The measurement of hyperon (Λ and $$\overline{\Lambda }$$ ) polarization along the beam axis in Pb-Pb collisions at $$\sqrt{{s}_{\text{N}\text{N}}}=5.36$$ TeV using the ALICE detector is presented. The polarization, arising from vorticity components induced by anisotropic flow, is studied relative to the second- and third-order event planes. The measured polarization exhibits clear azimuthal sine modulations, providing the first observation of polarization along the beam direction measured relative to the third-order event plane at the Large Hadron Collider. The values of the polarization measured with respect to the second-order event plane are consistent with previous measurements at $$\sqrt{{s}_{\text{N}\text{N}}}=5.02$$ TeV and show improved statistical precision owing to the larger data sample. Comparisons with hydrodynamic calculations indicate that the measured polarization is sensitive to the bulk viscosity and the vortical structure of the quark-gluon plasma, offering new constraints on its transport properties. In particular, the polarization measured relative to the third-order event plane is expected to provide an additional and independent input to constrain both bulk and shear viscosities of the quark-gluon plasma.

United States

D. Abdallah

I. Abualrob

Italy

S. Acharya

K. Agarwal

Switzerland

G. Aglieri Rinella

L. Aglietta

N. Agrawal

India

Z. Ahammed

S. Ahmad

Indonesia

Z. Akbar

Germany

V. Akishina

M. Al-Turany

B. Alessandro

Thailand

A. Alfarasyi

Mexico

R. Alfaro Molina

B. Ali

A. Alici

Norway

J. Alme

G. Alocco

T. Alt

I. Altsybeev

Romania

C. Andrei

United Kingdom

N. Andreou

A. Andronic

M. Angeletti

V. Anguelov

F. Antinori

P. Antonioli

N. Apadula

H. Appelshäuser

S. Arcelli

R. Arnaldi

I. Arsene

M. Arslandok

A. Augustinus

R. Averbeck

M. Azmi

South Korea

B. Kong

Japan

H. Baba

A. Babu

A. Badalà

J. Bae

Y. Bae

Y. Baek

China

X. Bai

R. Bailhache

France

Y. Bailung

R. Bala

A. Baldisseri

Poland

B. Balis

S. Bangalia

K. Barai

Slovakia

V. Barbasova

F. Barile

L. Barioglio

M. Barlou

B. Barman

Hungary

G. Barnaföldi

L. Barnby

E. Barreau

V. Barret

Brazil

L. Barreto

K. Barth

E. Bartsch

N. Bastid

G. Batigne

Czechia

D. Battistini

B. Batyunya

L. Baudino

D. Bauri

Peru

J. Bazo Alba

Denmark

I. Bearden

D. Behera

S. Behera

M. Behling

I. Belikov

V. Bella

F. Bellini

R. Bellwied

L. Beltran

Y. Beltran

G. Bencedi

Austria

O. Benchikhi

A. Bensaoula

S. Beole

A. Berdnikova

L. Bergmann

L. Bernardinis

L. Betev

P. Bhaduri

T. Bhalla

A. Bhasin

B. Bhattacharjee

L. Bianchi

J. Bielčík

J. Bielčíková

A. Bilandzic

A. Binoy

G. Biro

S. Biswas

Hyperon (Λ) polarization along the beam axis in Pb-Pb collisions at $$\sqrt{{s}_{\text{N}\text{N}}}=5.36$$ TeV

We propose a hybrid inflation model where a pseudo-Nambu-Goldstone boson inflaton couples to $\textit{N}$ waterfall scalar fields respecting a $\textit{Z}$ symmetry. We identify the phases for the inflation and the consequent waterfall transition, concretely, in $\textit{Z}$ , $\textit{Z}$ and $\textit{Z}$ cases. From the Coleman-Weinberg potential for the inflaton, we show that the quadratically divergent corrections coming from the waterfall sector are cancelled due to the $\textit{Z}$ symmetry, while the logarithmically divergent corrections are absent only for $\textit{N >}$ 2, ensuring the radiative stability of the inflaton potential. We show the parameter space for a successful inflation with the loop-corrected inflaton potential in each model and compare the results between different discrete symmetries. We further analyze the vacuum structure of the models and the reheating process due to the $\textit{Z}$ -invariant Higgs-portal couplings for the waterfall fields. We find that the maximum temperature can be smaller than the mass of the waterfall field condensate such that the $\textit{Z}$ symmetry is not restored after reheating and there is no domain wall problem in the models. We also comment on the possibility of multi-component dark matter from the $\textit{Z}$ partners of the waterfall field condensate.

Hyun Lee

Adriana Menkara

Pseudo-Nambu-Goldstone inflation with $\textit{Z}$ $\textit{N}$ symmetric waterfall fields

The interplay between toric Calabi-Yau 3-folds, cluster integrable systems, and 5-dimensional quantum field theories has proved fruitful. We extend this framework to generalized toric polygons (GTPs) and show that their integrable systems arise from refined birational transformations of known cluster integrable systems acting on the Casimirs and Hamiltonians as well as the Poisson structure and spectral curves. We argue that these transformations are realized as Hanany-Witten transitions producing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo stretchy="false">)</mo></math> 5-brane webs dual to GTPs. We show that the resulting <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5</mn><mi>D</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></math> theory is obtained by Higgsing a higher-rank theory whose associated toric Calabi-Yau has a toric diagram of the same shape as the GTP.

Minsung Kho

Kimyeong Lee

Norton Lee

Rak-Kyeong Seong

Integrable systems for generalized toric polygons and Higgsed 5D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></math> theories

We identify a mathematical structure in the gap equations of the large-$\textit{N}$ Gross–Neveu model at imaginary chemical potential in odd spacetime dimensions. Using this model as the primary example, the central observation is an elementary dimensional ladder: a single centred first difference with respect to $$\sigma ^2$$ relates the thermal part of the gap equation in dimension $\textit{d}$ to that in dimension $$d-2$$ , for every odd $\textit{d}$. Iterating this elementary step generates the higher-order finite-difference (discrete Laplacian) relations; for the distinguished sequence $$d=4k+3$$ , whose kernel exponent is even, the closed stencil hierarchy connects $\textit{d}$ to $$2d-3$$ through 2$\textit{k}$ iterates. We show that the gap equations can be written as the sum of two parts: one defined by higher-order finite-difference patterns and a cutoff-dependent part given by a truncated asymptotic expansion of a hypergeometric function. The same discrete finite-difference hierarchy is shown to arise in the thermal sector of large-$\textit{N}$ bosonic models, indicating that the underlying structure is not restricted to fermionic theories. We further argue that this picture suggests a relation between thermal field theories in these odd $\textit{d}$ dimensions and exactly solvable one-dimensional quantum problems. We find that the thermal mass at specific imaginary chemical potential values corresponds to points where internal-energy and entropy contributions balance, which is formally analogous to OPE inversion formula techniques where thermal mass values arise from sets of transcendental equations.

Greece

Evangelos Filothodoros

Discrete Laplacian structure and kernel reduction of the gap equation in odd-dimensional large-$\textit{N}$ vector models at imaginary chemical potential

Transfermium nuclei provide experimental access to the single-particle structure underlying the stability of superheavy nuclei. We present the first systematic shell-model description of the <math altimg='si1.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>150</mn></mrow></math> isotones using a new variation-after-projection shell-model approach. The ground-state and <math altimg='si19.svg'><mrow><msup><mi>K</mi><mi>&#960;</mi></msup><mo linebreak='goodbreak'>=</mo><msup><mn>2</mn><mo>&#8722;</mo></msup></mrow></math> bands are reproduced across the isotonic chain with a unified Hamiltonian, including the long-standing anomalous lowering of the <math altimg='si4.svg'><mrow><msup><mi>J</mi><mi>&#960;</mi></msup><mo linebreak='goodbreak'>=</mo><msup><mn>2</mn><mo>&#8722;</mo></msup></mrow></math> bandhead in 248Cf. We show that this anomaly originates from a local inversion of the neutron <italic>j</italic> <inf>15/2</inf> and <italic>g</italic> <inf>9/2</inf> orbitals, associated with the deformed [734]9/2 and [622]5/2 neutron orbitals near the Fermi surface. This is driven by the proton-neutron monopole interaction as proton occupations evolve along the isotonic chain. The same mechanism also reproduces the low-lying spectra of the neighboring <math altimg='si2.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>151</mn></mrow></math> isotones, without further adjustment, and predicts a low-lying <math altimg='si4.svg'><mrow><msup><mi>J</mi><mi>&#960;</mi></msup><mo linebreak='goodbreak'>=</mo><msup><mn>2</mn><mo>&#8722;</mo></msup></mrow></math> bandhead at 524 keV in 254Rf. This work establishes a microscopic shell-model benchmark for the key neutron single-particle levels in the heavy actinide and transfermium region and demonstrates the feasibility of large-scale shell-model calculations for superheavy nuclei.

Zhanjiang Lian

Zaochun Gao

Sweden

Chong Qi

Towards large-scale shell-model studies of superheavy nuclei: Spectroscopy of <italic>N</italic>&#8239;&#8764;&#8239;150 nuclei

Defect conformal field theories have special operators of protected dimension known as displacements and tilts. They arise due to the breaking of global symmetries by the defect and the normalisations of their two-point functions are characteristics of the defect. In the case of surface defects, these normalisations are related to some of the anomaly coefficients in the surface effective action. To study these operators and their flows between different defect renormalization group fixed points we present an elegant approach using conformal perturbation theory that easily reproduces the known examples from the critical Wilson-Fisher O($\textit{N}$) model in 4 − $\textit{ε}$ dimensions and allows us to construct new ones in other multiscalar theories. In all the systems that we study the flows are short and under full control, as is the change of the displacement and tilt normalizations. We point out some novel features like the existence of vortices when the defect conformal manifold is not simply connected. In addition to regular human labour, this work relied heavily on generative AI; see full disclosure in methodology section.

Jake Belton

Nadav Drukker

Biswajit Sahoo

Flowing with displacements and tilts: surface operators in O($\textit{N}$) models

We present the first experimental search for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-naturalness tower of neutrinos using a global analysis of publicly available neutrino data. As a potential solution to the hierarchy problem, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-naturalness model employs a varying Higgs mass parameter among <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> dark sectors and encodes the required fine-tuning of the placement of the sectors in a parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi></math>. We report exclusion limits on the parameter space (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>), for normal and inverted ordering and in case the neutrino is Majorana or Dirac. In the case of a Majorana neutrino, we can rule out <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>≤</mo><msup><mn>10</mn><mn>4</mn></msup></math> sectors with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi><mo>≥</mo><mn>0.1</mn></math>. This is particularly exciting as it shows that a gauge and gravitational unification around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>GUT</mi></msub></math>, which is a benchmark scenario of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-naturalness framework with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><msup><mn>10</mn><mn>4</mn></msup></math> without fine-tuning, is ruled out by neutrino experiments.

Sofia Lonardi

Manuel Ettengruber

Philipp Eller

Searching for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>-naturalness tower of neutrinos

We establish the multipole structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Δ</mi></math> transition at the level of the generalized parton distributions (GPDs). We decompose the four transition GPDs into one monopole, two dipole, and one quadrupole components in the transverse plane by a multipole expansion of the covariant transition matrix element in terms of the three-dimensional spin-transition tensors and the transverse momentum transfer. These multipole components are in one-to-one correspondence with the light-front helicity amplitudes. In the zero-skewness limit, the multipole GPDs define impact-parameter transition densities, which generalize the transverse transition charge densities to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>-dependent level. These transition densities arise from nondiagonal matrix elements between two distinct hadronic states and must therefore be distinguished from the diagonal densities of the nucleon and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi></math>. The multipole transition densities visualize the monopole, dipole, and quadrupole structures of the partonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Δ</mi></math> transition in the transverse plane.

June-Young Kim

Hyun-Chul Kim

Multipole structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Δ</mi></math> transition generalized parton distributions

The vast majority of extensions of the Standard Model affecting the number of effective relativistic neutrino species (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub></math>) do so additively, namely, they enhance this quantity with some light state contributing to dark radiation. In this work, we consider precisely the opposite case: new physics scenarios that can lead to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub><mo>&lt;</mo><mn>3</mn></math> that are consistent with all known cosmological, astrophysical, and laboratory data. We are motivated by three main reasons: (1) a recent measurement from Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT) in combination with Planck that leads to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub><mo>=</mo><mn>2.81</mn><mo>±</mo><mn>0.12</mn></math>, (2) by a new and powerful measurement of the primordial helium abundance, which anchors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub></math> to be very close to the Standard Model value one second after the big bang, (3) by the deployment of the Simons Observatory which will provide precise tests of the radiation content in the Universe and which may detect with a high significance cosmologies with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub><mo>&lt;</mo><mn>3</mn></math>. We survey the main theoretical possibilities and find that only a few simple scenarios can consistently give <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub><mo>=</mo><mn>2.81</mn><mo>±</mo><mn>0.12</mn></math>. One class consists of thermal electrophilic relics with masses <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo>∼</mo><mn>8</mn><mi>–</mi><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Another consists of out-of-equilibrium particles decaying to <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> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>γ</mi></math>, with a rather particular lifetime <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0.05</mn><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">s</mi><mo>≲</mo><mi>τ</mi><mo>≲</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>min</mi></mrow></math>, mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>250</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>≲</mo><mi>m</mi><mo>≲</mo><mn>600</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, and abundance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo>/</mo><msub><mi>ρ</mi><mi>γ</mi></msub><mo>∼</mo><mn>0.1</mn></math> at decay. Thermal electrophilic particles are especially interesting because they can account for the dark matter in the Universe and can be tested in experiments such as SENSEI, DAMIC-M, and Oscura, and their portals to the visible sector at experiments such as NA64 and LDMX. We conclude that if the Simons Observatory confirms that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>eff</mi></msub><mo>≃</mo><mn>2.8</mn></math>, it will point to very specific extensions of the Standard Model.

CERN

Miguel Escudero Abenza

Maksym Ovchynnikov

Neal Weiner

What does it take to have <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>eff</mi></mrow></msub><mrow><mo>&lt;</mo><mn>3</mn></mrow></mrow></math> at CMB times?

We consider the photon-energy spectrum of the inclusive radiative decay $\textit{B}$ → $\textit{X}$ $\textit{γ}$, induced by the electromagnetic dipole operator $\textit{O}$ , to next-to-next-to-next-to-leading order and calculate the complete corrections for light fermions, for the contributions with two closed massive fermion loops, and for the limit of large QCD colour factors $\textit{N}$ in the remaining part. We discuss the integrated decay rate both without and with a cut on the photon energy. In addition to the on-shell renormalization of the bottom-quark mass, we also consider the kinetic mass and the MSR mass schemes. The latter two lead to an improved perturbative behaviour of the decay rate.

Matteo Fael

Fabian Lange

Kay Schönwald

Matthias Steinhauser

The photon-energy spectrum in $\textit{B}$ → $\textit{X}$ $\textit{s}$ $\textit{γ}$ to N3LO: light-fermion and large-$\textit{N}$ c corrections