The production of heavy-quark (HQ) jets is a new area that addresses the mass effect of jet quenching in heavy-ion physics. This paper presents a theoretical study of HQ jet yield suppression in Pb+Pb collisions at the Large Hadron Collider (LHC) and focuses on the energy loss of HQ jets produced by different mechanisms. The $\textit{p+p}$ baseline is provided by the generator simulation of high-energy reactions of particles (SHERPA), and the jet-medium interactions are described by the SHELL transport model, which considers the elastic and inelastic partonic energy loss in the quark-gluon plasma (QGP). In $\textit{p+p}$ collisions, our numerical results indicate that the HQ jets from gluon splitting ( $ g \rightarrow Q $ -jet) are the dominant contribution at high $ p_T $ , displaying more dispersive structures than the HQ-initiated ( $ Q \rightarrow Q $ -jet). In nucleus-nucleus collisions, our calculations were consistent with the inclusive and b-jet $ R_{AA} $ recently measured by the ATLAS collaboration, revealing a remarkable manifestation of the mass effect of jet energy loss. As a result of the dispersive substructure, the $ g \rightarrow Q $ -jet loses more energy than the $ Q \rightarrow Q $ -jet in the QGP. Due to the significant contribution of $ g \rightarrow c $ -jet, the $ R_{AA} $ of $\textit{c}$-jet is comparable or even smaller than that of inclusive jet. To experimentally distinguish the $ g \rightarrow Q $ -jet and $ Q \rightarrow Q $ -jet, we propose event selection strategies based on their topological features and test their performances. By isolating the $ c \rightarrow c $ -jet, $ b \rightarrow b $ -jet, and the jets initiated by heavy quarks, we predicted that the order of their $ R_{AA} $ are in line with the mass hierarchy of energy loss. Future measurements on the $ R_{AA} $ of $ Q \rightarrow Q $ -jet and $ g \rightarrow Q $ -jet will provide a unique opportunity for testing the flavor/mass dependence of energy loss at the jet level.

China

Sa Wang

Shuang Li

Yao Li

Ben-Wei Zhang

Enke Wang

Probing the mass effect of heavy quark jets in high-energy nuclear collisions * Supported by the MajorProject of Basic and Applied Basic Research of Guangdong Province, China (2020B0301030008, 2023A1515011460), and the National Natural Science Foundation of China (11935007, 12035007, 12247127, 12375137). Sa Wang is supported by the Open Foundation of Key Laboratory of Quark and Lepton Physics (MOE) (QLPL2023P01) and the Talent Scientific Star-up Foundation of the China Three Gorges University, China (CTGU) (2024RCKJ013)

The direct CP asymmetry in the weak decay process of hadrons is commonly attributed to the weak phase of the CKM matrix and the indeterminate strong phase. We propose a method to generate a significant phase difference through the interference between ρ and ω mesons, taking into account the G-parity allowed decay process of   $\omega \rightarrow \pi^{+}\pi^{-}\pi^{0}$   and the G-parity-suppressed decay process of   $\omega \rightarrow \pi^{+}\pi^{-}\pi^{0}$   in B meson decays. This interference can lead to notable changes in the CP asymmetry within the interference region. Additionally, we calculate the integral results for different phase space regions of the four-body decay process. We hope that our work provides valuable theoretical guidance for future experimental investigations on CP asymmetry in these decays.

Xi-Liang Yuan

Gang Lü

Na Wang

Chao Wang

The resonance effect for the CP asymmetry associated with the process   

Elastic scattering off nuclei in target detectors, involving interactions with dark matter and coherent elastic neutrino nuclear recoil <math><mrow><mo>(</mo><mi>CE</mi><mi>ν</mi><mi>NS</mi><mo>)</mo></mrow></math>, results in the deposition of low energy within the nuclei, dissipating rapidly through a combination of heat and ionization. The primary energy loss mechanism for nuclear recoil is heat, leading to consistently smaller measurable scintillation signals compared to electron recoils of the same energy. The nuclear recoil quenching factor (QF), representing the ratio of scintillation light yield produced by nuclear recoil to that of electron recoil at the same energy, is a critical parameter for understanding dark matter and neutrino interactions with nuclei. The low energy QF of NaI(Tl) crystals, commonly employed in dark matter searches and <math><mrow><mi>CE</mi><mi>ν</mi><mi>NS</mi></mrow></math> measurements, is of substantial importance. Previous low energy QF measurements were constrained by contamination from photomultiplier tube (PMT)-induced noise, resulting in an observed light yield of approximately 15 photoelectrons per keVee (kilo-electron-volt electron-equivalent energy) and nuclear recoil energy above 5 keVnr (kilo-electron-volt nuclear recoil energy). Through enhanced crystal encapsulation, an increased light yield of around 26 photoelectrons per keVee is achieved. This improvement enables the measurement of the nuclear recoil QF for sodium nuclei at an energy of <math><mrow><mn>3.8</mn><mo>±</mo><mn>0.6</mn><mspace width="0.16em"></mspace><mi>keVnr</mi></mrow></math> with a QF of <math><mrow><mn>11.2</mn><mo>±</mo><mn>1.7</mn><mspace width="0.16em"></mspace><mo>%</mo></mrow></math>. Furthermore, a re-evaluation of previously reported QF results is conducted, incorporating enhancements in low energy events based on waveform simulation. The outcomes are generally consistent with various recent QF measurements for sodium and iodine.

South Korea

S.H. Lee

H.W. Joo

H.J. Kim

K.W. Kim

S.K. Kim

Y.D. Kim

Y.J. Ko

H.S. Lee

J.Y. Lee

H.S. Park

Y.S. Yoon

Measurements of low-energy nuclear recoil quenching factors for Na and I recoils in the NaI(Tl) scintillator

The ground states of the nuclei <math><mmultiscripts><mrow><mi>Mg</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>40</mn></mrow></mmultiscripts></math> and <math><mmultiscripts><mrow><mi>Na</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>39</mn></mrow></mmultiscripts></math> are investigated using the hyperspherical formalism. Since they are located at the edge of the “big island of inversion”, we concentrate on whether we are likely to find two-neutron Borromean halos in these nuclei. A three-body model with effective n-n and <math><mmultiscripts><mrow><mi>Mg</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>38</mn></mrow></mmultiscripts><mo>+</mo><mi>n</mi></math> interactions is built for <math><mmultiscripts><mrow><mi>Mg</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>40</mn></mrow></mmultiscripts></math> based on the available data. We also give predictions for the low-lying spectrum of <math><mmultiscripts><mrow><mi>Na</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>38</mn></mrow></mmultiscripts><msup><mrow><mo>=</mo></mrow><mrow><mn>37</mn></mrow></msup><mrow><mi>Na</mi></mrow><mo>+</mo><mi>n</mi></math> and two-neutron separation energy of the <math><mmultiscripts><mrow><mi>Na</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>39</mn></mrow></mmultiscripts></math> nucleus. Depending on parameter choice, we report an increase in the matter radii in the range 0.1-0.5 fm relative to those of the core nuclei. The results suggest a two-neutron halo structure in <math><mmultiscripts><mrow><mi>Mg</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>40</mn></mrow></mmultiscripts></math> for a subset of parameters, reinforcing the prediction of a Borromean halo nucleus. The calculations indicate that a two-neutron halo is even more likely for <math><mmultiscripts><mrow><mi>Na</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>39</mn></mrow></mmultiscripts></math>. As expected, the halo is linked to the disappearance of the shell gap in these nuclei due to the inversion of the <math><mn>2</mn><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math> and <math><mn>1</mn><msub><mrow><mi>f</mi></mrow><mrow><mn>7</mn><mo>/</mo><mn>2</mn></mrow></msub></math> orbitals. We study the total cross section for scattering of these nuclei from a carbon target using a Glauber model and show that these provide a clear signal to assess the halo structure.

Poland

United Kingdom

India

Japan

Jagjit Singh

Spain

J. Casal

W. Horiuchi

N.R. Walet

W. Satuła

Prediction of two-neutron halos in the = 28 Isotones Mg and Na

We present the novel   $ V\rightarrow K^{+}K^{-} (V=\phi, \rho, \omega) $   resonance, which generates a strong phase associated with vector meson resonances, leading to significant CP asymmetry in the interference region. The   $ V\rightarrow K^{+}K^{-} (V=\phi, \rho, \omega) $  ,   $ V\rightarrow K^{+}K^{-} (V=\phi, \rho, \omega) $  , and   $ V\rightarrow K^{+}K^{-} (V=\phi, \rho, \omega) $   resonances arise from the mixing of the vector mesons ϕ, ρ, and ω. We calculate the CP asymmetry from the decay mode of   $ V\rightarrow K^{+}K^{-} (V=\phi, \rho, \omega) $  . Meanwhile, the localized CP asymmetries are presented and a detailed analysis is performed. The CP asymmetry from the decay mode of   $ V\rightarrow K^{+}K^{-} (V=\phi, \rho, \omega) $   is also presented in our framework, which is highly consisted with that of the LHC experiment. The introduced CP asymmetry can provide a favorable theoretical support for experimental exploration in the future.

Li-Ying Zhang

Xin-Heng Guo

 Asymmetry From the Resonance Effect of the Meson Decay Process With And Final States  

In this paper, we consider 3D Young diagrams with at most N layers in z-axis direction, which can be constructed by N 2D Young diagrams on slice z = j, j = 1, 2, · · · , N from the Yang-Baxter equation. Using 2D Bosons {a  j,m , m ∈ ℤ} associated to 2D Young diagrams on the slice z = j, we constructed 3D Bosons. Then we show the 3D Boson representation of W 1+∞  algebra, and give the method to calculate the Littlewood-Richardson rule for 3-Jack polynomials.

Ke Wu

3D Bosons and W 1+∞ algebra

The symmetric functions <math><msub><mrow><mi>Y</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math> are a generalization of Schur functions <math><msub><mrow><mi>S</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math>, and <math><msub><mrow><mi>Y</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math> are symmetric about the x-axis and y-axis. As the Schur functions can be used to describe the tau functions of the KP hierarchy, in this paper, we define the symmetric KP hierarchy whose tau functions can be represented by <math><msub><mrow><mi>Y</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math>. The method we use is affine Yangian of <math><mrow><mi>gl</mi></mrow><mo>(</mo><mn>1</mn><mo>)</mo></math>. We also define the Boson-Fermion correspondence in the symmetric KP hierarchy.

The symmetric KP hierarchy and affine Yangian of

3D (3 dimensional) Young diagrams are a generalization of 2D Young diagrams. In this paper, We consider 3D Bosons and 3-Jack polynomials. We associate three parameters h 1, h 2, h 3 to y, x, z-axis respectively. 3-Jack polynomials are polynomials of P  n,j , n ≥ j with coefficients in ℂ(h 1, h 2, h 3), which are the generalization of Schur functions and Jack polynomials to 3D case. Similar to Schur functions, 3-Jack polynomials can also be determined by the vertex operators and the Pieri formulas.

3D bosons, 3-Jack polynomials and affine Yangian of   <math> <mi>gl</mi> <mfenced> <mn>1</mn> </mfenced> </math>  $$ \mathfrak{gl}(1) $$

In this paper, we define one kind of new Jack polynomials denoted by <math><mi>J</mi><msub><mrow><mi>k</mi></mrow><mrow><mi>λ</mi></mrow></msub></math>, which equal the standard Jack polynomials <math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>λ</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math> multiplied by a coefficient. We show that the structure constant <math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>λ</mi><mi>μ</mi></mrow><mrow><mi>ν</mi></mrow></msubsup></math> in <math><mi>J</mi><msub><mrow><mi>k</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>⋅</mo><mi>J</mi><msub><mrow><mi>k</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>ν</mi></mrow></msub><msubsup><mrow><mi>C</mi></mrow><mrow><mi>λ</mi><mi>μ</mi></mrow><mrow><mi>ν</mi></mrow></msubsup><mi>J</mi><msub><mrow><mi>k</mi></mrow><mrow><mi>ν</mi></mrow></msub></math> can be given from affine Yangian of <math><mrow><mi>gl</mi></mrow><mo>(</mo><mn>1</mn><mo>)</mo></math>. Then we give the Boson-Fermion correspondence for Jack polynomials <math><mi>J</mi><msub><mrow><mi>k</mi></mrow><mrow><mi>λ</mi></mrow></msub></math> and show that 3-Schur functions <math><msub><mrow><mi>S</mi></mrow><mrow><mi>π</mi></mrow></msub></math> equal Jack polynomials <math><mi>J</mi><msub><mrow><mi>k</mi></mrow><mrow><mi>λ</mi></mrow></msub></math> in the special case of <math><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mi>h</mi></math>, <math><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mo>−</mo><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, <math><msub><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mo>−</mo><mi>h</mi><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>.

Zhennan Cui

Yang Bai

Jack polynomials and affine Yangian

We study the   $ B_{c,u,d}\to X(3872)P $   decays in the perturbative QCD (PQCD) approach, involving the puzzling resonance   $ B_{c,u,d}\to X(3872)P $  , where P represents a light pseudoscalar meson (K or π). Assuming   $ B_{c,u,d}\to X(3872)P $   to be a   $ B_{c,u,d}\to X(3872)P $   charmonium state, we obtain the following results. (a) The branching ratios of the   $ B_{c,u,d}\to X(3872)P $   and   $ B_{c,u,d}\to X(3872)P $   decays are consistent with the results predicted by the covariant light-front approach within errors; however, they are larger than those given by the generalized factorization approach. (b) The branching ratio of the   $ B_{c,u,d}\to X(3872)P $   decay is predicted as   $ B_{c,u,d}\to X(3872)P $  , which is smaller than the previous PQCD calculation result but still slightly larger than the upper limits set by Belle and BaBar. Hence, we suggest that the  $ B_{c,u,d}\to X(3872)P $   decays should be precisely measured by the LHCb and Belle II experiments to help probe the inner structure of   $ B_{c,u,d}\to X(3872)P $  . (c) Compared with the   $ B_{c,u,d}\to X(3872)P $  decays, the   $ B_{c,u,d}\to X(3872)P $   decays have significantly smaller branching ratios, which drop to values as low as   $ B_{c,u,d}\to X(3872)P $  . (d) The direct CP violations of these considered decays are small (  $ B_{c,u,d}\to X(3872)P $  ) because the penguin contributions are loop suppressed compared to the tree contributions. The mixing-induced CP violation of the   $ B_{c,u,d}\to X(3872)P $   decay is highly consistent with the current world average value   $ B_{c,u,d}\to X(3872)P $  %. Experimentally testing the results for the branching ratios and CP violations, including the implicit   $ B_{c,u,d}\to X(3872)P $   and isospin symmetries of these decays, helps probe the nature of   $ B_{c,u,d}\to X(3872)P $  .