We propose an extension of the initial-condition model trento for sampling the number of partons inside the nucleons that participate in a heavy-ion collision. This sampling method is based on parton distribution functions and therefore has a natural dependence on the momentum transferred in the collision and the scale being probed during the collision. We examine the resulting distributions and their dependence on the momentum transfer. Additionally, we explore the sensitivity of different observables on the number of partons using the trento framework and the estimators available therein for final-state observables.

United States

Andreas Kirchner

Steffen A. Bass

Signals for fluctuating constituent numbers in small systems

In this study we apply the Remler formalism to charmonium production at Super Proton Synchrotron (SPS) and GSI/Facility for Antiproton and Ion Research (FAIR) energies in order to investigate the effects of baryon-rich matter on charmonium production and dissociation in heavy-ion collisions within the parton-hadron-string dynamics. As a first step the Remler formalism is tested in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></math> collisions and then applied to <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mo>+</mo><mi>A</mi></mrow></math> collisions in order to extract the nuclear absorption cross section of charmonium, which is then utilized in heavy-ion collisions. We find that the Remler formalism successfully describes charmonium production in heavy-ion collisions at SPS energies when an in-medium heavy quark potential is implemented, in which <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> dissociates near <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>c</mi></msub></math>. Finally, the same formalism is applied to the low CERN/SPS energy and GSI/FAIR energies, where we estimate charmonium production.

Germany

Taesoo Song

Jiaxing Zhao

France

Joerg Aichelin

Elena Bratkovskaya

Charmonium production at energies available at the CERN Super Proton Synchrotron and Facility for Antiproton and Ion Research

We calculate the valence parton distribution function (PDF) of pion within the theoretical approach based on spectral function representation of valence quarks in the pion. In this approach we assume that the soft partonic structure of pion is defined by the valence <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>q</mi><mover accent="true"><mi>q</mi><mo>¯</mo></mover></mrow></math> cluster, consisting of current quarks, embedded in the residual field of the pion. The valence PDF is calculated using phenomenological light-front wave functions for the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>q</mi><mover accent="true"><mi>q</mi><mo>¯</mo></mover></mrow></math> cluster and the residual field. Our result indicates that the peak position of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> weighted valence PDF (xPDF) depends on parameters characterizing the virtuality of the valence quark cluster and the mass of the residual system. Magnitudes of these parameters are obtained by fitting to the height and the peak position of empirical pion xPDF evaluated at starting <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Q</mi><mn>0</mn></msub></math>. They indicate that unlike the nucleon case, very little residual mass is needed to describe existing pion PDFs at intermediate <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>. They also indicate that the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>q</mi><mover accent="true"><mi>q</mi><mo>¯</mo></mover></mrow></math> cluster is highly virtual and on average the interacting quark carries almost all of the momentum of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>q</mi><mover accent="true"><mi>q</mi><mo>¯</mo></mover></mrow></math> cluster. This picture is consistent with the dominance of the Feynman mechanism leaving little room for the hard component in the PDF and practically describing <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>≈</mo><mo>(</mo><mn>1</mn><mo>−</mo><mi>x</mi><mo>)</mo></mrow></math> behavior observed recently at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>x</mi><mo>→</mo><mn>1</mn></mrow></math> limit. Our nontrivial observation is that the height and the peak position of xPDF define the analytic behavior of valence PDF at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>x</mi><mo>→</mo><mn>1</mn></mrow></math> limit.

Joseph Maerovitz

Misak Sargsian

Christopher Leon

Pion valence structure at intermediate <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> in the residual-field approach

We investigate the internal structure of two exotic tetraquark candidates, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mrow><mo>(</mo><mn>3872</mn><mo>)</mo></mrow></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mrow><mo>(</mo><mn>3875</mn><mo>)</mo></mrow></mrow></math>, whose masses lie within <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn><mspace width="0.28em"></mspace><mtext>MeV</mtext></mrow></math> of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>D</mi><mn>0</mn></msup><msup><mover accent="true"><mi>D</mi><mo>¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>D</mi><mn>0</mn></msup><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup></mrow></math> thresholds, respectively. Using the effective-range expansion (ERE) supplemented by resonance compositeness relations on the second Riemann sheet, we extract scattering lengths <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and effective ranges <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> directly from the experimental masses and widths and quantify the <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></mrow></math> molecular content through partial compositeness coefficients <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mi>j</mi></msub></math>. A two-channel framework couples each state's inelastic detection channel (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mspace width="0.16em"></mspace><mi>π</mi><mi>π</mi></mrow></math>; <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>D</mi><mn>0</mn></msup><msup><mi>D</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></mrow></math>) to the near-threshold molecular channel. Full Monte Carlo uncertainty propagation with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi><mo>=</mo><mn>50</mn><mspace width="0.16em"></mspace><mn>000</mn></mrow></math> Gaussian samples yields asymmetric <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>68</mn><mo>%</mo></mrow></math> confidence intervals for all observables. We find large negative scattering lengths <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>a</mi><mo>=</mo><mo>−</mo><mn>8</mn><mo>.</mo><msubsup><mn>49</mn><mrow><mo>−</mo><mn>1.05</mn></mrow><mrow><mo>+</mo><mn>0.93</mn></mrow></msubsup></mrow></math> fm for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mrow><mo>(</mo><mn>3872</mn><mo>)</mo></mrow></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>a</mi><mo>=</mo><mo>−</mo><mn>14</mn><mo>.</mo><msubsup><mn>57</mn><mrow><mo>−</mo><mn>1.66</mn></mrow><mrow><mo>+</mo><mn>1.70</mn></mrow></msubsup></mrow></math> fm for <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>, both far exceeding the natural hadronic scale <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>≈</mo><mn>1</mn><mo>/</mo><msub><mi>m</mi><mi>π</mi></msub></mrow></math> and dominant molecular components <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>X</mi><mn>2</mn></msub><mo>&gt;</mo><mn>0.95</mn></mrow></math> under full compositeness. The results are stable for total compositeness <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>X</mi><mo>∈</mo><mo>[</mo><mn>0.5</mn><mo>,</mo><mn>1.0</mn><mo>]</mo></mrow></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn><mo>−</mo><mi>X</mi></mrow></math> represents an upper bound on any compact/CDD-pole contribution. In the present study, we go beyond the pole-position Castillejo-Dalitz-Dyson (CDD) criterion by explicitly constructing the inverse amplitude as an ERE background plus a scanned CDD pole term, finding no region of physically reasonable bare-state parameter space that reproduces the pole while leaving a natural background; we fully propagate the loop-function subtraction constant <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>a</mi><mo>(</mo><msub><mi>μ</mi><mi>g</mi></msub><mo>)</mo></mrow></math> as a Monte Carlo nuisance parameter jointly with the experimental mass and width, confirming it contributes a negligible (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>&lt;</mo><mn>0.01</mn><mo>%</mo></mrow></math>) additional uncertainty; and we test robustness against an assumed correlation between <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>M</mi><mi>R</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">Γ</mi><mi>R</mi></msub></math>, finding all results stable over a broad range of correlation coefficients. We demonstrate analytically and numerically the scheme-independence of the compositeness coefficients, provide explicit derivations of all ERE formulas from the pole condition, clarify the analytic continuation procedure for closed channels, and compare our results quantitatively with independent ERE, effective-field theory, and other relevant studies. The <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>Z</mi><mi>c</mi></msub><mrow><mo>(</mo><mn>3900</mn><mo>)</mo></mrow></mrow></math> case is treated separately to show the breakdown of the two-channel approximation for above-threshold states. Graphical illustrations of the Monte Carlo distributions are included.

Cameroon

A.A. Atangana Likéné

Switzerland

A. Franck Rothen

J.M. Ema'a Ema'a

P. Pradyun Hebbar

United Kingdom

Saralees Nadarajah

Tobias Golling

G.H. Ben-Bolie

Near-threshold dynamics of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math>(3872) and <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>(3875) states via effective range expansion and Monte Carlo uncertainty propagation

Quantifying causal connections within fireballs resulting from high energy nucleus-nucleus collisions is pertinent to assessing the viability of several proposed mechanisms that directly influence particle production and correlations. Fireball causal connections have previously been studied in the context of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math> dimensional Bjorken flow. We expand into <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions using Gubser flow, which includes transverse expansion. Our findings suggest that the volume of these causally connected fireballs are on the order of 10–100 <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>fm</mi></mrow><mn>3</mn></msup></math> for observables dependent on the formation of the light quark condensates, but could be larger for other observables.

Olivia Chabowski

Joseph I. Kapusta

Causally connected regions in relativistic heavy ion collisions

We apply a constituent quark equal-velocity combination (EVC) model to study the elliptic flow (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math>) and triangular flow (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>3</mn></msub></math>) of light-flavor and single-charmed hadrons in Pb+Pb collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo></mrow></math> 2.76 and 5.02 TeV. <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></math> of hadrons in the EVC model can be expressed as a linear superposition of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub></math> of quarks at the same velocity as that of the hadrons. We find that available experimental data for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>3</mn></msub></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">Λ</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">Ξ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Ω</mi></math> as a function of transverse momentum (<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mi>T</mi></msub></math>) can be consistently explained by the EVC formula using the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> of up/down quarks and the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> of strange quarks. In comparison with <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> data of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mspace width="0.16em"></mspace><mn>2.76</mn></mrow></math> TeV, which can be naturally explained by the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> of strange quarks, explanation of the data of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math> mesons at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mspace width="0.16em"></mspace><mn>5.02</mn></mrow></math> TeV requires an additional contribution of two-kaon coalescence, which indicates approximately 20% influence of final-state hadronic rescattering on <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mspace width="0.16em"></mspace><mn>5.02</mn></mrow></math> TeV. Using <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>3</mn></msub></math> of light-flavor quarks obtained in studying light-flavor hadrons and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>3</mn></msub></math> of charm quarks determined from <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup></math> meson data, we apply the EVC model to predict the anisotropic flows of <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>D</mi><mrow><mi>s</mi></mrow><mo>+</mo></msubsup><mo>,</mo><mo> </mo><msubsup><mi mathvariant="normal">Λ</mi><mrow><mi>c</mi></mrow><mo>+</mo></msubsup><mo>,</mo><mo> </mo><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi></mrow><mn>0</mn></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">Ω</mi><mrow><mi>c</mi></mrow><mn>0</mn></msubsup></math> and compare them with the available experimental data. The preliminary data for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>D</mi><mn>0</mn></msup><mo>,</mo><mo> </mo><msubsup><mi>D</mi><mrow><mi>s</mi></mrow><mo>+</mo></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">Λ</mi><mrow><mi>c</mi></mrow><mo>+</mo></msubsup></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo></mrow></math> 5.36 TeV are found to be naturally described by the EVC model.

China

Yan-ting Feng

Rui-qin Wang

Feng-lan Shao

Jun Song

Anisotropic flows of light-flavor and charmed hadrons in Pb+Pb collisions at energies available at the CERN Large Hadron Collider

We investigate the exclusive semileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi><msup><mi>ℓ</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>ℓ</mi></msub><mspace width="4pt"></mspace><mrow><mo>(</mo><mi>ℓ</mi><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></mrow></math> within the standard model using the light-front quark model. The transition form factor behaviors of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi></mrow></math> are obtained from the effective treatment of nonvalence contributions in addition to the valence ones in the Drell-Yan-West frame due to the Bethe-Salpeter formalism. Based on these form factors, we obtain that the branching ratios of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi><msup><mi>e</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>e</mi></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><msup><mi>μ</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>μ</mi></msub></mrow></math>, including nonvalence contributions, are around <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>8.32</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1.31</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math>, which are consistent with the latest measurements from the BESIII Collaboration, respectively. Our results indicate that nonvalence contributions can play a non-negligible role in the semileptonic baryon decays within the light-front framework.

Chong-Chung Lih

Chao-Qiang Geng

Semileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">Λ</mi><mo>→</mo><mi>p</mi><msup><mi>ℓ</mi><mo>−</mo></msup><msub><mover accent="true"><mi>ν</mi><mo>¯</mo></mover><mi>ℓ</mi></msub></mrow></math> in light-front dynamics

We compare the longitudinal deposition of various conserved quantities in the initial condition models of a string based (SMASH) and a saturation based (McDipper) approach. SMASH has been shown to work reasonably well at lower collision energies as an initial condition for the SMASH-vHLLE hybrid approach, while McDipper, based on the color-glass-condensate, works well in the regime of perturbative quantum chromodynamics. The two models are capable of providing longitudinally resolved initial conditions, which is essential for three-dimensional hydrodynamical simulations. The goal of this study is to interface the different regions of applicability of the two models, to investigate the initial state dynamics in the intermediate energy regime. We analyze the deposition of transverse energy, charge and baryon number across a large range of collision energies (62.4 GeV to 5.02 TeV) and find that, while they are good agreement at lower energies, their energy and baryon deposition differs substantially at higher center of mass energies.

Lucas Constantin

Spain

Oscar Garcia-Montero

Niklas Götz

Hannah Elfner

3D initial-state dynamics across scales: A comparative study of saturation and string-based descriptions

The neutron-skin thickness in neutron-rich nuclei has traditionally been measured using low-energy hadronic and electronic scatterings at hadronic level. In this paper, we propose an alternative probe to the neutron-skin thickness through deep-inelastic scattering in high-energy electron-ion collisions, leveraging the intrinsic correlation between final-state jet charge distribution and initial-state partonic distributions in nucleons. Specifically, we demonstrate the sensitivity of jet charge distribution to the neutron skin-thickness and density profile in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>+</mo><mi>Pb</mi></mrow></math> collisions with varying centralities as determined using Glauber model, and in isobar collisions of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>+</mo><mi>Ru</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mo>+</mo><mi>Zr</mi></mrow></math>. We predict a strong suppression of positive jet charge distribution and an enhancement for negative jet charge distribution in peripheral electron-ion collisions, revealing the neutron-skin effect. Premised on the effective determination of centrality, this proposal can also be extended to photon and Z-boson tagged jet charge distribution in proton-nucleus collisions at the Large Hadron Collider, providing another similar access to neutron-skin structure.

Shan-Liang Zhang

Enke Wang

Xin-Nian Wang

Hongxi Xing

Probing the neutron skin thickness through jet charge in deep-inelastic scattering

It is well known that nonrelativistic or semirelativistic constituent quark models can describe a large number of the meson and baryon properties with surprising accuracy. In this work, we study the Killingbeck potential using the WKB approximation in the constituent quark model. The implicit approximate solutions for the energy eigenvalues, together with analytical expressions for the root-mean-square radii and the probability densities at the origin, of the Schrödinger equation are obtained by using appropriate quantization conditions. Finally, we discuss applications to double-heavy-meson spectroscopy within the Killingbeck potential.

Cheng-Qun Pang

Lhamo Chosto

Ya-Rong Wang

Zhi-Bin Gao

Hao Chen

Yu-Long Kang

Wei Li

WKB approximation under a Killingbeck potential and its application to double-heavy-meson spectroscopy