In this manuscript, we study the general scalar leptoquark contributions to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mi>g</mi><mo stretchy="false">→</mo><mi>Z</mi><mi>h</mi></math> process at a one-loop level. We find that the contributions only show up for the off diagonal Higgs and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson interactions with scalar leptoquarks, which can lead to new tensor structures different from the standard model. In the one-field and two-field models, the contributions vanish exactly; thus, the contributions are possible at least in the three-field models. We exemplify the contributions in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>S</mi><mn>1</mn></msub><mo>+</mo><msub><mover accent="true"><mi>R</mi><mo stretchy="false">˜</mo></mover><mn>2</mn></msub><mo>+</mo><msub><mi>S</mi><mn>3</mn></msub></math> model, which can appear in the presence of scalar leptoquark mass splittings and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation. In view of the heavy scalar leptoquark mass suppression, the leading contributions are typically small and difficult to observe at hadron colliders. However, this work offers a quantitative and systematic investigation of scalar leptoquark contributions, also making it valuable for the new physics studies in other models.

China

Shi-Ping He

Scalar leptoquark contributions to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mi>g</mi><mo stretchy="false">→</mo><mi>Z</mi><mi>h</mi></math> process

We combine existing perturbative results to show that a precise analytic determination of the charm-quark contribution to the hadronic light-by-light (HLbL) part of the muon anomalous magnetic moment is possible. Working in the <math altimg='si5.svg'><mover><mrow><mtext>MS</mtext></mrow><mo stretchy='true'>&#8254;</mo></mover></math> scheme, we include the NLO <math altimg='si6.svg'><mrow><mi mathvariant='script'>O</mi><mo>(</mo><msub><mi>&#945;</mi><mi>s</mi></msub><mo>)</mo></mrow></math> correction, which significantly reduces the residual renormalization-scale dependence and the perturbative uncertainty. Our final result is <math altimg='si7.svg'><mrow><msubsup><mi>a</mi><mrow><mi>&#956;</mi></mrow><mtext>HLbLc</mtext></msubsup><mo linebreak='goodbreak'>=</mo><mn>3.65</mn><mrow><mo>(</mo><mn>25</mn><mo>)</mo></mrow><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>11</mn></mrow></msup></mrow></math>, in good agreement with recent lattice determinations.

Sweden

Johan Bijnens

United Kingdom

Nils Hermansson-Truedsson

Spain

Antonio Rodríguez-Sánchez

On the charm contribution to the muon g - 2 light-by-light

We formulate a general fusion procedure for open $$\mathfrak{g}\mathfrak{l}(N)$$ spin chains. We construct the fused boundary reflection matrices and the corresponding fused reflection equations. By using the intertwining relation between the fused reflection matrices and the fusion operator, we identify the invariant subspace of the fused reflection matrices carrying the irreducible representations of $$\mathfrak{g}\mathfrak{l}(N)$$ . We also construct the fused transfer matrix and evaluate it explicitly in the total tensor product space and the invariant subspaces. Finally, we demonstrate that the ABJM spin chain model originates from such fusion procedure and derive three classes of boundary reflection matrices solutions on the anti-fundamental representation space of $$\mathfrak{s}\mathfrak{u}(4)$$ .

Nan Bai

A general fusion procedure for open $$\mathfrak{g}\mathfrak{l}(N)$$ spin chains: application to the ABJM spin chain

In this work we focus on the evaluation of the leading-order hadronic vacuum polarization contribution from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> channel to the muon anomalous magnetic moment <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math> by using the experimental <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>ν</mi><mi>τ</mi></msub></math> data. The isospin breaking corrections play the decisive role in this approach of computing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math>. One of such important isospin breaking sources is the long-distance electromagnetic correction factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>G</mi><mrow><mi>EM</mi></mrow></msub></math> of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>ν</mi><mi>τ</mi></msub></math> process from the real photon radiation. The latter effect can be calculated from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>ν</mi><mi>τ</mi></msub><mi>γ</mi></math> amplitude, which is revised in this work within the resonance chiral theory by simultaneously including the even-intrinsic-parity and odd-intrinsic-parity resonance operators. We update the determination of the only unknown resonance coupling through the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><mi>γ</mi></math> decay by including contributions from both the vector and scalar resonances. By taking other remaining contributions from the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math> White Paper 2025, we further revise the complete value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math>, which turns out to deviate from the newest world average result after Fermilab’s measurement at the level of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2.7</mn><mi>σ</mi></mrow></math>.

Zhi-Xin Li

Ao Li

Jin Hao

Chun-Gui Duan

Zhi-Hui Guo

Revisit of the electromagnetic correction to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>τ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mrow><mi>ν</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math> and its implication for muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math> based on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> data

We consider mixed strong-electroweak corrections to Higgs production via gluon fusion, in which the Higgs boson couples to the top quark. Using the method of differential equations, we compute all of the master integrals that contribute to this process at two loops through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mrow><mi>ϵ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math> in the dimensional regularization parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ϵ</mi><mo>=</mo><mo stretchy="false">(</mo><mi>d</mi><mo>−</mo><mn>4</mn><mo stretchy="false">)</mo><mo>/</mo><mn>2</mn></mrow></math>, keeping full analytic dependence on the top quark, Higgs, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson masses. We present the results for these master integrals in terms of iterated integrals whose kernels depend on elliptic curves.

Switzerland

Robin Marzucca

Andrew J. McLeod

Germany

Christoph Nega

Two-loop master integrals for mixed QCD-EW corrections to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>g</mi><mi>g</mi><mo stretchy="false">→</mo><mi>H</mi></mrow></math> through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mrow><mi mathvariant="normal">ϵ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math>

In neutrino physics, a class of models with local or global family symmetries may be invoked, and then a flavon field is needed to realize full neutrino mixing. This flavon may leave hints in lepton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math> and address their possible anomalies. In this work, we explore this idea in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow><msub><mo stretchy="false">)</mo><mrow><mi>i</mi><mi>j</mi></mrow></msub></math> gauge extension to the standard model (SM), in which realistic neutrino mixing requires both a SM singlet flavon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> and a vectorlike lepton (VLL) doublet. The dominant coupling between the flavon and leptons is in the manner of lepton-flavor-violation (LFV). Through an analytical analysis of the SM lepton-VLL mixing matrix, we find that the parameter space of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mover accent="true"><mi>μ</mi><mo stretchy="false">¯</mo></mover><mi>e</mi></math>-type flavon to explain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>μ</mi></msub></math> has been completely excluded by the specific LFV process, muonium-antimuonium oscillation. But the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mover accent="true"><mi>μ</mi><mo stretchy="false">¯</mo></mover><mi>τ</mi></math>-type flavon still has the opportunity to account for the excess in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>μ</mi></msub></math> or the deficit in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>e</mi></msub></math>; however, it faces the strong constraint from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi><mo stretchy="false">→</mo><mi>μ</mi></math> conservation and, in particular, the lepton flavor universality (LFU) test of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson decay, which arises due to our way to realize the LFV flavon. The surviving flavon is highly predictable, with mass in the narrow window <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>τ</mi></msub><mo>≲</mo><msub><mi>m</mi><mi>s</mi></msub><mo>≲</mo><mn>2</mn><msub><mi>m</mi><mi>τ</mi></msub></math> and LFV coupling strength <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup></math>. Besides, it leaves a TeV scale VLL with a multilepton signature at the LHC.

Shuyang Han

Zhaofeng Kang

Light lepton-flavor-violating flavon: The messenger of neutrino mixing and lepton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>

We are employing a supersymmetric variant of the worldline quantum field theory (WQFT) formalism to compute the far-field momentum-space gravitational waveform emitted during the scattering of two spinning black holes at next-to-leading order (NLO) in the post-Minkowskian expansion. Our results are accurate up to quadratic-in-spin contributions, which means we report for the very first time the waveform observable at the order 𝒪($\textit{G}$ 𝒮 ). Our computation is based on mapping $\textit{n}$-body tree-level amplitudes in such a way that we can obtain the ($\textit{n}$ – 2)-loop two-body waveform integrand. We discuss in detail this procedure and highlight the similarity of the resulting structures with those obtained in the scattering-amplitude approach. As a by product of our computational approach, we also obtain, for the first time, the leading-order waveform for three-body scattering of spinning black holes. We validated our results in various ways but most notably, we find exact agreement for the NLO waveform integrand obtained from the WQFT and the classical limit of scattering amplitudes in QFT.

Lara Bohnenblust

Harald Ita

Mexico

Manfred Kraus

Johannes Schlenk

Gravitational Bremsstrahlung in black-hole scattering at 𝒪($\textit{G}$

We propose a new inverse seesaw model based on hidden local <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> symmetry framework where the inverse seesaw mechanism is induced at one loop level. A Majorana mass term of singlet fermion is forbidden by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> symmetry and it is generated at one-loop level by introducing relevant particle contents to get loop diagram, inducing inverse seesaw mechanism. The same particle contents also contribute to lepton magnetic(electric) dipole moment and lepton flavor violating decays without chiral suppression. We can then obtain sizable muon anomalous magnetic dipole moment that accommodate with deviation from the standard model prediction. The constraints from lepton flavor violating decays and electron magnetic(electric) dipole moment are also discussed to explore testability of the model.

Takaaki Nomura

Japan

Hiroshi Okada

Radiative inverse seesaw model with hidden <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> gauge symmetry enhancing lepton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>

The Direct Detection (DD) experiments are vital for probing the particle nature of Dark Matter (DM). However, in the absence of a scattering event, DD searches result in stringent bounds on the corresponding parameter space. The paper has considered a $$ \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ -extension of the Standard Model (SM) and augmented the particle spectrum with SU(2) -singlet vector-like leptons and scalars. A discrete $\textit{Z}$ symmetry stabilizes the lightest SM-singlet vector-like lepton as the viable DM candidate. In the proposed model, amplitude-level cancellation can be achieved for both DM-electron and DM-quark scatterings, leading to a trivial explanation for the continuous null results in the DD experiments. The framework can also induce one-loop corrections to the lepton anomalous magnetic moments and $\textit{Zℓ}$ couplings. The experimental bounds on the $\textit{Z}$ → $\textit{ℓ}$ decays are instrumental in constraining the model parameters. Particularly, using the $\textit{Z}$ → $\textit{τ}$ $\textit{τ}$ decay, a stronger exclusion limit can be imposed on the $$ \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ parameter space. Further, in the presence of three heavy right-handed neutrinos, transforming as $\textit{Z}$ -even states, the model can explain all the neutrino mass and mixing constraints using the Type-I seesaw mechanism. Future experimental updates on the ($\textit{g}$ − 2) , $\textit{Z}$ → $\textit{ℓ}$ decays and improved bounds on the $$ \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ theory can be crucial to test the proposed model. Moreover, future DD experiments searching for a DM-muon scattering might be significant to probe the considered DM-SM interaction.

India

Bibhabasu De

Exploring the null results in the direct detection experiments, ($\textit{g}$ − 2)

In the heavy quarkonium decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo stretchy="false">→</mo><mi>g</mi><mi>g</mi><mi>g</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo>=</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>,</mo><mi mathvariant="normal">ϒ</mi></math>), making a definite prediction including relativistic corrections has so far remained a significant challenge. In this work, we study this decay process by taking into account the relativistic corrections in the Bethe-Salpeter formalism, where the relativistic bound-state wave function of quarkonium is obtained by solving the Bethe-Salpeter equation under the covariant instantaneous ansatz. Through analytical calculation, we find that some polarized decay widths vanish due to the helicity selection rule, which suppresses the corresponding helicity amplitudes. Owing to helicity flip symmetry and phase space symmetry, the nonvanishing polarized decay widths are not all independent; they are related through a set of symmetry relations. Then we obtain the unpolarized decay width formula <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">→</mo><mi>g</mi><mi>g</mi><mi>g</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mn>80</mn><mo stretchy="false">(</mo><msup><mi>π</mi><mn>2</mn></msup><mo stretchy="false">−</mo><mn>9</mn><mo stretchy="false">)</mo><msubsup><mi>α</mi><mi>s</mi><mn>3</mn></msubsup><msubsup><mi>N</mi><mi>V</mi><mn>2</mn></msubsup><msubsup><mi>β</mi><mi>V</mi><mn>3</mn></msubsup></mrow><mrow><mn>81</mn><msup><mi>π</mi><mrow><mn>9</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msup><mi>M</mi></mrow></mfrac><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>κ</mi><mfrac><msubsup><mi>β</mi><mi>V</mi><mn>2</mn></msubsup><msup><mi>M</mi><mn>2</mn></msup></mfrac><mo stretchy="false">)</mo></math>, where the factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mfrac><msubsup><mi>β</mi><mi>V</mi><mn>2</mn></msubsup><msup><mi>M</mi><mn>2</mn></msup></mfrac></math> arises from the relativistic corrections with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mo>≡</mo><mfrac><mrow><mn>3</mn><mo stretchy="false">(</mo><mn>112</mn><mo stretchy="false">+</mo><mn>25</mn><msup><mi>π</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow><mrow><mn>16</mn><mo stretchy="false">(</mo><msup><mi>π</mi><mn>2</mn></msup><mo stretchy="false">−</mo><mn>9</mn><mo stretchy="false">)</mo></mrow></mfrac></math>. Furthermore, including both relativistic and QCD radiative corrections within the factorization assumption, our predictions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">→</mo><mi>g</mi><mi>g</mi><mi>g</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">)</mo></math> agree well with their experimental data. As a crossing check, with the experimental value of the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mi>V</mi></msub><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">→</mo><mi>g</mi><mi>g</mi><mi>g</mi><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo stretchy="false">+</mo></msup><msup><mi>e</mi><mo stretchy="false">−</mo></msup><mo stretchy="false">)</mo></mrow></mfrac></math> and our result for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mi>V</mi></msub></math>, we extract <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">(</mo><msub><mi>M</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>/</mo><mn>2</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0.31</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">(</mo><msub><mi>M</mi><mi mathvariant="normal">ϒ</mi></msub><mo>/</mo><mn>2</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0.20</mn></math>, respectively.

Hong-Mei Jiang

Chao-Jie Fan

Jun-Kang He

Cui Kong

Heavy quarkonium decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo stretchy="false">→</mo><mi>g</mi><mi>g</mi><mi>g</mi></math> with both relativistic and QCD radiative corrections