We investigate the dynamics and mass spectra of charged pseudoscalar (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup></math>) and vector (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ρ</mi><mo>+</mo></msup></math>) mesons in a background magnetic field at finite temperature using the two-flavor Nambu-Jona–Lasinio model. By employing a quark propagator that isolates the Schwinger phase from its Landau level expansion, we formulate an analytically controlled phase-space framework utilizing the Wigner-Weyl transform and the Moyal star product. This approach enables the algebraic diagonalization of the Bethe-Salpeter equations for composite states with asymmetric fractional constituent charges. For the pseudoscalar channel, we analytically verify the exact cancellation between the dynamical random phase approximation spatial sum rules and the vacuum gap equation. This identity preserves the generalized Goldstone theorem, causing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup></math> pole mass to track the kinematic zero-point energy drift at order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>B</mi></math>. In the vector channel, our full phase-space evaluation reveals that the Zeeman spin-splitting emerges dynamically from microscopic threshold truncations governed by the chiral Dirac algebra. Notably, we find that the tachyonic instability of the spin-aligned <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ρ</mi><mo>+</mo></msup></math> state is quenched. The magnetic catalysis of the chiral condensate drives the continuum threshold (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>M</mi></math>) upwards, overtaking the Zeeman attraction and preventing vector meson condensation within this mean-field framework. Furthermore, finite-temperature evaluations show a monotonic thermal suppression of the meson masses driven by Pauli blocking, yet all modes remain bound without undergoing Mott dissociation prior to chiral symmetry restoration.

China

Jingyi Chao

Kun Xu

Mass spectra of charged mesons and the quenching of vector meson condensation via exact phase-space diagonalization

We revisit the traditional type I, II, and III seesaw mechanisms in the presence of a complex scalar field charged under a global <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> symmetry that can be identified with lepton number and the Peccei-Quinn symmetry. After symmetry breaking, the radial mode becomes heavy while the angular mode appears as an axionlike particle, traditionally dubbed the Majoron. We construct the effective field theory obtained after integrating out the heavy states and analyze two matching orders: first removing the radial mode and then the seesaw fields, and vice versa. Both procedures yield the same low-energy Lagrangian containing only Standard Model fields and the Majoron. Because a single vacuum expectation value fixes the mediator masses, the radial mode, and every Majoron coupling, these models predict relations among observables rather than their individual size, and it is these relations that are testable. Indeed, the invisible Higgs width is locked to the universal suppression of the Higgs couplings, while the Majoron-lepton coupling is fixed by the measured nonunitarity of the leptonic mixing matrix, and the two independently give comparable lower bounds on the same lepton-number-breaking scale, of the order of 1–10 TeV. Neutrinoless double beta decay with Majoron emission, by contrast, has no sensitivity in this class of models. The framework is, thus, falsifiable even when the new states lie far beyond experimental reach.

Italy

Carla Biggio

Spain

Marta Fuentes Zamoro

Xu Li

Luca Merlo

Luca Ottonello

How to identify a Majoron: Effective field theories of spontaneous lepton number breaking

We expand the treatment of the problem of the extraction of smeared spectral densities from Euclidean correlators, introduced in [Extraction of spectral densities from lattice correlators, <a href="http://dx.doi.org/10.1103/PhysRevD.99.094508">Phys. Rev. D 99, 094508 (2019)</a>.], providing an alternative which does not rely on the Backus-Gilbert regularization. This is possible due to the observation that the solution can be decomposed into a sum of terms, in the spirit of the singular value decomposition, where those with the largest contribution to the statistical noise happen to contribute the least to the central value of the smeared spectral density. The analysis of the systematics of the inverse problem is then shifted to finding the optimal truncation of such summation, so that the signal is saturated before the noise explodes. We scrutinize the performance and systematics of this approach either as a stand-alone procedure, or to complement the stability analysis required to extrapolate the unbiased result in the Backus-Gilbert regulated version of the solution.

France

Alessandro Lupo

Nazario Tantalo

Extraction of spectral densities from lattice correlators: Decoupling signal from noise

Quantum anomalies give rise to novel transport phenomena, including the generation of a current in a relativistic fluid due to the presence of magnetic field or vorticity. We present an exclusive and direct computation of the chiral anomaly in the adiabatic regime within the path integral for a massless fermion on a generic electromagnetic and curved background, including local temperature and chemical potential. We identify new quantum-thermodynamical contributions to the breaking of axial symmetry which induce the chiral separation and vortical effects.

Rémy Larue

Jérémie Quevillon

Diego Saviot

Examining the anomalous nature of chiral effects in thermodynamics

The COHERENT Collaboration reports the most precise measurement of the coherent elastic neutrino-nucleus scattering cross section to date. This measurement was performed with COHERENT’s germanium detector array, Ge-Mini, at the Spallation Neutron Source at Oak Ridge National Laboratory. A cumulative exposure of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>4.69</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>22</mn></mrow></msup></mrow></math> protons on target yielded a total number of observed counts of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mn>124</mn></mrow><mrow><mo>−</mo><mn>12</mn></mrow><mrow><mo>+</mo><mn>14</mn></mrow></msubsup></mrow></math> and a flux-averaged cross section of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0.98</mn><mo>±</mo><mn>0.10</mn><mrow><mo stretchy="false">(</mo><mi>statistical</mi><mo stretchy="false">)</mo></mrow><mo>±</mo><mn>0.10</mn><mrow><mo stretchy="false">(</mo><mi>systematic</mi><mo stretchy="false">)</mo></mrow></mrow></math> relative to the standard-model expectation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5.9</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>39</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>cm</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>. The well-understood energy and timing distributions of the neutrino source allow for independent measurements of muon- and electron-neutrino scattering rates. This information is used to improve constraints on nonstandard neutrino interactions mediated by heavy particles.

United States

M. Adhikari

South Korea

M. Ahn

D. Amaya Matamoros

P.S. Barbeau

Russia

V. Belov

I. Bernardi

C. Bock

A. Bolozdynya

R. Bouabid

A. Bracho

J. Browning

B. Cabrera-Palmer

N. Cedarblade-Jones

S. Chen

A.I. Colón Rivera

V. da Silva

Y. Efremenko

S.R. Elliott

Canada

A. Erlandson

L. Fabris

S. Foster

A. Galindo-Uribarri

E. Granados Vazquez

M.P. Green

B. Hackett

J. Hakenmüller

Japan

M. Harada

M.R. Heath

S.C. Hedges

Y. Hino

H. Huang

W. Huang

H. Jeong

B.A. Johnson

T. Johnson

H. Jones

A. Khromov

D. Kim

C. Koh

L. Kong

A. Konovalov

Y. Koshio

A. Kumpan

O. Kyzylova

Y. Lee

S.M. Lee

G. Li

L. Li

Z. Li

J.M. Link

J. Liu

Q. Liu

X. Lu

M. Luxnat

A. Major

D.M. Markoff

J. Mattingly

H. McLaurin

K. McMichael

N. Meredith

Y. Nakajima

F. Nakanishi

J. Newby

N. Ogoi

S.W. Oh

J. O’Reilly

A. Orvedahl

D.S. Parno

D. Pérez-Loureiro

D. Pershey

C.G. Prior

J. Queen

R. Rapp

H. Ray

O. Razuvaeva

D. Reyna

D. Rudik

J. Runge

D.J. Salvat

J. Sander

K. Scholberg

H. Sekiya

A. Shakirov

G. Simakov

J. Skweres

W.M. Snow

V. Sosnovtsev

M. Stringer

C. Su

T. Subedi

B. Suh

B. Sur

R. Tayloe

Y.T. Tsai

E.E. van Nieuwenhuizen

C.J. Virtue

G. Visser

K. Walkup

E.M. Ward

R. Wendell

Measurement of Coherent Elastic Neutrino-Nucleus Scattering on Germanium by COHERENT

We investigate the pion gravitational form factors (GFFs) at intermediate and large momentum transfer within the framework of QCD factorization. Our analysis centers on the non-Abelian <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mi>J</mi><mi>J</mi></math> correlator, which couples the local QCD energy-momentum tensor to two external gluon fields and explicitly encodes the perturbative effects of the trace anomaly. We demonstrate how this quantum anomaly induces a scalar, dilatonlike contribution to the hard-scattering kernel. To ensure field-theoretic consistency, a careful separation of the quark and gluon sectors is performed, accounting for the modifications introduced by gauge-fixing terms and Slavnov-Taylor identities on the off-shell gluonic structure. To obtain realistic phenomenological predictions and regulate soft-gluon endpoint divergences in the hard kernel, we implement the Sudakov resummation framework coupled with a Gaussian model for the pion’s transverse-momentum-dependent wave function. We show that the resulting anomaly-induced corrections significantly modify the behavior of the pion GFFs at large momentum transfer, leaving a unique imprint on the trace sector and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-term.

Claudio Corianó

Hsiang-Nan Li

Dario Melle

Leonardo Torcellini

Gravitational form factor of the pion in perturbative QCD with a dilaton interaction

We present a dispersive amplitude analysis of the low-energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> system in the radiative decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math>, using the mass-independent BESIII <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> intensities, the total spectrum, and the measured <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup><mo>−</mo><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup><mtext> </mtext><mtext> </mtext><mi>E</mi><mn>1</mn></math> phase difference. The isoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave is described by a coupled-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo>/</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> Muskhelishvili–Omnès representation, which implements the strong final-state interactions associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math>. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-wave is treated with a single-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> Muskhelishvili-Omnès representation, where we identify all kinematic constraints of helicity amplitudes before transforming them to the experimental <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi><mn>1</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mn>2</mn></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi><mn>3</mn></math> multipoles. Smooth short-distance production of a pseudoscalar-meson pair is encoded in subtraction polynomials, while left-hand-cut effects are estimated and found to be numerically subleading. We identify the negative solution of the BESIII <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup><mo>−</mo><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup><mtext> </mtext><mtext> </mtext><mi>E</mi><mn>1</mn></math> phase ambiguity, after using the modulo-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi></math> freedom of production amplitudes, as the phase solution compatible with unitarity constraints, showing that the measured phase information can be accommodated with the Omnès phase motion without requiring large additional phases. By normalizing the BESIII intensities with the extracted branching fraction, we fix the absolute scale of the fitted amplitudes, making them suitable as input for future dispersive studies of two-pion contributions to gravitational form factors.

Germany

Bai-Long Hoid

Igor Danilkin

Anna Testa

Marc Vanderhaeghen

Dispersive analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> process

We investigate the projected sensitivity of the Future Circular Collider in <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> mode (FCC-ee) in probing the lepton flavor violating (LFV) decay of the 125 GeV Higgs boson, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mo stretchy="false">→</mo><mi>μ</mi><mi>τ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mo stretchy="false">→</mo><mi>e</mi><mi>τ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mo stretchy="false">→</mo><mi>e</mi><mi>μ</mi></math> at center-of-mass energy of 240 GeV with an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>ab</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>. With the clean multilepton final states, we consider the Higgs production modes that contribute 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><mo stretchy="false">→</mo><mo>ℓ</mo><mo>ℓ</mo><mi>h</mi></math>, in particular, the Higgs-strahlung and the vector boson fusion production channels. The 95% confidence level upper limits on branching ratio are found to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.94</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6.28</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>7.37</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math> for the channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mo stretchy="false">→</mo><mi>μ</mi><mi>τ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mo stretchy="false">→</mo><mi>e</mi><mi>τ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mo stretchy="false">→</mo><mi>e</mi><mi>μ</mi></math>, respectively. In addition, we also consider the LFV decay of a new <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>CP</mi></mrow></math>-even Higgs boson with mass in the range of 110–200 GeV. The projected FCC-ee sensitivities are then compared to those from low-energy searches for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo><mo stretchy="false">→</mo><msup><mo>ℓ</mo><mo>′</mo></msup><mi>γ</mi></math> decay. We find that the FCC-ee sensitivity for the LFV decays of the Higgs boson in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo>−</mo><mi>τ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mo>−</mo><mi>τ</mi></math> channels is superior to the low-energy constraints. However, in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo>−</mo><mi>μ</mi></math> case, the low-energy search offers stronger constraints.

Thailand

Pongsakorn Sriling

Rutjanaret Uttho

Vichayanun Wachirapusitanand

CERN

Norraphat Srimanobhas

Patipan Uttayarat

Searching for lepton flavor violating decays of the Higgs boson into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mi>τ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>τ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>μ</mi></math> final states at FCC-ee

The Standard Model prediction for the rare <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mi>L</mi></msub><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> decay depends critically on the long-distance contribution coming from the exchange of two photons. Such a contribution can be computed using lattice QCD and an effective three-flavor theory including only the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> quarks, provided terms falling as the inverse square of the omitted charm quark mass, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msubsup><mi>m</mi><mi>c</mi><mn>2</mn></msubsup></math>, are neglected. Because of the missing Glashow-Iliopoulos-Maiani cancellation, this three-flavor theory contains additional low-energy constants that depend on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>c</mi></msub></math>. Here we show how these constants can be determined from a practical four-flavor lattice QCD calculation performed on a small volume with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math> quark masses that are heavier than physical.

En-Hung Chao

Norman Christ

Ceran Hu

Renormalizing a three-flavor lattice calculation of the two-photon contribution to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mi>L</mi></msub><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>

We study linear perturbations of static, spherically symmetric solutions of scalar-tensor theories (STT) of gravity from the Bergmann-Wagoner-Nordtvedt class, sourced by nonlinear electrodynamics (NED). We obtain a general expression for the effective potential $$V_\textrm{eff}$$ governing the perturbation dynamics for theories with arbitrary scalar-electromagnetic interaction of the form $$L(\psi , F)$$ , where $$\psi $$ is a scalar field and $$F = F_{\mu \nu }F^{\mu \nu }$$ the electromagnetic invariant. This consideration includes, in particular, arbitrary scalar self-interaction potentials and scalar fields that can be phantom in some regions of space-time (the so-called trapped ghosts). Only radial (monopole) perturbations are considered here as the most likely ones to cause an instability. It is shown, in particular, that if NED has a correct Maxwell weak field limit, the zero charge limit of $$V_\textrm{eff}$$ does not contain any trace of NED, and the perturbation dynamics is the same as for vacuum STT solutions. The previously obtained stability results for STT-Maxwell solutions are shown to be extended without change to STT-NED solutions with equal electric and magnetic charges, implying $$F =0$$ . As an example of a solution with $$F\not \equiv 0$$ , we consider a system with a massless scalar and truncated Born-Infeld NED, both minimally coupled to gravity, in GR, and show that almost all results previously obtained for $$F=0$$ are qualitatively preserved.

Kirill Bronnikov

Uzbekistan

Rustam Ibadov

Feruza Shaymanova

Najibullokhon Shukurullokhon

Nonlinear electrodynamics and stability of spherically symmetric space-times in scalar-tensor gravity