We propose the implementation of two ingredients in the phenomenological applications of the unitary approach based on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi></math>-expansion of hadronic form factors, commonly referred to as the Boyd-Grinstein-Lebed (BGL) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi></math>-expansion [<a href="http://dx.doi.org/10.1103/PhysRevLett.74.4603">Phys. Rev. Lett. 74, 4603 (1995)</a>.; <a href="http://dx.doi.org/10.1016/0370-2693(95)00480-9">Phys. Lett. B 353, 306 (1995)</a>.; <a href="http://dx.doi.org/10.1016/0550-3213(95)00653-2">Nucl. Phys. B461, 493 (1996)</a>.; [<a href="http://dx.doi.org/10.1103/PhysRevD.56.6895">Phys. Rev. D 56, 6895 (1997)</a>.] . The first ingredient is the explicit addition of a unitarity filter applied to a given set of input data for the hadronic form factors. This further constraint is not usually taken into account in the phenomenological applications of the BGL <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi></math>-expansion. We show that it follows from the equivalence between the BGL approach and the dispersion matrix (DM) method [<a href="http://dx.doi.org/10.1103/PhysRevD.104.054502">Phys. Rev. D 104, 054502 (2021)</a>.], which also describes hadronic form factors in a completely model-independent and nonperturbative way. The second ingredient is represented by the introduction of suitable kernel functions in the evaluation of unitarity bounds, leading to the application of multiple dispersive bounds to hadronic form factors, whenever data and/or (non)perturbative techniques allow to do so. This idea may be useful for the investigation of many physical processes, from the analysis of the electromagnetic form factors of mesons and baryons to the study of weak semileptonic decays of hadrons. An explicit numerical application will be presented in the companion paper [<a href="http://dx.doi.org/10.1103/g1q2-3pmq">Phys. Rev. D 113, 074018 (2026)</a>.], where the effects of subthreshold branch-cuts are analyzed.

Silvano Simula

Ludovico Vittorio

Multiple dispersive bounds. I. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>z</mi></math> expansion

We construct new half-BPS line defects in 3d $$ \mathcal{N}=2 $$ supersymmetric quiver gauge theories whose Higgs branches are complete flag manifolds $\textit{X}$ = Fl($\textit{n}$). Upon circle compactification, the bulk theory flows to a non-linear sigma model (NLSM) with target space $\textit{X}$ and the line defects flow to objects supported on Schubert varieties $\textit{X}$ ⊆ $\textit{X}$. These $\textit{Schubert line defects}$ form an important basis of the quantum K-theory of $\textit{X}$. They are realized as $$ \mathcal{N}=2 $$ supersymmetric quantum mechanics (SQM) quivers coupled to the 3d gauge theory. We show that the insertion of the Schubert line defect restricts the target space of the 3d gauged linear sigma model (GLSM) to the Schubert variety $\textit{X}$ , with the 1d degrees of freedom physically realizing a Bott-Samelson resolution of $\textit{X}$ . Moreover, we verify in examples that the 1d flavored Witten index of the quiver SQM reproduces the (equivariant) Chern character of the structure sheaf $$ {\mathcal{O}}_{X_w} $$ as a (double) quantum Grothendieck polynomial, generalizing previous results for $\textit{X}$ a Grassmannian manifold. Our construction thus provides a more direct realization of the 3d GLSM/quantum K-theory correspondence for complete flag manifolds. Finally, in the small-circle limit, we obtain a 0d-2d coupled system that realizes the Schubert classes [$\textit{X}$ ] in the quantum cohomology ring of $\textit{X}$.

United Kingdom

Cyril Closset

China

Wei Gu

France

Osama Khlaif

United States

Eric Sharpe

Hao Zhang

Hao Zou

Schubert line defects in 3d GLSMs. Part I. Complete flag manifolds and quantum Grothendieck polynomials

Recently, the study of long-lived particles (LLPs) has attracted increasing attention. In this work, we analyze the full parameter space of the Type-I Two-Higgs-Doublet Model (2HDM) that allows for light long-lived scalar ($\textit{H}$) and pseudoscalar ($\textit{A}$) particles. When involving a light beyongd Standard Model (BSM) Higgs, the ∆$\textit{S}$ could be the main contribution during the global fit of the oblique parameters, which is different to ∆$\textit{T}$ being the main factor for heavy BSM Higgs cases. By imposing theoretical constraints such as vacuum stability and perturbative unitarity, together with current experimental bounds, we summarize a complete region for a potential light $\textit{H}$ with cos($\textit{β}$ − $\textit{α}$) ≃ $$ \frac{1}{\tan \beta } $$ , light $\textit{A}$ with cos($\textit{β}$ − $\textit{α}$) ≃ $$ \frac{1}{\tan \beta}\frac{2{m}_H^2-{m}_h^2}{m_H^2-{m}_h^2} $$ , and point out the invisible Higgs decay is the most important constraint. We further identify viable regions for LLPs and propose four benchmark regions that simultaneously accommodate a light long-lived particle and the CDF-II measured $\textit{W}$ boson mass. For these benchmarks, we present the reaches of FASER and FASER 2, where FASER 2 improves the sensitivity by approximately two orders of magnitude compared to FASER.

Xueying Qi

South Korea

Huayang Song

Wei Su

Complete light long-lived particles searches in Type-I 2HDM

Results are presented on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></mrow></math> transitions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow><mo stretchy="false">→</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>3</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo></mrow></math> decays. The data were collected with the BABAR detector at the PEP-II 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 at SLAC. The integrated luminosity of the data sample is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>28.0</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, corresponding to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>121.3</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>3</mn><mi>S</mi><mo stretchy="false">)</mo></math> decays. Signals of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>b</mi><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo></math> are observed over a negligible background. Improved precision measurements of branching fractions are obtained. First measurements of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>b</mi><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo></math> angular distributions are performed. No evidence is found for the presence of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>χ</mi><mrow><mi>b</mi><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">→</mo><mi>ω</mi><mrow><mi mathvariant="normal">ϒ</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></mrow></mrow></math> decay mode.

J.P. Lees

V. Poireau

V. Tisserand

E. Grauges

A. Palano

G. Eigen

D.N. Brown

Yu. G. Kolomensky

M. Fritsch

H. Koch

R. Cheaib

C. Hearty

T.S. Mattison

J.A. McKenna

R.Y. So

V.E. Blinov

A.R. Buzykaev

V.P. Druzhinin

E.A. Kozyrev

E.A. Kravchenko

S.I. Serednyakov

Yu. I. Skovpen

E.P. Solodov

K. Yu. Todyshev

A.J. Lankford

B. Dey

J.W. Gary

O. Long

A.M. Eisner

W.S. Lockman

W. Panduro Vazquez

D.S. Chao

C.H. Cheng

B. Echenard

K.T. Flood

D.G. Hitlin

Y. Li

D.X. Lin

S. Middleton

T.S. Miyashita

P. Ongmongkolkul

J. Oyang

F.C. Porter

M. Röhrken

B.T. Meadows

M.D. Sokoloff

J.G. Smith

S.R. Wagner

D. Bernard

M. Verderi

D. Bettoni

C. Bozzi

R. Calabrese

G. Cibinetto

E. Fioravanti

I. Garzia

E. Luppi

V. Santoro

A. Calcaterra

R. de Sangro

G. Finocchiaro

S. Martellotti

P. Patteri

I.M. Peruzzi

M. Piccolo

M. Rotondo

A. Zallo

S. Passaggio

C. Patrignani

B.J. Shuve

H.M. Lacker

B. Bhuyan

U. Mallik

C. Chen

J. Cochran

S. Prell

A.V. Gritsan

N. Arnaud

M. Davier

F. Le Diberder

A.M. Lutz

G. Wormser

D.J. Lange

D.M. Wright

J.P. Coleman

D.E. Hutchcroft

D.J. Payne

C. Touramanis

A.J. Bevan

M. Bona

F. Di Lodovico

G. Cowan

Sw. Banerjee

C.L. Davis

A.G. Denig

W. Gradl

K. Griessinger

A. Hafner

K.R. Schubert

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></mrow></math> transitions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>3</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo></mrow></math> decays at BABAR

The reduced cross section of the semiexclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>l</mi><mo>,</mo><msup><mi>l</mi><mo>′</mo></msup><mi>p</mi><mo stretchy="false">)</mo></math> lepton scattering process irrespective of the type of interaction is determined mainly by the bound nucleon momentum distribution in the target and nucleon final state interaction with the residual nucleus. These cross sections can be identified with distorted nuclear spectral functions and therefore, they are similar up to Coulomb corrections for neutrino and electron scattering on nuclei. In this article, we exploit this similarity and use data with precise kinematics and large statistics for semiexclusive electron scattering on an oxygen target to test models employed in the genie neutrino event generator. We find that these models cannot reproduce well the measured reduced cross sections in all allowed kinematic regions and the genie event generator needs to describe better both the nuclear ground states and nucleon final state interaction. The approach presented in this paper provides a great opportunity to better test the accuracy of nuclear models of quasielastic neutrino-nucleus scattering, employed in neutrino event generators.

A.V. Butkevich

S.V. Luchuk

Test of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathsize="small">G</mi><mi mathsize="small">E</mi><mi mathsize="small">N</mi><mi mathsize="small">I</mi><mi mathsize="small">E</mi></mrow></math> neutrino event generator against reduced cross sections extracted from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mmultiscripts><mrow><mi mathvariant="normal">O</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>16</mn></mrow></mmultiscripts></mrow><mo stretchy="false">(</mo><mi>e</mi><mo>,</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>′</mo></mrow></msup><mi>p</mi><mo stretchy="false">)</mo></mrow></math> data

We investigate the nucleon and pion gravitational $\textit{D}$-form factors, by fitting a $\textit{σ}$/$\textit{f}$ (500)-meson pole, together with a background term, to lattice data at $\textit{m}$ ≈ 170 MeV. We find that the fitted residues are compatible with predictions from dilaton effective theory. In this framework, the $\textit{σ}$-meson takes on the role of the dilaton, the Goldstone boson of spontaneously broken scale symmetry. These results support the idea that QCD may be governed by an infrared fixed point and offer a physical interpretation of the $\textit{D}$-form factor (or $\textit{D}$-term) in the soft limit.

not found

Roy Stegeman

Roman Zwicky

Gravitational $\textit{D}$-form factor: the $\textit{σ}$-meson as a dilaton confronted with lattice QCD data I

We identify two distinct repulsive mechanisms in the Cho-Maison monopole-antimonopole pair (MAP) configuration. Our results show that the Higgs-mediated repulsion exhibits a nonmonotonic dependence on both topological charge and Higgs self-coupling, confirming its topological origin while revealing a mass-controlled range transition that deviates from the exponential form of a Yukawa potential. Simultaneously, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>-boson field generates localized repulsive cores of radius <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mi>c</mi></msub><mo>≈</mo><mn>0.8</mn><msubsup><mi>m</mi><mi>W</mi><mrow><mo>−</mo><mn>1</mn></mrow></msubsup></math>, consistent with the weak interaction scale. The collaborative effect of these mechanisms—operating in different physics regimes—counteracts the magnetic attraction, establishing a stabilization paradigm for the Cho-Maison MAP that extends naturally to other topological solitons in the Standard Model.

Dan Zhu

Xurong Chen

Khai-Ming Wong

Topological stabilization via Higgs and Z-boson mediated repulsions in electroweak monopole-antimonopole pairs

This is the first of two papers presenting a geometric framework for Planar QCD ( <italic>N<inf>c</inf></italic>&#8239;&#8594;&#8239;&#8734;). In this part, we establish the kinematic foundation of the theory by constructing the unique stable vacuum of the loop equation. We demonstrate that the Makeenko-Migdal loop equation admits a solution of the form <math altimg='si1.svg'><mrow><mi>W</mi><mrow><mo>[</mo><mi>C</mi><mo>]</mo></mrow><mo linebreak='goodbreak'>=</mo><msub><mi>W</mi><mrow><mi>p</mi><mi>e</mi><mi>r</mi><mi>t</mi></mrow></msub><mrow><mo>[</mo><mi>C</mi><mo>]</mo></mrow><mi>exp</mi><mrow><mo>&#8722;</mo><mi>&#954;</mi><mi>S</mi><mo>[</mo><mi>C</mi><mo>]</mo></mrow></mrow></math>, provided <italic>S</italic>[ <italic>C</italic>] is a specific minimal surface possessing a self-dual area derivative. We prove that such a surface exists and corresponds to the Hodge-dual projection of a minimal surface in <math altimg='si2.svg'><mrow><msup><mi mathvariant='double-struck'>R</mi><mn>3</mn></msup><mo>&#8855;</mo><msup><mi mathvariant='double-struck'>R</mi><mn>4</mn></msup></mrow></math>. Crucially, this confinement mechanism relies on the self-duality of the area derivative&#8212;a property that exists exclusively in four dimensions. This geometric constraint ensures stability only in <math altimg='si3.svg'><mrow><mi>D</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math>, distinguishing the resulting theory from standard string models which require higher critical dimensions. We relate the string tension parameter <italic>&#954;</italic> to the gluon condensate via the Operator Product Expansion. The dynamical quantization of the Fermi string on this rigid surface and the resulting meson spectrum are derived in the companion paper [1].

Alexander Migdal

Geometric QCD I: the Hodge-dual surface and quark confinement

The Galactic Center excess (GCE) of GeV <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> rays may hint at dark matter (DM), yet its origin remains debated. Motivated by this, we survey weakly interacting massive particle (WIMP) models that can fit the GCE while satisfying relic-density, direct-detection (DD), and indirect-detection (ID) bounds. We group candidates into hadronic (Higgs portals; simplified scalar/vector mediators), leptonic [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>i</mi></msub><mo>−</mo><msub><mi>L</mi><mi>j</mi></msub></mrow></msub></math>], and mixed [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>-portal] classes. Across all cases, present DD and dwarf-spheroidal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-ray limits exclude wide regions, leaving mainly narrow resonant funnels with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mrow><mi>DM</mi></mrow></msub><mo>≃</mo><msub><mi>m</mi><mrow><mi>med</mi></mrow></msub><mo>/</mo><mn>2</mn></math> and portal couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>≪</mo><mn>1</mn></math>. In hadronic setups, scalar and vector Higgs portals survive only in a thin strip near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>h</mi></msub><mo>/</mo><mn>2</mn><mo>≃</mo><mn>62.5</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> with portal couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, while the Dirac Higgs and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> portals are essentially excluded. The UV-complete vector Higgs portal retains resonant bands whose viable portal strength depends on the mixing angle. Simplified scalars allow small windows for complex-scalar or vector DM; Dirac DM is strongly disfavored, whereas a pseudoscalar with Dirac DM remains viable over a broader parameter range. For a simplified <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> mediator, a pure vector coupling leaves only a marginal region, while pure axial is excluded by DD/ID bounds. In leptonic scenarios, inverse-Compton emission is essential: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>e</mi></msub></math> (and, to a lesser extent, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math>) fits the GCE with near-thermal cross sections, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></math> is disfavored. Overall, viable WIMP explanations are constrained to the finely tuned resonant regime, with leptophilic vectors and pseudoscalar portals emerging as the most robust options.

Chuiyang Kong

Mattia Di Mauro

Comprehensive study of WIMP models explaining the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi><mi>e</mi><mi>r</mi><mi>m</mi><mi>i</mi></math>-LAT Galactic Center excess

This is the first of a series of papers devoted to a detailed analysis of isospin-breaking effects in the $\textit{ππ}$ scattering amplitude and the vector form factor of the pion. Isospin breaking originates from the mass difference between up and down quarks and from electromagnetic effects. The latter can be further split into effects due to the pion-mass difference and the remaining virtual and real photonic effects. In this paper, we derive the modifications to the Roy equations for $\textit{ππ}$ scattering due to the mass difference between the charged and the neutral pion. We solve the equations numerically after matching them to the chiral representation of the $\textit{ππ}$ scattering amplitude evaluated in the same approximation, which is also provided. Numerical results are presented and discussed in detail.

Switzerland

Gilberto Colangelo

Martina Cottini

Spain

Jacobo Ruiz de Elvira

Isospin-breaking in the $\textit{ππ}$ scattering amplitude. Part I. Effects due to the pion mass difference