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''

We revisit a theory that proposes a dark charge, <math><mi>D</mi></math>, as a dequantization of the electric charge, <math><mrow><mi>Q</mi></mrow></math>. We find that the general arguments of anomaly cancellation and fermion mass generation yield both <math><mi>D</mi></math> and <math><mi>Q</mi></math>, nontrivially unified with the weak isospin <math><msub><mi>T</mi><mi>i</mi></msub></math> <math><mo>(</mo><mi>i</mi><mo>=</mo><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow><mo>)</mo></math> in a novel gauge symmetry, <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>C</mi></mrow></msub><mo>⊗</mo><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>L</mi></mrow></msub><mo>⊗</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>Y</mi></mrow></msub><mo>⊗</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>N</mi></mrow></msub></mrow></math>, where <math><mi>Y</mi></math> and <math><mi>N</mi></math> determine <math><mi>Q</mi></math> and <math><mi>D</mi></math> through the <math><msub><mi>T</mi><mn>3</mn></msub></math> operator, i.e., <math><mi>Q</mi><mo>=</mo><msub><mi>T</mi><mn>3</mn></msub><mo>+</mo><mi>Y</mi></math> and <math><mi>D</mi><mo>=</mo><msub><mi>T</mi><mn>3</mn></msub><mo>+</mo><mi>N</mi></math>, respectively. A new observation is that fundamental particles possess a dynamical dark charge, which governs both neutrino mass and dark matter, where the neutrino mass is determined via a canonical seesaw, while the dark matter stability is ensured by electric and color charge conservations. We examine the mass spectra of fermions, scalars, and gauge bosons, as well as their interactions, taking into account the kinetic mixing effect of <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>Y</mi><mo>,</mo><mi>N</mi></mrow></msub></math> gauge fields. The new physics phenomena at colliders are examined. The dark matter relic density and detection are discussed.

Duong Van Loi

Cao H. Nam

Ngo Hai Tan

Phung Van Dong

Dark charge versus electric charge

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

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

In the Minimal Supersymmetric Standard Model (MSSM) searches for the heaviest CP-even and CP-odd Higgs H , A to tau-lepton pairs severely constrain the parameter region for large values of tan β and light Higgs bosons H , A . We demonstrate how the experimental constraint can be avoided by new decays to light third-generation sfermions, whose left-right couplings to H can be maximised in regions of large trilinear couplings A b , A τ for sbottoms and staus, or large supersymmetric (SUSY) Higgs mass μ for stops. Due to the tan β -enhancement in the production cross-sections via gluon-fusion and in association with bottom-quark pairs for H and A , we find that down-type sfermions, in particular, sbottoms perform a better job in allowing more parameter space than up-type sfermions such as stops, which require much larger values of μ to compensate for tan β . Vacuum stability as well as flavour observables constraints and direct searches for SUSY particles are imposed. We also associate the lightest CP-even Higgs with the observed 125 GeV SM-like Higgs and impose the experimental constraints from the LHC.

France

Argentina

Anibal Medina

Michael Schmidt

Enlarging regions of the MSSM parameter space for large tan β via SUSY decays of the heavy Higgs bosons

We present strategies to search for heavy neutral Higgs bosons decaying to top quark pairs, as often occurs at low tan β in type II two Higgs doublet models such as the Higgs sector of the MSSM. The resonant production channel is unsatisfactory due to interference with the SM background. We instead propose to utilize same-sign dilepton signatures arising from the production of heavy Higgs bosons in association with one or two top quarks and subsequent decay to a top pair. We find that for heavier neutral Higgs bosons the production in association with one top quark provides greater sensitivity than production in association with two top quarks. We obtain current limits at the LHC using Run I data at 8 TeV and forecast the sensitivity of a dedicated analysis during Run II at 14 TeV. Then we perform a detailed BDT study for the 14 TeV LHC and a future 100 TeV collider.