A future $ e^+e^- $ collider could run at the $\textit{Z}$-pole to perform important electroweak (EW) precision measurements, but such a run may not be viable for a future muon collider. However, this can be compensated for by measuring other EW processes utilizing the high energy and large luminosity of the muon collider. In this paper, we consider the measurements of the vector boson fusion processes of $ WW/WZ/W\gamma $ to a pair of fermions (along with a $ \nu_{\mu}\bar{\nu}_{\mu} $ or $ \nu_{\mu}\mu^+/\bar{\nu}_{\mu}\mu^- $ pair) at a high-energy muon collider and study their potential for probing EW observables. We consider two run scenarios for the muon collider with center-of-mass energies of 10 and 30 TeV, respectively, and focus on the processes involving $ f=b,c,\tau $ and the dimension-6 operators that directly modify the corresponding fermions coupling to the $ Z/W $ bosons. The invariant mass distribution of the $ f\bar{f} $ pair helps to separate the events from the $ Z/W $ and high-energy resonances, whereas the polar angle of the outing fermion provides additional information. Through a chi-squared analysis on the binned distributions and combining the information from the $\textit{WW}$ and $ WZ/W\gamma $ fusion processes, all relevant Wilson coefficients can be constrained simultaneously. The precision surpasses the current EW measurement constraints and is even competitive with future $ e^+e^- $ colliders. Our analysis can be included in a more complete framework that is required to fully determine the potential of muon colliders in EW precision measurements.

China

Hao-Qiao Li

Hai-Ning Yan

Jiayin Gu

Germany

Xiao-Ze Tan

Probing $\textit{Z}$/$\textit{W}$ pole physics at high-energy muon colliders via vector-boson-fusion processes * Supported by the National Natural Science Foundation of China (NSFC) (12035008, 12375091, 12347171), and the Innovation Program for Quantum Science and Technology (2024ZD0300101). Xiao-Ze Tan also acknowledges the support from Helmholtz – OCPC (Office of China Postdoctoral Council) Postdoctoral Fellowship Program

General one-loop formulas for loop-induced processes $gg/\gamma \gamma \rightarrow \phi_i\phi_j$ with $\phi_i\phi_j = hh,~hH,~HH$ are presented in this paper. The analytic expressions evaluated in this study are valid for a class of Higgs Extensions of the Standard Model, $\textit{e.g.,}$ Inert Doublet Higgs, Two Higgs Doublet, Zee-Babu, and Triplet Higgs Models$\textit{.}$ Analytic expressions for one-loop form factors are expressesd in terms of the basic scalar one-loop two-, three-, and four-point functions following the output format of the packages $ {\tt LoopTools}$ and $ {\tt Collier}$ . Hence, physical results can be evaluated numerically using one of these packages. The analytic results are tested using several checks such as the ultraviolet finiteness and infrared finiteness of the one-loop amplitudes. Furthermore, the amplitudes obey the ward identity due to massless gauge bosons in the initial states. This identity is also verified numerically. Regarding applications, we present the phenomenological results for the investigated processes in the Zee-Babu model as a typical example. In particular, production cross-sections for the processes $\gamma \gamma\rightarrow hh$ are scanned over the parameter space of the Zee-Babu Model.

Vietnam

Khiem Hong Phan

Dzung Tri Tran

Thanh Huy Nguyen

One-loop analytical expressions for $\textit{gg}$/$\textit{γγ}$ → ϕ$_{i}$ϕ$_{j}$ in Higgs extensions of the standard model and their applications * This research is supported by Vietnam National Foundation for Science and Technology Development (103.01-2023.16). Khiem Hong Phan and Dzung Tri Tran express their gratitude to all the valuable support from Duy Tan University, for the 30th anniversary of establishment (Nov. 11, 1994 - Nov. 11, 2024) towards ''Integral, Sustainable and Stable Development''

Current interpretations of the LHC results on two Higgs doublet models (2HDM) underestimate the sensitivity due to neglecting higher order effects. In this work, we revisit the impact of these effects using the current cross-section times branching ratio limits of the  $$A\rightarrow hZ, H \rightarrow VV$$  <math> <mrow> <mi>A</mi> <mo>→</mo> <mi>h</mi> <mi>Z</mi> <mo>,</mo> <mi>H</mi> <mo>→</mo> <mi>V</mi> <mi>V</mi> </mrow> </math>   and  $$H\rightarrow hh$$  <math> <mrow> <mi>H</mi> <mo>→</mo> <mi>h</mi> <mi>h</mi> </mrow> </math>   channels. With a degenerate heavy Higgs mass  $$m_\varPhi $$  <math> <msub> <mi>m</mi> <mi>Φ</mi> </msub> </math>  , we find that the LHC searches gain sensitivity to the small  $$\tan \beta $$  <math> <mrow> <mo>tan</mo> <mi>β</mi> </mrow> </math>   region after including loop corrections, even close to  $$\cos (\beta -\alpha )=0$$  <math> <mrow> <mo>cos</mo> <mo>(</mo> <mi>β</mi> <mo>-</mo> <mi>α</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </math>   which is not reachable at tree level for all types of 2HDM. For a benchmark point with  $$m_\varPhi =300$$  <math> <mrow> <msub> <mi>m</mi> <mi>Φ</mi> </msub> <mo>=</mo> <mn>300</mn> </mrow> </math>   GeV,  $$\tan \beta &lt;1.8(1.2)$$  <math> <mrow> <mo>tan</mo> <mi>β</mi> <mo>&lt;</mo> <mn>1.8</mn> <mo>(</mo> <mn>1.2</mn> <mo>)</mo> </mrow> </math>   can be probed for the Type-I(II) 2HDM model for  $$\cos (\beta -\alpha )=0$$  <math> <mrow> <mo>cos</mo> <mo>(</mo> <mi>β</mi> <mo>-</mo> <mi>α</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </math>  . When the deviation from  $$\cos (\beta -\alpha )=0$$  <math> <mrow> <mo>cos</mo> <mo>(</mo> <mi>β</mi> <mo>-</mo> <mi>α</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </math>   is larger, the region for which current searches have exclusion potential becomes larger.

Australia

Wei Su

Martin White

Anthony Williams

Canada

Yongcheng Wu

Exploring the low  $$\tan \beta $$  <math> <mrow> <mo>tan</mo> <mi>β</mi> </mrow> </math>   region of two Higgs doublet models at the LHC

We show that the four-dimensional Chern-Simons theory studied by Costello, Witten and Yamazaki, is, with Nahm pole-type boundary conditions, dual to a boundary theory that is a three-dimensional analogue of Toda theory with a novel 3d W-algebra symmetry. By embedding four-dimensional Chern-Simons theory in a partial twist of the five-dimensional maximally supersymmetric Yang-Mills theory on a manifold with corners, we argue that this three-dimensional Toda theory is dual to a two-dimensional topological sigma model with A-branes on the moduli space of solutions to the Bogomolny equations. This furnishes a novel 3d-2d correspondence, which, among other mathematical implications, also reveals that modules of the 3d W-algebra are modules for the quantized algebra of certain holomorphic functions on the Bogomolny moduli space.

Singapore

Meer Ashwinkumar

Kee-Seng Png

Meng-Chwan Tan

4d Chern-Simons theory as a 3d Toda theory, and a 3d-2d correspondence

We present an explicit matrix algebra regularization of the algebra of volume-preserving diffeomorphisms of the n-torus. That is, we approximate the corresponding classical Nambu brackets using   <math> <mi>sl</mi> <mfenced> <msup> <mi>N</mi> <mfenced> <mfrac> <mi>n</mi> <mn>2</mn> </mfrac> </mfenced> </msup> <mi>ℂ</mi> </mfenced> </math>  $$ \mathfrak{sl}\left({N}^{\left\lceil \frac{n}{2}\right\rceil },\mathrm{\mathbb{C}}\right) $$ -matrices equipped with the finite bracket given by the completely anti-symmetrized matrix product, such that the classical brackets are retrieved in the N → ∞ limit. We then apply this approximation to the super 4-brane in 9 dimensions and give a regularized action in analogy with the matrix regularization of the supermembrane. This action exhibits a reduced gauge symmetry that we discuss from the viewpoint of L  ∞ -algebras in a slight generalization to the construction of Lie 2-algebras from Bagger-Lambert 3-algebras.

Japan

Lennart Schmidt

Matrix regularization of classical Nambu brackets and super p-branes

Reliably computing the free energy in a gauge theory like QCD is a challenging and resource-demanding endeavor. We explore the possibility to obtain the associated thermodynamic anomaly from two-point functions based on a conjectured relation. This conjecture is triggered by the relation to the Tan contact in condensed matter systems. For this investigation we use state-of-the-art results for the Yang-Mills gluon two-point function from the lattice and the functional renormalization group, as well as novel Dyson-Schwinger results at finite temperature computed in the present work. This allows for a first, qualitative, test of this conjecture. The results from all methods reveal the same nontrivial temperature behavior of the subleading large momentum dependence of the gluon propagator relevant for the conjectured relation. The comparison with the expected behavior for SU(2) Yang-Mills theory is encouraging to further pursue this approach.

Austria

Ouraman Hajizadeh

Markus Q. Huber

Axel Maas

Jan M. Pawlowski

Exploring the Tan contact term in Yang-Mills theory

We discuss various improvements of the prediction for the light MSSM Higgs boson mass in the hybrid framework of the public code  $$\texttt {FeynHiggs}$$  <math> <mi>FeynHiggs</mi> </math>  , which combines fixed-order and effective field theory results. First, we discuss the resummation of logarithmic contributions proportional to the bottom-Yukawa coupling including two-loop  $$\Delta _b$$  <math> <msub> <mi>Δ</mi> <mi>b</mi> </msub> </math>   resummation. For large  $$\tan \beta $$  <math> <mrow> <mo>tan</mo> <mi>β</mi> </mrow> </math>  , these improvements can lead to large upward shifts of the Higgs mass compared to the existing fixed-order calculations. Second, we improve the implemented EFT calculation by fully taking into account the effect of  $$\mathcal{CP}$$  <math> <mi>CP</mi> </math>  -violating phases. As a third improvement, we discuss the inclusion of partial  $$\hbox {N}^3$$  <math> <msup> <mtext>N</mtext> <mn>3</mn> </msup> </math>  LL resummation. The presented improvements will be implemented into  $$\texttt {FeynHiggs}$$  <math> <mi>FeynHiggs</mi> </math>  .

Henning Bahl

Ivan Sobolev

Georg Weiglein

The light MSSM Higgs boson mass for large  $$\tan \beta $$  <math> <mrow> <mo>tan</mo> <mi>β</mi> </mrow> </math>   and complex input parameters

In a two Higgs-doublet model with <math><msub><mi>D</mi><mn>4</mn></msub></math> flavor symmetry we establish a relation between <math><mi>tan</mi><mi>β</mi></math> and the Cabibbo angle. Due to a small number of parameters, the quark Yukawa sector of the model is very predictive. The flavor changing neutral currents are small enough to allow for relatively light nonstandard scalars to pass through the flavor constraints.

Sweden

Dipankar Das

Relating the Cabibbo angle to <math><mi>tan</mi><mi>β</mi></math> in a two Higgs-doublet model

We propose two new benchmark scenarios for Higgs-boson searches in the Minimal Supersymmetric Standard Model (MSSM ). These scenarios are specifically designed for the low $$\tan \beta $$ <math><mrow><mo>tan</mo><mi>β</mi></mrow></math>  region. A light Higgs-boson mass prediction compatible with the observed value of $$125\,\hbox {GeV}$$ <math><mrow><mn>125</mn><mspace width="0.166667em"></mspace><mtext>GeV</mtext></mrow></math>  is ensured in almost the entire parameter space by employing a flexible supersymmetric (SUSY) mass scale, reaching values of up to $$10^{16}\,\hbox {GeV}$$ <math><mrow><msup><mn>10</mn><mn>16</mn></msup><mspace width="0.166667em"></mspace><mtext>GeV</mtext></mrow></math> . The MSSM Higgs-sector predictions are evaluated in an effective field theory (EFT ) framework that exhibits a Two-Higgs-Doublet-Model at the low scale. In the first scenario all SUSY particles are relatively heavy, whereas the second scenario features light neutralinos and charginos. Both scenarios are largely compatible with the most recent results from Run 2 of the LHC , and we highlight the main phenomenological features relevant for future LHC searches. In particular, we provide a detailed discussion of heavy Higgs-boson decays to neutralinos and charginos in the second scenario, and the arising collider signatures, in order to facilitate the design of dedicated LHC searches in the near future.

Stefan Liebler

Tim Stefaniak

MSSM Higgs benchmark scenarios for Run 2 and beyond: the low $$\tan \beta $$ <math><mrow><mo>tan</mo><mi>β</mi></mrow></math>  region

We describe supersymmetric A-branes and B-branes in open <math><mrow><mi>N</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></math> dynamically gauged nonlinear sigma models (GNLSM), placing emphasis on toric manifold target spaces. For a subset of toric manifolds, these equivariant branes have a mirror description as branes in gauged Landau-Ginzburg models with neutral matter. We then study correlation functions in the topological A-twisted version of the GNLSM and identify their values with open Hamiltonian Gromov-Witten invariants. Supersymmetry breaking can occur in the A-twisted GNLSM due to nonperturbative open symplectic vortices, and we canonically Becchi-Rouet-Stora-Tyutin quantize the mirror theory to analyze this phenomenon.

Equivariant branes and equivariant homological mirror symmetry