Evolution of Coupling Constant in Hot QCD

1997 ◽  
Vol 06 (01) ◽  
pp. 45-64
Author(s):  
M. Chaichian ◽  
M. Hayashi

The evolution of QCD coupling constant at finite temperature is considered by making use of the finite temperature renormalization group equation up to the one-loop order in the background field method with the Feynman gauge and the imaginary time formalism. The results are compared with the ones obtained in the literature. We point out, in particular, the origin of the discrepancies between different calculations, such as the choice of gauge, the breakdown of Lorentz invariance, imaginary versus real time formalism and the applicability of the Ward identities at finite temperature.

1989 ◽  
Vol 04 (03) ◽  
pp. 293-302 ◽  
Author(s):  
MEIUN SHINTANI

On the basis of the massive vector dipole theory as a model for strong interactions at large distances, we compute the counterterm Lagrangian at the one-loop level in the background field method. By smoothly relating the running coupling constant in the confining region to that in the asymptotically free region, we deduce a relationship between the string tension and the QCD scale parameter Λ QCD . With an input data of the string tension, we evaluate the value of Λ QCD . The lower bound to the distances where the dipole theory is valid relies on the number of flavors. The theory seems to be meaningful for six generations or less.


1990 ◽  
Vol 242 (3-4) ◽  
pp. 412-414 ◽  
Author(s):  
J. Antikainen ◽  
M. Chaichian ◽  
N.R. Pantoja ◽  
J.J. Salazar

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Tyler Corbett ◽  
Adam Martin ◽  
Michael Trott

Abstract We report consistent results for Γ(h → γγ), $$ \sigma \left(\mathcal{GG}\to h\right) $$ σ GG → h and $$ \Gamma \left(h\to \mathcal{GG}\right) $$ Γ h → GG in the Standard Model Effective Field Theory (SMEFT) perturbing the SM by corrections $$ \mathcal{O}\left({\overline{\upsilon}}_T^2/16{\pi}^2{\Lambda}^2\right) $$ O υ ¯ T 2 / 16 π 2 Λ 2 in the Background Field Method (BFM) approach to gauge fixing, and to $$ \mathcal{O}\left({\overline{\upsilon}}_T^4/{\Lambda}^4\right) $$ O υ ¯ T 4 / Λ 4 using the geometric formulation of the SMEFT. We combine and modify recent results in the literature into a complete set of consistent results, uniforming conventions, and simultaneously complete the one loop results for these processes in the BFM. We emphasize calculational scheme dependence present across these processes, and how the operator and loop expansions are not independent beyond leading order. We illustrate several cross checks of consistency in the results.


1996 ◽  
Vol 11 (28) ◽  
pp. 2259-2269 ◽  
Author(s):  
HISAO NAKKAGAWA ◽  
HIROSHI YOKOTA

We present a simple and effective procedure to improve the finite temperature effective potential so as to satisfy the renormalization group equation (RGE). With the L-loop knowledge of the effective potential and of the RGE coefficient function, this procedure carries out a systematic resummation of large-T as well as large-log terms up to the Lth-to-leading order, giving an improved effective potential which satisfies the RGE and is exact up to the Lth-to-leading T and log terms. Applications to the one- and two-loop effective potentials are explicitly performed.


2001 ◽  
Vol 10 (06) ◽  
pp. 483-499 ◽  
Author(s):  
Q. WANG ◽  
C.-W. KAO ◽  
G. C. NAYAK ◽  
W. GREINER

By using the background field method of QCD in a path integral approach, we derive the equation of motion for the classical chromofield and that for the gluon in a system containing the gluon and the classical chromofield simultaneously. This inhomogeneous field equation contains an induced current term, which is the expectation value of a combination of composite operators including linear, square and cubic terms of the gluon field. We also derive identities for the current from gauge invariance and calculate the current at the leading order where the current induced by the gluon is opposite in sign to that induced by the quark. This is just the feature of the non-Abelian gauge field theory which has asymptotic freedom. Physically, the induced current can be treated as a "displacement" current in the polarized vacuum, and its effect is equivalent to redefining the field and the coupling constant.


2006 ◽  
Vol 635 (4) ◽  
pp. 213-217 ◽  
Author(s):  
M. Loewe ◽  
S. Mendizabal ◽  
J.C. Rojas

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Ka-Hei Leung

Abstract We consider super Yang–Mills (SYM) theory in $N=1$ conformal supergravity. Using the background field method and the Faddeev–Popov procedure, the quantized action of the theory is presented. Its one-loop effective action is studied using the heat kernel method. We shall develop a non-iterative scheme, generalizing the non-supersymmetric case, to obtain the super heat kernel coefficients. In particular, the first three coefficients, which govern the one-loop divergence, will be calculated. We shall also demonstrate how to schematically derive the higher-order coefficients. The method presented here can be readily applied to various quantum theories. We shall, as an application, derive the full one-loop divergence of SYM in conformal supergravity.


1993 ◽  
Vol 71 (5-6) ◽  
pp. 237-240 ◽  
Author(s):  
M. A. van Eijck

We present a one-loop calculation of a gauge invariant quantum-chromodynamic β function at finite temperature with rules coming from the background field method in the Landau gauge and from the retarded and advanced formulation of finite-temperature field theory.


2014 ◽  
Vol 29 (34) ◽  
pp. 1450172
Author(s):  
Weijian Wang ◽  
Jia-Hui Huang

In this paper, the quantum corrections of gauge field propagator are investigated in the noncommutative (NC) scalar U(1) gauge theory with Seiberg–Witten map (SWM) method. We focus on the simplest case where the gauge boson couples with a massless complex scalar field. The one-loop divergent corrections at θ2-order are calculated using the background field method. It is found that the divergences can be absorbed by making field redefinitions, leading to a good renormalizability at θ2-order.


2014 ◽  
Vol 26 (01) ◽  
pp. 1330012 ◽  
Author(s):  
JOCHEN ZAHN

The definition of the locally covariant Dirac field is adapted such that it may be charged under a gauge group and in the presence of generic gauge and Yukawa background fields. We construct renormalized Wick powers and time-ordered products. It is shown that the Wick powers may be defined such that the current and the stress-energy tensor are conserved, and the remaining ambiguity is characterized. We sketch a variant of the background field method that can be used to determine the renormalization group flow at the one loop level from the nontrivial scaling of Wick powers.


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