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 Cabibbo-favored hadronic weak decay of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mi>η</mi><mrow><msup><mo stretchy="false">(</mo><mo>′</mo></msup><mo stretchy="false">)</mo></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> are studied in the nonrelativistic constituent quark model. By analyzing their decay mechanisms at the quark level we show that the pole terms are essential for understanding the transition dynamics in addition to the usually considered direct meson emission process and color suppressed process in the charmed baryon hadronic weak decays. The experimentally measurable asymmetry parameters are also predicted in order to further pin down the decay mechanism.

Peng-Yu Niu

Japan

Qian Wang

Qiang Zhao

Cabibbo-favored hadronic weak decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub></math> in the quark model

The observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>2900</mn><mo stretchy="false">)</mo></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>−</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math> decay process indicates the existence of open flavor tetraquark states. We investigate the production and decay of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>2900</mn><mo stretchy="false">)</mo></math> state with the final state interaction mechanism, where we calculate the strong vertices such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>K</mi><msub><mi>X</mi><mn>0</mn></msub></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup><msub><mi>X</mi><mn>0</mn></msub></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>K</mi></mrow></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msup><mi>K</mi><mo>*</mo></msup></mrow></msub></math> in the framework of the QCD sum rule method. We find that for the interpretation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> molecule of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>2900</mn><mo stretchy="false">)</mo></math>, the branching fraction of the production process and the decay width are consistent with the experimental results, indicating that the observed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>2900</mn><mo stretchy="false">)</mo></math> could be interpreted as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> molecule. However, we cannot exclude the possibility of a compact tetraquark interpretation within the uncertainty. More experimental and theoretical efforts are needed to fully understand the nature of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>2900</mn><mo stretchy="false">)</mo></math> state.

Zi-Yan Yang

Wei Chen

Production and decay of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>X</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>2900</mn><mo stretchy="false">)</mo></math> state with different interpretations

We employ the nuclear lattice effective field theory (NLEFT), an efficient tool for nuclear ab initio calculations, to solve the asymmetric multihadron systems. We take the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup><mi>K</mi></math> three-body system as an illustration to demonstrate the capability of the method. Here the two-body chiral interactions between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> are regulated with a soft lattice regulator and calibrated with the binding energies of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math> molecular states. We then calculate the three-body binding energy using the NLEFT and analyze the systematic uncertainties due to the finite volume effects, the sliding cutoff, and the leading-order three-body forces. Even when the three-body interaction is repulsive (even as large as the infinite repulsive interaction), the three-body system has a bound state unambiguously with binding energy no larger than the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo><mi>D</mi></math> threshold. To check the renormalization group invariance of our framework, we extract the first excited state. We find that when the ground state is fixed, the first excited states with various cutoffs coincide with each other when the cubic size goes larger. In addition, the standard angular momentum and parity projection technique is implemented for the quantum numbers of the ground and excited states. We find that both of them are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave states with quantum number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>−</mo></msup></math>. Because the three-body state contains two charm quarks, it is easier to be detected in the Large Hadron Collider.

Zhenyu Zhang

Xin-Yue Hu

Guangzhao He

Jun Liu

Jia-Ai Shi

Bing-Nan Lu

Binding of the three-hadron <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup><mi>K</mi></math> system from the lattice effective field theory

Whether the <math><mi>N</mi><mover><mi>N</mi><mo>¯</mo></mover></math> interaction could form a state or not is a long standing question, even before the observation of the <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> threshold enhancement in 2003. The recent high statistic measurement in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>γ</mi><mn>3</mn><mo>(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo></math> channel would provide a good opportunity to probe the nature of the peak structures around the <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> threshold in various processes. By constructing the <math><mi>N</mi><mover><mi>N</mi><mo>¯</mo></mover></math> interaction respecting chiral symmetry, we extract the pole positions by fitting the <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> and <math><mn>3</mn><mo>(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo></math> invariant mass distributions of the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>γ</mi><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> and <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>γ</mi><mn>3</mn><mo>(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo></math> processes. The threshold enhancement in the <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> invariant mass distribution is from the pole on the third Riemann sheet, which more couples to the isospin triplet channel. The broader structure in the <math><mn>3</mn><mo>(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo></math> invariant mass comes from the pole on the physical Riemann sheet, which more couples to the isospin singlet channel. Furthermore, the large compositeness indicates that there should exist <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> resonance based on the current experimental data. In addition, we also see a clear threshold enhancement in the <math><mi>n</mi><mover><mi>n</mi><mo>¯</mo></mover></math> channel, but not as significant as that in <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> channel, which is useful and compared with further experimental measurement.

Zhen-Yu Zhang

Yi-Yao Li

Pole structures of the <math><mi>X</mi><mo>(</mo><mn>1840</mn><mo>)</mo></math> or <math><mi>X</mi><mo>(</mo><mn>1835</mn><mo>)</mo></math> and the <math><mi>X</mi><mo>(</mo><mn>1880</mn><mo>)</mo></math>

The observation of the <math><msub><mi>T</mi><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover></mrow></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> indicates the potential existence of strange double charm pentaquarks based on the heavy antidiquark symmetry. We systematically study the mass spectra of strange double charm pentaquarks with strangeness <math><mi>S</mi><mo>=</mo><mo>−</mo><mn>1</mn></math> in both molecular and compact structures for quantum numbers <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>, <math><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>, <math><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>. By constructing the interpolating currents, the mass spectra can be extracted from the two-point correlation functions in the framework of QCD sum rule method. In the molecular picture, we find that the <math><mrow><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo><mo>+</mo></mrow></msubsup><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msup></mrow></math>, <math><mrow><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msup></mrow></math>, <math><mrow><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>*</mo><mo>+</mo><mo>+</mo></mrow></msubsup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>*</mo><mn>0</mn></mrow></msup></mrow></math>, and <math><msubsup><mi>Ω</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><msup><mi>ρ</mi><mo>+</mo></msup></math> may form molecular strange double charm pentaquarks. In both pictures, the masses of the <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> pentaquarks locate within the 4.2–4.6 GeV and 4.2–4.5 GeV regions, respectively. As all of them are above the thresholds of their strong decay channels, they behave as a broad state, making them challenging to be detected experimentally. On the other hand, the strange double charm pentaquark with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> lies below its strong decay channel, which may be a very narrow state and easy to identify experimentally. The best observed channel is its semileptonic decay to double charm baryon. As the result, we strongly suggest experiments to search for <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> strange double charm pentaquarks first.

Mass spectra of strange double charm pentaquarks with strangeness <math><mrow><mi>S</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow></math>

A novel approach is proposed to probe the nature of the double charm tetraquark through the prompt production asymmetry between $$T_{\bar{c}\bar{c}}^-$$ <math> <msubsup> <mi>T</mi> <mrow> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>-</mo> </msubsup> </math> and $$T_{cc}^+$$ <math> <msubsup> <mi>T</mi> <mrow> <mi>cc</mi> </mrow> <mo>+</mo> </msubsup> </math> in pp collisions. When comparing two theoretical pictures, i.e. the compact tetraquark and hadronic molecular pictures, we find that the former one exhibits a significantly larger production asymmetry, enabling the unambiguous determination of the tetraquark’s internal structure. Additionally, distinctive differences in the transverse momentum and rapidity distributions of $$T_{\bar{c}\bar{c}}^-$$ <math> <msubsup> <mi>T</mi> <mrow> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>-</mo> </msubsup> </math> and $$T_{cc}^+$$ <math> <msubsup> <mi>T</mi> <mrow> <mi>cc</mi> </mrow> <mo>+</mo> </msubsup> </math> cross sections emerge, particularly at $$p_\textrm{T}\approx 2~\textrm{GeV}$$ <math> <mrow> <msub> <mi>p</mi> <mtext>T</mtext> </msub> <mo>≈</mo> <mn>2</mn> <mspace width="3.33333pt"></mspace> <mtext>GeV</mtext> </mrow> </math> and $$y\approx \pm 6$$ <math> <mrow> <mi>y</mi> <mo>≈</mo> <mo>±</mo> <mn>6</mn> </mrow> </math> at a center-of-mass energy of 14 $$~\textrm{TeV}$$ <math> <mrow> <mspace width="3.33333pt"></mspace> <mtext>TeV</mtext> </mrow> </math> . The insignificant asymmetry in hadronic molecular picture is because that hadronic molecules are produced in hadronic phase, where the phase space of their constituents needs to be taken into account rigorously. Our work can be extended to the exploration of other double heavy tetraquark candidates, offering a versatile approach to advance our understanding of exotic hadrons.

Xue-Li Hua

Shuai Yang

Bing-Song Zou

Revealing the mystery of the double charm tetraquark in pp collision

In recent years many vector charmonium(like) states were reported by different electron-positron collider experiments above 4.2 GeV. However, so far, there not only exists sizable tension in the parameters of those states, but there is also no consensus on the number of the vector states in this energy range. To some extend, this might be caused by the fact that the experimental data were typically analyzed in single channel analyses employing overlapping Breit-Wigner functions, in particular ignoring the effect of opening thresholds. In this study, we focus on the mass range between 4.2 GeV and 4.35 GeV, conducting a comprehensive analysis of eight different final states in <math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> annihilation. Our findings demonstrate that, within this mass range, a single vector charmoniumlike state, exhibiting properties consistent with a <math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> molecular structure and characterized by a pole location <math><mrow><msqrt><mrow><msubsup><mrow><mi>s</mi></mrow><mrow><mi>pole</mi></mrow><mrow><mi>Y</mi><mo>(</mo><mn>4230</mn><mo>)</mo></mrow></msubsup></mrow></msqrt><mo>=</mo><mrow><mo>(</mo><mn>4227</mn><mo>±</mo><mn>4</mn><mo>−</mo><mfrac><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>(</mo><msubsup><mrow><mn>50</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow><mrow><mo>+</mo><mn>8</mn></mrow></msubsup><mo>)</mo><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></mrow></math>, can effectively describe all the collected data. This is made possible by allowing for an interference with the well-established vector charmonium <math><mi>ψ</mi><mo>(</mo><mn>4160</mn><mo>)</mo></math> along with the inclusion of the <math><msub><mi>D</mi><mn>1</mn></msub><mover><mi>D</mi><mo>¯</mo></mover></math> threshold effect. Moreover, in contrast to experimental analyses, our study reveals that the highly asymmetric total cross sections for <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi><mi>π</mi></math> and <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>K</mi><mover><mi>K</mi><mo>¯</mo></mover></math> around 4230 MeV stem from the same physics, rooted in the approximate SU(3) flavor symmetry of QCD.

Germany

Leon von Detten

Vadim Baru

Christoph Hanhart

Daniel Winney

How many vector charmoniumlike states lie in the mass range 4.2–4.35 GeV?

An approximated solution for the gluon distribution from DGLAP evolution equations with the NLO splitting function in the small-x limit is presented. We first obtain simplified forms of the LO and NLO splitting functions in the small-x limit. With these approximated splitting functions, we obtain the analytical gluon distribution using the Mellin transform. The free parameters in the boundary conditions are obtained by fitting the CJ15 gluon distribution data. We find that the asymptotic behavior of the gluon distribution is consistent with the CJ15 data; however, the NLO results considering the "ladder" structure of gluon emission are slightly better than the LO results. These results indicate that the corrections from NLO have a significant influence on the behavior of the gluon distribution in the small-x region. In addition, we investigate the DGLAP evolution of the proton structure function using the analytical solution of the gluon distribution. The differential structure function reveals that our results have a similar tendency to the CJ15 data at small-x.

Jingxuan Chen

Xiaopeng Wang

Yanbing Cai

Xurong Chen

Analysis of the gluon distribution with next-to-leading order splitting function at small-x  

We discuss recent lattice data for the <math><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>(</mo><mn>3875</mn><msup><mo>)</mo><mo>+</mo></msup></math> state to stress, for the first time, a potentially strong impact of left-hand cuts from the one-pion exchange on the pole extraction for near-threshold exotic states. In particular, if the left-hand cut is located close to the two-particle threshold, which happens naturally in the <math><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> system for the pion mass exceeding its physical value, the effective-range expansion is valid only in a very limited energy range up to the cut and as such is of little use to reliably extract the poles. Then, an accurate extraction of the pole locations requires the one-pion exchange to be implemented explicitly into the scattering amplitudes. Our findings are general and potentially relevant for a wide class of hadronic near-threshold states.

Meng-Lin Du

Arseniy Filin

Xiang-Kun Dong

Evgeny Epelbaum

Feng-Kun Guo

Slovenia

Portugal

Alexey Nefediev

Spain

Juan Nieves

Role of Left-Hand Cut Contributions on Pole Extractions from Lattice Data: Case Study for <math><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>(</mo><mn>3875</mn><msup><mo>)</mo><mo>+</mo></msup></math>