Early theoretical studies of the two-dimensional XY model with four-fold anisotropy (XY <italic>h</italic> <inf>4</inf>) predicted that any finite anisotropy should completely suppress Kosterlitz&#8211;Thouless (KT) transition of the isotropic system and replace it with a second-order phase transition. This prediction is inconsistent with Monte Carlo (MC) simulations, which suggested KT-like behavior at weak anisotropy. To resolve this discrepancy, we performed large-scale MC simulations to systematically examine the XY <italic>h</italic> <inf>4</inf> model across a wide range of anisotropic strengths. Our results indicate that while weak anisotropy can mimic KT behavior in small systems, a detailed finite-size scaling analysis of larger systems reveals that the temperature derivative of Binder ratio and the correlation length ratio displays scaling behaviors characteristic of a second-order transition even at the weak <italic>h</italic> <inf>4</inf> values. The critical exponent <italic>&#957;</italic> is non-universal and varies continuously with <italic>h</italic> <inf>4</inf> from weak to strong anisotropy. These findings confirm that XY <italic>h</italic> <inf>4</inf> model exhibits a second-order phase transition for weak finite anisotropy, effectively reconciling theoretical predictions with numerical observations.

Vietnam

Truong Thi Bach Yen

Le Thi Thao Vien

Nguyen Tri Tuan

Dinh Manh Tien

Nguyen Duc Dung

Hoang Mai Anh

Tran Truong Giang

Nguyen Vo Nguyen Huy

Le Chi Luan

Duong Xuan Nui

Dao Xuan Viet

Monte Carlo studies of the two-dimensional XY model with four-fold anisotropy

The JUNO collaboration has released its first measurement of reactor neutrino oscillations, obtaining <math altimg='si1.svg'><mrow><mi>sin</mi><msubsup><mi>&#952;</mi><mn>12</mn><mn>2</mn></msubsup><mo linebreak='goodbreak'>=</mo><mn>0.3092</mn><mo>&#177;</mo><mn>0.0087</mn></mrow></math>, an improvement in precision by a factor of 1.6 over previous combined results. We confront the minimally modified tri-bimaximal mixing pattern with the new data. Before the measurement of a nonzero <italic>&#952;</italic> <inf>13</inf> mixing angle, the tri-bimaximal mixing pattern was one of the most popular simple mixing scheme for neutrinos. Modifications have been proposed to keep some features of tri-bimaximal mixing and make it to be consistent with data. Minimal modifications preserving one column of the tri-bimaximal mixing matrix, yielding three patterns: a) unchanged third, b) unchanged second, and c) unchanged first column. Pattern a) is excluded since it keeps <math altimg='si2.svg'><mrow><msub><mi>&#952;</mi><mn>13</mn></msub><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>. Pattern b) predicts <math altimg='si3.svg'><mrow><msub><mi>V</mi><mrow><mi>e</mi><mn>2</mn></mrow></msub><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo linebreak='goodbreak'>/</mo><msqrt><mn>3</mn></msqrt></mrow></math> and specific CP-phase correlations, but JUNO&#8217;s smaller | <italic>V</italic> <inf><italic>e</italic>2</inf>| disfavors it at more than 3.5 <italic>&#963;</italic>. Pattern c), predicting <math altimg='si4.svg'><mrow><msub><mi>V</mi><mrow><mi>e</mi><mn>2</mn></mrow></msub><mo linebreak='goodbreak'>=</mo><mi>cos</mi><mi>&#964;</mi><mo linebreak='goodbreak'>/</mo><msqrt><mn>3</mn></msqrt></mrow></math>, can be in agreement with current data within 1 <italic>&#963;</italic>. It implies <math altimg='si5.svg'><mrow><msup><mi>sin</mi><mn>2</mn></msup><msub><mi>&#952;</mi><mn>12</mn></msub><mo linebreak='goodbreak'>=</mo><mrow><mo>(</mo><mn>1</mn><mo linebreak='badbreak'>&#8722;</mo><mn>3</mn><msup><mi>sin</mi><mn>2</mn></msup><msub><mi>&#952;</mi><mn>13</mn></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>/</mo><mn>3</mn><mrow><mo>(</mo><mn>1</mn><mo linebreak='badbreak'>&#8722;</mo><msubsup><mi>sin</mi><mn>13</mn><mn>2</mn></msubsup><mo>)</mo></mrow></mrow></math> and CP violating quantity sin&#8201; <italic>&#948;<inf>CP</inf></italic>&#8239;&#8764;&#8239;&#8239;&#177;&#8239;1. The current central values of NuFIT 6.1 for neutrino mixing data indicate the model with <math altimg='si6.svg'><mrow><mi>sin</mi><msub><mi>&#948;</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo>&#8776;</mo><mo>&#8722;</mo><mn>1</mn></mrow></math> fits data better which then requires neutrino mass to the inverted hierarchy. Upcoming experiments can further test this scenario and raise the confidence level to rule in or rule out the model.

China

Xiao-Gang He

Modified tri-bimaximal neutrino mixing confronted by JUNO <italic>&#952;</italic> <inf>12</inf> measurement

In this paper, we have studied the consequences of some representative neutrino flavor-symmetry models for tri-resonant leptogenesis (which is realized by having three nearly degenerate right-handed neutrinos). To be specific, we have considered a neutrino flavor-symmetry model realizing the TM1 mixing and modular $$\textrm{A}_4$$ , $$\textrm{S}_4$$ and $$\textrm{A}_5$$ symmetry models that have a right-handed neutrino mass matrix $$M_{\textrm{R}}$$ as shown in Eq. (6) which gives three exactly degenerate right-handed neutrino masses and consequently prohibits the leptogenesis mechanism to work successfully. For these models, we study the scenario that the desired right-handed neutrino mass splittings for leptogenesis to work are generated from the renormalization-group running effects. In such a scenario, we explore the parameter space that allows for the reproduction of the observed baryon-antibaryon asymmetry of the Universe.

Zhi-Cheng Liu

Zhen-hua Zhao

Renormalization group running triggered tri-resonant leptogenesis within neutrino flavor-symmetry models

We propose a minimal, ultraviolet-complete, and renormalizable extension of the Standard Model, in which the three generations of ordinary fermions are distinguished by family-dependent hypercharges, while three right-handed neutrinos are separated by a dark gauge symmetry that is trivial for all Standard Model fields. This setup yields a fully flipped inert doublet model. The model naturally realizes a hybrid scotoseesaw mechanism that accounts for the smallness of neutrino masses and the largeness of lepton mixing. Simultaneously, it explains the stability and relic abundance of dark matter through a residual dark parity and addresses the hierarchies of charged fermion masses and the suppression of quark mixing via higher-dimensional operators involving high-scale scalar singlets and vector-like fermions. We explore the phenomenological implications of the model and derive constraints from electroweak precision tests, collider searches, flavor-changing processes, and observations of dark matter.

Duong Loi

Chile

A. Hernández

Taiwan

Van Tran

N. Duy

Tri-hypercharge versus tri-darkcharge

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.

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 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

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