<p>We have investigated the prospects of probing the five-dimensional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> interactions in present and future muon dump experiments, namely, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>NA</mi><mn>6</mn><msub><mn>4</mn><mi>μ</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">M</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math>, MuSIC, and a future muon beam dump experiment. These experiments are classified into two categories: the first two can probe processes where feebly interacting massive particles go into invisible channels, while the latter two can probe processes where these states decay into muon pairs. These two types of experiments are complementary in that they allow exploration of different parameter regions of a model. In our scenario, the presence of multiple massive gauge bosons as Kaluza-Klein (KK) particles leads to an enhancement in the signal events compared to the corresponding four-dimensional scenario. In particular, the decay process into muon pairs enables mass reconstruction of the parent particle, making it possible to directly demonstrate the existence of multiple KK particles in at least some parameter regions. This can provide clear evidence that the origin of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> interaction lies in five dimensions. Furthermore, the muon (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>) value, which is now consistent with the Standard Model, can be used to exclude specific parameter regions for new particles interacting with muons. We also carefully discuss the nontrivial effects arising from nonzero kinetic mixing.</p>

India

Dibyendu Chakraborty

Arindam Chatterjee

Ayushi Kaushik

Kenji Nishiwaki

Muon beam dump experiments probe five-dimensional nature of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math>

<p>We propose a new scotogenic type model based on a global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>4</mn></msub></math> symmetry involving dark matter candidates. After the symmetry breaking as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>4</mn></msub></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>2</mn></msub></math> via the singlet scalar vacuum expectation value (VEV), the lightest Majorana fermion works as a viable thermal freeze-out dark matter (DM) candidate, and the mass terms for active neutrinos are generated as a finite quantum correction at the one-loop level. A key point of realizing our scotogenic structure is to introduce two types of Majorana fermions (heavy right-handed neutrinos) and inert Higgs doublets with opposite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>4</mn></msub></math> parities. Since a large VEV for the singlet scalar is not so harmful in an appropriate realization of the Higgs mechanism for the SM gauge symmetry, we can naturally realize a TeV-scale fermionic DM candidate, where constraints via direct detection experiments are less than those for sub-TeV DM. Our scenario involves the Higgs-portal DM interactions, which help the realization of the correct DM relic abundance. Relying on the structure of the model, it is possible to find a natural partner for coannihilation. Our scenario can be investigated via the measurement of the Higgs trilinear self-coupling at the Large Hadron Collider. The simplest way to evade the domain-wall problem, by adding a tiny soft <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>2</mn></msub></math> breaking term, works, keeping a sufficient longevity of the decaying DM lifetime.</p>

Noel Jonathan Jobu

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>4</mn></msub></math> scotogenic model with a Higgs portal

We discuss the future prospects of a minimally five-dimensional version of the well-motivated scenario for addressing the discrepancy in the muon anomalous magnetic moment, the <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> extension of the standard model gauge symmetry. Here, multiple associated massive gauge bosons appear thanks to the five-dimensional <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> gauge symmetry, and they contribute to the muon (<math><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>) and also other processes. We focus on the powerful probe of elastic neutrino-electron scatterings since the upcoming DUNE experiment will explore MeV-scale uncharted regions by previous experiments (e.g., CHARM-II and Borexino) in the near future. We found that even with small kinetic mixing parameters, much of the parameter space, including those satisfying the muon (<math><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>) process, can be probed using several years of data from the DUNE experiment, focusing on the near detector. In our scenario, interference effects between intermediate-state gauge bosons play an important role. Our results include comparisons between flat and warped extra dimensions.

Prospects of five-dimensional <math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>−</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math> gauge interactions in the light of elastic neutrino-electron scatterings: The scope of the DUNE near detector

We report calculations of a wave-packet amplitude of the two-body scattering <math><mi>ϕ</mi><mi>ϕ</mi><mo>→</mo><mi>Φ</mi><mo>→</mo><mi>ϕ</mi><mi>ϕ</mi></math>, which leads to the measured probability in realistic experiments. We elucidate the decay amplitude of <math><mi>Φ</mi><mo>→</mo><mi>ϕ</mi><mi>ϕ</mi></math> from this. In such an amplitude of wave packets, there are in and out time boundaries for the initial <math><mi>Φ</mi></math> and final <math><mi>ϕ</mi><mi>ϕ</mi></math> configurations, respectively. In this paper, we prove that the effect of the in time boundary of <math><mi>Φ</mi><mo>→</mo><mi>ϕ</mi><mi>ϕ</mi></math> emerges from <math><mi>ϕ</mi><mi>ϕ</mi><mo>→</mo><mi>Φ</mi><mo>→</mo><mi>ϕ</mi><mi>ϕ</mi></math> without assuming any time boundary a priori. This effect has been overlooked in the standard plane-wave formulation and can exhibit distinct phenomena in wide areas of science. We confirm the result in different integration orders. The result is also interpreted as a Stokes phenomenon in the Lefschetz-thimble decomposition.

Japan

Kenzo Ishikawa

Kin-ya Oda

New effect in wave-packet scattering of quantum fields

There is a long-standing anomaly in the ratio of the decay width for  $$\psi (3770)\rightarrow D^0\overline{D^0}$$  <math> <mrow> <mi>ψ</mi> <mrow> <mo>(</mo> <mn>3770</mn> <mo>)</mo> </mrow> <mo>→</mo> <msup> <mi>D</mi> <mn>0</mn> </msup> <mover> <msup> <mi>D</mi> <mn>0</mn> </msup> <mo>¯</mo> </mover> </mrow> </math>   to that for  $$\psi (3770)\rightarrow D^+D^-$$  <math> <mrow> <mi>ψ</mi> <mrow> <mo>(</mo> <mn>3770</mn> <mo>)</mo> </mrow> <mo>→</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <msup> <mi>D</mi> <mo>-</mo> </msup> </mrow> </math>   at the level of  $$9.5\,\sigma $$  <math> <mrow> <mn>9.5</mn> <mspace width="0.166667em"></mspace> <mi>σ</mi> </mrow> </math>  . A similar anomaly exists for the ratio of  $$\phi (1020)\rightarrow K_\text {L}^0K_\text {S}^0$$  <math> <mrow> <mi>ϕ</mi> <mrow> <mo>(</mo> <mn>1020</mn> <mo>)</mo> </mrow> <mo>→</mo> <msubsup> <mi>K</mi> <mtext>L</mtext> <mn>0</mn> </msubsup> <msubsup> <mi>K</mi> <mtext>S</mtext> <mn>0</mn> </msubsup> </mrow> </math>   to  $$\phi (1020)\rightarrow K^+K^-$$  <math> <mrow> <mi>ϕ</mi> <mrow> <mo>(</mo> <mn>1020</mn> <mo>)</mo> </mrow> <mo>→</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>K</mi> <mo>-</mo> </msup> </mrow> </math>   at  $$2.1\,\sigma $$  <math> <mrow> <mn>2.1</mn> <mspace width="0.166667em"></mspace> <mi>σ</mi> </mrow> </math>  . In this study, we reassess the anomaly through the lens of a Gaussian wave-packet formalism. Our comprehensive calculations include the localization of the overlap of the wave packets near the mass thresholds and the composite nature of the initial-state vector mesons. The results align within a  $$\sim 1 \sigma $$  <math> <mrow> <mo>∼</mo> <mn>1</mn> <mi>σ</mi> </mrow> </math>   confidence level with the Particle Data Group’s central values for a physically reasonable value of the form-factor parameter, indicating a resolution to these anomalies. We also check the deviation of a wave-packet resonance from the Briet–Wigner shape and find that wide ranges of the wave-packet size are consistent with the experimental data.

Osamu Jinnouchi

Wave-packet effects: a solution for isospin anomalies in vector-meson decay

The gauge-invariant two-point function of the Higgs field at the same spacetime point can make a natural gauge-invariant order parameter for spontaneous gauge symmetry breaking. However, this composite operator is ultraviolet divergent and is not well defined. We propose using a gradient flow to cure the divergence from putting the fields at the same spacetime point. As a first step, we compute it for the Abelian Higgs model with a positive mass squared at the one-loop order in the continuum theory using the saddle-point method to estimate the finite part. The order parameter consistently goes to zero in the infrared limit of the infinite flow time.

Kengo Kikuchi

Gradient-flowed order parameter for spontaneous gauge symmetry breaking

Abstract We compute an -channel  scalar scattering  in the Gaussian wave-packet formalism at the tree level. We find that wave-packet effects, including shifts of the pole and the width of the propagator of , persist even when we do not take into account the time boundary effect for  proposed earlier. An interpretation of the result is that a heavy scalar  decay , taking into account the production of , does not exhibit the in-state time boundary effect unless we further take into account in-boundary effects for the  scattering. We also show various plane-wave limits.

Scalar scattering amplitude in the Gaussian wave-packet formalism

Abstract We show that the observed quark/lepton mass hierarchy can be realized dynamically on an interval extra dimension with point interactions. In our model, the positions of the point interactions play a crucial role in controlling the quark/lepton mass hierarchy and are determined by the minimization of the Casimir energy. By use of the exact extra-dimensional coordinate-dependent vacuum expectation value of a gauge-singlet scalar, we find that there is a parameter set, where the positions of the point interactions are stabilized and fixed, which can reproduce the experimental values of the quark masses precisely enough, while the charged lepton part is less relevant. We also show that possible mixings among the charged leptons will improve the situation significantly.

Yukihiro Fujimoto

Kouhei Hasegawa

Croatia

Makoto Sakamoto

Kazunori Takenaga

Pedro Hugo Tanaka

Inori Ueba

Dynamical generation of quark/lepton mass hierarchy in an extra dimension

A new realization of extended quantum-mechanical supersymmetry (QM SUSY) with central extension is investigated. We first show that two different sets of <math><mi>d</mi><mo>+</mo><mn>2</mn></math> (<math><mi>d</mi><mo>+</mo><mn>1</mn></math>) supercharges for <math><mrow><mi>d</mi><mo>=</mo><mi>even</mi></mrow></math> (odd), each of which satisfies an <math><mi>N</mi><mo>=</mo><mi>d</mi><mo>+</mo><mn>2</mn></math> (<math><mi>d</mi><mo>+</mo><mn>1</mn></math>) extended QM SUSY algebra without central extension, are hidden in the four-dimensional mass spectrum of the (<math><mrow><mn>4</mn><mo>+</mo><mi>d</mi></mrow></math>)-dimensional Dirac action. We then find that the whole set of the supercharges forms an <math><mi>N</mi><mo>=</mo><mn>2</mn><mi>d</mi><mo>+</mo><mn>4</mn></math> (<math><mn>2</mn><mi>d</mi><mo>+</mo><mn>2</mn></math>) extended QM SUSY algebra with central charges for <math><mrow><mi>d</mi><mo>=</mo><mi>even</mi></mrow></math> (odd). The representation of the supersymmetry algebra is shown to be <math><mn>1</mn><mo>/</mo><mn>2</mn></math>-Bogomol’nyi-Prasad-Sommerfield states that correspond to a short representation for the supersymmetry algebra with a central extension. We explicitly examine the four-dimensional mass spectrum of the models with the hyperrectangle and the torus extra dimensions, and discuss their supersymmetric structures.

South Korea

Kentaro Tatsumi

Extended supersymmetry with central charges in higher dimensional Dirac action

We address the presently reported significant flavor anomalies in the Kaon and B meson systems such as the CP violating Kaon decay (ϵ′/ϵ) and lepton-flavor universality violation in B meson decays   <math> <mfenced> <mrow> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>*</mo> </mfenced> </msup> </msub> <mo>,</mo> <mspace width="0.25em"></mspace> <msub> <mi>R</mi> <msup> <mi>D</mi> <mfenced> <mo>*</mo> </mfenced> </msup> </msub> </mrow> </mfenced> </math>  $$ \left({R}_{K^{\left(*\right)}},\ {R}_{D^{\left(*\right)}}\right) $$ , by proposing flavorful and chiral vector bosons as the new physics constitution at around TeV scale. The chiral-flavorful vectors (CFVs) are introduced as a 63-plet of the global SU(8) symmetry, identified as the one-family symmetry for left-handed quarks and leptons in the standard model (SM) forming the 8-dimensional vector. Thus the CFVs include massive gluons, vector leptoquarks, and W′, Z′-type bosons, which are allowed to have flavorful couplings with left-handed quarks and leptons, and flavor-universal couplings to right-handed ones, where the latter arises from mixing with the SM gauge bosons. The flavor texture is assumed to possess a “minimal” structure to be consistent with the current flavor measurements on the K and B systems. Among the presently reported significant flavor anomalies in the Kaon and B meson systems (ϵ′/ϵ,   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>*</mo> </mfenced> </msup> </msub> <mo>,</mo> <mspace width="0.25em"></mspace> <msub> <mi>R</mi> <msup> <mi>D</mi> <mfenced> <mo>*</mo> </mfenced> </msup> </msub> </math>  $$ {R}_{K^{\left(*\right)}},\ {R}_{D^{\left(*\right)}} $$ ), the first two ϵ′/ϵ and   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>*</mo> </mfenced> </msup> </msub> </math>  $$ {R}_{K^{\left(*\right)}} $$  anomalies can simultaneously be interpreted by the presence of CFVs; the   <math> <msub> <mi>R</mi> <msup> <mi>D</mi> <mfenced> <mo>*</mo> </mfenced> </msup> </msub> </math>  $$ {R}_{D^{\left(*\right)}} $$  anomaly is predicted not to survive, due to the approximate SU(8) flavor symmetry. Remarkably, we find that as long as both of the ϵ′/ϵ and   <math> <msub> <mi>R</mi> <msup> <mi>K</mi> <mfenced> <mo>*</mo> </mfenced> </msup> </msub> </math>  $$ {R}_{K^{\left(*\right)}} $$  anomalies persist beyond the SM, the CFVs predict the enhanced   <math> <msup> <mi>K</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>π</mi> <mo>+</mo> </msup> <mi>ν</mi> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ {K}^{+}\to {\pi}^{+}\nu \overline{\nu} $$  and   <math> <msub> <mi>K</mi> <mi>L</mi> </msub> <mo>→</mo> <msup> <mi>π</mi> <mn>0</mn> </msup> <mi>ν</mi> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ {K}_L\to {\pi}^0\nu \overline{\nu} $$  decay rates compared to the SM values, which will readily be explored by the NA62 and KOTO experiments, and they will also be explored in new resonance searches at the Large Hadron Collider.