$\textit{CP}$ violation in the kaon system can manifest itself in decays to final states containing neutral kaons. The effect is governed by an efficiency function that reflects the specific experimental setup. We demonstrate that this efficiency function factorizes into two components: the kaon energy spectrum and a detector-dependent factor that is independent on the decay process. We show that matter effects on kaon oscillations can have a significant effect on $\textit{CP}$ asymmetries. We provide estimates of the theoretical prediction for some such $\textit{CP}$ asymmetries for a Belle II-type experiment.

United States

Yuval Grossman

Germany

Paolo Leo

Alberto Martini

Guglielmo Papiri

Armine Rostomyan

$\textit{CP}$ violation in decays into states with neutral kaons

Axions can naturally be very light due to the protection of an (approximate) shift symmetry. Because of their pseudoscalar nature, the long-range force mediated by the axion at tree level is spin dependent, which cannot lead to observable effects between two unpolarized macroscopic objects. At the one-loop level, however, the exchange of two axions does mediate a spin-independent force. This force is coherently enhanced in the presence of an axion background. In this work, we study the two-axion exchange force in a generic axion background. We find that the breaking of the axion shift symmetry plays a crucial role in determining this force. The background-induced axion force $\textit{V}$ vanishes in the shift-symmetry restoration limit. The shift symmetry can be broken either explicitly by non-perturbative effects or effectively by the axion background. When the shift symmetry is broken, $\textit{V}$ scales as 1$\textit{/r}$ and could be further enhanced by a large occupation number of the background axions. We investigate possible experimental probes of this effect in two distinct scenarios: an axion dark matter background and a solar axion flux, using fifth-force searches and atomic spectroscopy experiments. In the axion dark matter case, we find that the background-induced axion force can place strong constraints on axion couplings and masses, comparable to existing astrophysical bounds.

Bingrong Yu

China

Siyu Zhou

Axion forces in axion backgrounds

<p>We derive a complete expression for the neutrino-mediated quantum force beyond the four-Fermi approximation within the standard model. Using this new result, we study the effect of atomic parity violation caused by neutrinos. We find that the neutrino effect is sizable compared to the current experimental sensitivity and can also significantly affect the value of the Weinberg angle measured in atomic systems. This offers a promising method for detecting the neutrino force in the future and facilitates the application of precision atomic physics as a probe for neutrino physics and the electroweak sector of the standard model.</p>

Mitrajyoti Ghosh

Chinhsan Sieng

Neutrino Effects on Atomic Measurements of the Weinberg Angle

<p>The Standard Model predicts a long-range force mediated by a pair of neutrinos, known as “the neutrino force.” It scales as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>G</mi><mi>F</mi><mn>2</mn></msubsup><mo>/</mo><msup><mi>r</mi><mn>5</mn></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>G</mi><mi>F</mi></msub></math> is the Fermi constant. However, as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi><mo>≲</mo><msqrt><msub><mi>G</mi><mi>F</mi></msub></msqrt></math>, the four-Fermi theory breaks down and the neutrino force no longer has the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msup><mi>r</mi><mn>5</mn></msup></math> scaling. For the first time, we derive a complete expression for the neutrino force that is valid at all distances. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi><mo>≫</mo><msqrt><msub><mi>G</mi><mi>F</mi></msub></msqrt></math>, the result reduces to the known <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>G</mi><mi>F</mi><mn>2</mn></msubsup><mo>/</mo><msup><mi>r</mi><mn>5</mn></msup></math>; for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi><mo>≪</mo><msqrt><msub><mi>G</mi><mi>F</mi></msub></msqrt></math>, it scales as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><mi>r</mi></math>. We explore the implications of this result for atomic parity violation (APV) experiments. A key feature of the neutrino force is that it is a long-range effect compared to the atomic length scale. Thus, in general, it cannot be simply treated as a correction to the tree-level <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>-exchange diagram without considering the atomic wave functions. We calculate the effects in muonium and positronium, finding that the neutrino force contributes about 4% and 16%, respectively, compared to the leading <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> exchange. This indicates a significant impact on APV, with important implications for detecting the neutrino force and measuring the weak mixing angle in APV experiments.</p>

Neutrino force at all length scales

We point out that using current knowledge of $$ \mathcal{B}\left({K}_L^0\to {\mu}^{+}{\mu}^{-}\right) $$ and $$ \mathcal{B}\left({K}_L^0\to \gamma \gamma \right) $$ , one can extract short-distance information from the combined measurement of the time-integrated CP asymmetry, $\textit{A}$ ($\textit{K}$ $\textit{→ μ}$ $\textit{μ}$ ), and of $$ \mathcal{B}\left({K}_S^0\to {\mu}^{+}{\mu}^{-}\right) $$ . We discuss the interplay between this set of observables, and demonstrate that determining sign[$\textit{A}$ ($\textit{K}$ → $\textit{μ}$ $\textit{μ}$ )] would eliminate the discrete ambiguity in the Standard Model prediction for $$ \mathcal{B}\left({K}_L^0\to {\mu}^{+}{\mu}^{-}\right) $$ . We then move on to feasibility studies within an LHCb-like setup, using both time-integrated and time-dependent information, employing $\textit{K}$ and $$ {\overline{K}}^0 $$ tagging methods. We find that, within an optimistic scenario, the short-distance amplitude, proportional to the CKM parameter combination $$ \mid {A}^2{\lambda}^5\overline{\eta}\mid $$ , could be constrained by LHCb at the level of about 35% of its Standard Model value, and the discrete ambiguity in $$ \mathcal{B}{\left({K}_L^0\to {\mu}^{+}{\mu}^{-}\right)}_{\textrm{SM}} $$ could be resolved at more than 3$\textit{σ}$ by the end of the high luminosity LHC.

Italy

Giancarlo D’Ambrosio

Switzerland

Avital Dery

Japan

Teppei Kitahara

Radoslav Marchevski

Spain

Diego Santos

United Kingdom

Stefan Schacht

CP violation in $\textit{K → μ}$

Within the Standard Model, the branching fraction of the rare decay $$ {B}_s\to {K}^0{\overline{K}}^0 $$ is related to other decay rates and CP asymmetries through the approximate SU(3) flavor symmetry of the strong interactions and the heavy-quark limit. Three such relations were shown to be violated at a level of about 3$\textit{σ}$ each. By means of a systematic search for new-physics explanations of these puzzles, we find that possible solutions are highly fine-tuned and either excluded by other data or rather implausible. The tight correlation between $$ {B}_s\to K\overline{K} $$ and $\textit{B}$ → $\textit{πK}$ decays, which is maintained even in the presence of flavor-specific new-physics operators, plays a central role in our analysis.

Matthias Neubert

Israel

Yosef Nir

Yogev Shpilman

Yehonatan Viernik

$$ {B}_s\to {K}^0{\overline{K}}^0 $$ beyond the Standard Model

The ν  M  SM is defined as the SM extended to include dimension-5 operators. In this model neutrino masses violate lepton number, and two parameters of the lepton mixing matrix, the Majorana phases, are yet to be constrained. One combination of these phases and the neutrino masses, often denoted by m  ee , is probed by neutrinoless double beta decays (0νββ). We explore what information may be obtained beyond 0νββ, and how it depends on the lightest neutrino mass. We point out that with current central values of the mixing parameters, ∆L  e  = 2 and ∆L  e  = ∆L  μ  = 1 (or ∆L  e  = 2 and ∆L  μ  = 2) processes cannot simultaneously vanish, providing a no-lose theorem, in principle, for excluding the ν  M  SM, even in the case of normal mass ordering.

Stefania Gori

Zoltan Ligeti

Majorana phases beyond neutrinoless double beta decay

The neutrino force results from the exchange of a pair of neutrinos. A neutrino background can significantly influence this force. In this work, we present a comprehensive calculation of the neutrino force in various neutrino backgrounds with spin dependence taken into account. In particular, we calculate the spin-independent and spin-dependent parity-conserving neutrino forces, in addition to the spin-dependent parity-violating neutrino forces with and without the presence of a neutrino background for both isotropic and anisotropic backgrounds. Compared with the vacuum case, the neutrino background can effectively violate Lorentz invariance and lead to additional parity-violating terms that are not suppressed by the velocity of external particles. We estimate the magnitude of the effect of atomic parity-violation experiments, and it turns out to be well below the current experimental sensitivity.

Walter Tangarife

Xun-Jie Xu

South Korea

The neutrino force in neutrino backgrounds: Spin dependence and parity-violating effects

We study the penguin over tree ratio in <math><mi>D</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> decays. This ratio can serve as a probe for rescattering effects. Assuming the Standard Model and in the isospin limit, we derive expressions that relate both the magnitude and the phase of this ratio to direct <math><mi>C</mi><mi>P</mi></math> asymmetries and branching fractions. We find that the current data suggest that rescattering is large. A dedicated experimental analysis with current and future data will be able to significantly reduce the errors on these determinations, and enable us to check if indeed there is significant rescattering in <math><mi>D</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> decays.

Margarita Gavrilova

Determination of the <math><mi>D</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> ratio of penguin over tree diagrams

Accelerating classical systems that couple to a fermion-antifermion pair at the microscopic level can radiate pairs of fermions and lose energy in the process. In this work, we derive the generalization of the Larmor formula for fermion pair radiation. We focus on the case of a point-like classical source in an elliptical orbit that emits fermions through vector and scalar mediators. Ultra-light fermion emission from such systems becomes relevant when the mass of the mediator is larger than the frequency of the periodic motion. This enables us to probe regions of the parameter space that are inaccessible in on-shell bosonic radiation. We apply our results to pulsar binaries with mediators that couple to muons and neutrinos. Using current data on binary period decays, we extract bounds on the parameters of such models.

Taiwan

Tien-Hsueh Tsai

Fermion pair radiation from accelerating classical systems