Based on the holographic duality, we construct the new <italic>p</italic>-wave metal/superconductor phase transitions triggered by the electric and magnetic fields. Especially, using the axion field, we introduce simultaneously the spontaneous (SBT) and explicit (EBT) breaking of translation and then investigate how the SBT and EBT corrections influence on the critical temperature, vector condensate and the optical conductivity. Concretely, for the case with pure electric field, both the EBT correction with weak SBT correction and the SBT correction lower the critical temperature <math altimg='si1.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math> and soften the energy gap. Interestingly, for the strong enough SBT correction, the increasing EBT correction enhances firstly and then inhibits the phase transition. Meanwhile, the increasing EBT correction suppresses the SBT effect on <math altimg='si1.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>. At the lowest Landau energy level, the stronger SBT correction suppresses the phase transition for the weak magnetic field, whose inhibiting effect is finally eliminated by the strong enough magnetic field. The monotonic dependence of <math altimg='si1.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math> on the EBT correction only exists for the weak SBT correction. For the Landau energy level in the excited state, the monotonic dependence of <math altimg='si1.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math> on the EBT correction vanishes for the intermediate SBT correction with large magnetic field.

China

Bao-Ping Dong

Jun-Wang Lu

Ya-Bo Wu

Cheng-Yuan Zhang

Juan-Juan Luo

Jian-Xin Cheng

Hao Liao

Axion effects on new <italic>p</italic>-wave superconductors induced by electromagnetic fields

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.

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)

At the probe level, we investigate the holographic p-wave conductor/superconductor phase transition by both numerical and analytical methods. Especially, due to the nonlinear axion correction, the translational symmetry in superconductor is broken spontaneously. We then study the effects of the axion correction (or disorder) and the mass of vector field on the superconductor phase transition. Concretely, as the disorder parameter and the scaling dimension of vector operator increase, the critical temperature decreases and the stable value of condensate at the low temperature as well as the energy gap increase, which suggests that the larger mass of vector field and the disorder correction inhibit the phase transition, and increase the strength of interaction in superconductor. Near the critical point, the system always undergoes a second-order phase transition, which is independent of the disorder strength and the mass of vector field. According to the behaviors of grand potential and conductivity, the hairy state is verified to be thermodynamical favored and indeed superconducting state. Meanwhile, the analytical results uphold the numerical ones in terms of the critical behavior of condensate.

Yu Tang

Hui Zhu

Holographic -wave Superconductor With Spontaneously Broken Translation

The dineutron as a bound chargeless nucleus of two identical nucleons has been attracting attention for many decades. In addition to the study of the formation of a bound dineutron in the outgoing channel of specific nuclear reactions, cross-section estimates have been gaining interest as research targets. We used a traditional neutron activation technique to irradiate Lu samples followed by measurements of the induced activity with HPGe spectrometer in order to detect gamma-peaks of the 175Lu ( <italic>n</italic>, 2 <italic>n</italic>) 174 gLu reaction product when this reaction channel is not open for incident neutron energies. Based on two measurements of the instrumental gamma-ray spectra of Lu samples we reliably identified the presence of the 174 gLu isotope in the outgoing channel of the 175Lu ( <italic>n</italic>, 2 <italic>n</italic>) 174 gLu nuclear reaction. Also, the cross-section for this nuclear reaction was obtained and to be equal <math altimg='si1.svg'><mrow><mn>33</mn><mo>.</mo><msubsup><mn>5</mn><mrow><mo>&#8722;</mo><mn>6.7</mn></mrow><mrow><mo>+</mo><mn>7.0</mn></mrow></msubsup></mrow></math> mb. For the first time, the dineutron as a nuclearreaction product was indirectly detected via statistically significant observation of the induced activity of 174 gLu with a corresponding cross-section estimate.

Ukraine

Ihor Kadenko

Hungary

Barna Biró

Mihály Braun

András Fenyvesi

Kateryna Okopna

Nadiia Sakhno

Loránd Zakàny

Formation of bound dineutrons in the 175Lu ( <italic>n</italic>, 2 <italic>n</italic>) 174 gLu nuclear reaction and its cross-section

We revisit the proton emitter $^{149}$Lu utilizing the recently developed triaxial relativistic Hartree-Bogoliubov theory in continuum (TRHBc). By incorporating the microscopic nuclear structure properties from the TRHBc theory into the WKB approximation, we successfully reproduce the measured proton-emission half-life of $^{149}$Lu within experimental uncertainties. A triaxial ground state characterized by (<math><mi>β</mi><mo>=</mo><mn>0.17</mn><mo>,</mo><mi>γ</mi><mo>=</mo><msup><mrow><mn>31</mn></mrow><mrow><mo>∘</mo></mrow></msup></math>) has been clarified for $^{149}$Lu. The inclusion of triaxiality significantly changes nuclear density distributions and potentials, which results in enhanced binding of both the nuclear system and the proton-emitting orbital. As a result, a slightly extended half-life for the proton emission of $^{149}$Lu is achieved after considering triaxial deformation degrees of freedom. The examination of the dependence of the decay width on triaxial deformation parameters highlights the significance of microscopic description of nuclear deformation beyond the proton dripline.

Qi Lu

Kai-Yuan Zhang

Shi-Sheng Zhang

Triaxial shape of the one-proton emitter Lu

One-proton radioactivity in $^{149}$Lu, the latest identified proton emitter, is studied in the Wentzel-Kramers-Brillouin (WKB) approach with the proton-nucleus potential extracted from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) for the first time. The predicted half-life turns out to be consistent with the experimental measurement within uncertainties and (almost) independent of the density functionals in the DRHBc theory. Such a microscopic self-consistent calculation reveals that $^{149}$Lu is oblately deformed with a quadrupole deformation <math><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≈</mo><mo>−</mo><mn>0.18</mn></math>, and rules out the possibility of a prolate quadrupole deformation suggested in the nonadiabatic quasiparticle model. We also check the validity of this approach in the description of $^{150,151}$Lu and their isomeric states. The deviations of the predicted half-lives from their experimental counterparts are mostly smaller than those of the theoretical studies without considering deformation effects. Furthermore, we predict $^{148}$Lu to be a more oblately deformed proton-emitter with a longer half-life than that of $^{149}$Lu, which can be checked in the future. Our studies show that the DRHBc + WKB approach provides a new alternative method to evaluate the half-lives of well-deformed proton emitters.

Yang Xiao

Si-Zhe Xu

Ru-You Zheng

Germany

Xiang-Xiang Sun

Li-Sheng Geng

One-proton emission from Lu in the DRHBc+WKB approach

In the probe limit, we construct the p-wave conductor/superconductor phase transition with momentum relaxation originated from the axion fields by both numerical and analytical methods, and then study the effects of relaxation parameter (<math><mi>k</mi><mo>/</mo><mi>μ</mi></math>) on the superconductor model. Concretely, the increasing <math><mi>k</mi><mo>/</mo><mi>μ</mi></math> decreases monotonously the critical temperature and thus hinders the phase transition. The stable value of condensate (<math><msub><mrow><mi>C</mi></mrow><mrow><mn>00</mn></mrow></msub><mo>≡</mo><msup><mrow><mo>〈</mo><msub><mrow><mi>J</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>〉</mo></mrow><mrow><mn>1</mn><mo>/</mo><mo>(</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>/</mo><mi>μ</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>T</mi><mo>≈</mo><mn>0.15</mn><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msub></math>) and the coefficient (<math><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub></math>) of condensate (<math><mo>〈</mo><msub><mrow><mi>J</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>〉</mo><mo>/</mo><msup><mrow><mi>μ</mi></mrow><mrow><mn>1</mn><mo>/</mo><mo>(</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><msqrt><mrow><mn>1</mn><mo>−</mo><mi>T</mi><mo>/</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msqrt><msub><mrow><mo>|</mo></mrow><mrow><mi>T</mi><mo>≈</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msub></math>) always decrease with the larger <math><mi>k</mi><mo>/</mo><mi>μ</mi></math>. Near the critical point, the system suffers from a second order phase transition. Meanwhile, for fixed value of <math><mi>k</mi><mo>/</mo><mi>μ</mi></math>, the larger mass of vector field also suppresses the vector condensate to emerge. As for the above conclusions, the analytical results from the improved trial function agree with the numerical ones. The calculation of the ratio of energy gap to the critical temperature shows that the present superconductor indeed involves strong interaction, which increases with the increasing <math><mi>k</mi><mo>/</mo><mi>μ</mi></math>.

Huai-Fan Li

Yong Zheng

Holographic -wave Superconductors With Momentum Relaxation

At the probe approximation, we construct a holographic p-wave conductor/superconductor model in the five-dimensional Lifshitz black hole with the Weyl correction via both numerical and analytical methods, and study the effects of the Lifshitz parameter z as well as the Weyl parameter $$\gamma $$ <math> <mi>γ</mi> </math> on the superconductor model. As we take into account one of the two corrections separately, the increasing z ( $$\gamma $$ <math> <mi>γ</mi> </math> ) inhibits(enhances) the superconductor phase transition. When the two corrections are considered comprehensively, they display the obviously competitive effects on both the critical temperature and the vector condensate. In particular, the promoting effects of the Weyl parameter $$\gamma $$ <math> <mi>γ</mi> </math> on the critical temperature are obviously suppressed by the increasing Lifshitz parameter. Meanwhile, in the case of $$z&lt;2.35$$ <math> <mrow> <mi>z</mi> <mo>&lt;</mo> <mn>2.35</mn> </mrow> </math> ( $$z&gt;2.35$$ <math> <mrow> <mi>z</mi> <mo>&gt;</mo> <mn>2.35</mn> </mrow> </math> ), the condensate at lower temperature decreases(increases) with the increasing Weyl parameter $$\gamma $$ <math> <mi>γ</mi> </math> . What is more, the difference among the condensate with the fixed Weyl parameter( $$\gamma =-\frac{6}{100},0,\frac{4}{100}$$ <math> <mrow> <mi>γ</mi> <mo>=</mo> <mo>-</mo> <mfrac> <mn>6</mn> <mn>100</mn> </mfrac> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mfrac> <mn>4</mn> <mn>100</mn> </mfrac> </mrow> </math> ) decreases(increases) with the increasing Lifshitz parameter z in the region $$z&lt;2.35$$ <math> <mrow> <mi>z</mi> <mo>&lt;</mo> <mn>2.35</mn> </mrow> </math> ( $$z&gt;2.35$$ <math> <mrow> <mi>z</mi> <mo>&gt;</mo> <mn>2.35</mn> </mrow> </math> ). Furthermore, the increasing z obviously suppresses the real part of conductivity for all value of the Weyl parameter $$\gamma $$ <math> <mi>γ</mi> </math> . In addition, the analytical results agree well with the ones from the numerical method.

Yu Zhang

Holographic Lifshitz superconductors with Weyl correction

We describe predictions for top quark pair differential distributions at hadron colliders, by combining the next-to-next-to-leading order quantum chromodynamics calculations and next-to-leading order electroweak corrections with double resummation at the next-to-next-to-leading logarithmic accuracy of threshold logarithms and small-mass logarithms. To the best of our knowledge, this is the first study to present such a combination, which incorporates all known perturbative information. Numerical results are presented for the invariant-mass distribution, transverse-momentum distribution, and rapidity distributions.

Michał Czakon

United States

Andrea Ferroglia

United Kingdom

Alexander Mitov

Davide Pagani

Andrew S. Papanastasiou

Benjamin D. Pecjak

Netherlands

Darren J. Scott

Sweden

Ioannis Tsinikos

Xing Wang

Li Lin Yang

Italy

Marco Zaro

Top quark pair production at complete NLO accuracy with NNLO+NNLL′ corrections in QCD L. L. Yang and X. Wang are supported in part by the National Natural Science Foundation of China (11975030, 11635001, 11575004). X. Wang is also supported in part by the Cluster of Excellence PRISMA+ (project ID 39083149). D. J. S. is supported under the ERC grant ERC-STG2015-677323. The work of D. P. and I. T. is supported by the Alexander von Humboldt Foundation, in the framework of the Sofja Kovalevskaja Award Project "Event Simulation for the Large Hadron Collider at High Precision". D. P. is also supported by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy – EXC 2121"Quantum Univers" – 390833306. I. T. is also supported by the Swedish Research Council under contract number 2016-05996. The research of A. M. and A. P. has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (683211) as well as from UK STFC grants ST/L002760/1 and ST/K004883/1. The work of M. C. was supported in part by a grant of the BMBF and by the Deutsche Forschungs-gemeinschaft under grant 396021762 - TRR 257
						

Via both numerical and analytical methods, we build the holographic s-wave insulator/superconductor model in the five-dimensional AdS soliton with the Horndeski correction in the probe limit and study the effects of Horndeski parameter k on the superconductor model. For the fixed mass squared of the scalar field ($$m^2$$ <math><msup><mi>m</mi><mn>2</mn></msup></math> ), the critical chemical potential $$\mu _c$$ <math><msub><mi>μ</mi><mi>c</mi></msub></math> increases with the larger Horndeski parameter k, which means that the increasing Horndeski correction hinders the superconductor phase transition. Meanwhile, above the critical chemical potential, the obvious pole arises in the low frequency of the imaginal part of conductivity, which signs the appearance of superconducting state. What is more, the energy of quasiparticle excitation decreases with the larger Horndeski correction. Furthermore, the critical exponent of the condensate (charge density) is $$\frac{1}{2}$$ <math><mfrac><mn>1</mn><mn>2</mn></mfrac></math> (1), which is independent of the Horndeski correction. In addition, the analytical results agree well with the numerical results. Subsequently, the conductor/superconductor model with Horndeski correction is analytically realized in the four- and five-dimensional AdS black holes. It is observed that the increasing Horndeski correction decreases the critical temperature and thus hinders the superconductor phase transition, which agrees with the numerical result in the previous works.

Li-Gong Mi

Holographic s-wave superconductors with Horndeski correction