In previous work [D. Giusti, et al., Methods for high-precision determinations of radiative-leptonic decay form factors using lattice QCD, <a href="http://dx.doi.org/10.1103/PhysRevD.107.074507">Phys. Rev. D 107, 074507 (2023)</a>], we showed that form factors for radiative leptonic decays of pseudoscalar mesons can be determined efficiently and with high precision from lattice QCD using the “three-dimensional (3D) method,” in which three-point functions are computed for all values of the current insertion time and the time integral is performed at the data-analysis stage. Here, we demonstrate another benefit of the 3D method: the form factors can be extracted for any number of nonzero photon virtualities from the same three-point functions at no extra cost. We present results for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mi>s</mi></msub><mo stretchy="false">→</mo><mo>ℓ</mo><mi>ν</mi><msup><mi>γ</mi><mo>*</mo></msup></math> vector form factor as a function of photon energy and photon virtuality, for both positive and negative virtuality, for a single ensemble with 340 MeV pion mass and 0.11 fm lattice spacing. In our analysis, we separately consider the two different time orderings and the different quark flavors in the electromagnetic current. We discuss in detail the behavior of the unwanted exponentials contributing to the three-point functions, as well as the choice of fit models and fit ranges used to remove them for various values of the virtuality. While positive photon virtuality is relevant for decays to multiple charged leptons, negative photon virtuality suppresses soft contributions and is of interest in QCD-factorization studies of the form factors.

Germany

Davide Giusti

United States

Christopher F. Kane

Christoph Lehner

Stefan Meinel

Amarjit Soni

Efficient lattice QCD computation of radiative-leptonic-decay form factors at multiple positive and negative photon virtualities

We study the kinetic cooling (heating) of old neutron stars due to coherent scattering with relic neutrinos (sterile neutrino dark matter) via Standard Model neutral-current interactions. We take into account several important physical effects, such as coherent enhancement, gravitational clustering, neutron degeneracy, Pauli blocking and weak potential. We find that the anomalous cooling of neutron stars due to relic neutrino scattering is difficult to observe. However, the anomalous heating of neutron stars due to coherent scattering with keV-scale sterile neutrino dark matter may be observed by current and future telescopes operating in the optical to near-infrared frequency band, such as the James Webb Space Telescope (JWST), which would probe hitherto unexplored parameter space in the sterile neutrino mass-mixing plane.

Saurav Das

P.S. Bhupal Dev

Takuya Okawa

Old neutron stars as a new probe of relic neutrinos and sterile neutrino dark matter

We use vector meson dominance to calculate non-perturbative contributions to the branching ratio of the rare decay <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> $$ {K}^{\pm}\to {\pi}^{\pm}\nu \overline{\nu} $$ stemming from matrix elements involving up-quark loops. The importance of this observable as well as of K 0 → π 0 l + l − and of the direct CP violation parameter <math> <msubsup> <mi>ϵ</mi> <mi>K</mi> <mo>′</mo> </msubsup> </math> $$ {\epsilon}_K^{\prime } $$ is then discussed in the context of a Unitarity Triangle sqtudy based on Kaon sector observables only.

CERN

Switzerland

Enrico Lunghi

Light quark loops in <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> $$ {K}^{\pm}\to {\pi}^{\pm}\nu \overline{\nu} $$ from vector meson dominance and update on the Kaon Unitarity Triangle

We present a general analysis for the discovery potential of CP-violation (CPV) searches in scattering processes at TeV-scale colliders in an effective field theory framework, using the SMEFT basis for higher dimensional operators. In particular, we systematically examine the CP-violating sector of the SMEFT framework in some well motivated limiting cases, based on flavour symmetries of the underlying heavy theory. We show that, under naturality arguments of the underlying new physics (NP) and in the absence of (or suppressed) flavour-changing interactions, there is only a single operator, <math><msub><mrow><mi>Q</mi></mrow><mrow><mi>t</mi><mi>ϕ</mi></mrow></msub><mo>=</mo><msup><mrow><mi>ϕ</mi></mrow><mrow><mi>†</mi></mrow></msup><mi>ϕ</mi><mrow><mo>(</mo><msub><mrow><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>3</mn></mrow></msub><mi>t</mi><mo>)</mo></mrow><mover><mrow><mi>ϕ</mi></mrow><mrow><mo>˜</mo></mrow></mover></math> which alters the top-Yukawa coupling, that can generate a non-vanishing CP-violating effect from tree-level SM×NP interference terms. We find, however, that CPV from <math><msub><mrow><mi>Q</mi></mrow><mrow><mi>t</mi><mi>ϕ</mi></mrow></msub><mo>=</mo><msup><mrow><mi>ϕ</mi></mrow><mrow><mi>†</mi></mrow></msup><mi>ϕ</mi><mrow><mo>(</mo><msub><mrow><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>3</mn></mrow></msub><mi>t</mi><mo>)</mo></mrow><mover><mrow><mi>ϕ</mi></mrow><mrow><mo>˜</mo></mrow></mover></math> is expected to be at best of <math><mi>O</mi><mo>(</mo><mn>1</mn><mtext>%</mtext><mo>)</mo></math> and, therefore, very challenging if at all measurable at the LHC or other future high-energy colliders. We then conclude that a potentially measurable CP-violating effect of <math><mi>O</mi><mo>(</mo><mn>10</mn><mtext>%</mtext><mo>)</mo></math> can arise in high-energy scattering processes only if flavour-changing interactions are present in the underlying NP; in this case a sizable CPV can be generated at the tree-level by pure NP×NP effects and not from SM×NP interference. We provide several examples of CPV at the LHC and at a future <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> collider to support these statements.

Israel

Shaouly Bar-Shalom

Jose Wudka

Theoretical underpinnings of CP-violation at the high-energy frontier

In light of recently found deviations of the experimental data from predictions from QCD factorization for <math><msub><mi>B</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></msub><mo>→</mo><msub><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></msub><mi>P</mi></math> decays, where <math><mi>P</mi><mo>=</mo><mo>{</mo><mi>π</mi><mo>,</mo><mi>K</mi><mo>}</mo></math>, we systematically probe the current status of the <math><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>F</mi></msub></mrow></math> expansion from a fit to experimental branching ratio data without any further theory input. We find that the current data are in agreement with the power counting of the <math><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>F</mi></msub></mrow></math> expansion. While the <math><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>F</mi></msub></mrow></math> limit is excluded at <math><mo>&gt;</mo><mn>5</mn><mi>σ</mi></math>, amplitude-level <math><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>F</mi></msub></mrow></math>-breaking contributions of <math><mo>∼</mo><mn>20</mn><mo>%</mo></math> suffice for an excellent description of the data. <math><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>F</mi></msub></mrow></math> breaking is needed in tree (<math><mo>&gt;</mo><mn>5</mn><mi>σ</mi></math>) and color-suppressed tree (<math><mn>2.4</mn><mi>σ</mi></math>) diagrams. We are not yet sensitive to <math><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>F</mi></msub></mrow></math> breaking in exchange diagrams. From the underlying <math><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>F</mi></msub></mrow></math> parametrization we predict the unmeasured branching ratios <math><mrow><mi>B</mi><mo>(</mo><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo><mo>=</mo><mn>2</mn><mi>B</mi><mo>(</mo><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>)</mo><mo>=</mo><mo>[</mo><mn>0.3</mn><mo>,</mo><mn>7.2</mn><mo>]</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math> of suppressed decays that can be searched for at the LHCb experiment.

United Kingdom

Jonathan Davies

Stefan Schacht

Nicola Skidmore

Reappraisal of SU(3)-flavor breaking in <math><mi>B</mi><mo>→</mo><mi>D</mi><mi>P</mi></math>

A lattice QCD approach to the calculation of the long-distance contributions to <math><msub><mi>ε</mi><mi>K</mi></msub></math> is presented. This parameter describes indirect <math><mrow><mi>C</mi><mi>P</mi></mrow></math> violation in <math><mi>K</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> decay. While the short-distance contribution to <math><msub><mi>ε</mi><mi>K</mi></msub></math> can be accurately calculated in terms of standard model parameters and a single hadronic matrix element, <math><msub><mi>B</mi><mi>K</mi></msub></math>, there is a long-distance part which is estimated to be approximately 5% of the total and is more difficult to determine. A method for determining this small but phenomenologically important contribution to <math><msub><mi>ε</mi><mi>K</mi></msub></math> using lattice QCD is proposed and a complete exploratory calculation of the contribution is presented. This exploratory calculation uses an unphysical light quark mass corresponding to a 339 MeV pion mass and an unphysical charm quark mass of 968 MeV, expressed in the <math><mover><mi>MS</mi><mo>¯</mo></mover></math> scheme at 2 GeV. This calculation demonstrates that future work should be able to determine this long-distance contribution from first principles with a controlled error of 10% or less.

Ziyuan Bai

Norman H. Christ

Joseph M. Karpie

Christopher T. Sachrajda

Bigeng Wang

Long-distance contribution to <math><msub><mi>ε</mi><mi>K</mi></msub></math> from lattice QCD

In the early 1980s Sanda-san and collaborators wrote key papers on the direct and clean determination of the unitarity angle ϕ 1(&#946;). This motivated many of us to analogously come up with ways for direct and clean determinations of the other two unitarity angles, &#981; 2(&#945;) and &#981; 3(&#947;). This paper describes the current status of these direct determinations as well as our expectations for when Belle-II has 50 ab &#8722;1 of luminosity and LHCb is upgraded. In particular, it is emphasized that, for direct determination of &#981; 3, Belle-II should be able to handle final states in <italic>D</italic> 0 or <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\bar{D}^0$</tex-math></inline-formula> Dalitz decays, which contain one &#960; 0 (which are difficult for LHCb); then they may make further inroads in improving the accuracy of the &#981; 3 determination. Early lattice inputs for constraining the unitarity triangle (UT) are briefly recalled. Its crucial role in supporting the Kobayashi&#8211;Maskawa theory of <italic>CP</italic> violation is emphasized. Over the years significant progress has been made in lattice methods and the latest constraints from these for the UT will be discussed, as well as the compatibility with current direct determinations and some comments on the future outlook.

Theory of <italic>CP</italic> angle measurements

The longstanding muon <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><mo>)</mo></math> anomaly, as well as some hints of lepton flavor universality violation in B-meson decays, could be signaling new physics beyond the Standard Model (SM). A minimal R-parity-violating supersymmetric framework with light third-generation sfermions (dubbed as ‘RPV3’) provides a compelling solution to these flavor anomalies, while simultaneously addressing other pressing issues of the SM. We propose a new RPV3 scenario for the solution of the muon <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><mo>)</mo></math> anomaly, which leads to an interesting LHC signal of <math><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>τ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>τ</mi></mrow><mrow><mo>−</mo></mrow></msup></math> final state. We analyze the Run-2 LHC multilepton data to derive stringent constraints on the sneutrino mass and the relevant RPV coupling in this scenario. We then propose dedicated selection strategies to improve the bound even with the existing dataset. We also show that the high-luminosity LHC will completely cover the remaining muon <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><mo>)</mo></math>-preferred parameter space, thus providing a robust, independent test of the muon <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><mo>)</mo></math> anomaly.

Yoav Afik

Fang Xu

Probing the muon ( − 2) anomaly at the LHC in final states with two muons and two taus

We present a lattice calculation of the <math><mi>K</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> matrix elements and amplitudes with both the <math><mi>Δ</mi><mi>I</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> and <math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> channels and <math><msup><mi>ϵ</mi><mo>′</mo></msup></math>, the measure of direct <math><mi>C</mi><mi>P</mi></math> violation. We use periodic boundary conditions (PBC), where the correct kinematics of <math><mi>K</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> can be achieved via an excited two-pion final state. To overcome the difficulty associated with the extraction of excited states, our previous work [Z. Bai et al., Standard Model prediction for direct <math><mi>C</mi><mi>P</mi></math> violation in <math><mi>K</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> decay, Phys. Rev. Lett. 115, 212001 (2015); R. Abbott et al., Direct <math><mi>C</mi><mi>P</mi></math> violation and the <math><mi>Δ</mi><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math> rule in <math><mi>K</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> decay from the Standard Model, Phys. Rev. D 102, 054509 (2020).] successfully employed G-parity boundary conditions, where pions are forced to have nonzero momentum enabling the <math><mi>I</mi><mo>=</mo><mn>0</mn></math> two-pion ground state to express the on shell kinematics of the <math><mi>K</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> decay. Here instead we overcome the problem using the variational method which allows us to resolve the two-pion spectrum and matrix elements up to the relevant energy where the decay amplitude is on shell. In this paper we report an exploratory calculation of <math><mi>K</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> decay amplitudes and <math><msup><mi>ϵ</mi><mo>′</mo></msup></math> using PBC on a coarser lattice size of <math><msup><mn>24</mn><mn>3</mn></msup><mo>×</mo><mn>64</mn></math> with inverse lattice spacing <math><msup><mi>a</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><mn>1.023</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and the physical pion and kaon masses. The results are promising enough to motivate us to continue our measurements on finer lattice ensembles in order to improve the precision in the near future.

Thomas Blum

Peter A. Boyle

Daniel Hoying

Taku Izubuchi

Luchang Jin

Chulwoo Jung

Christopher Kelly

Masaaki Tomii

<math><mi>Δ</mi><mi>I</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> and <math><mi>Δ</mi><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math> channels of <math><mi>K</mi><mo>→</mo><mi>π</mi><mi>π</mi></math> decay at the physical point with periodic boundary conditions

We introduce a modification to the standard expression for tree-level <math><mi>C</mi><mi>P</mi></math> violation in scattering processes at the LHC, which is important when the initial state is not self-conjugate. Based on that, we propose a generic and model-independent search strategy for probing tree-level <math><mi>C</mi><mi>P</mi></math> violation in inclusive multilepton signals. We then use TeV-scale 4-fermion operators of the form <math><mrow><mi>t</mi><mi>u</mi><mo>ℓ</mo><mo>ℓ</mo></mrow></math> and <math><mi>t</mi><mi>c</mi><mo>ℓ</mo><mo>ℓ</mo></math> with complex Wilson coefficients as an illustrative example and show that it may generate <math><mrow><mi>O</mi><mo>(</mo><mn>10</mn><mo>%</mo><mo>)</mo></mrow></math> <math><mi>C</mi><mi>P</mi></math> asymmetries that should be accessible at the LHC with an integrated luminosity of <math><mi>O</mi><mo>(</mo><mn>1000</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mrow><msup><mrow><mi>fb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>.

Kuntal Pal

Generic Tests of <math><mi>C</mi><mi>P</mi></math> Violation in High-<math><msub><mi>p</mi><mi>T</mi></msub></math> Multilepton Signals at the LHC and Beyond