A Consistency Test of EFT Power Countings from Residual Cutoff Dependence
Harald W. Griesshammer
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15 pages LaTeX2e (pdflatex) including 5 figures as .pdf files using includegraphics. Final version to appear in Europ. J. Phys. A topical issue "The Tower of Effective (Field) Theories and the Emergence of Nuclear Phenomena". arXiv admin note: substantial text overlap with arXiv:1511.00490 Author's note: substantial corrections in key argument and expansions. Version appearing in Eur Phys J A
A method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories (EFT) which are non-perturbative at leading order is presented. The Renormalisation Group evolution of an observable predicts the functional form of its residual cutoff dependence on the breakdown scale of an EFT, on the low-momentum scales, and on the order of the calculation. Passing this test is a necessary but not sufficient consistency criterion for a suggested power counting whose exact nature is disputed. In Chiral Effective Field Theory (ChiEFT) with more than one nucleon, a lack of universally accepted analytic solutions obfuscates the convergence pattern in results. This led to proposals which predict different sets of Low Energy Coefficients (LECs) at the same chiral order, and at times even predict a different ordering long-range contributions. The method may independently check whether an observable is renormalised at a given order, and proves estimates of both the breakdown scale and the momentum-dependent order-by-order convergence pattern. Conversely, it helps identify those LECs (and long-range pieces) which ensure renormalised observables at a given order. I also discuss assumptions and the relation to Wilson's Renormalisation Group; useful observable and cutoff choices; the momentum window with likely best signals; its dependence on the values and forms of cutoffs as well as on the EFT parameters; the impact of fitting LECs to data; and caveats as well as limitations. Since the test is designed to minimise the use of data, it quantitatively falsifies if the EFT has been renormalised consistently. This complements other tests which quantify how an EFT compares to experiment. Its application in particular to the 3P0 and P2-3F2 partial waves of NN scattering in ChiEFT may elucidate persistent power-counting issues.
Consistency between renormalization group running of chiral operator and counting rule -- Case of chiral pion production operator --
在核手征微扰理论中，算子被定义在一个截止值可以在一定范围内变化的空间中。算子的运行是截止值变化的结果[重整化群（RG）运行]。为了使ChPT有用，操作者应该以与计数规则一致的方式运行;也就是说，手性计数器项的运行必须具有自然大小。我们使用威尔逊重整化群（WRG）方程改变截断，并检查这种一致性。作为一个例子，我们研究的s波π生产运营商的NN \to d π，来自ChPT。我们证明，WRG运行不会产生任何手征对称违反（CSV）的相互作用，只要我们开始与运营商不包含CSV项。我们分析表明，计数器项是如何产生的WRG运行的情况下，无穷小的截止减少。在此基础上，我们讨论了一个截断变分的范围，在这个范围内，反项的运行是自然大小的。然后，我们在数字上证实了这一点。
在建立手征核有效场论（EFT）的一致功率计数的基础上，以重整化群不变性为约束条件，讨论了核子-核子散射单重态通道中的次主导接触相互作用，即反项.我们认为，相当大的截止误差的领先幅度要求O（Q）的EFT扩展是非零的，相反，温伯格的原始功率计数。这一点，再加上扭曲波膨胀中两π介子交换的紫外发散，导致1 S 0反项的增强，并导致单重态通道的无π介子理论般的功率计数。
Universality in strongly interacting bosonic clusters
INFN-TIFPA Trento Institute of Fundamental Physics and Applications（INFN-TIFPA 特伦托基础物理与应用研究所）；European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Fondazione Bruno Kessler（欧洲核及相关领域理论研究中心（ECT*），布鲁诺·康德塞勒基金会）；Physics Department, University of Trento（特伦托大学物理系）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎-萨克雷大学，法国国家科学研究中心/法国国家核子和粒子物理研究所，IJCLab）；Department of Physics, University of Arizona（亚利桑那大学物理系）
Trapping-potential dependence of the unitary Fermi gas at the BCS-BEC crossover
University of Washington（华盛顿大学）；Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern（伯尔尼大学阿尔伯特·爱因斯坦基础物理中心理论物理研究所）；INFN sezione di Torino（都灵 INFN 分部）
Nuclear saturation in lowest-order Brueckner theory with two- and three-nucleon forces in view of chiral effective field theory
在手征有效场论（Ch-EFT）中，利用最低阶Brueckner理论，从双核子和三核子相互作用的角度讨论了核饱和机制.本文用现代核子-核子（NN）势及其低动量等效相互作用重新讨论了在计算各种NN力的饱和点时所观察到的Coester带，并详细地讨论了Ch-EFT相互作用的饱和曲线。通过折叠第三核子自由度，将三核子力（3 NF）简化为有效的两体相互作用。讨论了由于选择了3 NF低能常数$c_D$和$c_E$而导致的不稳定性。NN势的截止能量依赖性的降低通过证明$^1$ S $_0$和$^3$ S $_1$状态中的3 NF的作用来解释。
Finite-range EFT for the $E1$ strength distribution of ${}^6$He
Nuclear Physics Institute, Czech Academy of Sciences（捷克科学院核物理研究所）；Istituto Nazionale di Fisica Nucleare, Sezione di Pisa（意大利国家核物理研究所比萨分部）；Technische Universität Darmstadt（达姆施塔特工业大学）；ExtreMe Matter Institute EMMI and Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung GmbH（极端物质研究所EMMI和黑森亥姆霍兹FAIR研究学院(HFHf)，GSI重离子研究中心有限公司）；Ohio University（俄亥俄大学）；Chalmers University of Technology（查尔姆斯理工大学）
