Basing on Mellin-Barnes representations and Miller’s transformation, we present the Gel’fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of 4-loop vacuum Feynman integrals with arbitrary masses. Through the GKZ hypergeometric systems, the analytical hypergeometric solutions of 4-loop vacuum Feynman integrals with arbitrary masses can be obtained in neighborhoods of origin including infinity. The analytical expressions of Feynman integrals can be formulated as a linear combination of the fundamental solution systems in certain convergent region, which the combination coefficients can be determined by the integral at some regular singularities, the Mellin-Barnes representation of the integral, or some mathematical methods.

China

Hai-Bin Zhang

Tai-Fu Feng

GKZ hypergeometric systems of the four-loop vacuum Feynman integrals

<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson rare decays play a crucial role in exploring new physics beyond the standard model. In this study, we explore the rare decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> in a flavor violating extension of the Minimal Supersymmetric Standard Model (MSSM), namely, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math>-from-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ν</mi></math> SSM (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mi>ν</mi><mi>SSM</mi></math>). Combined with the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><msub><mi>X</mi><mi>s</mi></msub><mi>γ</mi></math>, the numerical results indicate that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mi>ν</mi><mi>SSM</mi></math> can successfully accommodate the experimental data for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> and additionally narrow down the parameter space.</p>

Kai-Kai Meng

Jin-Lei Yang

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> in a flavor violating extension of MSSM

Embedding Feynman integrals in Grassmannians, we can write Feynman integrals as some finite linear combinations of generalized hypergeometric functions. In this paper, we present a general method to obtain Gauss relations among those generalized hypergeometric functions. The hypergeometric expressions of Feynman integral are continued from a connected component to another by the inverse Gauss relations, then continued to the whole domain of definition by the Gauss-Kummer relations. The Laurent series of the Feynman integral around the space-time dimension <math><mi>D</mi><mo>=</mo><mn>4</mn></math> is obtained by the Gauss adjacent relations, where the coefficient of the term with power of <math><mi>D</mi><mo>−</mo><mn>4</mn></math> is given as the linear combinations of hypergeometric functions with integer parameters. As examples, we illustrate how to obtain the expressions for the Feynman integrals of the 1-loop self-energy and a 2-loop massless triangle diagram in the domains of definition.

Yang Zhou

Gauss relations in Feynman integrals

The next-to-minimal supersymmetric Standard Model with triplets is an attractive extension of the Standard Model. It combines the advantages of the next-to-minimal supersymmetric Standard Model and the minimal supersymmetric Standard Model with triplets to give three tiny Majorana neutrinos masses via a type-<math><mrow><mi>I</mi><mo>+</mo><mi>II</mi></mrow></math> seesaw mechanism. With the on-shell renormalization scheme, we consider the neutrino masses up to one loop approximation. Applying the effective Lagrangian method, we study the transition magnetic moments of Majorana neutrinos and consider the normal hierarchy and inverse hierarchy neutrino mass spectra within the constraints of experimental data on neutrino oscillations. The solar neutrino transition magnetic moment is further deduced, and compared with the XENONnT experiment limit.

Zhao-Yang Zhang

Transition magnetic moment of Majorana neutrinos in the triplets next-to-minimal MSSM

A flavor-dependent model (FDM) is proposed in this work. The model extends the Standard Model by an extra  $$U(1)_F$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>F</mi> </msub> </mrow> </math>   local gauge group, two scalar doublets, one scalar singlet and two right-handed neutrinos, where the additional  $$U(1)_F$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>F</mi> </msub> </mrow> </math>   charges are related to the particles’ flavor. The new fermion sector in the FDM can explain the flavor mixings puzzle and the mass hierarchy puzzle simultaneously, and the nonzero Majorana neutrino masses can be obtained naturally by the Type I see-saw mechanism. In addition, the B meson rare decay processes  $${\bar{B}} \rightarrow X_s\gamma ,$$  <math> <mrow> <mover> <mrow> <mi>B</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>→</mo> <msub> <mi>X</mi> <mi>s</mi> </msub> <mi>γ</mi> <mo>,</mo> </mrow> </math>    $$B_s^0 \rightarrow \mu ^+\mu ^-,$$  <math> <mrow> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> <mo>,</mo> </mrow> </math>   the top quark rare decay processes  $$t\rightarrow ch,$$  <math> <mrow> <mi>t</mi> <mo>→</mo> <mi>c</mi> <mi>h</mi> <mo>,</mo> </mrow> </math>    $$t\rightarrow uh$$  <math> <mrow> <mi>t</mi> <mo>→</mo> <mi>u</mi> <mi>h</mi> </mrow> </math>   and the  $$\tau $$  <math> <mi>τ</mi> </math>   lepton flavor violation processes  $$\tau \rightarrow 3e,$$  <math> <mrow> <mi>τ</mi> <mo>→</mo> <mn>3</mn> <mi>e</mi> <mo>,</mo> </mrow> </math>    $$\tau \rightarrow 3\mu ,$$  <math> <mrow> <mi>τ</mi> <mo>→</mo> <mn>3</mn> <mi>μ</mi> <mo>,</mo> </mrow> </math>    $$\mu \rightarrow 3e$$  <math> <mrow> <mi>μ</mi> <mo>→</mo> <mn>3</mn> <mi>e</mi> </mrow> </math>   predicted in the FDM are analyzed.

The flavor-dependent  $$U(1)_F$$  <math> <mrow> <mi>U</mi> <msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>F</mi> </msub> </mrow> </math>   model

Considering the hierarchical structure of fermionic masses and the fermionic flavor mixing puzzles in the Standard Model, we propose to relate them by the see-saw mechanism, i.e. only the third generation of quarks and charged leptons achieves the masses at the tree level, the first two generations achieve masses through the mixings with the third generation, and the neutrinos achieve tiny Majorana masses by the so-called Type-I see-saw mechanism. This new picture at the fermion sector can explain simultaneously the flavor mixing puzzle and mass hierarchy puzzle in the SM. In addition, a flavor-dependent model (FDM) is proposed to realize the new mechanism, and observing the top quark rare decay processes <math><mi>t</mi><mo>→</mo><mi>c</mi><mi>h</mi></math>, <math><mi>t</mi><mo>→</mo><mi>u</mi><mi>h</mi></math> and the lepton flavor violation processes <math><mi>μ</mi><mo>→</mo><mn>3</mn><mi>e</mi><mo>,</mo><mspace width="0.25em"></mspace><mi>τ</mi><mo>→</mo><mn>3</mn><mi>e</mi><mo>,</mo><mspace width="0.25em"></mspace><mi>μ</mi><mo>→</mo><mn>3</mn><mi>μ</mi></math> is effective to test the proposed FDM.

A mechanism relating the fermionic mass hierarchy to the flavor mixing

In this paper, we present an algorithm to construct the q  T  distribution at NLO accuracy to arbitrary power precision, including the assembly of suitable zero-bin subtrahends, in a mathematically well-defined way for a generic choice of rapidity-divergence regularisation prescription. In its derivation, we divide the phase space into two sectors, the interior of the integration domain as well as the integration boundary, which we include here for the first time. To demonstrate the applicability and usefulness of our algorithm, we calculate the N2LP corrections for Higgs hadroproduction for the first time. We observe that our approximate N2LP-accurate q  T  spectra replicate the asymptotic behaviour of the full QCD calculation to a much better degree than the previously available results, both within the q  T  → 0 limit and in the large-q  T  domain for all the involved partonic processes. While playing a minor role at larger transverse momenta, we show that the newly incorporated boundary contribution plays a vital role in the q  T  → 0 limit, where any subleading power accuracy would be lost without them. In particular, our N2LP-accurate q  T  expansion can approximate the exact q  T  distribution up to q  T  ≈ 30 GeV at the percent level for rapidities |Y  H  | ≲ 3.

Italy

Giancarlo Ferrera

Wan-Li Ju

United Kingdom

Marek Schönherr

Zero-bin subtraction and the q T spectrum beyond leading power

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

Shu-Min Zhao

Xi Wang

Yi-Tong Wang

Tong-Tong Wang

Jian-Bin Chen

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

The CMS and ATLAS Collaborations have recently reported their results searching for a light Higgs boson with mass around 95 GeV, based on the full run 2 dataset. In the framework of the <math><mi>C</mi><mi>P</mi></math>-violating (CPV) <math><mi>μ</mi></math>-from-<math><mi>ν</mi></math> supersymmetric standard model (SSM), we discuss an <math><mo>∼</mo><mrow><mn>2.9</mn><mi>σ</mi></mrow></math> (local) excess at 95 GeV in the light Higgs boson search in the diphoton decay mode as reported by ATLAS and CMS, together with an <math><mo>∼</mo><mrow><mn>2</mn><mi>σ</mi></mrow></math> excess (local) in the <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> final state at LEP in the same mass range. By introducing CPV phases as well as by mixing <math><mi>C</mi><mi>P</mi></math>-even Higgs and <math><mi>C</mi><mi>P</mi></math>-odd Higgs, a lighter Higgs boson in the <math><mi>μ</mi></math>-from-<math><mi>ν</mi></math> SSM can be produced, which can account for the “diphoton excess.”

Chang-Xin Liu

Xiao-Yu Zheng

Jiao Ma

95 GeV excess in a <math><mi>C</mi><mi>P</mi></math>-violating <math><mi>μ</mi></math>-from-<math><mi>ν</mi></math> 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).