We study the method to test the unitarity of the lepton mixing matrix by using only the long baseline neutrino oscillation experiments, such as the combination of the T2HK experiment and the one with the $\textit{ν}$ beam from a future neutrino factory at J-PARC. Without a specific parametrization, one can directly extract the elements of the lepton mixing matrix by observing the energy dependence of the oscillation probabilities. A non-trivial test of the unitarity under the three-generation assumption can thus be made possible by examining the orthogonality in a similar manner to the unitarity triangle in the quark sector. As the first trial, we perform the analysis based on the simplified situation where the matter effects in the neutrino oscillation can be neglected. Under this simplified analysis, we demonstrate that a violation of unitarity in the 3$\textit{×}$3 lepton mixing matrix can be observed, using a four-generation model as a concrete example of a non-unitary three-generation scenario. The statistically most significant measurement can be provided by the energy dependences of the combination of the CP conjugate modes, $\textit{ν}$ $\textit{→ ν}$ and $$ {\overline{\nu}}_{\mu}\to {\overline{\nu}}_e $$ , at T2HK and, independently, by the T conjugate modes, $\textit{ν}$ $\textit{→ ν}$ and $\textit{ν}$ $\textit{→ ν}$ , with the latter measured at the neutrino factory experiments.

Japan

Ryuichiro Kitano

Joe Sato

Sho Sugama

Unitarity test of lepton mixing via energy dependence of neutrino oscillation

The parity solution to the strong CP problem necessarily extends the Standard Model to include the SU(2) gauge sector and imposes restrictions on the structure of the Yukawa interactions. In this framework, one can consider an appealing structure of the neutrino sector in which the smallness of the neutrino masses is naturally explained, while lepton number symmetry is substantially violated at the TeV scale. Observation of distinctive lepton number violating signals at collider experiments can therefore be expected, since the rates are not suppressed by the small neutrino masses. We study the constraints from neutrinoless double beta decay and discuss the prospects for discovering new TeV-scale particles, such as the $\textit{W′}$ boson of SU(2) , via lepton number violating processes at a $\textit{μ}$ $\textit{μ}$ collider, $\textit{μ}$ $\textit{μ}$ → $\textit{W}$ $\textit{W′}$ . A $\textit{μ}$ $\textit{μ}$ collider with a center-of-mass energy of 10 TeV can probe the $\textit{W′}$ boson mass up to about 10 TeV through on-shell production, and the reach can extend to 16 TeV by studying processes involving off-shell $\textit{W′}$ boson.

United States

Keisuke Harigaya

Ryoto Takai

Lepton number violating signals of a parity symmetric model at $\textit{μ}$TRISTAN

The large $\textit{N}$ analysis of QCD states that the potential for the $\textit{η′}$ meson develops cusps at $\textit{η′}$ = $\textit{π}$/$\textit{N}$ , 3$\textit{π}$/$\textit{N}$ , ⋯ , with $\textit{N}$ the number of flavors. Furthermore, the recent discussion of generalized anomalies tells us that even for finite $\textit{N}$ there should be cusps if $\textit{N}$ and $\textit{N}$ are not coprime, as one can show that the domain wall configuration of $\textit{η′}$ should support a Chern-Simons theory on it, i.e., domains are not smoothly connected. On the other hand, there is a supporting argument for instanton-like, smooth potentials of $\textit{η′}$ from the analyses of softly-broken supersymmetric QCD for $\textit{N}$ = $\textit{N}$ − 1, $\textit{N}$, and $\textit{N}$ + 1. We argue that the analysis of the $\textit{N}$ = $\textit{N}$ case should be subject to the above anomaly argument, and thus there should be a cusp; while the $\textit{N}$ = $\textit{N}$ ± 1 cases are consistent, as $\textit{N}$ and $\textit{N}$ are coprime. We discuss how this cuspy/smooth transition can be understood. For $\textit{N}$ < $\textit{N}$, we find that the number of branches of the $\textit{η′}$ potential is gcd($\textit{N}$, $\textit{N}$ ), which is the minimum number allowed by the anomaly. We also discuss the condition for s-confinement in QCD-like theories, and find that in general the anomaly matching of the $\textit{θ}$ periodicity indicates that s-confinement can only be possible when $\textit{N}$ and $\textit{N}$ are coprime. The s-confinement in supersymmetric QCD at $\textit{N}$ = $\textit{N}$ + 1 is a famous example, and the argument generalizes for any number of fermions in the adjoint representation.

Ryutaro Matsudo

Lukas Treuer

On cusps in the $\textit{η′}$ potential

We present an exploratory study to determine the confinement-deconfinement transition temperature at finite $\textit{θ}$, $\textit{T}$ ($\textit{θ}$), for the 4d SU(2) pure Yang-Mills theory. Lattice numerical simulations are performed on three spatial sizes $\textit{N}$ = 24, 32, 48 with a fixed temporal size $\textit{N}$ = 8. We introduce a non-zero $\textit{θ}$-angle by the sub-volume method to mitigate the sign problem. By taking advantage of the universality in the second order phase transition and the Binder cumulant of the order parameter, the $\textit{θ}$-dependence of $\textit{T}$ is determined to be $\textit{T}$ ($\textit{θ}$)/$\textit{T}$ (0) = 1 $\textit{−}$ 0$\textit{.}$16(2) ($\textit{θ}$/$\textit{π}$) − 0$\textit{.}$03(4) ($\textit{θ}$/$\textit{π}$) up to $\textit{θ}$ ∼ 0.9 $\textit{π}$. The reliability of the extrapolations in the sub-volume method is extensively checked. We also point out that the temperature dependence of the topological susceptibility should exhibit a singularity with the exponent for the specific heat.

Norikazu Yamada

Masahito Yamazaki

$\textit{θ}$ dependence of T

We study Higgs boson production at <math><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math> colliders at high energy. Since both initial-state particles are positively charged, there is no <math><mi>W</mi></math> boson fusion at the leading order, as it requires a <math><msup><mi>W</mi><mo>+</mo></msup><msup><mi>W</mi><mo>−</mo></msup></math> pair. However, we find that the cross section of the higher-order, <math><mi>γ</mi></math>-and <math><mi>Z</mi></math>-mediated <math><mi>W</mi></math> boson fusion process is large at high center-of-mass energies <math><msqrt><mi>s</mi></msqrt></math>, growing as <math><mo>(</mo><mi>log</mi><mi>s</mi><msup><mo>)</mo><mn>3</mn></msup></math>. This is in contrast to the <math><mi>log</mi><mi>s</mi></math> behavior of the leading-order <math><mi>W</mi></math> boson fusion. Thus, even though it is a higher-order process, the rate of Higgs boson production for 10 TeV energies at <math><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math> colliders with polarized beams can be as high as about half of the one at <math><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> colliders, assuming the same integrated luminosity. To calculate the cross section of this process accurately, we carefully treat the collinear emission of the photon in the intermediate state. The thereby obtained large cross section furthermore shows the significance of Higgs production with an extra <math><mi>W</mi></math> boson in the final state also at <math><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> and <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders.

Germany

Yu Hamada

Shohei Okawa

Hiromasa Takaura

Higgs boson production at <math><mrow><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> colliders

Abstract We report the result of the numerical lattice computation of the lepton anomalous magnetic moment in quantum electrodynamics up to five loops. We concentrate on the contributions from diagrams without lepton loops, which are the most difficult part of the calculation in the Feynman diagram method, while the lattice formulation is the easiest. Good agreement with the results of the Feynman diagram method is observed.

QED Five-Loop on the Lattice

We study the possibility of measuring T (time reversal) violation in a future long baseline neutrino oscillation experiment. By assuming a neutrino factory as a staging scenario of a muon collider at the J-PARC site, we find that the ν  e  → ν  μ  oscillation probabilities can be measured with a good accuracy at the Hyper-Kamiokande detector. By comparing with the probability of the time-reversal process, ν  μ  → ν  e , measured at the T2K/T2HK experiments, one can determine the CP phase δ in the neutrino mixing matrix if |sin(δ)| is large enough. The determination of δ can be made with poor knowledge of the matter density of the earth as T violation is almost insensitive to the matter effects. The comparison of CP and T-violation measurements, à la the CPT theorem, provides us with a non-trivial check of the three neutrino paradigm based on the quantum field theory.

T violation at a future neutrino factory

We apply the previously-developed sub-volume method to study the θ-dependence of the four-dimensional SU(2) Yang-Mills theory at finite temperature. We calculate the first two coefficients, the topological susceptibility χ and the fourth cumulant b 2, in the θ-expansion of the free energy density around the critical temperature (T  c ) for the confinement-deconfinement transition. Lattice calculations are performed with three different spatial sizes 243 , 323 , 483 to monitor finite size effects, while the temporal size is fixed to be 8. The systematic uncertainty associated with the sub-volume extrapolation is studied with special care. The sub-volume method allows us to determine the values of b 2 much more accurately than the standard full-volume method, and we successfully identify the temperature dependence of b 2 around T  c . Our numerical results suggest that the θ-dependence of the free energy density near θ = 0 changes from 4χ(1 − cos(θ/2)) to χ(1 − cos θ) as the temperature crosses T  c .

Subvolume method for SU(2) Yang-Mills theory at finite temperature: topological charge distributions

A detection scheme is explored for light dark matter, such as axion dark matter or dark photon dark matter, using a Paul ion trap system. We first demonstrate that a qubit, constructed from the ground and first excited states of vibrational modes of ions in a Paul trap, can serve as an effective sensor for weak electric fields due to its resonant excitation. As a consequence, a Paul ion trap allows us to search for weak electric fields induced by light dark matter with masses around the neV range. Furthermore, we illustrate that an entangled qubit system involving N ions can enhance the excitation rate by a factor of N 2. The sensitivities of the Paul ion trap system to axion-photon coupling and gauge kinetic mixing can reach previously unexplored parameter space.

Asuka Ito

Wakutaka Nakano

Quantum entanglement of ions for light dark matter detection

Ignorance of the initial condition for the axion dynamics in the early Universe has led us to consider an O(1) valued initial amplitude, and that prefers the decay constant, F  a , of the QCD axion to be an intermediate scale such as 1012 GeV in order to explain the dark matter abundance. We explore a cosmological scenario of F  a  being much larger than 1012 GeV by considering the axion and modulus dynamics during inflation to set the initial amplitude. We show that if the volume modulus (radion) of the extra-dimension is stabilized mainly by the QCD contribution to the modulus potential during inflation, the QCD axion with the string-scale decay constant obtains a mass around the inflationary Hubble parameter. This means that the axion rolls down to the θ = 0 minimum during the inflation realizing almost vanishing initial amplitude, and the inflationary quantum fluctuation can be the dominant source of the current number density of axions. We find natural parameter regions where the axion explains the cold dark matter of the Universe, while the constraint on the isocurvature perturbation is avoided. The presence of the axion miniclusters or axion stars are predicted in a wide range of parameters, including the one explains the Subaru-HCS microlensing event.