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''

<p>The violation of the Lam-Tung relation in the high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>p</mi><mi>T</mi><mrow><mo>ℓ</mo><mo>ℓ</mo></mrow></msubsup></math> region of the Drell-Yan process at the LHC presents a longstanding discrepancy with the standard model prediction at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>3</mn></msubsup><mo stretchy="false">)</mo></math> accuracy. In this paper, we employed a model-independent analysis to investigate this phenomenon within the framework of the standard model effective field theory (SMEFT). Our findings revealed that the leading contributions from SMEFT to this violation appear at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msup><mi mathvariant="normal">Λ</mi><mn>4</mn></msup></math> order with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">)</mo></math> accuracy in quantum chromodynamics (QCD) interaction. Notably, we demonstrated that the quadratic effect of dimension-6 dipole operators, associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson, dominates the breaking effects induced by various dimension-6 and dimension-8 operators. This provides a possible explanation for the observed discrepancy with the Standard Model predictions at the LHC. Furthermore, the breaking effects could also serve as a powerful tool for constraining <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>-boson dipole interactions, highlighting their importance among potential sources of new physics in the Drell-Yan process.</p>

China

Xu Li

Bin Yan

United States

C.P. Yuan

Lam-Tung relation breaking in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson production as a probe of standard model effective field theory effects

We show that chiral higher-spin gravity with a vanishing cosmological constant admits a class of exact self-dual pp-wave solutions derived from harmonic scalar functions and two principal spinors. These solutions satisfy both the linear and non-linear equations of motion, as they annihilate all higher-order vertices, leading to the equations of motion for free fields on a self-dual background sourced by a positive-helicity spin-2 field. Our method employs a simple Kerr-Schild ansatz for positive-helicity chiral higher-spin fields adapted to the self-dual gravity framework.

South Korea

Tung Tran

Self-dual pp-wave solutions in chiral higher-spin gravity

We elaborate further on the one-loop effective action of the IKKT model on 3 + 1 dimensional covariant quantum spacetime in the presence of fuzzy extra dimensions. In particular, we describe the one-loop effective action in terms of a remarkable SO(1, 9) character, which allows to evaluate the pertinent traces over the internal modes explicitly. This also allows to estimate the higher-order contributions (in the internal flux $$ {\mathcal{F}}_{\textrm{IJ}} $$ ) to the one-loop effective action in a systematic way. We show that all higher-order contributions are generally suppressed and UV finite, which justifies the previous treatment of the induced gravitational action. We also obtain explicit expressions for the effective Newton constant, and determine the dynamics of the Kaluza-Klein scale $$ {\Delta }_{\mathcal{K}} $$ of the fuzzy extra dimensions $$ \mathcal{K} $$ .

Austria

Alessandro Manta

Harold Steinacker

$$ \mathfrak{hs} $$ -extended gravity from the IKKT matrix model

We study the interactions of the higher-spin gauge theory arising from the IKKT matrix model on a covariant quantum FLRW quantum space-time <math><msubsup><mrow><mi>M</mi></mrow><mrow><mi>J</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msubsup></math>, denoted as HS-IKKT. In particular, we elaborate some of the vertices and observe that they are not manifestly Lorentz invariant in the unitary formulation. We argue that Lorentz invariance of HS-IKKT can be recovered since Lorentz transformations are part of the gauge invariance in the covariant formulation. This statement is verified for some vertices with lowest number of derivatives. The lowest-derivative sector of this theory is expected to be governed by an “almost”-Lorentz-invariant Yang-Mills theory coupled to emergent gravity.

Harold C. Steinacker

Interactions in the IKKT matrix model on covariant quantum spacetime

We study the one-loop effective action of the higher-spin gauge theory induced by the IKKT matrix model on a <math><msup><mrow><mi>M</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msup><mo>×</mo><mi>K</mi></math> background, where <math><msup><mrow><mi>M</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msup></math> is an FLRW cosmological spacetime brane and <math><mi>K</mi></math> are compact fuzzy extra dimensions. In particular, we show that all non-abelian (<math><mi>hs</mi></math>-valued) gauge fields in this model acquire mass via quantum effects, thus avoiding no-go theorems. This leads to a massive non-abelian quantum <math><mi>hs</mi></math>-Yang-Mills theory, whose detailed structure depends on <math><mi>K</mi></math>. The stabilization of <math><mi>K</mi></math> at one loop is understood as a result of the coupling between <math><mi>K</mi></math> and the <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>-flux bundle on space-time. This flux stabilization induces the KK scale into the <math><mi>N</mi><mo>=</mo><mn>4</mn></math> SYM sector of the model, which break superconformal symmetry.

Quantum -Yang-Mills from the IKKT matrix model

We introduce a novel spinorial description for the higher-spin gauge theory induced by the IKKT matrix model on an FLRW spacetime with Lorentzian signature, called Lorentzian   <math> <mi>hs</mi> </math>  $$ \mathfrak{hs} $$ -IKKT theory. The new description is based on Weyl spinors transforming under the space-like isometry subgroup SL(2, ℂ) of the structure group SO(2, 4) ≃ SU(2, 2). It allows us to exploit the full power of the spinor formalism in Lorentzian signature, in contrast to a previous formalism based on the compact subgroup SU(2) L  × SU(2) R  of SU(2, 2). Some cubic vertices of the Yang-Mills sector and the corresponding scattering amplitudes are computed. We observe that the n-point (for n ≥ 4) tree-level amplitudes are typically non-trivial on-shell, but exponentially suppressed in the late-time regime. While Lorentz invariance of the higher-spin amplitudes is not manifest, it is expected to be restored by higher-spin gauge invariance.

Spinorial description for Lorentzian   <math> <mi>hs</mi> </math>  $$ \mathfrak{hs} $$ -IKKT

We explore the semi-classical relation between the fuzzy 4-hyperboloid   <math> <msubsup> <mi>H</mi> <mi>N</mi> <mn>4</mn> </msubsup> </math>  $$ {H}_N^4 $$  and non-compact quantized twistor space   <math> <msubsup> <mi>ℙ</mi> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msubsup> </math>  $$ {\mathbb{P}}_N^{1,2} $$  at large N. This provides two backgrounds of the IKKT matrix model via two natural stereographic projections, leading to higher-spin gauge theories with Euclidean and Minkowski signature denoted by HS-IKKT. The resulting higher-spin gauge theory can be understood as an uplift of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills to twistor space. The action of HS-IKKT is written using a spinor formalism in both in Euclidean and Minkowski signature. We then compute the tree-level amplitudes of the massless sector within the Yang-Mills part of the HS-IKKT model in the flat limit in Euclidean signature. All n-point tree-level scattering amplitudes for n ≥ 4 of this sector are found to vanish in the flat limit.

Belgium

Spinorial higher-spin gauge theory from IKKT model in Euclidean and Minkowski signatures

A covariant twistor action for chiral higher-spin theory in anti–de Sitter and flat space is constructed in term of a holomorphic Chern-Simons theory on twistor space. The action reproduces all known cubic vertices of chiral higher-spin theory in flat space. The spacetime action of the holomorphic Chern-Simons theory in flat space is also obtained.

Toward a twistor action for chiral higher-spin gravity

There are various no-go theorems that tightly constrain the existence of local higher-spin theories with non-trivial S-matrix in flat space. Due to the existence of higher-spin Yang-Mills theory with non-trivial scattering amplitudes, it makes sense to revisit Weinberg’s soft theorem — a direct consequence of the Lorentz invariance of the S-matrix that does not take advantage of unitarity and parity invariance. By working with the chiral representation — a representation originated from twistor theory, we show that Weinberg’s soft theorem can be evaded and non-trivial higher-spin S-matrix is possible. In particular, we show that Weinberg’s soft theorem is more closely related to the number of derivatives in the interactions rather than spins. We also observe that all constraints imposed by gauge invariance of the S-matrix are accompanied by polynomials in the soft momentum of the emitted particle where the zeroth order in the soft momentum is a charge conservation law.