We investigate the high-energy, small-angle limit of two-body gravitational scattering. Using power counting arguments and dispersion relations in an effective field theory for the Regge regime, we derive the general loop expansion that determines how the leading Regge logarithms and their complex structure arise as a power series in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mo>/</mo><mi>s</mi></math>. Focusing on the tower of multi-H diagrams that govern the leading logarithmic behavior, we compute the leading double logarithm at four loops (or equivalently fifth post-Minkowskian order, 5PM) using both effective field theory methods and the multi-Regge expansion, finding complete agreement. Finally, using the aforementioned dispersion relations, we extract the single logarithmic contribution to the imaginary part of the eikonal phase at 5PM in the Regge limit.

Italy

Francesco Alessio

Vittorio Del Duca

United Kingdom

Riccardo Gonzo

Emanuele Rosi

United States

Ira Z. Rothstein

Michael Saavedra

Analytic structure of the high-energy gravitational amplitude: Multi-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi></math> diagrams and classical 5PM logarithms

Generalised spin structures are necessary for placing fermions on manifolds that do not admit a standard spin structure. This is especially relevant in a dimensional reduction on such a manifold, which can then be compensated by using fermions that are appropriately charged under some Maxwell or Yang-Mills field defined on the internal manifold. A well known example in the physics literature is $$ {\mathbbm{CP}}^2 $$ , which has four real dimensions and is the coset SU(3)/U(2). In this paper we focus on a five-dimensional coset space, namely the Wu manifold SU(3)/SO(3) , where SO(3) is maximal in SU(3). Intriguingly, the Wu manifold does not admit a spin structure or spin structure, it does admit a spin structure. We provide a physical interpretation of the spin structure by considering spinors that are coupled to an SO(3) Yang-Mills field defined on the Wu manifold, but which carry half-integer “isospin,” thereby canceling the minus sign in the holonomy for uncharged spinors that provides the original obstruction to an ordinary spin structure. We also construct a gauge-covariantly constant spinor in the Wu manifold, and we show how this can be employed in order to construct spin spinor harmonics from scalar harmonics. We provide a very explicit construction of all the scalar and spin harmonics. In a follow-up paper, we shall employ the results we obtain here in order to discuss dimensional reductions and consistent reductions on the Wu manifold.

Cameron Gibson

Okan Günel

Gabriel Larios

C. Pope

Spin $\textit{h}$ structure, scalar and charged spinor eigenfunctions on the SU(3)/SO(3) Wu manifold

We search for 15 rare decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> mesons to hadrons accompanied by an electron-positron pair <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mo stretchy="false">→</mo><mi>h</mi><mo stretchy="false">(</mo><msup><mrow><mi>h</mi></mrow><mrow><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></mrow></msup><mo stretchy="false">)</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math>, based on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>20.3</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of <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> collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector at BEPCII. No significant signals are observed, and the corresponding upper limits on the branching fractions at the 90% confidence level are determined. The sensitivities of the results are at the level of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></math>. The upper limits on the branching fractions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>ρ</mi><mo>+</mo></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>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo>*</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>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><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>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></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>η</mi><mo>′</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> decay channels are measured for the first time. For the <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><mn>0</mn></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>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mi>η</mi><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>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><mi>ω</mi><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>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><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>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></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>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></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>D</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><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><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> decay channels, the upper limits on the branching fractions are determined, with an improvement of at least a factor of four compared to previous searches. The upper limits on the branching fractions for the <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>ρ</mi><mn>0</mn></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><mi>ϕ</mi><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> decay channels are set at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4.6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, respectively.

China

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

C.S. Akondi

Germany

R. Aliberti

A. Amoroso

Q. An

Y.H. An

Y. Bai

JINR

O. Bakina

H.R. Bao

X.L. Bao

M. Barbagiovanni

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

D. Cabiati

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.M. Chen

T. Chen

W. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J. Cheng

L.N. Cheng

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

X.C. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denisenko

M. Destefanis

F. De Mori

E. Di Fiore

X.X. Ding

Y. Ding

Y.X. Ding

Yi. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

Z.J. Dong

M.C. Du

S.X. Du

Shaoxu Du

X.L. Du

Y.Q. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

Jin Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

Search for the rare decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">→</mo><mi>h</mi><mo stretchy="false">(</mo><msup><mi>h</mi><mrow><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></mrow></msup><mo stretchy="false">)</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math>

Quantum gravity (QG) has a natural cutoff given by the Planck scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>pl</mi></msub></math>. However, it is known that the effective field theory (EFT) of gravity can break down at a lower scale, the species scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>s</mi></msub><mo>≲</mo><msub><mi>M</mi><mi>pl</mi></msub></math>, if there are light species of particles. Here we point out that there is a third scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub><mo>≲</mo><msub><mi mathvariant="normal">Λ</mi><mi>s</mi></msub><mo>≲</mo><msub><mi>M</mi><mi>pl</mi></msub></math>, which marks the inverse length (or the temperature) of the smallest black hole where the EFT gives a correct description of its entropy and free energy. This latter scale is hard to detect from the viewpoint of EFT as it represents a phase transition to a state with lower free energy. We illustrate this using examples drawn from consistent QG landscape. In particular <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> gets related to Gregory-Laflamme transition in the decompactification limits of quantum gravity and to the Horowitz-Polchinski solution in the light perturbative string limits. We propose the existence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> marking the temperature at which neutral black holes undergo a phase transition, as a new Swampland condition for all consistent quantum theories of gravity. In the asymptotic regimes of field space <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.

Alek Bedroya

Cumrun Vafa

David H. Wu

Tale of three scales: The Planck, the species, and the black hole scales

This study investigates the Higgs rare decays <italic>h</italic> 0&#8239;&#8594;&#8239; <italic>Z&#947;, VZ</italic> within the next to minimum B-L supersymmetric model(NB-LSSM), where <italic>V</italic> denotes a vector meson ( <italic>&#981;, J</italic>/ <italic>&#968;</italic>, &#933;(1 <italic>S</italic>), <italic>&#961;</italic> 0, <italic>&#969;</italic>). Compared with the minimal supersymmetric Standard Model(MSSM), the NB-LSSM introduces three singlet Higgs superfields, which mix with the Higgs doublets, thereby modifying the lightest Higgs boson mass and its couplings. The loop-induced contributions resulting from the effective <italic>h</italic> 0 <italic>Z&#947;</italic> coupling can generate new physics(NP) contributions, significantly affecting the theoretical predictions for these rare decays through the new parameters such as <italic>&#954;, &#955;</italic>, <math altimg='si23.svg'><mrow><msub><mi>&#955;</mi><mn>2</mn></msub><mo>,</mo><mo>&#8230;</mo></mrow></math>. The results of this work provide a useful reference for probing NP beyond the Standard Model(SM).

Portugal

Xing-Xing Dong

Cai Guo

Wen Lu

Shu-Min Zhao

Tai-Fu Feng

The rare decays <italic>h</italic> 0&#8239;&#8594;&#8239; <italic>Z&#947;, VZ</italic> in the NB-LSSM

By solving algebraic relations for the conditions of Haantjes structure on a Lie algebra <math altimg='si114.svg'><mi mathvariant='script'>G</mi></math> and by using the corresponding automorphism group we proceed to classify all inequivalent algebraic Haantjes structures on <math altimg='si114.svg'><mi mathvariant='script'>G</mi></math>. In this manner, we obtain 49 inequivalent algebraic Haantjes structures on the <italic>h</italic> <inf>4</inf> Lie algebra. We propose a new deformation of the chiral sigma model on a Lie group by using Haantjes structure on it. Then, we will try to obtain conditions on this structure such that the deformed sigma model remains to be integrable. Finally, using the <italic>h</italic> <inf>4</inf> Haantjes structures and solving the conditions on the integrability of the model, we find three new integrable sigma models on the <italic>H</italic> <inf>4</inf> Lie group.

Iran

Mirenayatollah Bahadori

Ali Eghbali

Adel Rezaei-Aghdam

Integrable sigma models with Haantjes structure on the <italic>H</italic> <inf>4</inf> Lie group

Motivated by the observation of the doubly charmed tetraquark $ T_{cc}(3875)^+ $ , we present a systematic study of doubly heavy tetraquarks ( $ T_{QQ'\bar{q}\bar{q}'} $ ) using heavy antiquark-diquark symmetry (HADS) within a constituent quark model. By calibrating model parameters to known hadron spectra and incorporating the effective mass formula, we predict the masses for 38 ground-state tetraquarks with $ cc $ , $ bb $ , and $ bc $ heavy quark pairs, including the non-strange, single-strange, and double-strange configurations with quantum numbers $ J^P = 0^+, 1^+ $ and $ 2^+ $ . Notably, we identify several stable states below the relevant meson-meson thresholds, particularly in the $ bb\bar{q}\bar{q}' $ sector. The explicit connection between the doubly heavy tetraquark and the heavy baryon spectra through HADS reduces model dependence and reveals the fundamental systematics in the heavy-quark hadron landscape.

Liu-Yu Zhang

Tian-Wei Wu

Yong-Liang Ma

Bridging doubly heavy tetraquark mass spectrum with heavy baryons utilizing heavy antiquark-diquark symmetry * The work of Tian-Wei Wu is supported by the National Natural Science Foundation of China (12405108). Yong-Liang Ma is supported in part by the National Science Foundation of China (NSFC) (12347103) and Gusu Talent Innovation Program (ZXL2024363)

Motivated by recent HAL QCD simulations of the <italic>&#981;N</italic> interaction in the 4 <italic>S</italic> <inf>3/2</inf> channel and its modification in the 2 <italic>S</italic> <inf>1/2</inf> channel, we develop a first-principles few-body framework that embeds these potentials into configuration-space Faddeev&#8211;Yakubovsky equations. We predict bound <math altimg='si30.svg'><mrow><msubsup><mrow /><mi>&#981;</mi><mn>4</mn></msubsup><mi mathvariant='normal'>H</mi></mrow></math>, <math altimg='si31.svg'><mrow><msubsup><mrow /><mi>&#981;</mi><mn>4</mn></msubsup><mtext>He</mtext></mrow></math>, and <math altimg='si32.svg'><mrow><msubsup><mrow /><mi>&#981;</mi><mn>5</mn></msubsup><mtext>He</mtext></mrow></math> nuclei by performing calculations for <italic>&#981;</italic>-mesic <italic>&#981;NNN</italic> and <italic>&#981;NNNN</italic> systems. Both spin-dependent and spin-independent <italic>&#981;N</italic> interactions are considered, leading to deeply and moderately bound states, respectively. The deeply bound states originate from the strong attraction in the 2 <italic>S</italic> <inf>1/2</inf> <italic>&#981;N</italic> channel. Coulomb shifts of the binding energies are evaluated. Our findings provide the binding mechanism and demonstrate the importance of short-range <italic>&#981;N</italic> attraction.

France

R. Lazauskas

R.Ya. Kezerashvili

I. Filikhin

Possible existence of <math altimg='si22.svg'><msubsup><mrow /><mi>&#981;</mi><mn>3</mn></msubsup></math>H, <math altimg='si23.svg'><msubsup><mrow /><mi>&#981;</mi><mn>4</mn></msubsup></math>H, <math altimg='si23.svg'><msubsup><mrow /><mi>&#981;</mi><mn>4</mn></msubsup></math>He, and <math altimg='si24.svg'><msubsup><mrow /><mi>&#981;</mi><mn>5</mn></msubsup></math>He nuclei

The decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math>, with a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry expected to be close to zero in the standard model, is theoretically clean and sensitive to potential new physics. An analysis of the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>±</mo></msup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi mathvariant="normal">S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>±</mo></msup></math> is performed using proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.4</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="script">A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msup><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mn>0.028</mn><mo>±</mo><mn>0.009</mn><mo>±</mo><mn>0.009</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="script">A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msup><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0.118</mn><mo>±</mo><mn>0.062</mn><mo>±</mo><mn>0.031</mn></mrow></math>, and the branching fraction ratio is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0.055</mn><mo>±</mo><mn>0.004</mn><mo>±</mo><mn>0.002</mn></mrow></math>, where the first uncertainties are statistical and the second are systematic. These results are the most precise measurements of these quantities to date. A search for the rare decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>±</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi mathvariant="normal">S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>±</mo></msup></math> is also performed. No significant signal is observed, and the upper limit on the product of the branching fraction ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo></mrow></math> and the fragmentation-fraction ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mi>c</mi></msub><mo>/</mo><msub><mi>f</mi><mi>u</mi></msub></math> is set to be 0.015 (0.016) at the 90% (95%) confidence level.

Netherlands

R. Aaij

A.S.W. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

A.A. Adefisoye

Spain

B. Adeva

M. Adinolfi

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

M. Akthar

P. Albicocco

J. Albrecht

R. Aleksiejunas

CERN

F. Alessio

P. Alvarez Cartelle

R. Amalric

Brazil

S. Amato

J.L. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

C. Arata

F. Archilli

Z. Areg

M. Argenton

Costa Rica

S. Arguedas Cuendis

Precision Measurement of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> Violation and Branching Fractions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>h</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>h</mi><mo>=</mo><mi>π</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi></mrow></math>) Decays and Search for the Rare Decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math>