The existence of p-form symmetry in (d + 1)-dimensional quantum field is known to always lead to the breakdown of the eigenstate thermalization hypothesis (ETH) for certain (d − p)-dimensional operators other than symmetry operators under some assumptions. The assumptions include the mixing of symmetry sectors within a given energy shell, which is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. We reconsider this assumption from the viewpoint of projective representations to avoid this difficulty. In the case of $mathbb {Z}_N$ symmetries, we can circumvent the difficulty by considering $mathbb {Z}_Ntimes mathbb {Z}_N$-symmetric theories with nontrivial projective phases, and perturbing the Hamiltonian while preserving one of the $mathbb {Z}_N$ symmetries of our interest. We also perform numerical analyses for (1 + 1)-dimensional spin chains and the (2 + 1)-dimensional $mathbb {Z}_2$ lattice gauge theory.
{"title":"Remarks on effects of projective phase on eigenstate thermalization hypothesis","authors":"Osamu Fukushima","doi":"10.1093/ptep/ptae039","DOIUrl":"https://doi.org/10.1093/ptep/ptae039","url":null,"abstract":"The existence of p-form symmetry in (d + 1)-dimensional quantum field is known to always lead to the breakdown of the eigenstate thermalization hypothesis (ETH) for certain (d − p)-dimensional operators other than symmetry operators under some assumptions. The assumptions include the mixing of symmetry sectors within a given energy shell, which is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. We reconsider this assumption from the viewpoint of projective representations to avoid this difficulty. In the case of $mathbb {Z}_N$ symmetries, we can circumvent the difficulty by considering $mathbb {Z}_Ntimes mathbb {Z}_N$-symmetric theories with nontrivial projective phases, and perturbing the Hamiltonian while preserving one of the $mathbb {Z}_N$ symmetries of our interest. We also perform numerical analyses for (1 + 1)-dimensional spin chains and the (2 + 1)-dimensional $mathbb {Z}_2$ lattice gauge theory.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140116656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In U(1) lattice gauge theory with compact U(1) variables, we construct the symmetry operator, i.e., the topological defect, for the axial U(1) non-invertible symmetry. This requires a lattice formulation of chiral gauge theory with an anomalous matter content and we employ the lattice formulation on the basis of the Ginsparg–Wilson relation. The invariance of the symmetry operator under the gauge transformation of the gauge field on the defect is realized, imitating the prescription by Karasik in continuum theory, by integrating the lattice Chern–Simons term on the defect over smooth lattice gauge transformations. The projection operator for allowed magnetic fluxes on the defect then emerges with lattice regularization. The resulting symmetry operator is manifestly invariant under lattice gauge transformations. In an appendix, we give another way of constructing the symmetry operator on the basis of a 3D $mathbb {Z}_N$ TQFT, the level-N BF theory on the lattice.
{"title":"Lattice realization of the axial U(1) non-invertible symmetry","authors":"Yamato Honda, Okuto Morikawa, Soma Onoda, Hiroshi Suzuki","doi":"10.1093/ptep/ptae040","DOIUrl":"https://doi.org/10.1093/ptep/ptae040","url":null,"abstract":"In U(1) lattice gauge theory with compact U(1) variables, we construct the symmetry operator, i.e., the topological defect, for the axial U(1) non-invertible symmetry. This requires a lattice formulation of chiral gauge theory with an anomalous matter content and we employ the lattice formulation on the basis of the Ginsparg–Wilson relation. The invariance of the symmetry operator under the gauge transformation of the gauge field on the defect is realized, imitating the prescription by Karasik in continuum theory, by integrating the lattice Chern–Simons term on the defect over smooth lattice gauge transformations. The projection operator for allowed magnetic fluxes on the defect then emerges with lattice regularization. The resulting symmetry operator is manifestly invariant under lattice gauge transformations. In an appendix, we give another way of constructing the symmetry operator on the basis of a 3D $mathbb {Z}_N$ TQFT, the level-N BF theory on the lattice.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we study the thermodynamic topology of a static, a charged static and a charged, rotating black hole in f(R) gravity. For charged static black holes, we work in two different ensembles: fixed charge(q) ensemble and fixed potential(φ) ensemble. For charged, rotating black hole, four different types of ensembles are considered: fixed (q, J), fixed (φ, J), fixed (q, Ω) and fixed (φ, Ω) ensemble, where J and Ω denotes the angular momentum and the angular frequency respectively. Using the generalized off-shell free energy method, where the black holes are treated as topological defects in their thermodynamic spaces, we investigate the local and global topology of these black holes via the computation of winding numbers at these defects. For static black hole we work in three model. We find that the topological charge for a static black hole is always −1 regardless of the values of the thermodynamic parameters and the choice of f(R) model. For a charged static black hole, in the fixed charge ensemble, the topological charge is found to be zero. Contrastingly, in the fixed φ ensemble, the topological charge is found to be −1. For charged static black holes, in both the ensembles, the topological charge is observed to be independent of the thermodynamic parameters. For charged, rotating black hole, in fixed (q, J) ensemble, the topological charge is found to be 1. In (φ, J) ensemble, we find the topological charge to be 1. In case of fixed (q, Ω) ensemble, the topological charge is 1 or 0 depending on the value of the scalar curvature(R). In fixed (Ω, φ) ensemble, the topological charge is −1, 0 or 1 depending on the values of R, Ω and φ. Therefore, we conclude that the thermodynamic topologies of the charged static black hole and charged rotating black hole are influenced by the choice of ensemble. In addition, the thermodynamic topology of the charged rotating black hole also depends on the thermodynamic parameters.
{"title":"Thermodynamic topology of black holes in f(R) gravity","authors":"Bidyut Hazarika, Prabwal Phukon","doi":"10.1093/ptep/ptae035","DOIUrl":"https://doi.org/10.1093/ptep/ptae035","url":null,"abstract":"In this work, we study the thermodynamic topology of a static, a charged static and a charged, rotating black hole in f(R) gravity. For charged static black holes, we work in two different ensembles: fixed charge(q) ensemble and fixed potential(φ) ensemble. For charged, rotating black hole, four different types of ensembles are considered: fixed (q, J), fixed (φ, J), fixed (q, Ω) and fixed (φ, Ω) ensemble, where J and Ω denotes the angular momentum and the angular frequency respectively. Using the generalized off-shell free energy method, where the black holes are treated as topological defects in their thermodynamic spaces, we investigate the local and global topology of these black holes via the computation of winding numbers at these defects. For static black hole we work in three model. We find that the topological charge for a static black hole is always −1 regardless of the values of the thermodynamic parameters and the choice of f(R) model. For a charged static black hole, in the fixed charge ensemble, the topological charge is found to be zero. Contrastingly, in the fixed φ ensemble, the topological charge is found to be −1. For charged static black holes, in both the ensembles, the topological charge is observed to be independent of the thermodynamic parameters. For charged, rotating black hole, in fixed (q, J) ensemble, the topological charge is found to be 1. In (φ, J) ensemble, we find the topological charge to be 1. In case of fixed (q, Ω) ensemble, the topological charge is 1 or 0 depending on the value of the scalar curvature(R). In fixed (Ω, φ) ensemble, the topological charge is −1, 0 or 1 depending on the values of R, Ω and φ. Therefore, we conclude that the thermodynamic topologies of the charged static black hole and charged rotating black hole are influenced by the choice of ensemble. In addition, the thermodynamic topology of the charged rotating black hole also depends on the thermodynamic parameters.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140054965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the convergence of the Ginzburg-Landau (GL) expansion in the context of the Bardeen-Cooper-Schrieffer (BCS) theory for superconductivity and the Nambu–Jona-Lasinio (NJL) model for chiral symmetry breaking at finite temperature T and chemical potential μ. We present derivations of the all-order formulas for the coefficients of the GL expansions in both systems under the mean-field approximation. We show that the convergence radii for the BCS gap Δ and dynamical quark mass M are given by Δconv = πT and $M_{rm conv} = sqrt{mu ^2 + (pi T)^2}$, respectively. We also discuss the implications of these results and the quantitative reliability of the GL expansion near the first-order chiral phase transition.
{"title":"Convergence of Ginzburg-Landau expansions: superconductivity in the BCS theory and chiral symmetry breaking in the NJL model","authors":"William Gyory, Naoki Yamamoto","doi":"10.1093/ptep/ptae032","DOIUrl":"https://doi.org/10.1093/ptep/ptae032","url":null,"abstract":"We study the convergence of the Ginzburg-Landau (GL) expansion in the context of the Bardeen-Cooper-Schrieffer (BCS) theory for superconductivity and the Nambu–Jona-Lasinio (NJL) model for chiral symmetry breaking at finite temperature T and chemical potential μ. We present derivations of the all-order formulas for the coefficients of the GL expansions in both systems under the mean-field approximation. We show that the convergence radii for the BCS gap Δ and dynamical quark mass M are given by Δconv = πT and $M_{rm conv} = sqrt{mu ^2 + (pi T)^2}$, respectively. We also discuss the implications of these results and the quantitative reliability of the GL expansion near the first-order chiral phase transition.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
T T Hong, V K Le, L T T Phuong, N C Hoi, N T K Ngan, N H T Nha
Two decay channels h → γγ, Zγ of the Standard Model-like Higgs in a left-right symmetry model are investigated under recent experimental data. We will show there exist one-loop contributions that affect the h → Zγ amplitude, but not the h → γγ amplitude. From numerical investigations, we show that the signal strength μZγ of the decay h → Zγ is still constrained strictly by that of h → γγ, namely $|Delta mu _{gamma gamma }|<38%$ results in max $|Delta mu _{Z gamma }|<46%$. On the other hand, the future experimental sensitivity $|Delta mu _{gamma gamma }|=4%$ still allows |ΔμZγ| reaches to values larger than the expected sensitivity $|Delta mu _{Z gamma }|=23%$.
根据最近的实验数据，我们研究了在左右对称模型中类似标准模型的希格斯粒子的两个衰变通道 h → γγ, Zγ。我们将证明存在影响 h → Zγ 振幅而不影响 h →γγ 振幅的一环贡献。通过数值研究，我们发现衰变h → Zγ的信号强度μZγ仍然严格受制于h → γ的信号强度μZγ，即$|Delta mu _{Z gamma }|<38%$ 结果为最大$|Delta mu _{Z gamma }|<46%$ 。另一方面，未来的实验灵敏度 $|Delta mu _{Z gamma }|=4%$ 仍然允许 |ΔμZγ| 达到比预期灵敏度 $|Delta mu _{Z gamma }|=23%$ 更大的值。
{"title":"Decays of standard model like higgs boson h → γγ, Zγ in a minimal left-right symmetric model","authors":"T T Hong, V K Le, L T T Phuong, N C Hoi, N T K Ngan, N H T Nha","doi":"10.1093/ptep/ptae029","DOIUrl":"https://doi.org/10.1093/ptep/ptae029","url":null,"abstract":"Two decay channels h → γγ, Zγ of the Standard Model-like Higgs in a left-right symmetry model are investigated under recent experimental data. We will show there exist one-loop contributions that affect the h → Zγ amplitude, but not the h → γγ amplitude. From numerical investigations, we show that the signal strength μZγ of the decay h → Zγ is still constrained strictly by that of h → γγ, namely $|Delta mu _{gamma gamma }|&lt;38%$ results in max $|Delta mu _{Z gamma }|&lt;46%$. On the other hand, the future experimental sensitivity $|Delta mu _{gamma gamma }|=4%$ still allows |ΔμZγ| reaches to values larger than the expected sensitivity $|Delta mu _{Z gamma }|=23%$.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider how gauge theories can be described by matrix models. Conventional matrix regularization is defined for scalar functions and is not applicable to gauge fields, which are connections of fiber bundles. We clarify how the degrees of freedom of gauge fields are related to the matrix degrees of freedom, by formulating the Seiberg-Witten map between them.
{"title":"Matrix regularization for gauge theories","authors":"Hiroyuki Adachi, Goro Ishiki, Satoshi Kanno","doi":"10.1093/ptep/ptae031","DOIUrl":"https://doi.org/10.1093/ptep/ptae031","url":null,"abstract":"We consider how gauge theories can be described by matrix models. Conventional matrix regularization is defined for scalar functions and is not applicable to gauge fields, which are connections of fiber bundles. We clarify how the degrees of freedom of gauge fields are related to the matrix degrees of freedom, by formulating the Seiberg-Witten map between them.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We describe how the general mechanism of partial deconfinement applies to large-N QCD and the partially-deconfined phase inevitably appears between completely-confined and completely-deconfined phases. Furthermore, we propose how the partial deconfinement can be observed in the real-world QCD with the SU(3) gauge group. For this purpose, we employ lattice configurations obtained by the WHOT-QCD collaboration and examine our proposal numerically. In the discussion, the Polyakov loop plays a crucial role in characterizing the phases, without relying on center symmetry, and hence, we clarify the meaning of the Polyakov loop in QCD at large N and finite N. Both at large N and finite N, the complete confinement is characterized by the Haar-random distribution of the Polyakov line phases. Haar-randomness, which is stronger than unbroken center symmetry, indicates that Polyakov loops in any nontrivial representations have vanishing expectation values, and deviation from the Haar-random distribution at higher temperatures is quantified with the loops. We discuss that the transitions separating the partially-deconfined phase are characterized by the behaviors of Polyakov loops in various representations. The lattice QCD data provide us with the signals exhibiting two different characteristic temperatures: deconfinement of the fundamental representation and deconfinement of higher representations. As a nontrivial test for our proposal, we also investigate the relation between partial deconfinement and instanton condensation and confirm the consistency with the lattice data. To make the presentation more easily accessible, we provide a detailed review of the previously known aspects of partial deconfinement.
我们描述了部分去约束的一般机制如何适用于大 N QCD，以及部分去约束相如何不可避免地出现在完全约束相和完全去约束相之间。此外，我们还提出了如何在具有 SU(3) 轨则群的真实 QCD 中观察到部分去约束。为此，我们采用了 WHOT-QCD 协作获得的晶格构型，并对我们的建议进行了数值检验。在讨论中，波里雅科夫环在表征相位方面发挥了关键作用，而无需依赖中心对称，因此我们澄清了波里雅科夫环在大 N 和有限 N 的 QCD 中的意义。哈尔-随机性比不破中心对称性更强，它表明任何非三维表示的波里雅科夫环具有消失的期望值，而在更高温度下偏离哈尔-随机分布的情况可以用环量化。我们讨论了分离部分解约束相的跃迁是由各种表征中的波里雅科夫环的行为所表征的。格子 QCD 数据为我们提供了表现出两种不同特征温度的信号：基本表征的解约束和更高表征的解约束。作为对我们建议的一个非简单测试，我们还研究了部分去抵消和瞬子凝聚之间的关系，并确认了与晶格数据的一致性。为了使介绍更容易理解，我们详细回顾了部分去协方性的先前已知方面。
{"title":"On thermal transition in QCD","authors":"Masanori Hanada, Hiromasa Watanabe","doi":"10.1093/ptep/ptae033","DOIUrl":"https://doi.org/10.1093/ptep/ptae033","url":null,"abstract":"We describe how the general mechanism of partial deconfinement applies to large-N QCD and the partially-deconfined phase inevitably appears between completely-confined and completely-deconfined phases. Furthermore, we propose how the partial deconfinement can be observed in the real-world QCD with the SU(3) gauge group. For this purpose, we employ lattice configurations obtained by the WHOT-QCD collaboration and examine our proposal numerically. In the discussion, the Polyakov loop plays a crucial role in characterizing the phases, without relying on center symmetry, and hence, we clarify the meaning of the Polyakov loop in QCD at large N and finite N. Both at large N and finite N, the complete confinement is characterized by the Haar-random distribution of the Polyakov line phases. Haar-randomness, which is stronger than unbroken center symmetry, indicates that Polyakov loops in any nontrivial representations have vanishing expectation values, and deviation from the Haar-random distribution at higher temperatures is quantified with the loops. We discuss that the transitions separating the partially-deconfined phase are characterized by the behaviors of Polyakov loops in various representations. The lattice QCD data provide us with the signals exhibiting two different characteristic temperatures: deconfinement of the fundamental representation and deconfinement of higher representations. As a nontrivial test for our proposal, we also investigate the relation between partial deconfinement and instanton condensation and confirm the consistency with the lattice data. To make the presentation more easily accessible, we provide a detailed review of the previously known aspects of partial deconfinement.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140003776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the early 80’s Sanda-san and collaborators wrote key papers on the direct and clean determination of the unitarity angle φ1 (β). This motivated many of us for analogously coming up with ways for direct and clean determinations of the other two unitarity angles, φ2(α) and φ3(γ). Current status of these direct determinations as well as our expectations for when Belle-II has 50 ab−1 of luminosity and LHCb with some upgrades, will be given. In particular, it is emphasized that for direct determination of φ3, Belle-II should be able to handle final states in D0 or $bar{D}^0$ Dalitz decays, that contain one π0 (which are difficult for LHCb) then they may make further inroads in improving the accuracy of φ3 determination. Early lattice inputs for constraining the unitarity triangle (UT) are briefly recalled. Its crucial role in supporting the Kobayashi-Maskawa theory of CP violation is emphasized. Over the years lattice methods have made significant progress and latest constraints from these for the UT will be discussed as well as compatibility with current direct determinations and some comments on future outlook will be made.
{"title":"Theory of CP angles measurements","authors":"Amarjit Soni","doi":"10.1093/ptep/ptae028","DOIUrl":"https://doi.org/10.1093/ptep/ptae028","url":null,"abstract":"In the early 80’s Sanda-san and collaborators wrote key papers on the direct and clean determination of the unitarity angle φ1 (β). This motivated many of us for analogously coming up with ways for direct and clean determinations of the other two unitarity angles, φ2(α) and φ3(γ). Current status of these direct determinations as well as our expectations for when Belle-II has 50 ab−1 of luminosity and LHCb with some upgrades, will be given. In particular, it is emphasized that for direct determination of φ3, Belle-II should be able to handle final states in D0 or $bar{D}^0$ Dalitz decays, that contain one π0 (which are difficult for LHCb) then they may make further inroads in improving the accuracy of φ3 determination. Early lattice inputs for constraining the unitarity triangle (UT) are briefly recalled. Its crucial role in supporting the Kobayashi-Maskawa theory of CP violation is emphasized. Over the years lattice methods have made significant progress and latest constraints from these for the UT will be discussed as well as compatibility with current direct determinations and some comments on future outlook will be made.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The ideal magnetohydrodynamics (MHD) as well as the ideal fluid dynamics is governed by the Hamilton equation with respect to the Lie-Poisson bracket. The Nambu bracket manifestly represents the Lie-Poisson structure in terms of derivative of the Casimir invariants. We construct a compact Nambu-bracket representation for the three-dimensional ideal MHD equations, with use of three Casimirs for the second Hamiltonians, the total entropy and the magnetic and cross helicities, whose coefficients are all constant. The Lie-Poisson bracket induced by this Nambu bracket does not coincide with the original one, but supplemented by terms with an auxiliary variable. The supplemented Lie-Poisson bracket qualifies the cross-helicity as the Casimir. By appealing to Noether’s theorem, we show that the cross-helicity is the integral invariant associated with the particle-relabeling symmetry. Employing the Lagrange label function, as the independent variable in the variational framework, facilitates implementation of the relabeling transformation. By incorporating the divergence symmetry, other known topological invariants are put on the same ground of Noether’s theorem.
{"title":"Nambu-bracket for three-dimensional ideal fluid dynamics and magnetohydrodynamics","authors":"Yasuhide Fukumoto, Rong Zou","doi":"10.1093/ptep/ptae025","DOIUrl":"https://doi.org/10.1093/ptep/ptae025","url":null,"abstract":"The ideal magnetohydrodynamics (MHD) as well as the ideal fluid dynamics is governed by the Hamilton equation with respect to the Lie-Poisson bracket. The Nambu bracket manifestly represents the Lie-Poisson structure in terms of derivative of the Casimir invariants. We construct a compact Nambu-bracket representation for the three-dimensional ideal MHD equations, with use of three Casimirs for the second Hamiltonians, the total entropy and the magnetic and cross helicities, whose coefficients are all constant. The Lie-Poisson bracket induced by this Nambu bracket does not coincide with the original one, but supplemented by terms with an auxiliary variable. The supplemented Lie-Poisson bracket qualifies the cross-helicity as the Casimir. By appealing to Noether’s theorem, we show that the cross-helicity is the integral invariant associated with the particle-relabeling symmetry. Employing the Lagrange label function, as the independent variable in the variational framework, facilitates implementation of the relabeling transformation. By incorporating the divergence symmetry, other known topological invariants are put on the same ground of Noether’s theorem.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Uncovering neutrinoless double beta decay (0ν2β) is crucial for confirming neutrinos’ Majorana characteristics. The decay rate of 0νββ is theoretically uncertain, influenced by nuclear matrix elements that vary across nuclides. To reduce this uncertainty, precise measurement of the half-life of neutrino-emitting double beta decay (2ν2β) in different nuclides is essential. We have launched the PIKACHU (Pure Inorganic scintillator experiment in KAmioka for CHallenging Underground sciences) project to fabricate high-purity Ce-doped Gd3Ga3Al2O12 (GAGG) single crystals and use them to study the double beta decay of 160Gd. Predictions from two theoretical models on nuclear matrix element calculations for 2ν2β in 160Gd show a significant discrepancy in estimated half-lives, differing by approximately an order of magnitude. If the lower half-life estimation holds true, detecting 2ν2β in 160Gd could be achievable with a sensitivity enhancement slightly more than an order of magnitude compared to prior investigations using Ce-doped Gd2SiO5 (GSO) crystal. We have successfully developed GAGG crystals with purity levels surpassing previous standards through refined purification and selection of raw materials. Our experiments with these crystals indicate the feasibility of reaching sensitivities exceeding those of earlier studies. This paper discusses the ongoing development and scintillator performance evaluation of High-purity GAGG crystals, along with the anticipated future prospects of the PIKACHU experiment.
{"title":"First Study of the PIKACHU Project: Development and Evaluation of High-Purity Gd3Ga3Al2O12:Ce Crystals for 160Gd Double Beta Decay Search","authors":"Takumi Omori, Takashi Iida, Azusa Gando, Keishi Hosokawa, Kei Kamada, Keita Mizukoshi, Yasuhiro Shoji, Masao Yoshino, Ken-Ichi Fushimi, Hisanori Suzuki, Kotaro Takahashi","doi":"10.1093/ptep/ptae026","DOIUrl":"https://doi.org/10.1093/ptep/ptae026","url":null,"abstract":"Uncovering neutrinoless double beta decay (0ν2β) is crucial for confirming neutrinos’ Majorana characteristics. The decay rate of 0νββ is theoretically uncertain, influenced by nuclear matrix elements that vary across nuclides. To reduce this uncertainty, precise measurement of the half-life of neutrino-emitting double beta decay (2ν2β) in different nuclides is essential. We have launched the PIKACHU (Pure Inorganic scintillator experiment in KAmioka for CHallenging Underground sciences) project to fabricate high-purity Ce-doped Gd3Ga3Al2O12 (GAGG) single crystals and use them to study the double beta decay of 160Gd. Predictions from two theoretical models on nuclear matrix element calculations for 2ν2β in 160Gd show a significant discrepancy in estimated half-lives, differing by approximately an order of magnitude. If the lower half-life estimation holds true, detecting 2ν2β in 160Gd could be achievable with a sensitivity enhancement slightly more than an order of magnitude compared to prior investigations using Ce-doped Gd2SiO5 (GSO) crystal. We have successfully developed GAGG crystals with purity levels surpassing previous standards through refined purification and selection of raw materials. Our experiments with these crystals indicate the feasibility of reaching sensitivities exceeding those of earlier studies. This paper discusses the ongoing development and scintillator performance evaluation of High-purity GAGG crystals, along with the anticipated future prospects of the PIKACHU experiment.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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