The weak decays of charmonium states such as $ J/\psi $ and $ \psi(2S) $ are instrumental in probing both nonperturbative QCD dynamics and the flavor structure of the Standard Model (SM). The extreme rarity of charmonium weak decays renders them highly sensitive to physics beyond the SM, particularly in channels that are heavily suppressed in the SM, such as flavor-changing neutral-current (FCNC) decays. This review highlights the critical role of the BESIII experiment, which leverages an unprecedented data sample of over $ 10^{10} $ $ J/\psi $ and $ 2.7\times10^{9} $ $ \psi(2S) $ events to achieve leading sensitivity in searches for charmonium weak decays. We present the latest and most stringent upper limits established by BESIII on various semileptonic, nonleptonic, and FCNC charmonium weak decay channels.

China

Xu-Ze Li

Kai-Xin Fan

Zheng-Yun You

Yu Zhang

Minggang Zhao

Mini-review of charmonium weak decays at BESIII * Supported in part by the National Key R&D Program of China (2023YFA1606000); the National Natural Science Foundation of China (NSFC) (12035009, 12175321, U1932101), and the National College Students' Science and Technology Innovation Project of Sun Yat-sen University

By introducing an extra stack of D6-branes to standard $$ \mathcal{N} $$ = 1 supersymmetric Pati-Salam models, we extend the landscape of its complete search. In this construction, the $\textit{d}$-stack of D6-branes is introduced besides the standard $\textit{a}$, $\textit{b}$, $\textit{c}$-stacks. More intersections from the extra stacks of D6-branes appear, and thus Higgs/Higgs-like particles arise from more origins. Among these models, we complete with 28 classes of $$ \mathcal{N} $$ = 1 supersymmetric Pati-Salam models under gauge symmetries $\textit{SU}$ (4) × $\textit{SU}$ (2) × $$ SU{(2)}_{R_1} $$ × $$ SU{(2)}_{R_2} $$ and $\textit{SU}$ (4) × $$ SU{(2)}_{L_1} $$ × $\textit{SU}$ (2) × $$ SU{(2)}_{L_2} $$ , where $\textit{d}$-stack of D6-branes carries the gauge symmetries $$ SU{(2)}_{R_2} $$ and $$ SU{(2)}_{L_2} $$ , respectively. The $$ SU{(2)}_{L_1/{R}_1} $$ × $$ SU{(2)}_{L_2/{R}_2} $$ can be broken down to the diagonal $\textit{SU}$ (2) gauge symmetry via bifundamental Higgs fields. In such a way, we for the first time successfully constructed three-family supersymmetric Pati-Salam models from non-rigid D6-branes with extra $\textit{d}$-stacks of D6-branes as visible sectors. Interestingly, by introducing extra stack of D6-branes to the standard supersymmetric Pati-Salam models, the number of filler brane reduces in general, and eventually the models without any $\textit{USp}$($\textit{N}$) gauge symmetry present. This reduces the exotic particles from filler brane intersection yet provides more vector-like particles from $$ \mathcal{N} $$ = 2 subsector that are useful in renormalization group equation evolution as an advantage. Moreover, interesting degeneracy behavior with the same gauge coupling ratio exists in certain class of models.

Haotian Huangfu

Tianjun Li

Qi Sun

Rui Sun

The $$ \mathcal{N} $$ = 1 supersymmetric Pati-Salam models with extra $$ SU{(2)}_{L_2/{R}_2} $$ gauge symmetry from intersecting D6-branes

The time-dependent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> decays is measured using proton-proton collision data corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, collected with the LHCb detector at a center-of-mass energy of 13 TeV during the years 2015–2018. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violation parameters for this process are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><msubsup><mrow><mi>β</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>d</mi></mrow><mrow><mi>eff</mi></mrow></msubsup><mo>=</mo><mn>0.710</mn><mo>±</mo><mn>0.084</mn><mo>±</mo><mn>0.051</mn><mtext> </mtext><mtext> </mtext><mi>rad</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">|</mo><mi>λ</mi><mo stretchy="false">|</mo><mo>=</mo><mn>1.019</mn><mo>±</mo><mn>0.034</mn><mo>±</mo><mn>0.024</mn></mrow></math>, where the first uncertainty is statistical and the second systematic. This constitutes the first observation of time-dependent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> decays. Assuming approximate SU(3) flavor symmetry, these results are combined with the previous consistent LHCb measurement to set the most stringent constraint on the penguin contribution, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>ϕ</mi><mi>s</mi></msub></math>, to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating phase <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ϕ</mi><mi>s</mi></msub></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mi>ϕ</mi><mo stretchy="false">(</mo><mn>1020</mn><mo stretchy="false">)</mo></math> decays, yielding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>ϕ</mi><mi>s</mi></msub><mo>=</mo><mn>5.0</mn><mo>±</mo><mn>4.6</mn><mtext> </mtext><mtext> </mtext><mi>mrad</mi></math>.

Netherlands

R. Aaij

United Kingdom

A.S.W. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

United States

A.A. Adefisoye

Spain

B. Adeva

M. Adinolfi

P. Adlarson

France

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Poland

M. Akthar

Italy

P. Albicocco

Germany

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

L. Arnone

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J.A. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J.J. Back

Z.B. Bai

P. Baladron Rodriguez

V. Balagura

A. Balboni

W. Baldini

Z. Baldwin

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I.R. Barbosa

R.J. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

S. Bashir

B. Batsukh

P.B. Battista

A. Bavarchee

A. Bay

A. Beck

M. Becker

F. Bedeschi

I.B. Bediaga

N.A. Behling

S. Belin

A. Bellavista

K. Belous

I. Belov

I. Belyaev

G. Benane

G. Bencivenni

E. Ben-Haim

A. Berezhnoy

R. Bernet

A. Bertolin

F. Betti

J. Bex

O. Bezshyyko

S. Bhattacharya

M.S. Bieker

N.V. Biesuz

A. Biolchini

M. Birch

F.C.R. Bishop

A. Bitadze

A. Bizzeti

T. Blake

Observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> Violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> Decays

The decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> is studied at LHCb for the first time using proton-proton collision data recorded by the LHCb experiment at a center-of-mass energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>, 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 branching ratio relative to 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 mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mrow><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup></mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> 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><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mrow><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup></mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>/</mo><mo stretchy="false">[</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 mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mrow><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup></mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>=</mo><mn>0.53</mn><mo>±</mo><mn>0.05</mn><mo>±</mo><mn>0.05</mn></mrow></math> where the first uncertainty is statistical and the second is systematic. Evidence is found for contributions from two resonant states, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2923</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2939</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>, in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mi>K</mi><mi mathvariant="normal">S</mi><mn>0</mn></msubsup></math> system. The two states show a significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3.9</mn><mi>σ</mi></math> relative to the nonresonant hypothesis. These two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup></math> states are consistent with being the isospin partners of the states observed in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msup><mi>K</mi><mo>−</mo></msup></math> system.

M. Abdelfatah

F. Blanc

J.E. Blank

S. Blusk

Study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msubsup><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> decay

We develop a local reconstruction framework between $$\Phi (R,\phi ,X)$$ theories with linear dependence on $$X$$ and generalized hybrid metric-Palatini gravity. The construction is formulated in vacuum in the Einstein frame, where both formulations can be written as two-scalar theories with the same field-space geometry. The framework provides a practical method for finding $$\Phi (R,\phi ,X)$$ and $$f(R,\mathcal {R})$$ functions that describe the same regular Einstein-frame two-scalar sector. Starting from a given $$\Phi (R,\phi ,X)$$ model, we derive the equation that determines the compatible hybrid functions $$f(R,\mathcal {R})$$ and show that it has a Clairaut-type structure. We also show that the inverse reconstruction is not unique: a regular hybrid Einstein-frame potential determines a family of compatible $$\Phi (R,\phi ,X)$$ theories, parametrized by the kinetic coupling. Explicit examples illustrate the reconstruction procedure, its domain of validity, and the translation of model parameters between the $$\Phi (R,\phi ,X)$$ and $$f(R,\mathcal {R})$$ formulations.

Jonathan Ramírez

Reconstruction between generalized hybrid metric-Palatini gravity and $$\Phi (R,\phi ,X)$$ theories

We ask whether two classical time-machine geometries, the Ori (2005) compact-vacuum-core metric and the Ahmed (2018) four-dimensional generalisation of Misner space, remain admissible exact solutions when the gravitational sector is enlarged to the recently proposed $$f(R,\mathcal {L}_{m},\Phi ,X)$$ class, an extension of $$f(R,\mathcal {L}_{m})$$ that couples curvature, the matter Lagrangian density, a scalar field $$\Phi $$ , and its kinetic invariant $$X = g^{\mu \nu }\nabla _{\mu }\Phi \nabla _{\nu }\Phi $$ . Working with the explicit model $$f = R + \mathcal {L}_{m} + (\lambda /2)\,X$$ and a vanishing scalar potential, we compute the curvature invariants, the modified field equations, and the effective stress-energy components produced by the harmonic scalar profile $$\Phi (x,y) = a(x^{2}-y^{2})/2$$ in both backgrounds. The Ricci scalar vanishes for the Ori metric and obeys $$R = e^{f}(f_{,xx}+f_{,yy})$$ for the Ahmed metric; the kinetic invariant takes the explicit forms $$X = a^{2}(x^{2}+y^{2})$$ and $$X = a^{2}e^{f}(x^{2}+y^{2})$$ , respectively. Both metrics solve the field equations of the modified theory with anisotropic matter sources, and the chronology-violating regions $$g_{zz}<0$$ (Ori) and $$g_{\psi \psi }<0$$ (Ahmed) survive the modification. Energy-density profiles measured by a closed-timelike-curve observer match those measured by a static observer outside the chronology horizon, so the additional scalar degree of freedom in $$f(R,\mathcal {L}_{m},\Phi ,X)$$ gravity does not enforce a chronology-protection mechanism in either background. The conclusion mirrors the parallel result for the Li time-machine and supplies a consistency test for scalar-extended modified gravity in non-globally-hyperbolic settings.

India

Faizuddin Ahmed

Jordan

Ahmad Al-Badawi

Türkiye

İzzet Sakallı

Are Petrov type-N and D spacetimes admitting CTCs valid in $$f(R,\mathcal {L}_m,\Phi ,X)$$ gravity?

In this study, within the framework of <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> modified gravity, we investigate the influence of coupling parameter ( <italic>&#955;</italic>), magnetic field and anisotropy parameter on the neutron star structure. This work employs an accurate equation of state (EoS), derived from realistic microscopic calculations based on the AV18 nucleon-nucleon potential, to compute the structure of this compact object. Here, determination of Schwarzschild radius, compactness, gravitational surface redshift and Kretschmann scalar within the <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity, confirms that our theoretical results are consistent with the observational constraints. While established physical EoSs within the framework of Einstein gravity have successfully characterized a broad range of compact objects, they remain inadequate in explaining certain massive objects residing within the mass gap ( <math altimg='si82.svg'><mrow><mn>2.5</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>5</mn><msub><mi>M</mi><mo>&#8857;</mo></msub></mrow></math>). We show that some compact objects residing in the mass gap can be interpreted as candidates of neutron stars within the framework of <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity. Motivated by the observation of objects within this mass range, we employ a framework that simultaneously incorporates <math altimg='si83.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><mi mathvariant='script'>R</mi><mo linebreak='goodbreak'>+</mo><mn>2</mn><mi>&#955;</mi><mi>T</mi></mrow></math> gravity and Bowers-Liang anisotropy model. Our study concludes that an increase in the star&#8217;s surface magnetic field (which dominates the softening of the EoS) leads to a reduction in the maximum masses and corresponding radii. Furthermore, at a fixed <italic>&#955;</italic>, larger values of the anisotropy parameter <italic>&#946;</italic> result in increased masses and radii. Conversely, for fixed <italic>&#946;</italic>, a decrease in <italic>&#955;</italic> yields an increasing trend in both masses and radii. Finally, we compare our results with the observational data from LIGO/Virgo/KAGRA and NICER, setting the parameters of the <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> theory and anisotropy to successfully reproduce the masses and radii of the GW170817, PSR J0952-0607 and PSR J0740+6620 and the masses of the secondary components of GW190814 ( <math altimg='si84.svg'><mrow><msub><mi>m</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn><mo>.</mo><msubsup><mn>59</mn><mrow><mo>&#8722;</mo><mn>0.09</mn></mrow><mrow><mo>+</mo><mn>0.08</mn></mrow></msubsup><msub><mi>M</mi><mo>&#8857;</mo></msub></mrow></math>) and GW200210-092254 ( <math altimg='si85.svg'><mrow><msub><mi>m</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn><mo>.</mo><msubsup><mn>83</mn><mrow><mo>&#8722;</mo><mn>0.42</mn></mrow><mrow><mo>+</mo><mn>0.47</mn></mrow></msubsup><msub><mi>M</mi><mo>&#8857;</mo></msub></mrow></math>).

Iran

M. Savari

G.H. Bordbar

J. Sedaghat

A. Sheykhi

Structure of anisotropic magnetized neutron stars in <math altimg='si3.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity with realistic equation of state

We investigate the interplay of the Weak Gravity Conjecture (WGC) and the Weak Cosmic Censorship Conjecture (WCCC) in $\textit{F}$($\textit{R}$)-Euler-Heisenberg black holes in Anti-de Sitter and de Sitter backgrounds. The solution is characterized by the electric charge $\textit{q}$, the $\textit{F}$($\textit{R}$) deviation $$ {f}_{R_0} $$ , the Euler-Heisenberg coupling $\textit{λ}$, and the constant scalar curvature $\textit{R}$ . We establish a universal entropy-extremality relation that provides thermodynamic evidence for the WGC independently of $$ {f}_{R_0} $$ and $\textit{R}$ . Photon sphere analysis from both geodesic and topological perspectives confirms the simultaneous compatibility of the WGC and WCCC, with the Euler-Heisenberg coupling restoring photon spheres in the naked singularity regime. Gravitational lensing in the strong- and weak-deflection limits reveals that the photon sphere radius is independent of the cosmological background while the critical impact parameter nearly doubles in de Sitter. Black hole shadow images under isotropic accretion are constructed. Within the Barrow entropy framework, we uncover van der Waals-type phase transitions and analyze Joule-Thomson expansion, identifying the small black hole phase as the WGC-compatible thermodynamic regime accessible via isenthalpic cooling.

Saeed Noori Gashti

Erdem Sucu

Mohammad Alipour

Ankit Anand

Mohammad Afshar

Azerbaijan

Behnam Pourhassan

Jafar Sadeghi

Testing the weak gravity conjecture via gravitational lensing, black hole shadows, and Barrow thermodynamics in F(R)-Euler-Heisenberg (A)dS black holes

This paper presents a study of the charmless three-body decays $$ {B}_{(s)}^0\to {K}_{\mathrm{S}}^0{h}^{+}h{\prime}^{-} $$ (where $\textit{h}$ $\textit{′}$ = $\textit{π, K}$), using a sample of $\textit{pp}$ collision data collected by the LHCb experiment during Runs 1 and 2 of the LHC, corresponding to an integrated luminosity of 9 fb . The decay $$ {B}_s^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-} $$ is observed for the first time, and the following ratios of branching fractions are measured:

A. Abdelmotteleb

A. Adefisoye

Sweden

H. Afsharnia

C. Aidala

Z. Aliouche

J. Amey

A. Andreianov

D. Andreou

J. Back

I. Barbosa

R. Barlow

M. Bartolini

J. Basels

G. Bassi

P. Battista

I. Bediaga

N. Behling

V. Bellee

S. Bernet Andres

E. Bertholet

C. Betancourt

Ia. Bezshyiko

J. Bhom

M. Bieker

N. Biesuz

P. Billoir

F. Bishop

Improved branching-fraction measurements of $$ {B}_{(s)}^0\to {K}_{\mathrm{S}}^0{h}^{+}h{\prime}^{-} $$ decays and first observation of $$ {B}_s^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-} $$

An analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo stretchy="false">(</mo><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><mo stretchy="false">)</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> decay is presented using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>8.4</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The full set of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-averaged and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-asymmetric angular observables is determined in bins of the invariant mass squared of the dimuon system, as well as the branching fraction relative to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></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></mrow></math> decay. For the first time, the full set of observables pertaining to the <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></math> S-wave contribution to the final state are presented and consideration is given to effects arising from the mass of the muons. The extracted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-asymmetry observables show no significant deviations from zero. The measurements of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-averaged observables and the branching fractions continue to exhibit the pattern of tensions with the standard model predictions that have been seen in previous analyses that use part of the dataset considered in this Letter.

Comprehensive Analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> Decay