<p>We develop the method adjusting the Faddeev-Popov factorization procedure for the quantization of generic reducible gauge theories with linearly dependent generators and apply it to the first stage reducible model of second rank antisymmetric fermion in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math>-dimensional anti–de Sitter (AdS) spacetime. The method consists of nested factorizations of the gauge group volume for the determination of the consistently defined delta function of reduced gauge conditions, group integration measure, and gauge-fixed contribution of ghosts. It is compared to the Batalin-Vilkovisky (BV) formalism of quantizing theories with linearly dependent generators and shown to be equivalent to it for first stage reducible theories. Nevertheless, the method under consideration, unlike the BV formalism, from the very beginning leads to the functional integral with fewer number of ghosts. Using this method, we quantized the variant of fermionic totally antisymmetric tensor-spinor theory in AdS space and derived its effective action in terms of the functional determinants of special Dirac-type operators. Limitations of the method are also discussed along with the prospects of its extension to higher reducibility stages and higher rank models of antisymmetric fermions.</p>

Russia

Andrei Barvinsky

JINR

Ioseph Buchbinder

Vladimir Krykhtin

Dmitry Nesterov

Adjustment of Faddeev-Popov quantization to reducible gauge theories: Antisymmetric tensor fermion in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></math> space

The present work extends scotogenic and its modular <math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math> variation a step forward and demonstrates scotogenic modular <math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math> non-supersymmetric realization. To achieve this non-holomorphic modular symmetries come to rescue. Advantage of the current construction is the compactness of the model content and absence of the supersymmetric fields. Neutrino mass is generated through a canonical scotogenic mechanism. The allowed values of the VEV of the τ modulus are <math><mi>τ</mi><mo>≃</mo><mi>w</mi></math> and Im<math><mo>[</mo><mi>τ</mi><mo>]</mo><mo>≈</mo><mn>2</mn></math>. The non-holomorphic modular <math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math> symmetry leads to correlations among the neutrino observables.

China

Takaaki Nomura

Hiroshi Okada

Oleg Popov

Non-holomorphic modular Symmetric Scotogenic Model

The current article presents an extension of the classical scotogenic neutrino mass paradigm, where the three issues in particle physics: dark matter, smallness of neutrino mass, and stability of the proton are interconnected. The scenario encompasses the neutrino mass as well as the proton decay as a consequence of an existence of the dark matter. The study successfully achieves the correlation between the naturally small neutrino masses and naturally long proton lifetime in the present paradigm. Furthermore, all relevant cosmological, collider, and flavor physics constraints are incorporated in the detailed analysis. The scotogenic fermionic dark matter with the mass in the range from 100 GeV to 10 TeV successfully satisfies all relevant constraints. The valid range of <math><mn>2.51</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><mo>&lt;</mo><mi>λ</mi><mo>&lt;</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> is obtained for the 2HDM <math><mi>λ</mi></math> coupling. We give a brief discussion, as well as outline some of the future prospects.

Extended scotogenic model of neutrino mass and proton decay

Modular symmetries offer a dynamic approach to understanding the flavor structure of leptonic mixing. Using the modular <math><msub><mi>A</mi><mn>4</mn></msub></math> flavor symmetry integrated in a type-II seesaw, we propose a simple and minimalistic model that restricts the neutrino oscillation parameter space and, most importantly, introduces a sum rule in the physical neutrino masses. When combined with the mass squared differences observed in neutrino oscillations, this sum rule determines the absolute neutrino mass scale. This has significant implications for cosmology, neutrinoless double beta decay experiments, and direct neutrino mass measurements. In particular, the model predicts <math><msub><mo>∑</mo><mi>i</mi></msub><msub><mi>m</mi><mi>i</mi></msub><mo>≈</mo><mn>0.1</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></math> for both normal and inverted ordering, and thus can be fully probed by the current generation of cosmological probes in the upcoming years.

Germany

Salvador Centelles Chuliá

India

Ranjeet Kumar

Rahul Srivastava

Neutrino mass sum rules from modular <math><msub><mi>A</mi><mn>4</mn></msub></math> symmetry

In the present letter, a Dirac neutrino mass model is presented in the view of the new result on W boson mass of <math><msubsup><mrow><mi>m</mi></mrow><mrow><mi>W</mi></mrow><mrow><mi>C</mi><mi>D</mi><mi>F</mi><mo>−</mo><mi>I</mi><mi>I</mi></mrow></msubsup><mo>=</mo><mn>80.4335</mn><mo>±</mo><mn>0.0094</mn></math> GeV, recently reported by the CDF-II experimental collaboration. The newly measured value of the W mass anomaly shows a 7-σ deviation from that predicted by the standard model. The model explains the CDF-II W boson mass anomaly by extending the standard model with hypercharge zero vector-like fermion triplet. Symmetry is amended with a global <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> which is broken with an hypercharge zero electroweak triplet. It is demonstrated that the model can successfully explain CDF-II result, Dirac neutrino mass origin, while satisfying standard model precision constraints and collider constraints with scalar and fermion triplet masses in the ranger 1.4 TeV−5.2 TeV and 100 TeV <math><mo>−</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>13</mn></mrow></msup></math> GeV, respectively.

South Korea

The triplet Dirac seesaw in the view of the recent CDF-II W mass anomaly

The goal of this work is to find the simplest UV completion of Accidental Composite Dark Matter Models (ACDM) that can dynamically generate an asymmetry for the DM candidate, the lightest dark baryon (DCb), and simultaneously annihilate the symmetric component. In this framework the DCb is a bound state of a confining SU(N)DC gauge group, and can interact weakly with the visible sector. The constituents of the DCb can possess non-trivial charges under the Standard Model gauge group. The generation of asymmetry for such candidate is a two-flavor variation of the out-of-equilibrium decay of a heavy scalar, with mass M  ϕ  ≳ 1010 GeV. Below the scale of the scalars, the models recover accidental stability, or long-livedness, of the DM candidate. The symmetric component is annihilated by residual confined interactions provided that the mass of the DCb m DCb ≲ 75 TeV. We implement the mechanism of asymmetry generation, or a variation of it, in all the original ACDM models, managing to generate the correct asymmetry for DCb of masses in this range. For some of the models found, the stability of the DM candidate is not spoiled even considering generic GUT completions or asymmetry generation mechanisms in the visible sector.

Italy

Salvatore Bottaro

Marco Costa

Asymmetric accidental composite dark matter

We propose a minimal extension of the Standard Model where neutrino masses are generated radiatively at one-loop level via Scotogenic scenario. The model is augmented with <math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math> modular symmetry as a scotogenic and flavor symmetry. With minimal number of parameters, the model makes predictions for neutrino oscillation data, Majorana and Dirac phases, dark matter characteristics, and neutrinoless double beta decay.

A modular Symmetric Scotogenic Model

The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point. In this note, we consider a doubled and at the same time gauged particle action, and show that its BRST formulation including Faddeev-Popov ghosts matches with the graded Poisson geometry that has been recently used to describe the symmetries of Double Field Theory. Besides, by requiring target spacetime diffeomorphisms at the quantum level, we derive quantum corrections to the classical action involving dilaton, which might be comparable with the Fradkin-Tseytlin term on string worldsheet.

Thomas Basile

Euihun Joung

Jeong-Hyuck Park

A note on Faddeev-Popov action for doubled-yet-gauged particle and graded Poisson geometry

Dark matter stability can result from a residual matter-parity symmetry, following naturally from the spontaneous breaking of the gauge symmetry. Here we explore this idea in the context of the <math><mi>SU</mi><msub><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mrow><mi>c</mi></mrow></msub><mo>⊗</mo><mi>SU</mi><msub><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mrow><mi>L</mi></mrow></msub><mo>⊗</mo><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub><mo>⊗</mo><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>N</mi></mrow></msub></math> electroweak extension of the standard model. The key feature of our new scotogenic dark matter theory is the use of a triplet scalar boson with anti-symmetric Yukawa couplings. This naturally implies that one of the light neutrinos is massless and, as a result, there is a lower bound for the <math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math> decay rate.

Brazil

Spain

Julio Leite

José W.F. Valle

A theory for scotogenic dark matter stabilised by residual gauge symmetry

We propose that neutrino Dirac masses can be generated through a scotogenic scenario while violating the lepton number by four units by extending the standard model to have an anomaly free <math><mrow><mi>U</mi><mo>(</mo><mn>1</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></mrow></math>, which is spontaneously broken to a residual <math><msub><mi>Z</mi><mn>4</mn></msub></math> symmetry. <math><msub><mi>Z</mi><mn>4</mn></msub></math> symmetry ensures the Dirac nature of neutrinos and simultaneously stabilizes dark matter. Although neutrinoless double beta decay is exactly absent, this model predicts a nonzero neutrinoless quadruple beta decay (<math><mn>0</mn><mi>ν</mi><mn>4</mn><mi>β</mi></math>). It is shown that the <math><mn>0</mn><mi>ν</mi><mn>4</mn><mi>β</mi></math> can be enhanced thanks to the introduction of a new scalar field without affecting tiny neutrino masses and the relic density of dark matter. We perform numerical analysis for a <math><mn>0</mn><mi>ν</mi><mn>4</mn><mi>β</mi></math>, dark matter, and direct detection by imposing cosmological, collider, and theoretical constraints.

Arnab Dasgupta

Sin Kyu Kang

Radiative Dirac neutrino mass, neutrinoless quadruple beta decay, and dark matter in <math><mi>B</mi><mo>−</mo><mi>L</mi></math> extension of the standard model