Motivated by the work of Cardoso et al. (2022) <cross-ref refid='br0150' id='crf0030'>[15]</cross-ref> on black holes in galaxies, we derive a new black hole solution surrounded by a Dekel-Zhao (DZ) dark matter profile. The derived metric, influenced by DZ profile parameters, exhibits two distinct regimes: for <math altimg='si1.svg'><mi>r</mi><mo>&#8810;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> is a characteristic radius), exponential corrections dominate, producing significant deviations from the Schwarzschild solution near dense cores, while for <math altimg='si3.svg'><mi>r</mi><mo>&#8811;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>, these corrections vanish, restoring the Schwarzschild metric at large distances. These findings ensure consistency with general relativity in vacuum. The black hole shadow and deflection angle are analyzed, demonstrating that the shadow radius increases with black hole mass ( <math altimg='si4.svg'><msub><mrow><mi>M</mi></mrow><mrow><mi mathvariant='normal'>BH</mi></mrow></msub></math>), while higher central densities ( <math altimg='si5.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mi mathvariant='normal'>ch</mi></mrow></msub></math>) result in smaller shadows, reflecting the environmental impact of dense dark matter halos. Photon dynamics reveal how DZ profiles modify critical impact parameters and effective potentials, with gravitational lensing effects highly sensitive to the characteristic radius ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>). Smaller <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> values lead to larger deflection angles due to stronger gravitational effects near compact cores. This work highlights the significance dark matter profiles in shaping black hole observables, providing a theoretical foundation for future observational studies and advancing the understanding of dark matter-black hole interactions in astrophysical and cosmological contexts.

Türkiye

Ali Övgün

Philippines

Reggie C. Pantig

Black hole in the Dekel-Zhao dark matter profile

We study diffractive vector meson production at small-x in the collision of electrons and polarized deuterons <math><mi>e</mi><mo>+</mo><msup><mrow><mi>d</mi></mrow><mrow><mo>↑</mo></mrow></msup></math>. We consider the polarization dependence of the nuclear wave function of the deuteron, which results in an azimuthal angular dependence of the produced vector meson when the deuteron is transversely polarized. The Fourier coefficients extracted from the azimuthal angular dependence of the vector meson differential cross-section exhibit notable differences between longitudinally and transversely polarized deuterons. The angular dependence of the extracted effective deuteron radius provides direct insight into the structure of the polarized deuteron wave function. Furthermore, we observe slightly increased gluon saturation effects when the deuteron is longitudinally polarized compared to the transversely polarized case. The small-x observables studied in this work will be accessible at the future Electron-Ion Collider.

Finland

Heikki Mäntysaari

United States

Farid Salazar

Björn Schenke

Chun Shen

Wenbin Zhao

Spatial imaging of polarized deuterons at the Electron-Ion Collider

Using Bayesian inference, we determine probabilistic constraints on the parameters describing the fluctuating structure of protons at high energy. We employ the color glass condensate framework supplemented with a model for the spatial structure of the proton, along with experimental data from the ZEUS and H1 Collaborations on coherent and incoherent diffractive <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production in e+p collisions at HERA. This data is found to constrain most model parameters well. This work sets the stage for future global analyses, including experimental data from e+p, p+p, and p+A collisions, to constrain the fluctuating structure of nucleons along with properties of the final state.

Bayesian inference of the fluctuating proton shape

In this paper we introduce a light Dirac particle ψ as thermal dark matter candidate in a <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>−</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></msub></math> model. Together with the new gauge boson X, we find a possible parameter space with <math><msub><mrow><mi>m</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>≃</mo><mn>20</mn></math> MeV, <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>−</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></msub></math> coupling <math><msub><mrow><mi>g</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>≃</mo><mn>5</mn><mo>⋅</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> and <math><msub><mrow><mi>m</mi></mrow><mrow><mi>ψ</mi></mrow></msub><mo>≳</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>/</mo><mn>2</mn></math> where the <math><msub><mrow><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>μ</mi></mrow></msub></math> anomaly, dark matter, the Hubble tension, and (part of) the excess of 511 keV photons from the region near the galactic center can be explained simultaneously. This model is safe from current experimental and astrophysical constraints, but can be probed by the next generation of neutrino experiments as well as low–energy <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> colliders.

Germany

Manuel Drees

For Light Dark Matter, − 2, the 511 keV excess and the Hubble tension

Hydrodynamics and jet quenching are responsible for the elliptic flow <math><msub><mi>v</mi><mn>2</mn></msub></math> and suppression of large transverse momentum (<math><msub><mi>p</mi><mi>T</mi></msub></math>) hadrons, respectively, two of the most important phenomena leading to the discovery of a strongly coupled quark-gluon plasma in high-energy heavy-ion collisions. A consistent description of the hadron suppression factor <math><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> and <math><msub><mi>v</mi><mn>2</mn></msub></math>, especially at intermediate <math><msub><mi>p</mi><mi>T</mi></msub></math>, however, remains a challenge. We solve this long-standing <math><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub><mo>⊗</mo><msub><mi>v</mi><mn>2</mn></msub></math> puzzle by including quark coalescence for hadronization and final state hadron cascade in the coupled linear Boltzmann transport-hydro model that combines concurrent jet transport and hydrodynamic evolution of the bulk medium. We illustrate that quark coalescence and hadron cascade, two keys to solving the puzzle, also lead to a splitting of <math><msub><mi>v</mi><mn>2</mn></msub></math> for pions, kaons, and protons in the intermediate <math><msub><mi>p</mi><mi>T</mi></msub></math> region. We demonstrate for the first time that experimental data on <math><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub></math>, <math><msub><mi>v</mi><mn>2</mn></msub></math>, and their hadron flavor dependence from low to intermediate and high <math><msub><mi>p</mi><mi>T</mi></msub></math> in high-energy heavy-ion collisions can be understood within this coupled framework.

China

Weiyao Ke

Wei Chen

Spain

Tan Luo

Xin-Nian Wang

From Hydrodynamics to Jet Quenching, Coalescence, and Hadron Cascade: A Coupled Approach to Solving the <math><msub><mi>R</mi><mrow><mi>A</mi><mi>A</mi></mrow></msub><mo>⊗</mo><msub><mi>v</mi><mn>2</mn></msub></math> Puzzle

Using the nucleon coalescence model based on kinetic freeze-out nucleons from the 3D MUSIC+UrQMD and the 2D VISHNU hybrid model with a crossover equation of state, we study the multiplicity dependence of deuteron (d) and triton (t) production from central to peripheral Au+Au collisions at <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>NN</mi></mrow></msub></mrow></msqrt><mo>=</mo></math> 7.7, 14.5, 19.6, 27, 39, 62.4 and 200 GeV and Pb+Pb at <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>NN</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>2.76</mn></math> TeV, respectively. It is found that the ratio <math><msub><mrow><mi>N</mi></mrow><mrow><mi>t</mi></mrow></msub><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>/</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math> of the proton yield <math><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub></math>, deuteron yield <math><msub><mrow><mi>N</mi></mrow><mrow><mi>d</mi></mrow></msub></math> and triton yield <math><msub><mrow><mi>N</mi></mrow><mrow><mi>t</mi></mrow></msub></math> exhibits a scaling behavior in its multiplicity dependence, i.e., decreasing monotonically with increasing charged-particle multiplicity. A similar multiplicity scaling of this ratio is also found in the nucleon coalescence calculation based on kinetic freeze-out nucleons from a multiphase transport (AMPT) model. The scaling behavior of <math><msub><mrow><mi>N</mi></mrow><mrow><mi>t</mi></mrow></msub><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>/</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math> can be naturally explained by the interplay between the sizes of light nuclei and the nucleon emission source. We further argue that the multiplicity scaling of <math><msub><mrow><mi>N</mi></mrow><mrow><mi>t</mi></mrow></msub><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>/</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math> can be used to validate the production mechanism of light nuclei, and the collision energy dependence of this yield ratio can further serve as a baseline in the search for the QCD critical point in relativistic heavy-ion collisions.

Kai-jia Sun

Che Ming Ko

Xiaofeng Luo

Multiplicity scaling of light nuclei production in relativistic heavy-ion collisions

In this paper, we investigate the hydrodynamic collectivity in proton-proton collisions at  $$\sqrt{s}=$$  <math> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> </mrow> </math>   13 TeV, using iEBE-VISHNU with three different initial conditions, namely, HIJING, super-MC and TRENTo. With properly tuned parameters, hydrodynamics gives reasonable descriptions of the measured two-particle correlations, including the integrated and  $$p_\mathrm{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>  -differential flow. However, the hydrodynamic simulations fail to describe the negative four-particle cumulant  $$c_2^v\{4\}$$  <math> <mrow> <msubsup> <mi>c</mi> <mn>2</mn> <mi>v</mi> </msubsup> <mrow> <mo>{</mo> <mn>4</mn> <mo>}</mo> </mrow> </mrow> </math>   as measured in experiments. The four-particle cumulant  $$c_2^v\{4\}$$  <math> <mrow> <msubsup> <mi>c</mi> <mn>2</mn> <mi>v</mi> </msubsup> <mrow> <mo>{</mo> <mn>4</mn> <mo>}</mo> </mrow> </mrow> </math>   is always positive after hydrodynamic evolutions. Further investigations show that the non-linear response between the final  $$v_2$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   and the initial  $$\varepsilon _2$$  <math> <msub> <mi>ε</mi> <mn>2</mn> </msub> </math>   becomes significant in p-p systems. This leads to a large deviation from linear eccentricity scaling and generates additional flow fluctuations, which results in a positive  $$c_2^v\{4\}$$  <math> <mrow> <msubsup> <mi>c</mi> <mn>2</mn> <mi>v</mi> </msubsup> <mrow> <mo>{</mo> <mn>4</mn> <mo>}</mo> </mrow> </mrow> </math>   even with a negative  $$c_2^\varepsilon \{4\}$$  <math> <mrow> <msubsup> <mi>c</mi> <mn>2</mn> <mi>ε</mi> </msubsup> <mrow> <mo>{</mo> <mn>4</mn> <mo>}</mo> </mrow> </mrow> </math>   from the initial state. We also presented the first hydrodynamic calculations of mixed harmonic azimuthal correlations in p-p collisions. Although many qualitative features are reproduced by the hydrodynamic simulations, the measured negative normalized Symmetric-Cumulant  $$nsc_{2,3}\{4\}$$  <math> <mrow> <mi>n</mi> <mi>s</mi> <msub> <mi>c</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </msub> <mrow> <mo>{</mo> <mn>4</mn> <mo>}</mo> </mrow> </mrow> </math>   cannot be reproduced. Obviously hydrodynamic calculations have a general difficulty to describe the data. It triggers that whether hydrodynamics with a new initial state could solve this puzzle, or hydrodynamics itself is not the appreciated mechanism of the observed collectivity, and the non-hydrodynamic modes become important in p-p collisions at the LHC.

Denmark

You Zhou

Koichi Murase

Huichao Song

Searching for small droplets of hydrodynamic fluid in proton–proton collisions at the LHC

In this paper, we implement principal component analysis (PCA) to study the single particle distributions generated from thousands of $$\mathtt {VISH2+1}$$ <math><mrow><mi>VISH</mi><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>  hydrodynamic simulations with an aim to explore if a machine could directly discover flow from the huge amount of data without explicit instructions from human-beings. We found that the obtained PCA eigenvectors are similar to but not identical with the traditional Fourier bases. Correspondingly, the PCA defined flow harmonics $$v_n^\prime $$ <math><msubsup><mi>v</mi><mi>n</mi><mo>′</mo></msubsup></math>  are also similar to the traditional $$v_n$$ <math><msub><mi>v</mi><mi>n</mi></msub></math>  for $$n=2$$ <math><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></math>  and 3, but largely deviated from the Fourier ones for $$n\ge 4$$ <math><mrow><mi>n</mi><mo>≥</mo><mn>4</mn></mrow></math> . A further study on the symmetric cumulants and the Pearson coefficients indicates that mode-coupling effects are reduced for these flow harmonics defined by PCA.

Ziming Liu

Principal component analysis of collective flow in relativistic heavy-ion collisions

In this paper, we investigate the hydrodynamic collectivity in proton–proton (p–p) collisions at 13 TeV, using iEBE-VISHNU hybrid model with HIJING initial conditions. With properly tuned parameters, our model simulations can remarkably describe all the measured 2-particle correlations, including integrated and differential elliptic flow coefficients for all charged and identified hadrons (<math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math>, Λ). However, our model calculations show positive 4-particle cumulant <math><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>{</mo><mn>4</mn><mo>}</mo></math> in high multiplicity pp collisions, and can not reproduce the negative <math><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>{</mo><mn>4</mn><mo>}</mo></math> measured in experiment. Further investigations on the HIJING initial conditions show that the fluctuations of the second order anisotropy coefficient <math><msub><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow></msub></math> increases with the increase of its mean value, which leads to a similar trend of the flow fluctuations. For a simultaneous description of the 2- and 4- particle cumulants within the hydrodynamic framework, it is required to have significant improvements on initial condition for pp collisions, which is still lacking of knowledge at the moment.

Hao-jie Xu

Weitian Deng

Hydrodynamic collectivity in proton–proton collisions at 13 TeV

In this paper, we study and predict flow observables in 2.76 and 5.02 A TeV PbÂ +Â Pb collisions, using the iEBE-VISHNU hybrid model with TRENTo and AMPT initial conditions and with different forms of the QGP transport coefficients. With properly chosen and tuned parameter sets, our model calculations can nicely describe various flow observables in 2.76 A TeV PbÂ +Â Pb collisions, as well as the measured flow harmonics of all charged hadrons in 5.02 A TeV PbÂ +Â Pb collisions. We also predict other flow observables, including vn(pT) of identified particles, event-by-event vn distributions, event-plane correlations, (normalized) symmetric cumulants, non-linear response coefficients and pT -dependent factorization ratios, in 5.02 A TeV PbÂ +Â Pb collisions. We find many of these observables to remain approximately the same values as the ones in 2.76 A TeV PbÂ +Â Pb collisions. Our theoretical studies and predictions could shed light to the experimental investigations in the near future.