diminished fine-tuning in spite of a large superpotential <math><mi>μ</mi></math> parameter. We set up a computer code to calculate such spectra, which are then susceptible to a variety of constraints: (1) possible charge-or-color breaking (CCB) minima in the scalar potential, (2) unbounded from below (UFB) scalar potential, (3) improper electroweak symmetry breaking, (4) a charged or sneutrino lightest SUSY particle (LSP), (5) generating <math><msub><mi>m</mi><mi>h</mi></msub><mo>∼</mo><mn>125</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, (6) consistency with LHC sparticle mass limits, and (7) naturalness. We find this bevy of constraints leaves little or no viable parameter space for the case where hidden sector dynamics dominates minimal supersymmetric standard model (MSSM) running, even for the case of nonuniversal gaugino masses. For the case with moderate HS running with comparable MSSM running, and with universal gaugino masses, then the fine-tuning is ameliorated, but nonetheless remains high. Viable spectra with moderate HS running and with low fine-tuning and large <math><mi>μ</mi></math> can be found for nonuniversal gaugino masses.

Dakotah Martinez

Supersymmetry with scalar sequestering

Supersymmetric models with the anomaly-mediated supersymmetry (SUSY) breaking (AMSB) form for soft SUSY breaking terms arise in two different settings: (1) extra-dimensional models where SUSY breaking occurs in a sequestered sector, and (2) <math><mn>4</mn><mo>−</mo><mi>d</mi></math> models with dynamical SUSY breaking in a hidden sector where scalars gain masses of order the gravitino mass <math><msub><mi>m</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math>, but gaugino masses and trilinear soft terms are assumed to be of the AMSB form. Both models run into serious conflicts with (1) LHC sparticle and Higgs mass constraints, (2) constraints from winolike weakly interacting massive particle dark matter searches, and (3) bounds from naturalness. These conflicts may be avoided by introducing minor changes to the underlying phenomenological models consisting of nonuniversal bulk scalar Higgs masses and <math><mi>A</mi></math> terms, providing a setting for 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 sorts of spectra are expected to emerge when nAMSB arises from a string landscape setting: While model 2 can only be natural for a Higgs mass <math><msub><mi>m</mi><mi>h</mi></msub><mo>≲</mo><mn>123</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, model 1 can accommodate naturalness along with <math><msub><mi>m</mi><mi>h</mi></msub><mo>∼</mo><mn>125</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> while still respecting LHC bounds on sparticle masses. We explore the LHC phenomenology of nAMSB models where we find that for Higgsino pair production, typically larger dilepton mass gaps arise from the soft dilepton-plus-jets signature than in models with gaugino mass unification. For wino-pair production, the higher <math><msub><mi>m</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math> portion of nAMSB parameter space is excluded by recent LHC bounds from gaugino pair production searches. We characterize the dominant LHC signatures arising from the remaining lower <math><msub><mi>m</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub><mo>∼</mo><mn>90</mn><mi>–</mi><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> range of parameter space, which should be fully testable at high-luminosity LHC via EWino pair production searches.

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

In natural supersymmetric models defined by no worse than a part in thirty electroweak fine-tuning, winos and binos are generically expected to be much heavier than Higgsinos. Moreover, the splitting between the Higgsinos is expected to be small, so that the visible decay products of the heavier Higgsinos are soft, rendering the Higgsinos quasi-invisible at the LHC. Within the natural supersymmetry (SUSY) framework, heavy electroweak gauginos decay to <math><mi>W</mi></math>, <math><mi>Z</mi></math> or <math><mi>h</mi></math> bosons plus Higgsinos in the ratio <math><mrow><mo>∼</mo><mn>2</mn><mo>∶</mo><mn>1</mn><mo>∶</mo><mn>1</mn></mrow></math>, respectively. This is in sharp contrast to models with a binolike lightest superpartner and very heavy Higgsinos, where the charged (neutral) wino essentially always decays to a <math><mi>W</mi></math> (<math><mi>h</mi></math>) boson and an invisible bino. Wino pair production at the LHC, in natural SUSY, thus leads to <math><mi>V</mi><mi>V</mi></math>, <math><mi>V</mi><mi>h</mi></math> and <math><mi>h</mi><mi>h</mi><mo>+</mo><msub><mi>E</mi><mi>T</mi></msub></math> final states (<math><mrow><mi>V</mi><mo>=</mo><mi>W</mi></mrow></math>, <math><mrow><mi>Z</mi></mrow></math>) where, for TeV scale winos, the vector bosons and <math><mi>h</mi></math> daughters are considerably boosted. We identify eight different channels arising from the leptonic and hadronic decays of the vector bosons and the decay <math><mi>h</mi><mo>→</mo><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math>, each of which offers an avenue for wino discovery at the high luminosity LHC (HL-LHC). By combining the signal in all eight channels we find, assuming <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>14</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> and an integrated luminosity of <math><mn>3000</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, that the discovery reach for winos extends to <math><mi>m</mi><mo>(</mo><mi>w</mi><mi>i</mi><mi>n</mi><mi>o</mi><mo>)</mo><mo>∼</mo><mn>1.1</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>, while the 95% CL exclusion range extends to a wino mass of almost 1.4 TeV. We also identify “Higgsino specific channels” which could serve to provide <math><mn>3</mn><mi>σ</mi></math> evidence that winos lighter than 1.2 TeV decay to light Higgsinos rather than to a binolike lightest supersymmetric particle, should a wino signal appear at the HL-LHC.

Xerxes Tata

Winos from natural SUSY at the high luminosity LHC

Supersymmetric models with low electroweak fine-tuning are expected to be more prevalent on the string landscape than fine-tuned models. We assume a fertile patch of landscape vacua containing the minimal supersymmetric standard model as low energy/weak scale effective field theory. Then, a statistical pull by the landscape to large soft terms is balanced by the requirement of a derived value of the weak scale which is not too far from its measured value in our Universe. Such models are characterized by light Higgsinos in the few hundred GeV range whilst top squarks are in the 1–2.5 TeV range with large trilinear soft terms which helps to push <math><msub><mi>m</mi><mi>h</mi></msub><mo>∼</mo><mn>125</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. Other sparticles are generally beyond current LHC reach and the <math><mi>BR</mi><mo>(</mo><mi>b</mi><mo>→</mo><mi>s</mi><mi>γ</mi><mo>)</mo></math> branching fraction is nearly equal to its standard model value. The light top-squarks decay comparably via <math><msub><mover><mi>t</mi><mo>˜</mo></mover><mn>1</mn></msub><mo>→</mo><mi>b</mi><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mo>+</mo></msubsup></math> and <math><msub><mover><mi>t</mi><mo>˜</mo></mover><mn>1</mn></msub><mo>→</mo><mi>t</mi><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow><mn>0</mn></msubsup></math> yielding mixed final states of <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover><mo>+</mo><msub><mi>E</mi><mi>T</mi></msub></math>, <math><mi>t</mi><mover><mi>b</mi><mo>¯</mo></mover><mo>/</mo><mover><mi>t</mi><mo>¯</mo></mover><mi>b</mi><mo>+</mo><msub><mi>E</mi><mi>T</mi></msub></math>, and <math><mi>t</mi><mover><mi>t</mi><mo>¯</mo></mover><mo>+</mo><msub><mi>E</mi><mi>T</mi></msub></math>. We evaluate prospects for top squark discovery at high-luminosity LHC for the well-motivated case of natural SUSY from the landscape. We find for high luminosity LHC a <math><mn>5</mn><mi>σ</mi></math> reach out to <math><msub><mi>m</mi><msub><mover><mi>t</mi><mo>˜</mo></mover><mn>1</mn></msub></msub><mo>∼</mo><mn>1.65</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> and a 95% CL exclusion reach to <math><msub><mi>m</mi><msub><mover><mi>t</mi><mo>˜</mo></mover><mn>1</mn></msub></msub><mo>∼</mo><mn>1.95</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>. These reaches cover most (but not all) of the allowed stringy natural parameter space.

Top squarks from the landscape at high luminosity LHC

We revisit the various measures of practical naturalness for models of weak-scale supersymmetry (SUSY) including: 1. electroweak (EW) naturalness; 2. naturalness via sensitivity to high-scale (HS) parameters [Ellis-Enquist-Nanopoulos-Zwirner/Barbieri-Giudice (EENZ/BG)]; 3. sensitivity of Higgs soft terms due to high-scale radiative corrections; and 4. stringy naturalness (SN) from the landscape. The EW measure is most conservative and seems unavoidable. We debut a new numerical routine for calculating the EENZ/BG measure from any SUSY Les Houches Accord file. We implement a careful analysis and comparison of these measures in the mSUGRA/CMSSM and NUHMi model parameter spaces and via parameter-space scans. We demonstrate the reasoning behind why—and the extent to which—the EENZ/BG and HS measures overestimate the degree of fine-tuning. We find the overestimation can range up to a factor of over 1000. While EENZ/BG and HS have ambiguities when applied to models such as anomaly- and mirage-mediation, the EW measure has no such ambiguity and so we display the natural parameter space regions of these models. SN depends on the landscape distribution of soft terms, but is closely related to EW naturalness via the atomic principle.