We investigated the effect of an isospin chemical potential ( $ \mu_{I} $ ) within the quark-meson model, which approximates quantum chromodynamics (QCD) by modeling low-energy phenomena such as chiral symmetry breaking and phase structure under varying conditions of temperature and chemical potential. Using the functional renormalization group (FRG) flow equations, we calculated the phase diagram in the chiral limit within the two-flavor quark-meson model in a finite $ \mu_{I} $ with $\textit{ρ}$ vector meson interactions. Fluctuation effects significantly decrease the critical chemical potential from the mean-field (MF) value $\mu_{I,{\rm MF}} \gt m_\rho$ to a lower value at which the $\textit{ρ}$ vector meson condensates alongside the chiral condensate once the isospin chemical potential exceeds the critical value $ \mu_{I}^{{\rm{crit}}} $ . This $\textit{ρ}$ condensation was investigated numerically for different meson coupling strengths. The $\textit{ρ}$ meson dominated region is delineated from other phases by a second-order phase transition at lower $ \mu_{I} $ and a first-order transition at slightly higher $ \mu_{I} $ .

China

Mohammed Osman

Defu Hou

Wentao Wang

United States

Hui Zhang

Functional renormalization group study of $\textit{ρ}$ meson condensate at a finite isospin chemical potential in the quark meson model * Supported in part by the National Key Research and Development Program of China (2022YFA1604900). This work is also partly supported by the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Hui Zhang acknowledges the financial support from the Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008) and the National Natural Science Foundation of China (12047523, 12105107)

We analyze the latest cosmic microwave background (CMB) constraints on the scalar spectral index <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub></math> and tensor-to-scalar ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi></math> from Planck 2018, BICEP/Keck 2018, the Atacama Cosmology Telescope Data Release 6 (ACT DR6), and the South Pole Telescope (SPT-3G) data, focusing on their implications for attractor models of inflation. We compare systematically observational bounds with theoretical predictions for both E-model (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi></math>-Starobinsky) and T-model potentials. The observational constraints accommodate E-models with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo>≲</mo><mn>25</mn></math>, with the canonical Starobinsky model (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo>=</mo><mn>1</mn></math>) predicting <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub><mo>=</mo><mn>0.958</mn><mi>–</mi><mn>0.963</mn></math> for reheating temperatures between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>100</mn><mo>−</mo><msup><mn>10</mn><mn>10</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, in good agreement with Planck 2018 data and within the 95% CL region determined by the Planck-ACT-SPT combination, but below the 95% confidence region of the Planck-ACT-DESI combination. Higher reheating temperatures from near-instantaneous reheating improve the compatibility. T-models predict slightly lower <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub></math> values (0.956–0.961), in some tension with Planck 2018 data, and we find an upper limit of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo>≲</mo><mn>11</mn></math> in these models. We extend our analysis to generalized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi></math>-attractors with monomial potentials <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo stretchy="false">(</mo><mi>φ</mi><mo stretchy="false">)</mo><mo>∝</mo><msup><mi>φ</mi><mi>k</mi></msup></math> near the minimum, demonstrating that models with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi><mo>≥</mo><mn>6</mn></math> naturally predict <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub><mo>≃</mo><mn>0.965</mn><mi>–</mi><mn>0.968</mn></math> for typical number of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi></math>-folds, in better agreement with the ACT DR6 data. We also consider deformed E- and T-models, which allow significantly higher values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub></math> for low values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mo>≃</mo><mn>1</mn></math>.

CERN

John Ellis

Mexico

Marcos A.G. Garcia

Keith A. Olive

Sarunas Verner

Constraints on attractor models of inflation and reheating from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi><mi>l</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>k</mi></math>, BICEP/Keck, ACT DR6, and SPT-3G data

In this work, we perform a comprehensive investigation of the production of high-spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mi>J</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mi>J</mi></msub></math> mesons (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>2</mn></math>, 3, 4, 5) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>−</mo></msup><mi>p</mi></math> reactions using an effective Lagrangian approach. By constructing the relevant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel processes and calibrating the model with a single adjustable parameter fitted to existing data, we successfully reproduce the measured total and differential cross sections for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>3</mn></math> states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mn>3</mn></msub><mo stretchy="false">(</mo><mn>1670</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mn>3</mn></msub><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo></math>. Within the same framework, we predict the production cross sections for their lower- and higher-spin partners; <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1975</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1940</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mn>4</mn></msub><mo stretchy="false">(</mo><mn>2250</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mn>4</mn></msub><mo stretchy="false">(</mo><mn>2230</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mn>5</mn></msub><mo stretchy="false">(</mo><mn>2350</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mn>5</mn></msub><mo stretchy="false">(</mo><mn>2350</mn><mo stretchy="false">)</mo></math>. Our results show that these states exhibit measurable cross sections with characteristically forward-peaked angular distributions, underscoring their strong potential for observation in future <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>p</mi></math> meson-beam experiments.

Ting-Yan Li

Zi-Yue Bai

Xiang Liu

Production of high-spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mi>J</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ρ</mi><mi>J</mi></msub></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>=</mo><mn>2</mn></mrow></math>, 3, 4, 5) mesons in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>−</mo></msup><mi>p</mi></math> reactions

Feynman integrals with generic propagator powers in one and two spacetime dimensions are investigated from various perspectives. In particular, we argue that the class of track integrals with massless propagators at any loop order is fixed by the recently found $$ \hat{\textrm{P}} $$ -symmetries of Yangian type. All track integrals up to six external points (and four loops) are bootstrapped explicitly as well as the full family of one-loop integrals at any multiplicity. Moreover, the triangle tracks at generic loop order, which constitute the most generic family of track-type integrals, are bootstrapped in this way. The results are compared to the direct evaluation via a spectral transform from the integrability toolbox that turns out to be particularly efficient for position-space tree integrals in lower dimensions. We prove that all $$ \hat{\textrm{P}} $$ -symmetries of these integrals can be derived from the framework of Aomoto-Gelfand hypergeometric functions, which applies to integrals in one and two dimensions. Finally, we also demonstrate the method’s applicability to conformal integrals by deriving the complete results for all comb-channel conformal partial waves as well as the conformal double-box integral. We explicitly go through all examples of the above integrals in 1D and then provide a straightforward recipe for how to read off their 2D counterparts.

Germany

Gwenaël Ferrando

Florian Loebbert

Amelie Pitters

Sven Stawinski

Hypergeometry from $$ \hat{\textrm{P}} $$ -symmetry: Feynman integrals in one and two dimensions

Based on a sample of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>10087</mn><mo>±</mo><mn>44</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mtext> </mtext><mtext> </mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></math> events collected with the BESIII detector, a partial-wave analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mover accent="true"><mi mathvariant="normal">Σ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mi>η</mi><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></math> is performed for the first time. The dominant contributions are found to be excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mi mathvariant="normal">Λ</mi></math> mass spectra. The measured masses and widths are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mo>=</mo><mn>1668.8</mn><mo>±</mo><mn>3.1</mn><mo>±</mo><mn>21.2</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo>=</mo><mn>52.7</mn><mo>±</mo><mn>4.2</mn><mo>±</mo><mn>17.8</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1670</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mo>=</mo><mn>1881.5</mn><mo>±</mo><mn>16.5</mn><mo>±</mo><mn>20.3</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo>=</mo><mn>82.4</mn><mo>±</mo><mn>18.2</mn><mo>±</mo><mn>8.9</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1810</mn><mo stretchy="false">)</mo></math>, respectively. The branching fraction is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mover accent="true"><mi mathvariant="normal">Σ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mi>η</mi><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>3.44</mn><mo>±</mo><mn>0.11</mn><mo>±</mo><mn>0.13</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>. The first uncertainties are statistical and the second systematic.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Italy

C.S. Akondi

R. Aliberti

A. Amoroso

Q. An

Y.H. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

X.L. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.M. Chen

T. Chen

W. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J. Cheng

L.N. Cheng

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

X.C. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denisenko

M. Destefanis

F. De Mori

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

X.L. Du

Y.Q. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

Amplitude analysis and branching fraction measurement of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mover accent="true"><mi mathvariant="normal">Σ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mi>η</mi><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></math>

It is demonstrated that, within the eikonal approach, the Coulomb corrections to the elastic electromagnetic nonflip and spin-flip proton-nucleus amplitudes are identical when the two amplitudes share the same exponential form factors. This result allows Coulomb corrections to be computed numerically, and with high precision, for both electromagnetic and hadronic elastic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>p</mi><mo stretchy="false">↑</mo></msup><mi>A</mi></math> amplitudes in the massless-photon limit, including the effects of soft magnetic photon exchange. The method relies on analytical expressions and numerical integrations over a finite impact-parameter range with nonsingular integrands, providing a practical and systematically controlled framework for phenomenological applications.

A.A. Poblaguev

Coulomb corrections for the nonflip and spin-flip electromagnetic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>p</mi><mo stretchy="false">↑</mo></msup><mi>A</mi></math> amplitudes

We report a search for ultraheavy dark matter (UHDM) with the CDEX-10 experiment at the China Jinping Underground Laboratory. Using a Monte Carlo framework that incorporates Earth shielding effects, we simulated UHDM propagation and energy deposition in p-type point-contact germanium detectors. Analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>205.4</mn><mtext> </mtext><mtext> </mtext><mi>kg</mi><mo>·</mo><mi>day</mi></mrow></math> exposure in the 0.16–4.16 keVee range showed no excess above background. Our results exclude the spin-independent UHDM-nucleon scattering with two cross section scales, with the UHDM mass from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mn>6</mn></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mn>11</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, and provide the most stringent constraints with solid-state detectors below <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mn>8</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.

Y.F. Wang

L.T. Yang

Q. Yue

K.J. Kang

Y.J. Li

H.P. An

Taiwan

Greeshma C.

J.P. Chang

H. Chen

Y.H. Chen

J.P. Cheng

J.Y. Cui

W.H. Dai

Z. Deng

Y.X. Dong

C.H. Fang

H. Gong

Q.J. Guo

T. Guo

X.Y. Guo

L. He

J.R. He

H.X. Huang

T.C. Huang

S. Karmakar

Y.S. Lan

H.B. Li

H.Y. Li

J.M. Li

J. Li

M.C. Li

Q.Y. Li

R.M.J. Li

X.Q. Li

Y.L. Li

Y.F. Liang

B. Liao

F.K. Lin

S.T. Lin

J.X. Liu

R.Z. Liu

S.K. Liu

Y.D. Liu

Y. Liu

Y.Y. Liu

H. Ma

Y.C. Mao

A. Mureed

H. Pan

N.C. Qi

J. Ren

X.C. Ruan

M.B. Shen

H.Y. Shi

M.K. Singh

T.X. Sun

W.L. Sun

C.J. Tang

Y. Tian

Constraints on ultraheavy dark matter from the CDEX-10 experiment at the China Jinping Underground Laboratory