We compute the energy scales of perturbative unitarity violation in VLVL → VLVLh processes and compare them to VLVL → hhh process, where VL refers to a longitudinal mode of Z or W boson, and h the Higgs boson. Using these energy scales, we determine which process is more sensitive to potential modifications in the Higgs sector at high-energy colliders. Within the Higgs Effective Field Theory (HEFT), we consider the Higgs cubic coupling and other interactions with and without derivatives. Any HEFT interactions predict the perturbative unitarity violation at a finite scale, and in a generic case, the minimalistic process is 2 → 3 scattering. Our analysis reveals that the energy scales for unitarity violation in VLVL → VLVLh and VLVL → hhh processes are similar across all scenarios considered. If the backgrounds are similar, VLVLh final states are more feasible because VLVLh has higher branching ratios in cleaner decay modes than hhh. We also investigate HEFT derivative interactions derived from various UV models. In these cases, both VLVL → VLVL and VLVL → hh processes exhibit unitarity violating behavior. We demonstrate that the energy scales for unitarity violation in VLVL final states are comparable to or even lower than those in the hh final state.
{"title":"Energy growth in VLVL → VLVL, VLVLh scattering to probe Higgs cubic and HEFT interactions","authors":"Shameran Mahmud, Kohsaku Tobioka","doi":"10.1007/jhep09(2024)073","DOIUrl":"https://doi.org/10.1007/jhep09(2024)073","url":null,"abstract":"<p>We compute the energy scales of perturbative unitarity violation in <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub> → <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub><i>h</i> processes and compare them to <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub> → <i>hhh</i> process, where <i>V</i><sub><i>L</i></sub> refers to a longitudinal mode of <i>Z</i> or <i>W</i> boson, and <i>h</i> the Higgs boson. Using these energy scales, we determine which process is more sensitive to potential modifications in the Higgs sector at high-energy colliders. Within the Higgs Effective Field Theory (HEFT), we consider the Higgs cubic coupling and other interactions with and without derivatives. Any HEFT interactions predict the perturbative unitarity violation at a finite scale, and in a generic case, the minimalistic process is 2 → 3 scattering. Our analysis reveals that the energy scales for unitarity violation in <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub> → <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub><i>h</i> and <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub> → <i>hhh</i> processes are similar across all scenarios considered. If the backgrounds are similar, <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub><i>h</i> final states are more feasible because <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub><i>h</i> has higher branching ratios in cleaner decay modes than <i>hhh</i>. We also investigate HEFT derivative interactions derived from various UV models. In these cases, both <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub> → <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub> and <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub> → <i>hh</i> processes exhibit unitarity violating behavior. We demonstrate that the energy scales for unitarity violation in <i>V</i><sub><i>L</i></sub><i>V</i><sub><i>L</i></sub> final states are comparable to or even lower than those in the <i>hh</i> final state.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 next-to-leading order weak-coupling shear viscosity of QCD was computed 6 years ago. However, these results have never been applied at finite baryon chemical potential μ, even though intermediate-energy heavy ion collisions and merging neutron stars may explore the Quark-Gluon Plasma in a regime where baryon chemical potentials are large. Here, we extend the next-to-leading order shear viscosity calculations to finite μ, and we show that, while the convergence of the weak-coupling expansion is questionable for achievable plasmas, it is somewhat better at μ > T than at μ = 0.
{"title":"Hot and dense QCD shear viscosity at (almost) NLO","authors":"Isabella Danhoni, Guy D. Moore","doi":"10.1007/jhep09(2024)075","DOIUrl":"https://doi.org/10.1007/jhep09(2024)075","url":null,"abstract":"<p>The next-to-leading order weak-coupling shear viscosity of QCD was computed 6 years ago. However, these results have never been applied at finite baryon chemical potential <i>μ</i>, even though intermediate-energy heavy ion collisions and merging neutron stars may explore the Quark-Gluon Plasma in a regime where baryon chemical potentials are large. Here, we extend the next-to-leading order shear viscosity calculations to finite <i>μ</i>, and we show that, while the convergence of the weak-coupling expansion is questionable for achievable plasmas, it is somewhat better at <i>μ</i> > <i>T</i> than at <i>μ</i> = 0.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 present analytic techniques for parametric integrations of massive two-loop four-point Feynman integrals at high energies, and their implementation in the toolbox AsyInt. In the high-energy region, the Feynman integrals involving external and internal massive particles, such as the top quark, Higgs and vector bosons, can be asymptotically expanded and directly calculated in the small-mass limit. With this approach, analytic results for higher-order terms in the expansion parameter and the dimensional regulator can be obtained with AsyInt. These results are important ingredients for the two-loop electroweak and QCD corrections for 2 → 2 scattering processes in the large transverse momenta region, which is relevant to both precision collider phenomenology and new physics searches at current and future high-energy colliders. In this paper, analytic results of representative planar and non-planar Feynman integrals are presented.
{"title":"Massive two-loop four-point Feynman integrals at high energies with AsyInt","authors":"Hantian Zhang","doi":"10.1007/jhep09(2024)069","DOIUrl":"https://doi.org/10.1007/jhep09(2024)069","url":null,"abstract":"<p>We present analytic techniques for parametric integrations of massive two-loop four-point Feynman integrals at high energies, and their implementation in the toolbox AsyInt. In the high-energy region, the Feynman integrals involving external and internal massive particles, such as the top quark, Higgs and vector bosons, can be asymptotically expanded and directly calculated in the small-mass limit. With this approach, analytic results for higher-order terms in the expansion parameter and the dimensional regulator can be obtained with AsyInt. These results are important ingredients for the two-loop electroweak and QCD corrections for 2 → 2 scattering processes in the large transverse momenta region, which is relevant to both precision collider phenomenology and new physics searches at current and future high-energy colliders. In this paper, analytic results of representative planar and non-planar Feynman integrals are presented.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
Christian Capanelli, Leah Jenks, Edward W. Kolb, Evan McDonough
Dark photons are a theorized massive spin-1 particle which can be produced via various mechanisms, including cosmological gravitational particle production (GPP) in the early universe. In this work, we extend previous results for GPP of dark photons to include nonminimal couplings to gravity. We find that nonminimal couplings can induce a ghost instability or lead to runaway particle production at high momentum and discuss the constraints on the parameter space such that the theory is free of instabilities. Within the instability-free regime we numerically calculate the particle production and find that the inclusion of nonminimal couplings can lead to an enhancement of the particle number. As a result, GPP of nonminimally coupled dark photons can open the parameter space for production of a cosmological relevant relic density (constituting all or part of the dark matter) as compared to the minimally-coupled theory. These results are independent of the choice of inflation model, which we demonstrate by repeating the analysis for a class of rapid-turn multi-field inflation models.
{"title":"Gravitational production of completely dark photons with nonminimal couplings to gravity","authors":"Christian Capanelli, Leah Jenks, Edward W. Kolb, Evan McDonough","doi":"10.1007/jhep09(2024)071","DOIUrl":"https://doi.org/10.1007/jhep09(2024)071","url":null,"abstract":"<p>Dark photons are a theorized massive spin-1 particle which can be produced via various mechanisms, including cosmological gravitational particle production (GPP) in the early universe. In this work, we extend previous results for GPP of dark photons to include nonminimal couplings to gravity. We find that nonminimal couplings can induce a ghost instability or lead to runaway particle production at high momentum and discuss the constraints on the parameter space such that the theory is free of instabilities. Within the instability-free regime we numerically calculate the particle production and find that the inclusion of nonminimal couplings can lead to an enhancement of the particle number. As a result, GPP of nonminimally coupled dark photons can open the parameter space for production of a cosmological relevant relic density (constituting all or part of the dark matter) as compared to the minimally-coupled theory. These results are independent of the choice of inflation model, which we demonstrate by repeating the analysis for a class of rapid-turn multi-field inflation models.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142247917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 investigate various aspects of capacity of entanglement in certain setups whose entanglement entropy becomes extensive and obeys a volume law. In particular, considering geometric decomposition of the Hilbert space, we study this measure both in the vacuum state of a family of non-local scalar theories and also in the squeezed states of a local scalar theory. We also evaluate field space capacity of entanglement between interacting scalar field theories. We present both analytical and numerical evidences for the volume law scaling of this quantity in different setups and discuss how these results are consistent with the behavior of other entanglement measures including Renyi entropies. Our study reveals some generic properties of the capacity of entanglement and the corresponding reduced density matrix in the specific regimes of the parameter space. Finally, by comparing entanglement entropy and capacity of entanglement, we discuss some implications of our results on the existence of consistent holographic duals for the models in question.
{"title":"Capacity of entanglement and volume law","authors":"M. Reza Mohammadi Mozaffar","doi":"10.1007/jhep09(2024)068","DOIUrl":"https://doi.org/10.1007/jhep09(2024)068","url":null,"abstract":"<p>We investigate various aspects of capacity of entanglement in certain setups whose entanglement entropy becomes extensive and obeys a volume law. In particular, considering geometric decomposition of the Hilbert space, we study this measure both in the vacuum state of a family of non-local scalar theories and also in the squeezed states of a local scalar theory. We also evaluate field space capacity of entanglement between interacting scalar field theories. We present both analytical and numerical evidences for the volume law scaling of this quantity in different setups and discuss how these results are consistent with the behavior of other entanglement measures including Renyi entropies. Our study reveals some generic properties of the capacity of entanglement and the corresponding reduced density matrix in the specific regimes of the parameter space. Finally, by comparing entanglement entropy and capacity of entanglement, we discuss some implications of our results on the existence of consistent holographic duals for the models in question.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 investigate the parity-violating effects in primordial gravitational waves (GWs) due to null energy condition (NEC) violation in two very early universe scenarios: bounce-inflation and intermediate NEC violation during inflation. In both scenarios, we numerically solve the power spectra of parity-violating primordial GWs generated by coupling the background field and the spectator field with the Nieh-Yan term, respectively. We find that the background field can significantly enhance parity-violating effects at scales corresponding to the maximum of the GW power spectra. In contrast, the parity-violating effects produced by the spectator show significantly weaker observability even if the coupling constant is large. Therefore, in NEC-violating scenarios, the significant observable parity-violating effects in primordial GWs primarily arise from the physics directly related to NEC violation. This result highlights the potential of primordial GWs as crucial tools for exploring NEC-violating and parity-violating physics.
我们研究了在两种极早期宇宙场景中由于违反空能条件(NEC)而导致的原始引力波(GWs)的违反奇偶性效应:反弹-膨胀和膨胀过程中的中间违反 NEC。在这两种情况下,我们分别对背景场和旁观者场与聂扬项耦合产生的违反奇偶性的原始引力波的功率谱进行了数值求解。我们发现,在对应于 GW 功率谱最大值的尺度上,背景场可以显著增强违反奇偶校验的效应。相比之下,即使耦合常数很大,旁观者产生的违反奇偶性效应也会明显减弱可观测性。因此,在违反 NEC 的情况下,原始 GW 中显著的可观测奇偶性破坏效应主要来自与违反 NEC 直接相关的物理学。这一结果凸显了原始全球瓦作为探索违反 NEC 和违反奇偶性物理的重要工具的潜力。
{"title":"Parity-violating primordial gravitational waves from null energy condition violation","authors":"Zi-Wei Jiang, Yong Cai, Fei Wang, Yun-Song Piao","doi":"10.1007/jhep09(2024)067","DOIUrl":"https://doi.org/10.1007/jhep09(2024)067","url":null,"abstract":"<p>We investigate the parity-violating effects in primordial gravitational waves (GWs) due to null energy condition (NEC) violation in two very early universe scenarios: bounce-inflation and intermediate NEC violation during inflation. In both scenarios, we numerically solve the power spectra of parity-violating primordial GWs generated by coupling the background field and the spectator field with the Nieh-Yan term, respectively. We find that the background field can significantly enhance parity-violating effects at scales corresponding to the maximum of the GW power spectra. In contrast, the parity-violating effects produced by the spectator show significantly weaker observability even if the coupling constant is large. Therefore, in NEC-violating scenarios, the significant observable parity-violating effects in primordial GWs primarily arise from the physics directly related to NEC violation. This result highlights the potential of primordial GWs as crucial tools for exploring NEC-violating and parity-violating physics.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
A dark matter model based on QCD-like SU(Nc) gauge theory with electroweakly interacting dark quarks is discussed. Assuming the dark quark mass m is smaller than the dynamical scale Λd ~ 4πfd, the main component of the dark matter is the lightest G-parity odd dark pion associated with chiral symmetry breaking in the dark sector. We show that nonzero dark quark mass induces the universal mass contribution to both G-parity odd and even pions, and their masses tend to be degenerate. As a result, dark pion annihilation into heavier G-parity even dark pion also affects the dark matter relic abundance. Thus, our setup naturally accommodates forbidden dark matter scenario and realizes heavy dark matter whose mass is ( mathcal{O} )(1–100) TeV, which is different from conventional electroweakly interacting dark matter such as minimal dark matter. We also discuss CP-violation from the θ-term in the dark gauge sector and find that the predicted size of the electron electric dipole moment can be as large as ∼ 10−32e cm.
本文讨论了一个基于类似 QCD 的 SU(Nc) 轨则理论、具有电弱相互作用暗夸克的暗物质模型。假定暗夸克质量 m 小于动力学尺度Λd ~ 4πfd,暗物质的主要成分是与暗扇区中手性对称破缺相关的最轻 G 偶奇暗先驱。我们的研究表明,非零暗夸克质量诱导了对G-奇偶性粒子的普遍质量贡献,而且它们的质量趋于退化。因此,暗先驱湮灭成较重的G-奇偶暗先驱也会影响暗物质遗迹丰度。因此,我们的设置自然地容纳了禁止暗物质情景,实现了质量为 ( mathcal{O} )(1-100) TeV的重暗物质,这与传统的电弱相互作用暗物质(如最小暗物质)是不同的。我们还讨论了暗规部门中θ项的CP违背,发现电子电偶极矩的预言大小可以达到 ∼ 10-32 e cm。
{"title":"Composite dark matter with forbidden annihilation","authors":"Tomohiro Abe, Ryosuke Sato, Takumu Yamanaka","doi":"10.1007/jhep09(2024)064","DOIUrl":"https://doi.org/10.1007/jhep09(2024)064","url":null,"abstract":"<p>A dark matter model based on QCD-like SU(<i>N</i><sub><i>c</i></sub>) gauge theory with electroweakly interacting dark quarks is discussed. Assuming the dark quark mass <i>m</i> is smaller than the dynamical scale Λ<sub><i>d</i></sub> ~ 4<i>πf</i><sub><i>d</i></sub>, the main component of the dark matter is the lightest <i>G</i>-parity odd dark pion associated with chiral symmetry breaking in the dark sector. We show that nonzero dark quark mass induces the universal mass contribution to both <i>G</i>-parity odd and even pions, and their masses tend to be degenerate. As a result, dark pion annihilation into heavier <i>G</i>-parity even dark pion also affects the dark matter relic abundance. Thus, our setup naturally accommodates forbidden dark matter scenario and realizes heavy dark matter whose mass is <span>( mathcal{O} )</span>(1–100) TeV, which is different from conventional electroweakly interacting dark matter such as minimal dark matter. We also discuss CP-violation from the <i>θ</i>-term in the dark gauge sector and find that the predicted size of the electron electric dipole moment can be as large as ∼ 10<sup><i>−</i>32</sup> <i>e</i> cm.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
Given a manifold ( mathbbm{M} ) admitting a maximally supersymmetric consistent truncation, we show how to formulate new consistent truncations by restricting to a set of Kaluza-Klein modes on ( mathbbm{M} ) invariant under some subgroup of the group of isometries of ( mathbbm{M} ). These truncations may involve either finite or infinite sets of modes. We provide their global description using exceptional generalised geometry to construct a ‘deformed’ generalised parallelisation starting with that on ( mathbbm{M} ). This allows us to explicitly embed known consistent truncations directly into exceptional generalised geometry/exceptional field theory, and to obtain the equations governing situations where the consistent truncation retains an infinite tower of modes.
{"title":"Infinite and finite consistent truncations on deformed generalised parallelisations","authors":"Chris D. A. Blair, Martín Pico, Oscar Varela","doi":"10.1007/jhep09(2024)065","DOIUrl":"https://doi.org/10.1007/jhep09(2024)065","url":null,"abstract":"<p>Given a manifold <span>( mathbbm{M} )</span> admitting a maximally supersymmetric consistent truncation, we show how to formulate new consistent truncations by restricting to a set of Kaluza-Klein modes on <span>( mathbbm{M} )</span> invariant under some subgroup of the group of isometries of <span>( mathbbm{M} )</span>. These truncations may involve either finite or infinite sets of modes. We provide their global description using exceptional generalised geometry to construct a ‘deformed’ generalised parallelisation starting with that on <span>( mathbbm{M} )</span>. This allows us to explicitly embed known consistent truncations directly into exceptional generalised geometry/exceptional field theory, and to obtain the equations governing situations where the consistent truncation retains an infinite tower of modes.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}
It is known that perturbative expansions in powers of the coupling in quantum mechanics (QM) and quantum field theory (QFT) are asymptotic series. This can be useful at weak coupling but fails at strong coupling. In this work, we present two types of series expansions valid at strong coupling. We apply the series to a basic integral as well as a QM path integral containing a quadratic and quartic term with coupling constant λ. The first series is the usual asymptotic one, where the quartic interaction is expanded in powers of λ. The second series is an expansion of the quadratic part where the interaction is left alone. This yields an absolutely convergent series in inverse powers of λ valid at strong coupling. For the basic integral, we revisit the first series and identify what makes it diverge even though the original integral is finite. We fix the problem and obtain, remarkably, a series in powers of the coupling which is absolutely convergent and valid at strong coupling. We explain how this series avoids Dyson’s argument on convergence. We then consider the QM path integral (discretized with time interval divided into N equal segments). As before, the second series is absolutely convergent and we obtain analytical expressions in inverse powers of λ for the nth order terms by taking functional derivatives of generalized hypergeometric functions. The expressions are functions of N and we work them out explicitly up to third order. The general procedure has been implemented in a Mathematica program that generates the expressions at any order n. We present numerical results at strong coupling for different values of N starting at N = 2. The series matches the exact numerical value for a given N (up to a certain accuracy). The continuum is formally reached when N → ∞ but in practice this can be reached at small N.
众所周知,量子力学(QM)和量子场论(QFT)中耦合幂的微扰展开是渐近级数。这在弱耦合时可能有用,但在强耦合时就失效了。在这项工作中,我们提出了两种在强耦合时有效的级数展开。第一个数列是通常的渐近数列,其中四元相互作用以λ的幂级数展开。这产生了一个在强耦合条件下有效的以λ的反幂为单位的绝对收敛级数。对于基本积分,我们重温了第一个数列,并找出了在原始积分是有限的情况下使其发散的原因。我们解决了这个问题,得到了一个在强耦合时绝对收敛且有效的耦合度幂级数。我们解释了这个数列如何避免戴森关于收敛性的论证。然后,我们考虑 QM 路径积分(离散化,时间间隔分为 N 个等分段)。与之前一样,第二序列是绝对收敛的,我们通过求广义超几何函数的函数导数,得到了 n 阶项的λ反幂解析表达式。这些表达式是 N 的函数,我们明确地将它们计算到三阶。我们给出了从 N = 2 开始的不同 N 值的强耦合数值结果。该序列与给定 N 的精确数值相匹配(达到一定精度)。当 N → ∞ 时,形式上达到了连续性,但在实践中,小 N 也能达到连续性。
{"title":"Two types of series expansions valid at strong coupling","authors":"Ariel Edery","doi":"10.1007/jhep09(2024)063","DOIUrl":"https://doi.org/10.1007/jhep09(2024)063","url":null,"abstract":"<p>It is known that perturbative expansions in powers of the coupling in quantum mechanics (QM) and quantum field theory (QFT) are asymptotic series. This can be useful at weak coupling but fails at strong coupling. In this work, we present two types of series expansions valid at strong coupling. We apply the series to a basic integral as well as a QM path integral containing a quadratic and quartic term with coupling constant <i>λ</i>. The first series is the usual asymptotic one, where the quartic interaction is expanded in powers of <i>λ</i>. The second series is an expansion of the quadratic part where the interaction is left alone. This yields an absolutely convergent series in inverse powers of <i>λ</i> valid at strong coupling. For the basic integral, we revisit the first series and identify what makes it diverge even though the original integral is finite. We fix the problem and obtain, remarkably, a series in powers of the coupling which is absolutely convergent and valid at strong coupling. We explain how this series avoids Dyson’s argument on convergence. We then consider the QM path integral (discretized with time interval divided into <i>N</i> equal segments). As before, the second series is absolutely convergent and we obtain analytical expressions in inverse powers of <i>λ</i> for the <i>n</i>th order terms by taking functional derivatives of generalized hypergeometric functions. The expressions are functions of <i>N</i> and we work them out explicitly up to third order. The general procedure has been implemented in a Mathematica program that generates the expressions at any order <i>n</i>. We present numerical results at strong coupling for different values of <i>N</i> starting at <i>N</i> = 2. The series matches the exact numerical value for a given <i>N</i> (up to a certain accuracy). The continuum is formally reached when <i>N</i> → ∞ but in practice this can be reached at small <i>N</i>.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 eigenstate thermalization hypothesis (ETH) is the leading conjecture for the emergence of statistical mechanics in generic isolated quantum systems and is formulated in terms of the matrix elements of operators. An analog known as the ergodic bipartition (EB) describes entanglement and locality and is formulated in terms of the components of eigenstates. In this paper, we significantly generalize the EB and unify it with the ETH, extending the EB to study higher correlations and systems out of equilibrium. Our main result is a diagrammatic formalism that computes arbitrary correlations between eigenstates and operators based on a recently uncovered connection between the ETH and free probability theory. We refer to the connected components of our diagrams as generalized free cumulants. We apply our formalism in several ways. First, we focus on chaotic eigenstates and establish the so-called subsystem ETH and the Page curve as consequences of our construction. We also improve known calculations for thermal reduced density matrices and comment on an inherently free probabilistic aspect of the replica approach to entanglement entropy previously noticed in a calculation for the Page curve of an evaporating black hole. Next, we turn to chaotic quantum dynamics and demonstrate the ETH as a sufficient mechanism for thermalization, in general. In particular, we show that reduced density matrices relax to their equilibrium form and that systems obey the Page curve at late times. We also demonstrate that the different phases of entanglement growth are encoded in higher correlations of the EB. Lastly, we examine the chaotic structure of eigenstates and operators together and reveal previously overlooked correlations between them. Crucially, these correlations encode butterfly velocities, a well-known dynamical property of interacting quantum systems.
特征态热化假说(ETH)是在一般孤立量子系统中出现统计力学的主要猜想,它是根据算子的矩阵元素提出的。被称为 "遍历双分区"(EB)的类似理论描述了纠缠和局域性,并以特征态的分量来表述。在本文中,我们对 EB 进行了重大概括,并将其与 ETH 统一起来,将 EB 扩展到研究更高的相关性和非平衡系统。我们的主要成果是一种图解形式主义,它基于最近发现的 ETH 与自由概率论之间的联系,计算特征状态与算子之间的任意相关性。我们把图中的连接成分称为广义自由积。我们从几个方面应用我们的形式主义。首先,我们专注于混沌特征状态,并建立了所谓的子系统 ETH 和佩奇曲线,作为我们构造的结果。我们还改进了已知的热还原密度矩阵计算,并对之前在蒸发黑洞佩奇曲线计算中注意到的纠缠熵复制方法的内在自由概率方面进行了评论。接下来,我们转向混沌量子动力学,并证明 ETH 是一般热化的充分机制。特别是,我们证明了还原密度矩阵会松弛到其平衡形式,并且系统在晚期服从佩奇曲线。我们还证明,纠缠增长的不同阶段是由 EB 的较高相关性编码的。最后,我们一起研究了特征状态和算子的混沌结构,并揭示了它们之间以前被忽视的相关性。最重要的是,这些相关性编码了蝴蝶速度,这是相互作用量子系统的一个众所周知的动力学特性。
{"title":"Generalized free cumulants for quantum chaotic systems","authors":"Siddharth Jindal, Pavan Hosur","doi":"10.1007/jhep09(2024)066","DOIUrl":"https://doi.org/10.1007/jhep09(2024)066","url":null,"abstract":"<p>The eigenstate thermalization hypothesis (ETH) is the leading conjecture for the emergence of statistical mechanics in generic isolated quantum systems and is formulated in terms of the matrix elements of operators. An analog known as the ergodic bipartition (EB) describes entanglement and locality and is formulated in terms of the components of eigenstates. In this paper, we significantly generalize the EB and unify it with the ETH, extending the EB to study higher correlations and systems out of equilibrium. Our main result is a diagrammatic formalism that computes arbitrary correlations between eigenstates and operators based on a recently uncovered connection between the ETH and free probability theory. We refer to the connected components of our diagrams as generalized free cumulants. We apply our formalism in several ways. First, we focus on chaotic eigenstates and establish the so-called subsystem ETH and the Page curve as consequences of our construction. We also improve known calculations for thermal reduced density matrices and comment on an inherently free probabilistic aspect of the replica approach to entanglement entropy previously noticed in a calculation for the Page curve of an evaporating black hole. Next, we turn to chaotic quantum dynamics and demonstrate the ETH as a sufficient mechanism for thermalization, in general. In particular, we show that reduced density matrices relax to their equilibrium form and that systems obey the Page curve at late times. We also demonstrate that the different phases of entanglement growth are encoded in higher correlations of the EB. Lastly, we examine the chaotic structure of eigenstates and operators together and reveal previously overlooked correlations between them. Crucially, these correlations encode butterfly velocities, a well-known dynamical property of interacting quantum systems.</p>","PeriodicalId":635,"journal":{"name":"Journal of High Energy Physics","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}