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SUMMARY:Seeing Effective Field Theory of Neutron Decay through of Double C
 ategories
DTSTART;VALUE=DATE-TIME:20260923T134000Z
DTEND;VALUE=DATE-TIME:20260923T140000Z
DTSTAMP;VALUE=DATE-TIME:20260914T045140Z
UID:indico-contribution-500@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Stepan Moskaliuk (Bogoliubov Institute for Theoretic
 al Physics)\nIn this talk the Standard Model of the neutron decay is descr
 ibed by the exchange of the electroweak $W$ boson. However\, energy scales
  for this process ($\\sim \\mathrm{MeV}$) are well below the electroweak s
 cale ($\\sim 100~\\mathrm{GeV}$). Consequently\, the historical descriptio
 n within the low-energy effective field theory (EFT) is the correct physic
 s picture for the neutron decay\, on the one hand. On the other hand\, exp
 ansion of the categorical point of view on many areas of  mathematical phy
 sics will cause to deeper understanding of genuine features of these probl
 ems. New applications of categorical methods are\nconnected with new addit
 ional structures on categories. One of such structures\, a double category
 \, is considered in this talk. The double category structure is defined as
  generalization of the bicategory\nstructure. The use of EFT techniques an
 d category-theoretical methods is not a mere reformulation of the problem.
    Different formulations of EFTs lead to identical mappings of one set  o
 f finite quantities (parameters of the theory) to another set of finite qu
 antities (results of measurements\,  cross-sections\, etc.).  It means tha
 t the presence of infinities (quartic\,  quadratic and etc.) is formalism 
 dependent\, and thus their absence or presence should not be served as an 
 argument for selecting this or that physical theory. This shows that the s
 o-called technical hierarchy problem (the sensitivity of low-energy physic
 s \nto high-energy physics) depends on the formulation of quantum field th
 eory\, and\, therefore\, is devoid of physical meaning\, at least for reno
 rmalisable theories.   The  EFT also provides a rigorous way to connect sc
 ales and estimate uncertainties. Moreover\, EFT methods can  bring new ins
 ights to the problem. In fact\,  by providing a simple framework to analyz
 e hadronic correlation functions\,  the study of neutron decay to $\\mathc
 al{O} (G_F \\alpha)$ in Heavy Baryon Chiral Perturbation Theory (HBChPT) h
 as uncovered a new \\%-level ``inner" correction to the ratio $g_A/g_V$ of
  axial-vector to vector nucleon couplings\, missed in previous analyses ba
 sed on current algebra. The leading-order amplitude for the neutron decay 
 is proportional to the Fermi coupling constant $\\mathrm{G}_\\mathrm{F}$\,
  which is precisely determined from the muon decay. Charged currents with 
 quarks introduce the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $V_{ud
 }$ to the neutron beta decay amplitude. At low energies\, the neutron deca
 y is described by two coupling constants: the vector $g_\\mathrm{V}$ and t
 he axial-vector $g_\\mathrm{A}$. In the reference of this talk\, there are
  presented all theoretical works rely on the precise evaluation of electro
 weak\, quantum chromodynamics (QCD)\, and long-distance hadronic contribut
 ions to these coupling constants. \n  In the HBChPT framework for single-n
 ucleon weak charged-current (CC) processes\, the active degrees of freedom
  are the light leptons\, photons\, pions\, and nucleons. The effect of bot
 h electroweak- and other hadronic-scale physics is encoded in a number of 
 low-energy constants (LECs). The goal of this talk is to develop a matchin
 g procedure  to express the relevant LECs in terms of perturbatively calcu
 lable Wilson coefficients and hadronic correlation functions that can then
  be estimated with  non-perturbative methods\, such as dispersive methods 
 or lattice QCD. Since there are multiple thresholds\, the electroweak scal
 e $\\sim M_{W\,Z}$\, the chiral symmetry breaking scale $\\Lambda_\\chi \\
 sim m_N\\sim$~GeV\, with $m_N$ the mass of nucleon\, and the pion mass\, w
 e adopt a multi-step matching strategy. The first step connects the  Stand
 ard Model EFT to  the  low-energy effective theory (LEFT) below the weak s
 cale\, which coincides with the $V-A$ theory of weak interactions augmente
 d by QED and QCD. This is a perturbative matching step. The second step co
 nnects the double category of  LEFT to the double category of HBChPT by do
 uble category functors and involves non-perturbative physics.  The third s
 tep consists of integrating out the pions\, by matching the double categor
 y of HBChPT onto a  double category of pionless EFT.\n\nhttps://indico.bit
 p.kiev.ua/event/18/contributions/500/
LOCATION:Bogolyubov Institute for Theoretical Physics Conference Hall
URL:https://indico.bitp.kiev.ua/event/18/contributions/500/
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