We investigate three intriguing anomalies within the framework of the general next-to-minimal supersymmetric standard model. These anomalies include a significant deviation of the experimental results for the muon anomalous magnetic moment from its standard model prediction, with a confidence level of <math><mn>5.1</mn><mi>σ</mi></math>; a joint observation by the CMS and ATLAS Collaborations of a diphoton excess with a local significance of <math><mn>3.1</mn><mi>σ</mi></math> in the invariant mass distribution around 95.4 GeV; and a reported excess in the <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> production at the Large Electron-Positron Collider with a local significance of <math><mn>2.3</mn><mi>σ</mi></math>. Through analytical and numerical analyses, we provide unified interpretations across an extensive parameter space that remain consistent with current experimental restrictions from data on the Higgs boson at 125 GeV, <math><mi>B</mi></math>-physics measurements, and dark matter observables, as well as existing searches for supersymmetry and extra Higgs bosons. We attribute the muon anomaly to loops involving muon-smuon-neutralino and muon-sneutrino-chargino interactions, while attributing the diphoton and <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> excesses to the resonant production of a singlet-dominated scalar. These proposed solutions are poised for experimental tests at the high-luminosity LHC and future linear colliders.

China

Junjie Cao

Xinglong Jia

Jingwei Lian

Unified interpretation of the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly, the 95 GeV diphoton, and <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> excesses in the general next-to-minimal supersymmetric standard model

In the General Next-to-Minimal Supersymmetric Standard Model (GNMSSM), singlet particles may form a secluded sector of dark matter (DM), in which Singlino-like DM could achieve the observed relic abundance through various channels such as   <math> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mn>1</mn> <mn>0</mn> </msubsup> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mn>1</mn> <mn>0</mn> </msubsup> <mo>→</mo> <msub> <mi>h</mi> <mi>s</mi> </msub> <msub> <mi>h</mi> <mi>s</mi> </msub> </math>  $$ {\overset{\sim }{\chi}}_1^0{\overset{\sim }{\chi}}_1^0\to {h}_s{h}_s $$ , A  s  A  s , h  s  A  s , where h  s  and A  s  represent singlet-dominated CP-even and CP-odd Higgs bosons. We provide analytical formulas for both the spin-independent and spin-dependent cross sections of Singlino DM scattering with nucleons, illustrating their dependence on the model’s parameters in a clear manner. We also present analytic expressions for the annihilation cross sections of these three important channels. Based on these preparations, we conducted Bayesian analyses of the GNMSSM and concluded that the theory significantly favored Singlino-dominated DM over Bino-like DM across a much broader range of parameters. The combined results from our numerical analyses and the formulas distinctly highlight crucial aspects of DM physics within the GNMSSM.

Lei Meng

Fei Li

Shenshen Yang

Dark Matter physics in general NMSSM

The CMS and ATLAS Collaborations recently published their results searching for light Higgs bosons, using the complete Run 2 data of the LHC. Both reported an excess in the diphoton invariant mass distribution at <math><msub><mi>m</mi><mrow><mi>γ</mi><mi>γ</mi></mrow></msub><mo>≃</mo><mn>95.4</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> with compatible signal strengths. The combined result corresponded to a local significance of <math><mn>3.1</mn><mi>σ</mi></math>. Besides, the mass of the diphoton signal coincided with that of the <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> excess observed at the Large Electron Positron. Given the remarkable theoretical advantages of the general next-to-minimal supersymmetric Standard Model, we interpret these excesses by the resonant productions of the singlet-dominated <math><mi>C</mi><mi>P</mi></math>-even Higgs boson predicted by the theory. Using both analytic formulas and numerical results, we show that the idea can interpret the excesses by broad parameter space without contradicting current experimental restrictions, including those from the 125 GeV Higgs data, the dark matter relic abundance and direct detection experiments, and the collider searches for supersymmetry and extra Higgs bosons. Although the explanations are scarcely affected by present Higgs data and the LHC search for supersymmetry, the dark matter physics may leave footprints on them. We also survey the other signals of the light Higgs boson at the LHC.

95 GeV diphoton and <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> excesses in the general next-to-minimal supersymmetric standard model

Inspired by the recent measurements of the muon and electron anomalous magnetic moments, the rapid progress of the LHC search for supersymmetry, and the significantly improved sensitivities of dark matter direct detection experiments, we studied the supersymmetric contribution to the electron <math><mi>g</mi><mo>−</mo><mn>2</mn></math>, <math><msubsup><mi>a</mi><mi>e</mi><mi>SUSY</mi></msubsup></math>, in the Next-to-Minimal Supersymmetric Standard Model with a discrete <math><msub><mi>Z</mi><mn>3</mn></msub></math> symmetry. We concluded that <math><msubsup><mi>a</mi><mi>e</mi><mi>SUSY</mi></msubsup></math> was mainly correlated with <math><msubsup><mi>a</mi><mi>μ</mi><mi>SUSY</mi></msubsup></math> by the formula <math><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>e</mi></mrow><mrow><mi>SUSY</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>m</mi></mrow><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>≃</mo><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>SUSY</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>m</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></math>, and significant violations of this correlation might occur only in rare cases. As a result, <math><msubsup><mi>a</mi><mi>e</mi><mi>SUSY</mi></msubsup></math> was typically around <math><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>14</mn></mrow></msup></math> when <math><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>SUSY</mi></mrow></msubsup><mo>≃</mo><mn>2.5</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>9</mn></mrow></msup></mrow></math>. We also concluded that the dark matter direct detection and LHC experiments played crucial roles in determining the maximum reach of <math><msubsup><mi>a</mi><mi>e</mi><mi>SUSY</mi></msubsup></math>. Concretely, <math><msubsup><mi>a</mi><mi>e</mi><mi>SUSY</mi></msubsup></math> might be around <math><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>13</mn></mrow></msup></math> in the optimum cases if one used the XENON-1T experiment to limit the supersymmetry parameter space. This prediction, however, was reduced to <math><mn>1.5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>13</mn></mrow></msup></math> after implementing the LZ restrictions and <math><mn>1.0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>13</mn></mrow></msup></math> when further considering the LHC restrictions.

Yuanfang Yue

Electron and muon anomalous magnetic moments in the <math><msub><mi>Z</mi><mn>3</mn></msub></math>-NMSSM

With the rapid progress of dark matter direct detection experiments, the attractiveness of the popular bino-dominated dark matter in economical supersymmetric theories is fading. As an alternative, the singlino-dominated dark matter in general Next-to-Minimal Supersymmetric Standard Model (NMSSM) is paying due attention. This scenario has the following distinct characteristics: free from the tadpole problem and the domain-wall problem of the NMSSM with a Z 3-symmetry, predicting more stable vacuum states than the Z 3-NMSSM, capable of forming an economical secluded dark matter sector to yield the dark matter experimental results naturally, and readily weaken the restrictions from the LHC search for SUSY. Consequently, it can explain the muon g-2 anomaly in broad parameter space that agrees with various experimental results while simultaneously breaking the electroweak symmetry naturally. In this study, we show in detail how the scenario coincides with the experiments, such as the SUSY search at the LHC, the dark matter search by the LZ experiment, and the improved measurement of the muon g-2. We provide a simple and clear picture of the physics inherent in the general NMSSM.

Di Zhang

Status of the singlino-dominated dark matter in general Next-to-Minimal Supersymmetric Standard Model

The new measurement of <math><mi>W</mi></math>-boson mass by the CDF collaboration revealed a remarkable <math><mn>7</mn><mi>σ</mi></math> disagreement with the Standard Model (SM) prediction. If confirmed by other experiments, then the disagreement strongly indicates the existence of new physics beyond the SM. In this work, seven vectorlike quark (VLQ) extensions of the SM are investigated to interpret the anomaly, and it is found that three can explain the anomaly in broad parameter space. The explanations are consistent with the constraints from oblique parameters, the LHC search for VLQs, the measurements of the properties for the top quark, bottom quark, and Higgs boson, and the perturbativity criterion. The typical size of the involved Yukawa coupling is around 1, which is comparable to the top quark Yukawa coupling in the SM. The other extensions, however, either predict a negative correction to the mass in reasonable parameter space or explain the anomaly by unnatural theoretical input parameters.

Liangliang Shang

Shiyu Wang

Bingfang Yang

Interpreting the <math><mi>W</mi></math>-mass anomaly in vectorlike quark models

The General Next-to-Minimal Supersymmetric Standard Model (GNMSSM) is an attractive theory that is free from the tadpole problem and the domain-wall problem of Z 3-NMSSM, and can form an economic secluded dark matter (DM) sector to naturally predict the DM experimental results. It also provides mechanisms to easily and significantly weaken the constraints from the LHC search for supersymmetric particles. These characteristics enable the theory to explain the recently measured muon anomalous magnetic moment, (g − 2) μ , in a broad parameter space that is consistent with all experimental results and at same time keeps the electroweak symmetry breaking natural. This work focuses on a popular scenario of the GNMSSM in which the next-to-lightest CP-even Higgs boson corresponds to the scalar discovered at the Large Hadron Collider (LHC). Both analytic formulae and a sophisticated numerical study show that in order to predict the scenario without significant tunings of relevant parameters, the Higgsino mass μ tot ≲ 500 GeV and tan β ≲ 30 are preferred. This character, if combined with the requirement to account for the (g − 2) μ  anomaly, will entail some light sparticles and make the LHC constraints very tight. As a result, this scenario can explain the muon anomalous magnetic moment in very narrow corners of its parameter space.

Yusi Pan

Impact of recent (g − 2) μ  measurement on the light CP-even Higgs scenario in general Next-to-Minimal Supersymmetric Standard Model

Very recently, a Fermilab report of muon g − 2 showed a 4.2σ discrepancy between it and the standard model (SM) prediction. Motivated by this inspiring result and the increasing tension in supersymmetric interpretation of the anomalous magnetic moment, it is argued that in the general next-to-minimal supersymmetric standard model (GNMSSM), a singlino-dominated neutralino can act as a feasible dark matter (DM) candidate in explaining the discrepancy naturally. In this case, the singlino-dominated DM and singlet-dominated Higgs bosons can form a secluded DM sector with   <math> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mn>1</mn> <mn>0</mn> </msubsup> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mn>1</mn> <mn>0</mn> </msubsup> </math>  $$ {\overset{\sim }{\chi}}_1^0{\overset{\sim }{\chi}}_1^0 $$  → h  s  A  s  responsible for the measured DM relic abundance when   <math> <msub> <mi>m</mi> <msubsup> <mover> <mi>χ</mi> <mo>~</mo> </mover> <mn>1</mn> <mn>0</mn> </msubsup> </msub> </math>  $$ {m}_{{\overset{\sim }{\chi}}_1^0} $$  ≳ 150 GeV and the Yukawa coupling κ is around 0.2. This sector communicates with the SM sector by weak singlet-doublet Higgs mixing, so the scatterings of the singlino-dominated DM with nucleons are suppressed. Furthermore, due to the singlet nature of the DM and the complex mass hierarchy, sparticle decay chains in the GNMSSM are lengthened in comparison with the prediction of the minimal supersymmetric standard model. These characteristics lead to sparticle detection at the Large Hadron Collider (LHC) being rather tricky. This study surveys a specific scenario of the GNMSSM, which extends the ℤ3-NMSSM by adding an explicit μ-term, to reveal the features. It indicates that the theory can readily explain the discrepancy of the muon anomalous magnetic moment without conflicting with the experimental results in DM and Higgs physics, and the LHC searches for sparticles.

Pengxuan Zhu

Improved (g − 2) μ  measurement and singlino dark matter in μ-term extended ℤ3-NMSSM

The recently improved observation of the fine structure constant has led to a negative <math><mn>2.4</mn><mi>σ</mi></math> anomaly of electron <math><mi>g</mi><mo>−</mo><mn>2</mn></math>. Combined with the long-existing positive <math><mn>4.2</mn><mi>σ</mi></math> discrepancy of the muon anomalous magnetic moment, it is interesting and difficult to explain these two anomalies with a consistent model without introducing flavor violations. We show that they can be simultaneously explained in the inverse seesaw extended next-to-minimal supersymmetric standard model by the Higgsino-sneutrino contributions to <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>e</mi></msub></math> and <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>μ</mi></msub></math>. The spectrum features prefer light <math><mi>μ</mi></math>, which can predict <math><msub><mi>m</mi><mi>Z</mi></msub></math> naturally, and it is not difficult to obtain a <math><mi>τ</mi></math>-type sneutrino dark matter candidate that is compatible with the observed dark matter relic density and the bounds from dark matter direct detection experiments. Due to the compressed spectra and the undetectable decay mode of selectrons, they can evade the current Large Hadron Collider constraints.

Yangle He

Electron and muon anomalous magnetic moments in the inverse seesaw extended NMSSM

Singlino-dominated dark matter properties are investigated in the <math><msub><mi>Z</mi><mn>3</mn></msub></math> next-to-minimal supersymmetric Standard Model, producing superweak interactions with nucleons involved in dark matter direct-detection experiments. Approximate analytical formulas describing the dark matter abundance and cross section in the scattering with nucleons are used to illustrate a dependence on theoretical parameters in the neutralino and Higgs sectors. It is shown that the measured abundance requires a sizable singlet-doublet Higgs coupling parameter <math><mi>λ</mi></math>, while the experimental detection results prefer a small <math><mi>λ</mi></math>. The parameter space is then surveyed using a nest sampling technique guided by a likelihood function containing various observables in dark matter, Higgs, and <math><mi>B</mi></math> physics, such as the abundance and the scattering cross section. It is demonstrated that dark matter can achieve the correct abundance through <math><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mn>0</mn></msubsup><msubsup><mover><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mn>0</mn></msubsup><mo>→</mo><mi>t</mi><mover><mi>t</mi><mo>¯</mo></mover></math> or coannihilation with Higgsinos. The former process provides significantly larger Bayesian evidence than the latter, but this will be examined by the near-future PandaX-4T experiment. If the experiment shows no signs of dark matter, it will become highly disfavored. Furthermore, four cases are summarized to suppress dark matter scattering with nucleons, namely, a small <math><mi>λ</mi></math> and three kinds of cancellation between different contributions.