Motivated by the work of Cardoso et al. (2022) <cross-ref refid='br0150' id='crf0030'>[15]</cross-ref> on black holes in galaxies, we derive a new black hole solution surrounded by a Dekel-Zhao (DZ) dark matter profile. The derived metric, influenced by DZ profile parameters, exhibits two distinct regimes: for <math altimg='si1.svg'><mi>r</mi><mo>&#8810;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> is a characteristic radius), exponential corrections dominate, producing significant deviations from the Schwarzschild solution near dense cores, while for <math altimg='si3.svg'><mi>r</mi><mo>&#8811;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>, these corrections vanish, restoring the Schwarzschild metric at large distances. These findings ensure consistency with general relativity in vacuum. The black hole shadow and deflection angle are analyzed, demonstrating that the shadow radius increases with black hole mass ( <math altimg='si4.svg'><msub><mrow><mi>M</mi></mrow><mrow><mi mathvariant='normal'>BH</mi></mrow></msub></math>), while higher central densities ( <math altimg='si5.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mi mathvariant='normal'>ch</mi></mrow></msub></math>) result in smaller shadows, reflecting the environmental impact of dense dark matter halos. Photon dynamics reveal how DZ profiles modify critical impact parameters and effective potentials, with gravitational lensing effects highly sensitive to the characteristic radius ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>). Smaller <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> values lead to larger deflection angles due to stronger gravitational effects near compact cores. This work highlights the significance dark matter profiles in shaping black hole observables, providing a theoretical foundation for future observational studies and advancing the understanding of dark matter-black hole interactions in astrophysical and cosmological contexts.

Türkiye

Ali Övgün

Philippines

Reggie C. Pantig

Black hole in the Dekel-Zhao dark matter profile

It is well known that the muon magnetic dipole moment (MDM) has close relation with the new physics (NP) in the development of the Standard Model (SM). Combined with the Fermilab National Accelerator Laboratory (FNAL) and the Brookhaven National Laboratory (BNL) E821 result, the departure from the SM prediction is about 5.0 $$\sigma .$$ We study the electroweak corrections from several type two-loop SUSY diagrams and the virtual SUSY particles include chargino, neutralino, scalar lepton and scalar neutrino. Based on the latest experimental constraints, we study the muon anomalous MDM under the next to the minimal supersymmetric extension of the SM with local B-L gauge symmetry (N-B-LSSM). The abundant numerical results verify that $$\tan {\beta },$$ $$T_{e22}$$ , $$~M^2_L,~M^2_e,~M_{BB'}$$ play an important role in muon anomalous MDM. $$M^2_e,~\tan {\beta }$$ and $$~T_{e22}$$ are sensitive parameters to muon anomalous MDM. From the data obtained in all the figures of the numerical results, most of the values of $$a_{\mu }^{NBL}$$ are in 2 $$\sigma $$ interval, which can compensate the departure between the experiment data and the SM prediction.

China

Xing-Yu Han

Shu-Min Zhao

Long Ruan

Xi Wang

Portugal

Xing-Xing Dong

Study some two loop contribution to muon anomalous MDM in the N-B-LSSM

In an extension of MSSM with two triplets and a singlet, called the TNMSSM, there are seven neutralinos which can enrich the study of cold dark matter if one expects that the weakly interacting massive particle (WIMP) is responsible for the observation of Planck satellite. Such a model, compared to the MSSM, can naturally offer a solution to the  $$\mu $$  <math> <mi>μ</mi> </math>   problem, and its lightest neutralino, which is bino-like, can also provide a correct relic density by using the coannihilation mechanism due to the newly added triplinos. Taking into account the related experimental measurements, such as the bound on the SM-like Higgs mass, the B meson rare decays, the anomalous magnetic moment of the muon  $$a_\mu $$  <math> <msub> <mi>a</mi> <mi>μ</mi> </msub> </math>  , the Large Hadron Collider (LHC) measurements and the latest dark matter direct detection experiment LUX-ZEPLIN (LZ), the TNMSSM parameter space can be strictly limited. In respect to all the constraints mentioned above, we find that a bino-like neutralino with a mass in the region  $$[100, 450]~\textrm{GeV}$$  <math> <mrow> <mo>[</mo> <mn>100</mn> <mo>,</mo> <mn>450</mn> <mo>]</mo> <mspace width="3.33333pt"></mspace> <mtext>GeV</mtext> </mrow> </math>   can successfully account for the correct dark matter relic density. Additionally, most of the viable parameter space can be tested in the near future experiments such as the Xenon-nT experiment or LHC.

Zhong-Jun Yang

Jin-Lei Yang

Xing-Gang Wu

Tai-Fu Feng

Neutralino dark matter in the extension of MSSM with two triplets and singlet

In the U(1) X SSM, we delve into the quark flavor violation of h → bs, where h is identified as the SM-like Higgs boson discovered at the LHC. As the U(1) extension of the minimal supersymmetric standard model (MSSM), the U(1) X SSM has new super fields such as right-handed neutrinos and three Higgs singlets. We conduct a thorough analysis of the underlying mechanisms and parameter dependencies of h → bs in the U(1) X SSM. In the U(1) X SSM, we discover that the Br(h → bs) for the Higgs decay to bs could significantly differ from the expectation in the standard model (SM), depending on the values of the new parameters introduced in the model. Our research not only contributes to a deeper understanding of Higgs physics within the U(1) X SSM, but also provides valuable guidance for new physics (NP).

Song Gao

Ming-Yue Liu

The Higgs boson decay h → bs in the U(1) X SSM

In the present study, we investigated the decays of the top quark:   $ t\rightarrow c\gamma $  ,   $ t\rightarrow c\gamma $  ,   $ t\rightarrow c\gamma $  , and   $ t\rightarrow c\gamma $  . They are extremely rare processes in the standard model (SM). As the   $ t\rightarrow c\gamma $   extension of the minimal supersymmetric standard model (MSSM), the   $ t\rightarrow c\gamma $   SSM features new superfields such as the right-handed neutrinos and three Higgs singlets. We analyzed the effects of different sensitive parameters on the results and made reasonable theoretical predictions, thereby providing a useful reference for future experimental development. Considering the constraint set by the updated experimental data, the numerical results show that the branching ratios of the four processes, i.e.,   $ t\rightarrow c\gamma $  , can reach the same order of magnitude as their experimental upper limits. Among them,   $ t\rightarrow c\gamma $   has the most evident effect on these processes and is the main parameter;   $ t\rightarrow c\gamma $  ,   $ t\rightarrow c\gamma $  ,   $ t\rightarrow c\gamma $  ,   $ t\rightarrow c\gamma $  ,   $ t\rightarrow c\gamma $  ,   $ t\rightarrow c\gamma $  , and   $ t\rightarrow c\gamma $   are also important parameters for the processes, and have effects on the numerical results.

Top-quark rare decays with flavor violation  

People extend the MSSM with the local gauge group <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></math> to obtain the <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></math>SSM. In the framework of the <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></math>SSM, we study the flavor transition process <math><mi>b</mi><mo>→</mo><mi>s</mi><mi>γ</mi></math> with the mass insertion approximation (MIA). By the MIA method and some reasonable parameter assumptions, we can intuitively find the parameters that have obvious effect on the analytic results of the flavor transition process <math><mi>b</mi><mo>→</mo><mi>s</mi><mi>γ</mi></math>. By means of the influences of different sensitive parameters, we can obtain reasonable results to better fit the experimental data.

Xin-Xin Long

Yi-Tong Wang

Tong-Tong Wang

Jian-Bin Chen

Hai-Bin Zhang

The flavor transition process → In the (1) SSM with the mass insertion approximation

Charged lepton flavor violation (CLFV) represents a clear new physics (NP) signal beyond the standard model (SM). In this work, we investigate CLFV processes <math><mrow><msubsup><mrow><mi>l</mi></mrow><mrow><mi>j</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>l</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mi>γ</mi></mrow></math> utilizing mass insertion approximation (MIA) in the minimal supersymmetric extension of the SM with local <math><mi>B</mi><mo>−</mo><mi>L</mi></math> gauge symmetry (<math><mi>B</mi><mo>−</mo><mi>L</mi></math> SSM). The MIA method can provide a set of simple analytic formulas for the form factors and the associated effective vertices, so that the movement of the CLFV decays <math><mrow><msubsup><mrow><mi>l</mi></mrow><mrow><mi>j</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>l</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mi>γ</mi></mrow></math> with the sensitive parameters will be intuitively analyzed. Considering the SM-like Higgs boson mass and the muon anomalous dipole moment (MDM) within <math><mn>4</mn><mi>σ</mi></math>, <math><mn>3</mn><mi>σ</mi></math>, and <math><mn>2</mn><mi>σ</mi></math> regions, we discuss the corresponding constraints on the relevant parameter space of the model.

Jia-Peng Huo

Charged lepton flavor violation in the <math><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></math> symmetric SSM

In this paper, we study the lepton flavor violating decays of the <math><msub><mrow><mi>l</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>→</mo><msub><mrow><mi>l</mi></mrow><mrow><mi>i</mi></mrow></msub><mi>γ</mi><mi>γ</mi></math> (j=2, 3; i=1, 2) processes under the <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></math>SSM. The <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></math>SSM is the addition of three singlet new Higgs superfields and right-handed neutrinos to the minimal supersymmetric standard model (MSSM). Based on the latest experimental constraints of <math><msub><mrow><mi>l</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>→</mo><msub><mrow><mi>l</mi></mrow><mrow><mi>i</mi></mrow></msub><mi>γ</mi><mi>γ</mi></math>, we analyze the effects of different sensitive parameters on the results and made reasonable predictions for future experimental development. Numerical analysis shows that many parameters have a greater or lesser effect on lepton flavor violation (LFV), but the main sensitive parameters and sources leading to LFV are the non-diagonal elements involving the initial and final leptons. This work could provide a basis for the discovery of the existence of new physics (NP).

Lepton flavor violating decays →

In the <math><mrow><mi>U</mi><mo>(</mo><mn>1</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></mrow></math> extension of the minimal supersymmetric standard model, there are three Higgs singlets and the corresponding trilinear terms in the Higgs effective potential. These new terms can allow a strongly first-order electroweak phase transition (EWPT) for a wide parameter space. We use codes cosmotransitions to analyze the thermal evolution of the Higgs effective potential and calculate nucleation temperature. To find reasonable parameter spaces for strongly first-order EWPT, we randomly scan many parameters, which is numerically expensive. The diagrams are shown, that can lead to the 125 GeV Higgs mass and satisfy the first-order EWPT. This work benefits the phenomenology of <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> SSM and exploring new physics beyond the SM.

Jian-Fei Zhang

Strong first-order electroweak phase transition in the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math>-extended MSSM

$$R_{D^{(*)}}$$  <math> <msub> <mi>R</mi> <msup> <mi>D</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> </msub> </math>   is the ratio of branching ratio  $$\overline{B} \rightarrow D^{(*)}\tau \overline{\nu }_{\tau }$$  <math> <mrow> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> <mi>τ</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </mrow> </math>   to  $$\overline{B} \rightarrow D^{(*)}l\overline{\nu }_{l}~(l=e,~\mu )$$  <math> <mrow> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> <mi>l</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>l</mi> </msub> <mspace width="3.33333pt"></mspace> <mrow> <mo>(</mo> <mi>l</mi> <mo>=</mo> <mi>e</mi> <mo>,</mo> <mspace width="3.33333pt"></mspace> <mi>μ</mi> <mo>)</mo> </mrow> </mrow> </math>  . There is a gap of 2 $$\sigma _{exp}$$  <math> <msub> <mi>σ</mi> <mrow> <mi>exp</mi> </mrow> </msub> </math>   or more between its experimental value and the prediction under the standard model (SM). People extend the MSSM with the local gauge group  $$U(1)_X$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>X</mi> </msub> </mrow> </math>   to obtain the  $$U(1)_X$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>X</mi> </msub> </mrow> </math>  SSM. Compared with MSSM,  $$U(1)_X$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>X</mi> </msub> </mrow> </math>  SSM has more superfields and effects. In  $$U(1)_X$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>X</mi> </msub> </mrow> </math>  SSM, we research the semileptonic decays  $$\overline{B} \rightarrow D^{(*)}l\overline{\nu }_{l}$$  <math> <mrow> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> <mi>l</mi> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>l</mi> </msub> </mrow> </math>   and calculate  $$R_{D^{(*)}}$$  <math> <msub> <mi>R</mi> <msup> <mi>D</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> </msub> </math>  . The numerical results of  $$R_{D^{(*)}}$$  <math> <msub> <mi>R</mi> <msup> <mi>D</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> </msub> </math>   are further corrected under  $$U(1)_X$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>X</mi> </msub> </mrow> </math>  SSM, which are much better than the SM predictions. After correction, the theoretical value of  $$R_{D^{(*)}}$$  <math> <msub> <mi>R</mi> <msup> <mi>D</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> </msub> </math>   can reach one  $$\sigma _{exp}$$  <math> <msub> <mi>σ</mi> <mrow> <mi>exp</mi> </mrow> </msub> </math>   range of the averaged experiment central value.

Theoretical corrections of  $$R_D$$  <math> <msub> <mi>R</mi> <mi>D</mi> </msub> </math>   and  $$R_{D^*}$$  <math> <msub> <mi>R</mi> <msup> <mi>D</mi> <mo>∗</mo> </msup> </msub> </math>