Coulomb branches of vacua are the most universal moduli spaces that arise in local unitary interacting 4d $$ \mathcal{N} $$ = 2 superconformal field theories (SCFTs). In these theories, 1/2-BPS primaries parameterize the Coulomb branches and form (anti-)chiral rings. We define the notion of a Coulomb branch operator algebra, $$ {\mathcal{A}}_{\mathcal{C}} $$ , that contains these chiral and anti-chiral rings along with infinitely many more operators and products that are less protected by supersymmetry. Using a universal symmetry, $$ \mathcal{I}\cong {\mathbb{Z}}_2 $$ , that arises from studying the superconformal group, we give $$ \mathcal{I} $$ selection rules for $$ {\mathcal{A}}_{\mathcal{C}} $$ and, more generally, for arbitrary products in the local operator algebra of any 4d $$ \mathcal{N} $$ = 2 SCFT. Defining the notion of a “Coulombic” SCFT, we propose explanations for certain phenomena in a 4d/2d correspondence involving 4d $$ \mathcal{N} $$ = 2 theories and 2d vertex operator algebras. Finally, by considering deformations of $$ \mathcal{I} $$ , we explore the case of $$ \mathcal{N} $$ > 2 SCFTs.

United Kingdom

Matthew Buican

Coulomb branch operator algebras and universal selection rules for $$ \mathcal{N} $$ = 2 SCFTs

Using data samples of 102 million <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math> events and 158 million <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> events 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 search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><mi>u</mi><mi>d</mi><mi>s</mi><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">]</mo></math> pentaquark states decaying to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math>. Using the first observations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo>,</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> inclusive decays to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math>, we find evidence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> state with a local significance of 3.3 standard deviations, including statistical and systematic uncertainties. We measure the mass and width of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>4471.7</mn><mo>±</mo><mn>4.8</mn><mo>±</mo><mn>0.6</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>22</mn><mo>±</mo><mn>13</mn><mo>±</mo><mn>3</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, respectively. The branching fractions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> production are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo>/</mo><msub><mrow><mover accent="true"><mrow><mi>P</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi>anything</mi><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">(</mo><mn>3.5</mn><mo>±</mo><mn>2.0</mn><mo>±</mo><mn>0.2</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo>/</mo><mspace linebreak="goodbreak"></mspace><msub><mrow><mover accent="true"><mrow><mi>P</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi>anything</mi><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">(</mo><mn>2.9</mn><mo>±</mo><mn>1.7</mn><mo>±</mo><mn>0.4</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math>. The inclusive branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo>,</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi><mo>/</mo><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi><mo>/</mo><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi>anything</mi><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">(</mo><mn>36.9</mn><mo>±</mo><mn>5.3</mn><mo>±</mo><mn>2.4</mn><mo stretchy="false">)</mo><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"><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi><mo>/</mo><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi>anything</mi><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">(</mo><mn>22.3</mn><mo>±</mo><mn>5.7</mn><mo>±</mo><mn>3.1</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>. We measure the visible cross section <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>σ</mi><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><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi><mo>/</mo><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo>+</mo><mi>anything</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>90</mn><mo>±</mo><mn>14</mn><mo>±</mo><mn>6</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mrow><mi>fb</mi></mrow></mrow></math> for the continuum production at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>10.52</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. In all cases, the first uncertainties are statistical and the second are systematic.

I. Adachi

L. Aggarwal

H. Ahmed

J.K. Ahn

H. Aihara

N. Akopov

M. Alhakami

A. Aloisio

N. Althubiti

D.M. Asner

H. Atmacan

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

D. Biswas

D. Bodrov

A. Bolz

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

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

B.G. Cheon

K. Chilikin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

J. Cochran

L. Corona

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. De Nardo

G. De Pietro

R. de Sangro

M. Destefanis

S. Dey

R. Dhamija

F. Di Capua

J. Dingfelder

Z. Doležal

I. Domínguez Jiménez

T.V. Dong

X. Dong

D. Dossett

K. Dugic

G. Dujany

P. Ecker

J. Eppelt

P. Feichtinger

T. Ferber

T. Fillinger

C. Finck

G. Finocchiaro

F. Forti

B.G. Fulsom

A. Gabrielli

E. Ganiev

M. Garcia-Hernandez

G. Gaudino

Search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4338</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo>,</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> Inclusive Decays at Belle

We study Carrollian amplitudes of massless scalars in (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>+</mo><mn>2</mn></mrow></math>) Minkowski space. Using the prescription recently shown by Alday et al. [Carrollian amplitudes from holographic correlators, <a href="http://dx.doi.org/10.1007/JHEP03(2025)158">J. High Energy Phys. 03 (2025) 158</a>] originally designed for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> Witten diagrams, we show that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> Witten diagrams in position space in the flat space limit reduce to Carrollian amplitudes. The flat space limit in the bulk is implemented by the Carrollian limit at the boundary. Focusing on four-point correlators with contact and exchange diagrams, we show that the Carrollian limit makes the universality of the bulk point singularity manifest upon performing analytic continuation to the Lorentzian signature of the boundary correlators. Unlike four-point Carrollian amplitudes in (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>+</mo><mn>3</mn></mrow></math>) dimensions, the (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>+</mo><mn>2</mn></mrow></math>) dimensional ones are nondistributional, having analytic properties simpler than the AdS correlators. We also observe for the first time a double copy structure of Carrollian amplitudes.

Iustin Surubaru

Bin Zhu

Carrollian amplitudes and holographic correlators in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>/</mo><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>

We explore the Faddeev-Jackiw symplectic Hamiltonian reduction of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>l</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> affine Toda model coupled to matter, which includes new parametrizations for a scalar field and a Grassmannian fermionic field. The structure of constraints and symplectic potentials primarily dictates the strong-weak dual coupling sectors of the theory, ensuring the equivalence between the Noether and topological currents. The analytical calculations encompass the fermion-kink classical solution, the excited fermion bound states localized on the kink, and the scattering states, all of which account for the fermion backreaction on the soliton. The total energy, which includes the classical fermion-soliton interaction energy, the bound-state fermion energy, and the fermion vacuum polarization energy, is determined by the topological charge of the kink. This system satisfies first-order differential equations and a chiral current conservation equation. Our results demonstrate that the excited fermion bound states and scattering states significantly alter the properties of the kink. Notably, they give rise to a pumping mechanism for the topological charge of the in-gap kink due to fermionic backreaction, as well as the appearance of kink states in the continuum.

Brazil

H. Blas

R. Quicaño

Fermionic backreaction on kink and topological charge pumping in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mi>l</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></math> affine Toda model coupled to matter

Hybrid mesons occupy a unique position in the hadronic spectrum, offering a valuable insight into the non-perturbative nature of the glue field. Hybrid states with exotic $$J^{PC}$$ quantum numbers, such as the $$1^{-+}$$ , $$0^{+-}$$ and $$2^{+-}$$ , cannot mix with conventional $$q\bar{q}$$ mesons, making them critical for establishing the full spectrum of hybrid mesons. In this work, we investigate the masses and the strong decays of $$0^{+-}$$ and $$2^{+-}$$ hybrid mesons, which could be regarded as the first orbitally excited states of the $$\pi _1(1600)$$ and $$\eta _1(1855)$$ mesons. We develop a constituent gluon model and apply it to study the mass spectra and decay modes of these exotic states. Our results suggest that experiment may searched for these $$0^{+-}$$ and $$2^{+-}$$ hybrid mesons in the mass region between 2.0 and 2.4 GeV. Additionally, we identify some key decay channels which should be targeted in future experiments.

China

Bing Chen

Xiang Liu

Investigating hybrid mesons with $$0^{+-}$$ and $$2^{+-}$$ exotic quantum numbers

We investigate phenomenological implications of vector bosons $\textit{V}$ transforming as (1, 2, -3/2) under the standard model (SM) product gauge group SU(3) , SU(2) and U(1) . These vector bosons can couple to two SM leptons at tree-level forming dimension-4 operators. These operators dictate $\textit{V}$ to have two units of global lepton number, ∆$\textit{L}$ = 2. The operators generated conserve the global lepton number but can violate generational lepton numbers. We study constraints on the couplings $\textit{Y}$ of $\textit{V}$ to SM particles using tree-level processes such as $$ {l}_{\alpha}^{-}\to {l}_{\beta}^{+}{l}_{\rho}^{-}{l}_{\sigma}^{-} $$ , muonium and antimuonium oscillation, neutrino trident scattering, inverse muon decay, $\textit{e}$ $\textit{e}$ → $\textit{l}$ $\textit{l}$ , and also one-loop level processes such as the magnetic dipole moment of a charged lepton and $\textit{l}$ → $\textit{l}$ $\textit{γ}$. Strong constraints are obtained from $$ {l}_{\alpha}^{-}\to {l}_{\beta}^{+}{l}_{\rho}^{-}{l}_{\sigma}^{-} $$ with | $$ {Y}_{ee}{Y}_{\mu e}^{\ast } $$ | $\textit{<}$ 3$\textit{.}$29 × 10 ($\textit{m}$ $\textit{/}$GeV) $\textit{,}$ $$ \mid {Y}_{ee}{Y}_{\mu e}^{\ast}\mid $$ $\textit{<}$ 3$\textit{.}$29 × 10 ($\textit{m}$ $\textit{/}$GeV) and from $\textit{l}$ → $\textit{l}$ $\textit{γ}$ with $$ \mid {Y}_{\tau e}{Y}_{\mu \tau}^{\ast}\mid $$ $\textit{<}$ 3$\textit{.}$46 × 10 ($\textit{m}$ $\textit{/}$GeV) $\textit{,}$ $$ \mid {Y}_{e\tau}{Y}_{\tau \mu}^{\ast}\mid $$ $\textit{<}$ 3$\textit{.}$46 × 10 ($\textit{m}$ $\textit{/}$GeV) , respectively. Interestingly, the imaginary part of the coupling constant in our model induces CP violation, which is constrained by experimental limits on the electric dipole moment.

Zhong-Lv Huang

Xiao-Gang He

Constraints on ∆$\textit{L}$ = 2 vector bosons with tree couplings to SM particles

In order to reach a precision of 0$\textit{.}$2% on the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon, ($\textit{g}$ – 2) , such that the full Standard-Model prediction matches in precision the direct experimental measurement, it is crucial to include the leading, O($\textit{α}$) electromagnetic corrections to HVP. In this work, we determine an important contribution to the latter from a diagram comprised of two two-point quark-loops, connected by the internal photon and gluons. This ultraviolet-finite correction is calculated from lattice QCD using a coordinate-space formalism, where photons are treated in the continuum and infinite volume. Our result amounts to a (−0.89 ± 0.18)% correction to the leading-order HVP contribution to ($\textit{g}$ – 2) . To overcome the worsening statistical noise at large distances, our analysis is combined with phenomenological models featuring light pseudoscalar mesons with masses below 1 GeV. In particular, our data show a very steep mass dependence as dictated by the charged pion loop. Similarly, the other diagrams appearing in the O($\textit{α}$)-corrections to the HVP with the internal photon connecting two separate quark loops are also ultraviolet-finite and can be computed with the same formalism.

Germany

Julian Parrino

Volodymyr Biloshytskyi

United States

En-Hung Chao

Harvey Meyer

Vladimir Pascalutsa

Computing the UV-finite electromagnetic corrections to the hadronic vacuum polarization in the muon ($\textit{g}$ − 2) from lattice QCD

The arguably most promising avenue towards testing physics beyond the Standard Model in the anomalous magnetic moment of the $\textit{τ}$ proceeds via suitably constructed asymmetries in $\textit{e}$ $\textit{e}$ → $\textit{τ}$ $\textit{τ}$ in the presence of a polarized electron beam. Such a program, as could be realized at Belle II assuming a polarization upgrade of the SuperKEKB $\textit{e}$ $\textit{e}$ collider, crucially relies on a careful consideration of radiative corrections. In this work, we present the complete one-loop result for the fully polarized $\textit{e}$ $\textit{e}$ → $\textit{τ}$ $\textit{τ}$ process and its implementation in the Monte-Carlo integrator M M . As an application, we discuss projections relevant for measurements at Belle II, both with and without electron polarization, and outline the necessary steps for a generalization to next-to-next-to-leading order.

Switzerland

Joël Gogniat

Martin Hoferichter

Yannick Ulrich

Towards testing ($\textit{g}$ − 2)

The renormalization of a parity-even massless U(1) × U(1) quantum electrodynamics in three space-time dimensions (QED ) is studied by adopting the Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein (BPHZL) renormalization method. The presence of two massless fermions requires the Lowenstein-Zimmermann (LZ) subtraction scheme to renormalize the infrared divergences induced by the ultraviolet subtractions at 1- and 2-loops, moreover due to the model superrenormalizability the ultraviolet divergences are bounded up to 2-loops. Finally, through the BPHZL renormalization method together with the LZ subtraction scheme the ultraviolet and infrared finiteness of the model is proved up to 2-loops and beyond.

D. Azevedo

O. Cima

L. Lima

E. Miranda

The BPHZL renormalization of a planar quantum electrodynamics up to 2-loops and beyond

We present a Bayesian holographic model constructed by integrating the equation of state and baryon number susceptibility at zero chemical potential from lattice quantum chromodynamics (QCD). The model incorporates error estimates derived from lattice data. With this model, we systematically investigate the thermodynamic properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>-flavor QCD system. Using Bayesian inference, we perform precise calibration of the model parameters and determined the critical end point (CEP) position under the maximum a posterior (MAP) estimation to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>T</mi><mi>c</mi></msup><mo>,</mo><msubsup><mi>μ</mi><mi>B</mi><mi>c</mi></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>0.0859</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>,</mo><mn>0.742</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo stretchy="false">)</mo></math>. Additionally, we predict the CEP positions within 68% and 95% confidence levels, yielding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>T</mi><mi>c</mi></msup><mo>,</mo><msubsup><mi>μ</mi><mi>B</mi><mi>c</mi></msubsup><msub><mo stretchy="false">)</mo><mrow><mn>68</mn><mo>%</mo></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mn>0.0820</mn><mo>−</mo><mn>0.0889</mn><mo>,</mo><mn>0.71</mn><mo>−</mo><mn>0.77</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>T</mi><mi>c</mi></msup><mo>,</mo><msubsup><mi>μ</mi><mi>B</mi><mi>c</mi></msubsup><msub><mo stretchy="false">)</mo><mrow><mn>95</mn><mo>%</mo></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mn>0.0816</mn><mo>−</mo><mn>0.0898</mn><mo>,</mo><mn>0.71</mn><mo>−</mo><mn>0.79</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, respectively. Moreover, to validate the reliability and predictive power of our approach, we conduct a comprehensive comparison between our predictions and potential CEP locations proposed by other theoretical models. This work not only establishes a novel Bayesian framework for holographic modeling but also provides valuable insights and theoretical support for exploring phase transitions in strongly interacting matter under extreme conditions.

Liqiang Zhu

Italy

Xun Chen

Kai Zhou

Hanzhong Zhang

Mei Huang

Bayesian inference of the critical end point in a (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor system from holographic QCD