Using data samples collected by the Belle and Belle II experiments at the Υ(4$\textit{S}$) resonance with integrated luminosities of 571 fb and 365 fb , respectively, we measure the pseudoscalar $\textit{B}$-meson mass difference to be $\textit{m}$($\textit{B}$ ) − $\textit{m}$($\textit{B}$ ) = (0$\textit{.}$495 ± 0$\textit{.}$024 ± 0$\textit{.}$005) MeV/$\textit{c}$ . The results are based on a simultaneous fit to the variable $${\overline{M} }_{bc}$$ , which is related to the $\textit{B}$ momentum, for $\textit{B}$ and $\textit{B}$ candidates; and to the energy dependence of $$\mathcal{R}=\sigma ({e}^{+}{e}^{-}\to {B}^{0}{\overline{B} }^{0}) / \sigma ({e}^{+}{e}^{-}\to {B}^{+}{B}^{-})$$ , which is measured using changes in the average center-of-mass energy over the data taking periods. The phase-space hypothesis $$\mathcal{R}={({p}_{{B}^{0}} /{p}_{{B}^{+}})}^{3}$$ , upon which previous measurements rely, is strongly disfavored by our fit; the measured mass-difference value for the phase-space hypothesis also differs significantly from our measurement. We constrain $$\mathcal{R}$$ in a broader energy range than covered by the direct measurement and extract the energy dependence of $$\mathcal{R}$$ in the range from the $$B\overline{B }$$ threshold up to 10.59 GeV. We interpret the results using a phenomenological model and constrain the parameters of the $$B\overline{B }$$ potential in the isovector channel.

M. Abumusabh

I. Adachi

L. Aggarwal

H. Ahmed

Y. Ahn

H. Aihara

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

N. Althubiti

K. Amos

N. Anh Ky

C. Antonioli

D. Asner

H. Atmacan

T. Aushev

R. Ayad

V. Babu

N. Baghel

S. Bahinipati

P. Bambade

Sw. Banerjee

M. Barrett

M. Bartl

J. Baudot

A. Beaubien

F. Becherer

J. Becker

J. Bennett

F. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

V. Bhardwaj

F. Bianchi

T. Bilka

D. Biswas

D. Bodrov

A. Bondar

G. Bonvicini

J. Borah

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

R. Briere

T. Browder

A. Budano

S. Bussino

Q. Campagna

M. Campajola

G. Casarosa

C. Cecchi

P. Chang

P. Cheema

L. Chen

B. Cheon

C. Cheshta

H. Chetri

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

S. Chutia

J. Colorado-Caicedo

I. Consigny

L. Corona

J. Cui

E. Cruz-Burelo

S. Motte

G. Marino

G. Nardo

G. Pietro

R. Sangro

M. Destefanis

S. Dey

A. Canto

Z. Doležal

I. Domínguez Jiménez

T. Dong

X. Dong

M. Dorigo

G. Dujany

P. Ecker

J. Eppelt

R. Farkas

P. Feichtinger

T. Ferber

T. Fillinger

C. Finck

G. Finocchiaro

F. Forti

B. Fulsom

Measurements of the mass difference $\textit{m}$($\textit{B}$ 0) $\textit{− m}$($\textit{B}$ +) and the energy dependence of the cross-section ratio $$\sigma ({e}^{+}{e}^{-}\to {B}^{0}{\overline{B} }^{0})/\sigma ({e}^{+}{e}^{-}\to {B}^{+}{B}^{-})$$ at Belle and Belle II

Starting from the most general effective |∆$\textit{B}$| = 1 Hamiltonian describing non-leptonic $\textit{b}$-quark decays $$ b\to {q}_1{\overline{q}}_2{q}_3 $$ , we compute analytic expressions for all matching coefficients of the two-quark operator contributions in the heavy quark expansion (HQE) of a $\textit{B}$ meson, up to mass-dimension-six. In addition, we calculate the weak-annihilation contributions, which enter the matching of four-quark operators in the HQE at dimension-six and were previously missing. Our results complete the calculation of beyond Standard Model (BSM) effects in non-leptonic, tree-level, $\textit{b}$-quark decays relevant for $\textit{B}$ meson lifetimes and lifetime ratios such as $$ \tau \left({B}_s^0\right)/\tau \left({B}_d^0\right) $$ . Such BSM contributions naturally arise in generic extensions of the Standard Model (SM) that aim to address the observed tensions between experimental measurements and theoretical predictions based on QCD factorisation in several colour-allowed non-leptonic $\textit{B}$-meson decays. As a by-product of our calculation, we also determine the matching coefficients in the HQE induced by the QCD-penguin operators within the SM, including both the interference between current-current and penguin operators and the contributions quadratic in the penguin operators. Owing to the suppression of the QCD-penguin Wilson coefficients within the SM, these effects are typically regarded as corrections of order $\textit{α}$ and $$ {\alpha}_s^2 $$ in the strong coupling, respectively. Our results reproduce the known expressions at dimension-three and provide new results for the coefficients of the chromomagnetic operator at dimension-five and of the Darwin operator at dimension-six.

Germany

Martin Lang

Alexander Lenz

Ali Mohamed

Netherlands

Maria Piscopo

Aleksey Rusov

$\textit{B}$-meson decay width up to $$ 1/{m}_b^3 $$ corrections within and beyond the Standard Model

We continue the investigation of symmetries and anomalies of $\textit{T}$[$\textit{M}$] theories obtained by compactifying 6d SCFTs on an internal manifold $\textit{M}$. We extend the notion of “polarizations on a manifold $\textit{M}$” to cases where $\textit{M}$ may have boundaries or defects. Through examples with $\textit{M}$ of dimension two, three, and four, we illustrate recurring themes in compactifications — for instance, the important roles played by Kaluza-Klein modes, and how the generalized symmetries (including higher-group and non-invertible ones) of $\textit{T}$[$\textit{M}$], together with their anomalies, arise from non-trivial combinations of the parent 6d symmetries and the geometric structures of the internal manifold. For each dimension, we also focus on several topics that are especially interesting in that setting. These include: for 2-manifolds, the geometry of the “full moduli space” of $\textit{T}$[$\textit{M}$ ] and its interaction with polarizations and symmetries; for 3-manifolds, the effect of torsion in homology on the spectrum of line operators in $\textit{T}$[$\textit{M}$ ], together with applications to the study of quantum invariants such as $$ {\hat{Z}}_a\left({M}_3,q\right) $$ ; and for 4-manifolds, predictions for VOA[$\textit{M}$ ] following from symmetries of $\textit{T}$[$\textit{M}$ ], as well as the construction of a new invariant of 4-manifolds that depends on two “$\textit{q}$-parameters.” Along the way, we discuss a range of topics that are of independent interest, such as how non-invertible symmetries in higher dimensions can become invertible under compactification, how to classify defects in quantum field theory via their response to a change of framing, and the interplay between $$ {\hat{Z}}_a $$ and volume conjectures.

United States

Sergei Gukov

United Kingdom

Po-Shen Hsin

Denmark

Du Pei

Sunghyuk Park

Generalized global symmetries of $\textit{T}$[$\textit{M}$] theories. Part II

We explore the leptonic sector of a recently proposed supersymmetric SO(10) model with supersymmetry breaking in the 3–10 TeV range. A new ingredient in this work is the requirement that the observed baryon asymmetry is explained via non-thermal leptogenesis, which can be realized in a large class of supersymmetric hybrid inflation models including SO(10). We provide estimates for the masses of the three Standard Model neutrinos (with the lightest mass $\textit{m}$ ≈ 5 meV) as well as the three right-handed neutrinos ($\textit{M}$ ≈ 10 GeV and $\textit{M}$ ≈ 10 GeV). The best fit estimate for the leptonic CP violating parameter $\textit{δ}$ ≈ 235$\textit{°}$, and the value of the neutrinoless double beta decay mass parameter $\textit{m}$ ≈ 0.18 meV. A numerical analysis broadens the predicted range for $\textit{δ}$ (100$\textit{°}$–300$\textit{°}$), but leaves largely intact the predictions for the six (light and heavy) neutrino masses and $\textit{m}$ . Our statistical analysis, which yields the likelihood-predicted ranges of the observables, is fully consistent with JUNO’s newly released first measurement of reactor neutrino oscillations in the $$ \Delta {m}_{12}^2 $$ -sin $\textit{θ}$ plane, with JUNO improving the precision by a factor of 1.6 relative to the combination of all previous measurements. The implementation of successful non-thermal leptogenesis allows us to provide estimates for the inflaton mass ($\textit{m}$ ≈ 7 × 10 GeV) and the reheating temperature ($\textit{T}$ ≈ 4 × 10 GeV).

Slovenia

Shaikh Saad

Qaisar Shafi

Neutrino masses, $\textit{δ}$ PMNS, and $\textit{m}$ $\textit{ββ}$ in SO(10)

<p>In all previous calculations of the nonlocal subleading contribution to the inclusive penguin decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><msub><mi>X</mi><mi>s</mi></msub><mi>γ</mi></math> due to the interference of the electroweak operators <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">O</mi><mn>1</mn><mi>c</mi></msubsup><mo>−</mo><msub><mi mathvariant="script">O</mi><mrow><mn>7</mn><mi>γ</mi></mrow></msub></math> the local Voloshin term was subtracted. In view of the ongoing analysis at order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math>, we present a calculation of the complete nonlocal contribution which takes into account the high correlation between the uncertainties of the local Voloshin and the nonlocal term of the previous analyses. The new calculation has a high impact on the range of the nonlocal contribution.</p>

Michael Benzke

Maria Vittoria Garzelli

Tobias Hurth

Addendum to “Resolved <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msub><mi>m</mi><mi>b</mi></msub></math> contributions to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><msub><mi>X</mi><mrow><mi>s</mi><mo>,</mo><mi>d</mi></mrow></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><msub><mi>X</mi><mi>s</mi></msub><mi>γ</mi></math>”

This study presents a novel interpretation of complexity in the formalism of <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity, where <italic>R</italic> specifies the Ricci scalar, <math altimg='si2.svg'><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub></math> is written as matter Lagrangian that describes characteristics of the matter fields, and <math altimg='si3.svg'><mi mathvariant='script'>T</mi></math> represents the trace of energy-momentum tensor. We commence with the contemplation of the inner sector as a cylindrical configuration having anisotropic matter and linked with the exterior region through a hypersurface. We determine the modified field equations associated with <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity and assume the preliminarily established relations between the conformal tensor and the intrinsic curvature. We consider the generally employed mathematical expressions for Tolman mass and C-Energy and evaluate their relationship with the conformal tensor. The structural scalars are calculated from orthogonal splitting of Riemann tensor, out of which <italic>Y<inf>TF</inf></italic> is categorized as complexity factor for the inferred fluid composition. It is important to specify that the complexity factor is eradicated in the framework of uniform matter configuration and also in the scenario when anisotropic terms are canceled with each other. Significant results related to the Weyl scalar, Tolman mass, and the complexity factor are derived in <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity. The vanishing complexity constraint is considered in order to deal with the modified field equations that have extra degrees of freedom and to find particular solutions corresponding to the specific models.

Pakistan

A. Rehman

Azerbaijan

M. Yousaf

Uzbekistan

Bekzod Rahmatov

Javlon Rayimbaev

Munisbek Akhmedov

Complexity evaluation related to the cylindrically symmetric anisotropic matter in <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> theory

Accurate measurements of fundamental cosmological parameters, especially the Hubble constant ( $$H_0$$ ) and present-day matter density ( $$\Omega _\mathrm{{m} 0}$$ ), are crucial for constraining dark energy (DE) evolution. We analyze the sensitivities of cosmological observables ($\textit{H}$($\textit{z}$), $$D_L(z)$$ , $$\text {E}_{\text {G}}$$ ) to $$\Omega _\mathrm{{m} 0}$$ , $$\omega _{0}$$ , and $$\omega _{a}$$ under different parametrizations. Our results show observables are far more sensitive to $$\Omega _\mathrm{{m} 0}$$ than to DE equation of state parameters (e.g., at $$z \sim 0.5$$ , $\textit{H}$($\textit{z}$)’s $$\Omega _\mathrm{{m} 0}$$ sensitivity is $$\sim 0.7$$ vs. $$\omega _{a}$$ ’s $$\sim 0.04$$ ). This hierarchy mandates high-precision $$\Omega _\mathrm{{m} 0}$$ measurements to accurately constrain time-varying DE. We also find DE parameter sensitivity highly depends on parametrization; the standard CPL form shows low sensitivity to $$\omega _{a}$$ , but $$\omega (z) = \omega _{0}+ \omega _{a}\ln (1+z)$$ significantly enhances it. Our analysis of DESI DR1/DR2 data confirms these theoretical limits: standalone DESI data primarily provides only upper limits for $$\omega _{a}$$ , underscoring insufficient constraining power for a definitive time-varying DE detection. While combined datasets offer tighter constraints, interpretation requires caution due to parametrization influence. We further confirm this point using simulated Supernovae MCMC data. In conclusion, improving $$\Omega _\mathrm{{m} 0}$$ precision and adopting optimized parametrizations are imperative for future surveys like DESI to fully probe dark energy’s nature.

South Korea

Seokcheon Lee

Probing time-varying dark energy with DESI: the crucial role of precision matter density ( $$\Omega _\mathrm{{m} 0}$$ ) measurements

<p>We propose and evaluate a source-equals-detector search for the deexcitation of the long-lived isomer <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Ta</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>180</mn><mi mathvariant="normal">m</mi></mrow></mmultiscripts></mrow></math> in natural tantalum (Ta), using a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-ray transition-edge-sensor (TES) array. Two capabilities absent in conventional high-purity germanium (HPGe) searches are exploited: (i) near-unity containment of low-energy secondaries [internal-conversion (IC) electrons and characteristic x-rays] and of the nuclear recoil, enabling a calorimetric, event-by-event measurement of the total deposited energy in the absorber; and (ii) a delayed-coincidence tag using the subsequent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Ta</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>180</mn></mrow></mmultiscripts></mrow></math> electron-capture (EC) decay to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Hf</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>180</mn></mrow></mmultiscripts></mrow></math>. We evaluate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mi>σ</mi></math> discovery reach for IC and for dark-matter (DM)-induced deexcitation in two benchmark scenarios: a strongly interacting DM subcomponent and inelastic DM with off diagonal couplings. Using a background model based on intrinsic radioactivity in the Ta absorber and realistic detector performance, we show that arrays with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>TES</mi></mrow></msub><mo>=</mo><mn>256</mn></mrow></math> and 1,000 pixels can reach the theoretically expected IC half-life within 2.6 yr and 0.66 yr, respectively. For an array with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>TES</mi></msub><mo>=</mo><msup><mn>10</mn><mn>4</mn></msup></math> and a five-year exposure, the projected sensitivity to DM-induced de-excitation surpasses limits inferred from HPGe nonobservations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Ta</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>180</mn><mi mathvariant="normal">m</mi></mrow></mmultiscripts></mrow></math> and probes regions of parameter space not covered by current direct-detection experiments.</p>

Japan

A. Gando

K. Ichimura

K. Ishidoshiro

T. Kikuchi

T. Kishimoto

A. Takeuchi

R. Sato

R. Smith

Probing internal conversion and dark-matter-induced deexcitation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>Ta</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>180</mn><mi mathvariant="normal">m</mi></mrow></mmultiscripts></mrow></math> with a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-ray TES array

As double heavy quarkonia, charmonium and bottomonium are generally considered to have small relativistic corrections and can be treated using nonrelativistic models. However, this is not always the case. In this paper, we employ the relativistic Bethe-Salpeter (BS) equation method to calculate the electromagnetic (EM) radiative decays of heavy quarkonium where the $\textit{M}$1 transition provides the leading-order contribution. Compared to nonrelativistic method which only computes $\textit{M}$1 transition, our calculations include $\textit{M}$1 + $\textit{E}$2 + $\textit{M}$3 + $\textit{E}$4 transitions, where the higher-order multipoles, $\textit{E}$2, $\textit{M}$3, and $\textit{E}$4, account for relativistic corrections. The study finds that relativistic effects are large in such transitions even for bottomonium. For instance: the relativistic corrections in the decays $\textit{ψ}$($\textit{nS}$) → $\textit{γη}$ ($\textit{mS}$) ($\textit{n}$ ≥ $\textit{m}$) range from 68$\textit{.}$1% to 83$\textit{.}$2%, while those for ϒ($\textit{nS}$) → $\textit{γη}$ ($\textit{mS}$) range between 65$\textit{.}$9% and 75$\textit{.}$2%.

China

Su-Yan Pei

Wei Li

Wen-Yuan Ke

Yi-Yi Rui

Qiang Li

Guo-Li Wang

Large relativistic corrections to nonrelativistic $\textit{M}$1 transitions in heavy quarkonium

We derive decomposition formulas for supercharacters of quantum affine orthosymplectic superalgebras and twisted quantum affine superalgebras into supercharacters of their finite-type quantum sub-superalgebras, by employing Cauchy-type identities for supersymmetric Schur functions. These formulas are obtained via a folding (reduction) procedure applied to the supercharacters of the finite-dimensional general linear Lie superalgebra <math altimg='si5.svg'><mrow><mi mathvariant='fraktur'>gl</mi><mo>(</mo><mi>M</mi><mo>|</mo><mi>N</mi><mo>)</mo></mrow></math>. As a special case, our results provide explicit character formulas for a class of Kirillov-Reshetikhin modules of quantum affine algebras (and their Yangian counterparts), thereby proving a previously proposed conjecture derived from Bethe ansatz analysis.

Zengo Tsuboi

Character formulas for Kirillov-Reshetikhin modules via folding of supercharacters of <math altimg='si5.svg'><mrow><mi mathvariant='fraktur'>gl</mi><mo>(</mo><mi>M</mi><mo>|</mo><mi>N</mi><mo>)</mo></mrow></math>