We perform the first computation of phase-transition parameters to cubic order in $ \lambda\sim m^2/T^2 $ , where $\textit{m}$ is the scalar mass and $\textit{T}$ is the temperature, in a simple model resembling the Higgs sector of the SMEFT. We use dimensional reduction, including 1-loop matching corrections for terms of dimension 6 (in 4-dimensional units), 2-loop contributions for dimension-4 ones and 3-loops for the squared mass. We precisely quantify the size of the different corrections, including renormalization-group running as well as quantum effects from light fields in the effective theory provided by the Coleman-Weinberg potential, and discuss briefly the implications for gravitational waves. Our results suggest that, for strong phase transitions, 1-loop corrections from dimension-6 operators can compete with 2-loop ones from quartic couplings and largely surpass those from 3-loop thermal masses.

Spain

Mikael Chala

Luis Gil

Zhe Ren

Phase transitions in dimensional reduction up to three loops * Supported by MCIN/AEI (10.13039/501100011033) and ERDF (grants PID2021-128396NB-I00 and PID2022-139466NB-C22), from the Junta de Andalucía grants FQM 101 and P21-00199 and from Consejería de Universidad, Investigación e Innovación, Gobierno de España and Unión Europea – NextGenerationEU under grants AST22 6.5 and CNS2022-136024. MC and LG are further supported by the RyC and FPU programs under contract numbers RYC2019-027155-I and FPU23/02026, respectively.

In this work, we study the contribution of invisible light particles to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msub><mrow><mi>E</mi></mrow><mrow><mi>miss</mi></mrow></msub></mrow></math>, particularly the three-body decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mi>ϕ</mi><mover accent="true"><mrow><mi>ϕ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mi>ψ</mi><mover accent="true"><mi>ψ</mi><mo stretchy="false">¯</mo></mover></math>. The differential branching ratio of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msub><mi>E</mi><mrow><mi>miss</mi></mrow></msub></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math>-dependent longitudinal polarization asymmetry of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> in scenarios explaining the Belle II excess are presented. In the chiral basis, we investigate the correlations between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">→</mo><mi>K</mi><msub><mrow><mi>E</mi></mrow><mrow><mi>miss</mi></mrow></msub><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msub><mrow><mi>E</mi></mrow><mrow><mi>miss</mi></mrow></msub><mo stretchy="false">)</mo></mrow></math>, as well as between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">→</mo><mi>K</mi><msub><mi>E</mi><mrow><mi>miss</mi></mrow></msub><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mi>L</mi><mi mathvariant="normal">Λ</mi></msubsup></math>, in eight distinct new physics scenarios. We find that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mi>L</mi><mi mathvariant="normal">Λ</mi></msubsup></math> can be used to distinguish the chirality of the hadronic current part in the effective operators, which is similar to the cases in the two-body decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mi>ϕ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mi>V</mi></math>.

China

Quan-Yi Hu

Zhi-Bin Duan

Influence of invisible light particles on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msub><mi>E</mi><mrow><mi>miss</mi></mrow></msub></math>

A scan of the beam energy across the top quark pair $$ \left(\textrm{t}\overline{\textrm{t}}\right) $$ production threshold is part of the program of future Higgs, top, and electroweak factory projects. In this paper, we provide projections for the achievable precision in the top quark mass ($\textit{m}$ ), width (Γ ), and Yukawa coupling ($\textit{y}$ ) at the electron-positron (e e ) stage of the Future Circular Collider (FCC-ee). The study includes a detailed assessment of parametric and systematic uncertainties, as well as a rigorous estimate of the effect of point-to-point correlations. We project that $\textit{m}$ and Γ can be determined with an experimental precision of 6.8 and 11.5 MeV, respectively, when $\textit{m}$ is defined in the potential-subtracted (PS) scheme. The impact of theoretical uncertainties due to missing higher orders is found to be of about 35 (25) MeV on $\textit{m}$ (Γ ) at N LO in non-relativistic QCD. Therefore, improvements in the theoretical accuracy, which is an active area of development, are key to match the achievable experimental precision at a future e e collider. We also explore the prospects for a measurement of $\textit{y}$ at FCC-ee via a dedicated run above the $$ \textrm{t}\overline{\textrm{t}} $$ production threshold.

Switzerland

Matteo Defranchis

Jorge Blas

Ankita Mehta

Michele Selvaggi

Marcel Vos

A detailed study on the prospects for a $$ \textrm{t}\overline{\textrm{t}} $$ threshold scan in $\textit{e}$

The PADME Experiment at the Frascati DAΦNE linear accelerator has searched for a hypothetical particle with mass around 17 MeV, commonly referred to as the X17, using a positron beam incident on a fixed target. The beam energy was varied between 262 and 296 MeV, corresponding to center-of-mass energies $$\sqrt{s}$$ between 16.4 and 17.4 MeV. The X17 should be produced resonantly via $\textit{e}$ $\textit{e}$ annihilation when $$\sqrt{s}$$ approaches its mass, inducing an excess of events with a two-body final state over the background expectation. The beam energy spacing was fixed to less than half the expected width of the resonance’s line shape. Uncertainties below 1% per $$\sqrt{s}$$ point were achieved. A blind analysis has been performed. The data are consistent with the expected background in most of the explored energy range, and limits are set in previously unexplored regions of the available parameter space. The most significant deviation is found for $$\sqrt{s}\approx 16.90$$ MeV, corresponding to a global significance of approximately 2 standard deviations over the null hypothesis expectation.

Italy

F. Bossi

R. Sangro

C. Giulio

E. Meco

D. Domenici

G. Finocchiaro

L. Foggetta

M. Garattini

P. Gianotti

M. Mancini

I. Sarra

T. Spadaro

C. Taruggi

E. Vilucchi

Bulgaria

K. Dimitrova

S. Ivanov

Sv. Ivanov

K. Kostova

V. Kozhuharov

R. Simeonov

F. Ferrarotto

E. Leonardi

P. Valente

E. Long

G. Organtini

M. Raggi

United States

A. Frankenthal

Search for a new 17 MeV resonance via $\textit{e}$

We critically examine the back-to-back limit of the energy-energy correlation (EEC) in $\textit{e}$ $\textit{e}$ annihilation as a potential source of information on the Collins-Soper kernel and the strong coupling constant. The analysis is performed within the framework of transverse momentum dependent (TMD) factorization at next-to-next-to-next-to-next-to-leading logarithmic (N LL) accuracy, using a global fit to all available experimental data. Contrary to previous claims, we demonstrate that the current data do not provide meaningful constraints on either the Collins-Soper kernel or $\textit{α}$ .

Alejandro Cuerpo

Ignazio Scimemi

Alexey Vladimirov

Assessing the sensitivity of energy-energy correlations in $\textit{e}$

Within the framework of the next-to-minimal supersymmetric (SUSY) extension of the Standard Model (SM) with a local B-L gauge symmetry (N-B-LSSM), we study lepton flavor violating (LFV) $ \tau\rightarrow e M^+ M^- $ decays: $ \tau \rightarrow e \pi^+\pi^- $ , $ \tau \rightarrow e \pi^+K^- $ , and $ \tau \rightarrow e K^+K^- $ . Based on the latest experimental data, the influence of different sensitive parameters on the branching ratios is considered. It can be seen from the numerical analysis that the main sensitive parameters and LFV sources are non-diagonal elements corresponding to the initial and final leptons. This work can provide a basis for discovering the existence of new physics (NP).

Rong-Zhi Sun

Shu-Min Zhao

Shuang Di

Portugal

Xing-Xing Dong

Study of ${\boldsymbol\tau\rightarrow {\boldsymbol e M^+ M^-}}$ decays in N-B-LSSM * Supported by National Natural Science Foundation of China (NNSFC) (12075074), Natural Science Foundation of Hebei Province (A2023201040, A2022201022, A2022201017, A2023201041), Natural Science Foundation of Hebei Education Department (QN2022173), Post-graduate's Innovation Fund Project of Hebei University (HBU2024SS042), the Project of the China Scholarship Council (CSC) (202408130113). X. Dong acknowledges support from Fundação para a Ciência e a Tecnologia (FCT, Portugal) through the projects CFTP FCT Unit (UIDB/00777/2020, UIDP/00777/2020)

Recent anomalies observed in $ e^+e^- $ nuclear transitions of $ ^8 {{\rm{Be}}} $ , $ ^4 {\rm{He}} $ , and $ ^{12} {\rm{C}} $ by the ATOMKI collaboration may hint at the existence of a vector boson with a mass around 17 MeV, which is referred to as X17. If it exists, this boson would affect similar processes in particle physics, including the Dalitz decays of vector mesons. Recently, the BESIII collaboration measured the Dalitz decay $ D^{*0}\to D^0e^+e^- $ for the first time and reported a $ 3.5\sigma $ excess over the theoretical prediction based on the vector meson dominance (VMD) model. This excess may be another signal of X17. In this study, we investigate the possible effects of X17 on the Dalitz decays $ D^*_{(s)}\to D_{(s)}e^+e^- $ , $ B^*_{(s)}\to B_{(s)}e^+e^- $ , and $ J/\psi\to \eta_ce^+e^- $ . The required hadronic form factors are calculated within the framework of our covariant confined quark model without relying on heavy quark effective theory or the VMD model. We present predictions for the Dalitz decay widths and the ratios $ R_{ee}(V)\equiv \Gamma(V\to Pe^+e^-)/\Gamma(V\to P\gamma) $ within the standard model and in several new physics scenarios involving modifications attributed to X17. Our results are compared with other theoretical calculations.

Vietnam

C.T. Tran

Russia

M.A. Ivanov

A.T.T. Nguyen

Probing the ATOMKI X17 vector boson using Dalitz decays $\textit{V}$ → $\textit{Pe}$ $^{+}$ $\textit{e}$ $^{−}$ * Supported by Ho Chi Minh City University of Technology and Education (T2024-65)

We present a study of the rare charm meson decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mrow><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> using a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>942</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> dataset collected by the Belle detector at the KEKB asymmetric-energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collider. We identify <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup></math> candidates via the charge of the pion from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math> decays and normalize the branching fractions to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup></math> decays. The branching fraction for decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>39.6</mn><mo>±</mo><mn>4.5</mn><mtext> </mtext><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo><mo>±</mo><mn>2.9</mn><mtext> </mtext><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup></mrow></math>, with the dielectron mass in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo>/</mo><mi>ω</mi></math> mass region <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>675</mn><mo>&lt;</mo><msub><mi>m</mi><mrow><mi>e</mi><mi>e</mi></mrow></msub><mo>&lt;</mo><mn>875</mn><mtext> </mtext><mtext> </mtext><mrow><mrow><mi>MeV</mi><mo>/</mo></mrow><msup><mi>c</mi><mn>2</mn></msup></mrow></math>. We also search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>h</mi><mo>−</mo></msup><msup><mi>h</mi><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>h</mi><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><mi>K</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>π</mi></mrow></math>) decays with the dielectron mass near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> resonances, and away from these resonances for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> modes. For these modes, we find no significant signals and set 90% confidence level upper limits on their branching fractions at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup></mrow><mo stretchy="false">)</mo></mrow></math> level.

I. Adachi

L. Aggarwal

H. Ahmed

Y. Ahn

H. Aihara

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

N. Althubiti

K. Amos

M. Angelsmark

N. Anh Ky

C. Antonioli

D.M. Asner

H. Atmacan

T. Aushev

V. Aushev

M. Aversano

R. Ayad

V. Babu

H. Bae

N.K. Baghel

S. Bahinipati

P. Bambade

Sw. Banerjee

S. Bansal

M. Barrett

M. Bartl

J. Baudot

A. Baur

A. Beaubien

F. Becherer

J. Becker

J.V. Bennett

F.U. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

V. Bhardwaj

B. Bhuyan

F. Bianchi

L. Bierwirth

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

A. Bolz

A. Bondar

J. Borah

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

N. Brenny

R.A. Briere

T.E. Browder

A. Budano

S. Bussino

Q. Campagna

M. Campajola

L. Cao

G. Casarosa

C. Cecchi

J. Cerasoli

M.C. Chang

P. Chang

R. Cheaib

P. Cheema

C. Chen

L. Chen

B.G. Cheon

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

J. Cochran

I. Consigny

L. Corona

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. de Marino

G. De Nardo

G. De Pietro

R. de Sangro

M. Destefanis

S. Dey

R. Dhamija

A. Di Canto

F. Di Capua

J. Dingfelder

Z. Doležal

I. Domínguez Jiménez

Measurement of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> branching fraction and search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> decays at Belle

Atomic electron motion is responsible for well-studied effects observed in low-energy (MeV-scale) processes. Recently, interest in this phenomenon has also emerged within the high-energy physics community, due to its potential to increase significantly the center-of-mass energy in fixed-target experiments. However, direct experimental evidence of this effect in high energy collisions has yet to be observed. We argue that a striking manifestation of atomic electron momenta could be revealed by the NA64 experiment at CERN during the proposed run with a 40 GeV positron beam. At this energy, $\textit{μ}$ $\textit{μ}$ production via positron annihilation on electrons at rest is kinematically forbidden. The detection of $\textit{μ}$ $\textit{μ}$ pairs from the annihilation channel would thus constitute direct evidence of an increase in the center-of-mass energy resulting from atomic electron motion. We also investigate the expected signatures for the proposed 60 GeV run, as well as for the data already collected at 70 GeV. Intriguingly, in both these cases, the predicted number of $\textit{μ}$ $\textit{μ}$ pairs from positron annihilation is reduced compared to the electron-at-rest approximation.

Fernando Arias-Aragón

Giovanni Cortona

Estonia

Enrico Nardi

Unveiling atomic electron motion effects in $\textit{e}$

High-precision measurements of the lepton’s electromagnetic dipole moments provide a powerful probe for testing the Standard Model. A nonzero value of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> lepton’s electric(weak) dipole moment (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>d</mi><mi>τ</mi><mi>γ</mi></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>d</mi><mi>τ</mi><mi>Z</mi></msubsup></math>) would serve as a smoking gun of the new physics. On the one hand, current and future high energy colliders offer an ideal environment for such measurements. On the other hand, it is essential to investigate the optimal measurement method for extracting not only <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>d</mi><mi>τ</mi><mi>γ</mi></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>d</mi><mi>τ</mi><mi>Z</mi></msubsup></math>, but also the anomalous magnetic dipole moment (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>τ</mi></msub></math>). In this work, we analyze the precision of observables, particularly optimal observables, for determining these physics quantities through the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>γ</mi><mo>*</mo></msup><mo>/</mo><mi>Z</mi><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> leptons undergoing (semi)leptonic and hadronic decays at the center-of-mass energies at the Z pole mass and significantly below <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>Z</mi></msub></math>. By considering the full kinematic information of the decay products, we find that the sensitivities to the weak dipole moments, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Im</mi><mo stretchy="false">[</mo><msubsup><mi>d</mi><mi>τ</mi><mi>Z</mi></msubsup><mo stretchy="false">]</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Re</mi><mo stretchy="false">[</mo><msubsup><mi>d</mi><mi>τ</mi><mi>Z</mi></msubsup><mo stretchy="false">]</mo></math>, can reach <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>21</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>e</mi><mtext> </mtext><mi>cm</mi></mrow></math> at CEPC with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><msub><mi>m</mi><mi>Z</mi></msub></math>. This compares to sensitivities for the electric dipole moments, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Im</mi><mo stretchy="false">[</mo><msubsup><mi>d</mi><mi>τ</mi><mi>γ</mi></msubsup><mo stretchy="false">]</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Re</mi><mo stretchy="false">[</mo><msubsup><mi>d</mi><mi>τ</mi><mi>γ</mi></msubsup><mo stretchy="false">]</mo></math>, of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>20</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>e</mi><mtext> </mtext><mi>cm</mi></math> at Belle-II <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo></math> resonance and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>17</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>e</mi><mtext> </mtext><mi>cm</mi></math> at BEPCII <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> resonance. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>τ</mi></msub></math>, we find that precisions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Im</mi><mo stretchy="false">[</mo><msub><mi>a</mi><mi>τ</mi></msub><mo stretchy="false">]</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Re</mi><mo stretchy="false">[</mo><msub><mi>a</mi><mi>τ</mi></msub><mo stretchy="false">]</mo></math> can be attained at Belle-II <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>10.58</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.

Peng-Cheng Lu

Zong-Guo Si

Han Zhang

Probing the electromagnetic dipole moment of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> lepton in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>γ</mi><mo>*</mo></msup><mo>/</mo><mi>Z</mi><mo stretchy="false">→</mo><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math> reaction