We analyse dynamics of the closed Type IIA and IIB string on various tri-vector deformed background searching for signatures of integrability. Using numerical methods we construct Poincaré sections for particular embeddings of the string and show that these are not destroyed under tri-vector deformation. We find that the corresponding Lyapunov exponents decay showing that trajectories do not diverge.

Russia

Edvard Musaev

Gleb Zverev

On integrability of tri-vector deformed Type II string

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''

Abstract The first analytic expressions for one-loop-induced contributions for the decay of CP-even Higgs H → hγγ, with  being the Standard-Model-like Higgs boson within the framework of the two-Higgs doublet model, are presented in this paper. The one-loop form factors for the decay processes are written in terms of scalar one-loop Passarino–Veltman functions following the input notations of both the LoopTools and Collier packages. Subsequently, physical results for the decay processes can be generated numerically by using one of the above-mentioned packages. The analytic expressions shown in this paper are verified by several numerical checks, e.g. the ultraviolet and infrared finiteness of the one-loop amplitude. Furthermore, the amplitude satisfies the Ward identity due to on-shell photons in final states. The identity is also checked numerically in this work. In phenomenological studies, the differential decay rates for H → hγγ as a function of the invariant mass of two photons in final states are first examined in the parameter space of the two-Higgs doublet models.

Decay of CP-Even Higgs in the Two-Higgs Doublet Model: One-Loop Analytic Results and Ward Identity Checks

We extend the formalism of tri-vector deformations to the full SL(5) exceptional field theory with no truncation assumed thus covering 11D backgrounds of any form. We derive explicit transformation rules for 11D supergravity component fields and prove that these generate solutions given the same algebraic conditions hold: generalized Yang–Baxter equation and the unimodularity condition.

Sergei Barakin

Kirill Gubarev

Tri-vector deformations with external fluxes

In this work, we present the first full NLO predictions for the process pp → μ + ν  μ e+ ν ejj at the LHC in a typical tri-boson phase space. The NLO corrections reach 50% at the level of the fiducial cross section and have a very different hierarchy with respect to vector-boson-scattering phase spaces. By comparing the cross section of the full off-shell process with the sum of contributing on-shell electroweak-boson production subchannels, we find that the process is dominated by WWW and WH production, while vector-boson-scattering topologies still play a non-negligible role. In addition, NLO QCD predictions matched to parton shower which are supplemented by approximate electroweak corrections are provided. For the fiducial cross section, the electroweak corrections turn out to be small but the QCD corrections reach 47%. For the inclusive cross section, matching to parton shower affects the predictions by 7%. However, for differential distributions corrections due to the parton shower can be much more sizeable, depending on the region of phase space.

Germany

Ansgar Denner

Mathieu Pellen

United Kingdom

Marek Schönherr

Steffen Schumann

Tri-boson and WH production in the W + W + jj channel: predictions at full NLO accuracy and beyond

The tri-hypercharge proposal introduces a separate gauged weak hypercharge assigned to each fermion family as the origin of flavour. This is arguably one of the simplest setups for building “gauge non-universal theories of flavour” or “flavour deconstructed theories”. In this paper we propose and study two minimal but ultraviolet complete and renormalisable tri-hypercharge models. We show that both models, which differ only by the heavy messengers that complete the effective theory, are able to explain the observed patterns of fermion masses and mixings (including neutrinos) with all fundamental coefficients being of   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (1). In fact, both models translate the complicated flavour structure of the Standard Model into three simple physical scales above electroweak symmetry breaking, completely correlated with each other, that carry meaningful phenomenology. In particular, the heavy messenger sector determines the origin and size of fermion mixing, which controls the size and nature of the flavour-violating currents mediated by the two heavy Z′ gauge bosons of the theory. The phenomenological implications of the two minimal models are compared. In both models the lightest Z′ remains discoverable in dilepton searches at the LHC Run 3.

Mario Fernández Navarro

Stephen King

Spain

Avelino Vicente

Minimal complete tri-hypercharge theories of flavour

Abstract We present one-loop formulas for the decay of the CP-odd Higgs  with  and  in Higgs extensions of the Standard Model, considering a two Higgs doublet model with an extra complex (and real) scalar, a two Higgs doublet model as well as a triplet Higgs model. Analytic results for one-loop amplitudes are expressed in terms of the basic Passarino–Veltman functions following the standard notations of LoopTools. As a result, physical results can be generated numerically by using the package. In the phenomenological results, the total decay widths and the differential decay rates with respect to the invariant mass of a lepton pair are analyzed for two typical models such as the two Higgs doublet model and the triplet Higgs model.

One-Loop Contributions for → With ≡ And ≡ γ , in Higgs Extensions of the Standard Model

In this paper we discuss SU(5)3 with cyclic symmetry as a possible grand unified theory (GUT). The basic idea of such a tri-unification is that there is a separate SU(5) for each fermion family, with the light Higgs doublet(s) arising from the third family SU(5), providing a basis for charged fermion mass hierarchies. SU(5)3 tri-unification reconciles the idea of gauge non-universality with the idea of gauge coupling unification, opening the possibility to build consistent non-universal descriptions of Nature that are valid all the way up to the scale of grand unification. As a concrete example, we propose a grand unified embedding of the tri-hypercharge model  $${\text{U}}{\left(1\right)}_{Y}^{3}$$  based on an SU(5)3 framework with cyclic symmetry. We discuss a minimal tri-hypercharge example which can account for all the quark and lepton (including neutrino) masses and mixing parameters. We show that it is possible to unify the many gauge couplings into a single gauge coupling associated with the cyclic SU(5)3 gauge group, by assuming minimal multiplet splitting, together with a set of relatively light colour octet scalars. We also study proton decay in this example, and present the predictions for the proton lifetime in the dominant e + π 0 channel.

Mario Navarro

Tri-unification: a separate SU(5) for each fermion family

A direct investigation of the self-couplings of gauge bosons, completely described by the non-Abelian gauge symmetry of the Standard Model, is extremely valuable in understanding the gauge structure of the SM. Any deviation from the SM predictions on gauge boson self-coupling is to give a hint at the existence of a new physics beyond the SM, which is defined with a modification of the self-interactions using an effective field theory approach. In this paper, we present a detailed Monte Carlo study searching for anomalous quartic gauge dimension-8 couplings related to <math altimg='si1.svg'><mi>&#947;</mi><mi>&#947;</mi><mi>&#947;</mi><mi>&#947;</mi></math> and <math altimg='si2.svg'><mi>&#947;</mi><mi>&#947;</mi><mi>&#947;</mi><mi>Z</mi></math> vertices at the future hadron-hadron collider (FCC-hh) via tri-photon production at a 100 TeV center of mass energy with an integrated luminosity L <math altimg='si3.svg'><msub><mrow /><mrow><mi>i</mi><mi>n</mi><mi>t</mi></mrow></msub></math> =30 ab <sup>&#8722;1</sup>. Events that have been parton showered and include detector effects are analyzed with a Toolkit for Multivariate Data Analysis (TMVA) using a boosted decision tree to help distinguish between signal and background events to achieve the best sensitivities on anomalous quartic gauge couplings. Our obtained results reveal that the limits on anomalous quartic gauge couplings <math altimg='si4.svg'><msub><mrow><mi>f</mi></mrow><mrow><mi>T</mi><mn>8</mn></mrow></msub><mo stretchy='false'>/</mo><msup><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>4</mn></mrow></msup></math> and <math altimg='si5.svg'><msub><mrow><mi>f</mi></mrow><mrow><mi>T</mi><mn>9</mn></mrow></msub><mo stretchy='false'>/</mo><msup><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mn>4</mn></mrow></msup></math> at 95% C.L. without systematic errors are about three orders of magnitude stronger compared to the best current experimental limits reported by the ATLAS collaboration at the LHC. Considering a realistic systematic uncertainty such as 10% from possible experimental sources, our obtained limits of anomalous quartic couplings get worse by about one order of magnitude compared to those without systematic uncertainty but are still two orders of magnitude better than those recently reported by ATLAS.

Türkiye

A. Senol

H. Denizli

C. Helveci

Sensitivity of anomalous quartic gauge couplings via tri-photon production at FCC-hh

We search for tri-nucleon decays of  $$^{76}$$  <math> <msup> <mrow></mrow> <mn>76</mn> </msup> </math>  Ge in the dataset from the GERmanium Detector Array (GERDA) experiment. Decays that populate excited levels of the daughter nucleus above the threshold for particle emission lead to disintegration and are not considered. The ppp-, ppn-, and pnn-decays lead to  $$^{73}$$  <math> <msup> <mrow></mrow> <mn>73</mn> </msup> </math>  Cu,  $$^{73}$$  <math> <msup> <mrow></mrow> <mn>73</mn> </msup> </math>  Zn, and  $$^{73}$$  <math> <msup> <mrow></mrow> <mn>73</mn> </msup> </math>  Ga nuclei, respectively. These nuclei are unstable and eventually proceed by the beta decay of  $$^{73}$$  <math> <msup> <mrow></mrow> <mn>73</mn> </msup> </math>  Ga to  $$^{73}$$  <math> <msup> <mrow></mrow> <mn>73</mn> </msup> </math>  Ge (stable). We search for the  $$^{73}$$  <math> <msup> <mrow></mrow> <mn>73</mn> </msup> </math>  Ga decay exploiting the fact that it dominantly populates the 66.7 keV  $$^{73m}$$  <math> <msup> <mrow></mrow> <mrow> <mn>73</mn> <mi>m</mi> </mrow> </msup> </math>  Ga state with half-life of 0.5 s. The nnn-decays of  $$^{76}$$  <math> <msup> <mrow></mrow> <mn>76</mn> </msup> </math>  Ge that proceed via  $$^{73m}$$  <math> <msup> <mrow></mrow> <mrow> <mn>73</mn> <mi>m</mi> </mrow> </msup> </math>  Ge are also included in our analysis. We find no signal candidate and place a limit on the sum of the decay widths of the inclusive tri-nucleon decays that corresponds to a lower lifetime limit of 1.2 $$\times $$  <math> <mo>×</mo> </math>  10 $$^{26}$$  <math> <msup> <mrow></mrow> <mn>26</mn> </msup> </math>   yr (90% credible interval). This result improves previous limits for tri-nucleon decays by one to three orders of magnitude.

M. Agostini

A. Alexander

Switzerland

G. Araujo

A. Bakalyarov

Italy

M. Balata

I. Barabanov

L. Baudis

C. Bauer

S. Belogurov

A. Bettini

L. Bezrukov

V. Biancacci

E. Bossio

V. Bothe

R. Brugnera

A. Caldwell

S. Calgaro

C. Cattadori

A. Chernogorov

P.J. Chiu

T. Comellato

V. D’Andrea

E. Demidova

A. Giacinto

N. Marco

E. Doroshkevich

F. Fischer

JINR

M. Fomina

A. Gangapshev

A. Garfagnini

C. Gooch

P. Grabmayr

V. Gurentsov

K. Gusev

United States

J. Hakenmüller

S. Hemmer

W. Hofmann

Belgium

M. Hult

L. Inzhechik

J. Janicskó Csáthy

J. Jochum

M. Junker

V. Kazalov

Y. Kermaïdic

H. Khushbakht

T. Kihm

K. Kilgus

I. Kirpichnikov

A. Klimenko

K. Knöpfle

O. Kochetov

V. Kornoukhov

P. Krause

V. Kuzminov

M. Laubenstein

M. Lindner

I. Lippi

A. Lubashevskiy

B. Lubsandorzhiev

G. Lutter

C. Macolino

B. Majorovits

W. Maneschg

L. Manzanillas

G. Marshall

Poland

M. Misiaszek

M. Morella

Y. Müller

I. Nemchenok

M. Neuberger

L. Pandola

K. Pelczar

L. Pertoldi

P. Piseri

A. Pullia

L. Rauscher

M. Redchuk

S. Riboldi

N. Rumyantseva

C. Sada

S. Sailer

F. Salamida

S. Schönert

J. Schreiner

M. Schütt

A.K. Schütz

O. Schulz

M. Schwarz

B. Schwingenheuer

O. Selivanenko

E. Shevchik

M. Shirchenko

L. Shtembari

H. Simgen

A. Smolnikov

D. Stukov

S. Sullivan

A. Vasenko

A. Veresnikova

C. Vignoli

Search for tri-nucleon decays of  $$^{76}$$  <math> <msup> <mrow></mrow> <mn>76</mn> </msup> </math>  Ge in GERDA