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SUMMARY:NLO Scattering in ϕ^4 Theory Finite System Size Correction
DTSTART;VALUE=DATE-TIME:20220321T171000Z
DTEND;VALUE=DATE-TIME:20220321T172500Z
DTSTAMP;VALUE=DATE-TIME:20260309T033113Z
UID:indico-contribution-2267@indico.tlabs.ac.za
DESCRIPTION:Speakers: Jean Du Plessis (Stellenbosch University)\nPreviousl
 y an equation of state for the relativistic hydrodynamics encountered in h
 eavy-ion collisions at the LHC has been calculated using lattice QCD metho
 ds. This leads to a prediction of very low viscosity\, due to the trace an
 omaly. Finite system corrections to this trace anomaly could challenge thi
 s calculation\, since the lattice QCD calculation was preformed in an effe
 ctively infinite system. To verify this trace anomaly it is beneficial to 
 add the finite system corrections that will be encountered. We construct a
  massive $\\phi^4$ theory while imposing periodic boundary conditions on n
  of the 3 spatial dimensions. $2\\rightarrow2$ NLO scattering is then comp
 uted\, while analytically making sure the optical theorem holds\, to ensur
 e unitarity remains intact despite the pathological nature of the finite s
 ystem. In order to develop a solid mathematical basis that will carry forw
 ard into the thermal field theory context\, some small and large argument 
 analysis (in terms of the incoming energy as well as the length scales of 
 the finite dimensions) is performed on the s\,t and u channels separately.
  Finally the finite size corrections to the total cross section\, running 
 coupling and effective coupling is explored numerically\, in order to esti
 mate the size of such finite system corrections in massive field theories.
 \n\nThe size of these effects appears to depend very sensitively on the le
 ngth scales of the finite dimensions\, the number of finite dimensions\, t
 he energy of the scattering as well as the size of the renormalized coupli
 ng. For parameters comparable to what is found for QCD at the LHC it is un
 clear if the corrections would be detectable or not. Due to the pathologic
 al nature of the system it is also found that there are energies at which 
 the total cross section becomes infinite when there are 2 finite dimension
 s\, and that the cross section is infinite for all physical energies when 
 all three spatial dimensions are finite. This makes interpretation difficu
 lt\, and suggests the need to consider scattering happening in a finite ti
 me-span. It does however suggest that a fuller treatment of finite-system 
 time-independent QCD may reveal detectable finite system effects\, possibl
 y challenging or confirming the low viscosity of the relativistic Quark Gl
 uon Plasma generated in heavy-ion collisions\, as calculated as a conseque
 nce of the numerically calculated lattice QCD equation of state.\n\nhttps:
 //indico.tlabs.ac.za/event/109/contributions/2267/
LOCATION:
URL:https://indico.tlabs.ac.za/event/109/contributions/2267/
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