Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeneral scalar renormalisation group equations at three-loop order
130
0
0.0
(
0
)
Authors
Tom Steudtner
Ask ChatGPT about the research
No Arabic abstract
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $overline{text{MS}}$ scheme. Utilising pre-existing literature expressions for a specific model, loop integrals are avoided and templates for general theories are obtained. We reiterate known four-loop expressions, and derive $beta$ functions for scalar masses and cubic interactions from it. As an example, the results are applied to compute all renormalisation group equations in $U(n) times U(n)$ scalar theories.
rate research
Read More
For arbitrary four-dimensional quantum field theories with scalars and fermions, renormalisation group equations in the $overline{text{MS}}$ scheme are investigated at three-loop order in perturbation theory. Collecting literature results, general expressions are obtained for field anomalous dimensions, Yukawa interactions, as well as fermion masses. The renormalisation group evolution of scalar quartic, cubic and mass terms is determined up to a few unknown coefficients. The combined results are applied to compute the renormalisation group evolution of the gaugeless Litim-Sannino model.
We consider the scalar sector of a general renormalizable theory and evaluate the effective potential through three loops analytically. We encounter three-loop vacuum bubble diagrams with up to two masses and six lines, which we solve using differential equations transformed into the favorable $epsilon$ form of dimensional regularization. The master integrals of the canonical basis thus obtained are expressed in terms of cyclotomic polylogarithms up to weight four. We also introduce an algorithm for the numerical evaluation of cyclotomic polylogarithms with multiple-precision arithmetic, which is implemented in the Mathematica package cyclogpl.m supplied here.
We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which cannot be done using any known method by introducing counterterms.
We present the complete 2-loop renormalisation group equations of the superpotential parameters for the supersymmetric standard model including the full set of R-parity violating couplings. We use these equations to do a study of (a) gauge coupling unification, (b) bottom-tau unification, (c) the fixed-point structure of the top quark Yukawa coupling, and (d) two-loop bounds from perturbative unification. For large values of the R-parity violating coupling, the value of alpha_S(M_Z) predicted from unification can be reduced by 5% with respect to the R-parity conserving case, bringing it to within 2sigma of the observed value. Bottom-tau Yukawa unification becomes potentially valid for any value of tanbetasim 2-50. The prediction of the top Yukawa coupling from the low tanbeta, infra-red quasi fixed point can be lowered by up to 10%, raising tanbeta up to a maximum of 5 and relaxing experimental constraints upon the quasi-fixed point scenario. For heavy scalar fermion masses of order 1 Tev the limits on the higher family Delta L ot=0 operators from perturbative unification are competitive with the indirect laboratory bounds. We calculate the dependence of these bounds upon tan beta.
Functional renormalisation group approach is applied to a system of kaons with finite chemical potential. A set of approximate flow equations for the effective couplings is derived and solved. At high scale the system is found to be at the normal phase whereas at some critical value of the running scale it undergoes the phase transition (PT) to the phase with a spontaneously broken symmetry with the kaon condensate as an order parameter. The value of the condensate turns out to be quite sensitive to the kaon-kaon scattering length.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
