We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the ...computation of simple quantities in the various schemes, we point out similarities and differences between them.
A new mathematical framework for the diagonalization of the nondiagonal vector–scalar and axial-vector–pseudoscalar mixing in the effective meson Lagrangian is described. This procedure has ...unexpected connections with the Hadamard product of n×n matrices describing the couplings, masses, and fields involved. The approach is argued to be much more efficient as compared with the standard methods employed in the literature. The difference is especially noticeable if the chiral and flavor symmetry is broken explicitly. The paper ends with an illustrative application to the chiral model with broken U(3)L×U(3)R symmetry.
We compute the two-loop
β
-function of scalar and spinorial quantum electrodynamics as well as pure Yang–Mills and quantum chromodynamics using the background field method in a fully ...quadridimensional setup using implicit regularization (IREG). Moreover, a thorough comparison with dimensional approaches such as conventional dimensional regularization (CDR) and dimensional reduction (DRED) is presented. Subtleties related to Lorentz algebra contractions/symmetric integrations inside divergent integrals as well as renormalisation schemes are carefully discussed within IREG where the renormalisation constants are fully defined as basic divergent integrals to arbitrary loop order. Moreover, we confirm the hypothesis that momentum routing invariance in the loops of Feynman diagrams implemented via setting well-defined surface terms to zero deliver non-abelian gauge invariant amplitudes within IREG just as it has been proven for abelian theories.
In this manuscript, we report the outcome of the topical workshop:
paving the way to alternative NNLO strategies
(
https://indico.ific.uv.es/e/WorkStop-ThinkStart_3.0
), by presenting a discussion ...about different frameworks to perform precise higher-order computations for high-energy physics. These approaches implement novel strategies to deal with infrared and ultraviolet singularities in quantum field theories. A special emphasis is devoted to the local cancellation of these singularities, which can enhance the efficiency of computations and lead to discover novel mathematical properties in quantum field theories.
A realization of the composite Higgs scenario in the context of the effective model with the
S
U
(
2
)
L
×
U
(
1
)
R
symmetric four-Fermi interactions proposed by Miransky, Tanabashi and Yamawaki is ...studied. The model implements Nambu’s mechanism of dynamical electroweak symmetry breaking leading to the formation of
t
¯
t
and
b
¯
b
quark condensates. We explore the vacuum structure and spectrum of the model by using the Schwinger proper-time method. As a direct consequence of this mechanism, the Higgs acquires a mass in accord with its experimental value. The present prediction essentially differs from the known overestimated value,
m
χ
=
2
m
t
, making more favourable the top condensation scenario presented here. The mass formulas for the members of the second Higgs doublet are also obtained. The Nambu sum rule is discussed. It is shown that the anomalous
U
(
1
)
A
symmetry breaking modifies this rule at next to leading order in
1
/
N
c
.
We extend a known multiquark three-flavor Lagrangian of the Nambu-Jona-Lasinio type, which includes a set of effective interactions proportional to the current quark masses, to include the multiquark ...interactions of vector and axial-vector types. It is shown that the mass spectrum of the four low-lying meson nonets are in agreement with current phenomenological expectations. The role of the new interactions is analyzed in detail.
We considered a QED scattering (AB→AB), in which B is initially entangled with a third particle (C) that does not participate directly in the scattering. The effect of the scattering over C's final ...state was evaluated and we noted coherence (off-diagonal) terms were created, which led to non-null values for ⟨σx⟩ and ⟨σy⟩ that are, in principle, measurable in a Stern-Gerlach apparatus. We chose a particular QED scattering (e+e−→μ+μ−) and found that ⟨σx⟩ and ⟨σy⟩ are proportional to the total cross section (σtotal) of the AB scattering, besides being maximal if BC's initial state is taken as a Bell basis. Furthermore, we calculated the initial and final mutual information IAC and IBC, and noticed an increase (decrease) in IAC (IBC), which indicates that, after AB interact, the total amount of correlations (quantum+classical) is distributed among the 3 subsystems.
It is shown that flavor mixing of the strange and light quarks allows for existence of a much larger baryonic chemical potential window for the formation of a stable dual chiral-wave state as ...compared to the well-known two-flavor case. In addition, strangeness catalyzes the occurrence of a new branch of nonhomogeneous solutions at moderate densities. This case study is addressed at zero temperature within the SU(3) flavor Nambu-Jona-Lasinio model with the't Hooft determinanta! flavor mixing interaction. The modulation of the chiral condensates in the light quark sector is taken to be one dimensional, while strangeness is embedded as a homogeneous condensate in the spontaneously broken phase of chiral symmetry. A finite current quark mass for the strange quark is incorporated, while the up and down current masses are set to zero. In that case the modulation considered provides an exact analytic solution for the system. Despite the simplicity of the ansatz, the emerging phase diagram displays a very rich structure.
The radiative induction of the CPT and Lorentz violating Chern–Simons (CS) term is reassessed. The massless and massive models are studied. Special attention is given to the preservation of gauge ...symmetry at higher orders in the background vector
b
μ
when radiative corrections are considered. Both the study of the odd and even parity sectors of the complete vacuum polarization tensor at one-loop order and a non-perturbative analysis show that this symmetry must be preserved by quantum corrections. As a complement we obtain the result that transversality of the polarization tensor does not fix the value of the coefficient of the induced CS term.
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