A
bstract
The couplings of the electroweak effective theory contain information on the heavy-mass scales which are no-longer present in the low-energy Lagrangian. We build a general effective ...Lagrangian, implementing the electroweak chiral symmetry breaking SU(2)
L
⊗ SU(2)
R
→ SU(2)
L
+
R
, which couples the known particle fields to heavier states with bosonic quantum numbers
J
P
= 0
±
and 1
±
. We consider colour-singlet heavy fields that are in singlet or triplet representations of the electroweak group. Integrating out these heavy scales, we analyze the pattern of low-energy couplings among the light fields which are generated by the massive states. We adopt a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs, without making any assumption about its possible doublet structure. Special attention is given to the different possible descriptions of massive spin-1 fields and the differences arising from naive implementations of these formalisms, showing their full equivalence once a proper short-distance behaviour is required.
Toy models for hierarchy studies Álvarez-Luna, Clara; Cembranos, José A. R.; Sanz-Cillero, Juan José
European physical journal. C, Particles and fields,
11/2022, Volume:
82, Issue:
11
Journal Article
Peer reviewed
Open access
We provide a simple computation in order to estimate the probability of a given hierarchy between two scales. In particular, we work in a model provided with a gauge symmetry, with two scalar ...doublets. We start from a scale-invariant classical Lagrangian, but by taking into account the Coleman–Weinberg mechanism, we obtain masses for the gauge bosons and the scalars. This approach typically provides a
light
(
L
) and a
heavy
(
H
) sector related to the two different vacuum expectation values of the two scalars. We compute the size of the hypervolume of the parameter space of the model associated with an interval of mass ratios between these two sectors. We define the probability as proportional to this size and conclude that probabilities of very large hierarchies are not negligible in the type of models studied in this work.
Gravitational Coleman-Weinberg mechanism Álvarez-Luna, Clara; de la Calle-Leal, Sergio; Cembranos, José A. R. ...
The journal of high energy physics,
02/2023, Volume:
2023, Issue:
2
Journal Article
Peer reviewed
Open access
A
bstract
The Coleman-Weinberg mechanism provides a procedure by which a scalar field, which initially has no mass parameters, acquires a mass due to the anomalous nature of scale symmetry. Loop ...corrections trigger a spontaneous symmetry breaking and the appearance of a non-trivial vacuum. We first review the basic example of the Coleman-Weinberg mechanism, scalar Quantum Electrodynamics, in a perturbative regime where the scalar particle becomes massive through photon loops. We then present the main results of this article, what we name the gravitational Coleman-Weinberg mechanism: we analyse the same effect in a gravitational theory without explicit energy scales at tree-level. Finally, we also study the mechanism for two scalar fields in the mentioned gravitational theory. We will derive the gravitational Coleman-Weinberg potentials, analyse the parameter space where we have a symmetry breaking, and obtain the value of the corresponding scalar masses.
A
bstract
We analyze heavy states from generic ultraviolet completions of the Standard Model in a model-independent way and investigate their implications on the low-energy couplings of the ...electroweak effective theory. We build a general effective Lagrangian, implementing the electroweak symmetry breaking SU(2)
L
⊗ SU(2)
R
→ SU(2)
L
+
R
with a non-linear Nambu-Goldstone realization, which couples the known particles to the heavy states. We generalize the formalism developed in previous works
1
,
2
to include colored resonances, both of bosonic and fermionic type. We study bosonic heavy states with
J
P
= 0
±
and
J
P
= 1
±
, in singlet or triplet SU(2)
L
+
R
representations and in singlet or octet representations of SU(3)
C
, and fermionic resonances with
J
=
1
2
that are electroweak doublets and QCD triplets or singlets. Integrating out the heavy scales, we determine the complete pattern of low-energy couplings at the lowest non-trivial order. Some specific types of (strongly- and weakly-coupled) ultraviolet completions are discussed to illustrate the generality of our approach and to make contact with current experimental searches.
The anomalous 〈VVP〉 Green function and related form-factors (π0→γ⁎γ⁎ and τ−→X−ντ vector form-factors, with X−=(KKπ)−, φ−γ, (φV)−) are analyzed in this letter in the large-NC limit. Within the single ...(vector and pseudoscalar) resonance approximation and the context of Resonance Chiral Theory, we show that all these observables overdetermine in a consistent way a unique set of compatible high-energy constraints for the resonance couplings. This result is in agreement with analogous relations found in the even intrinsic-parity sector of QCD like, e.g., FV2=3F2. The antisymmetric tensor formalism is considered for the spin-one resonance fields. Finally, we have also worked out and provide here the relation between the two bases of odd intrinsic-parity Lagrangian operators commonly employed in the literature.
Software tools for computing EW chiral amplitudes Martínez Martín, Javier; Sanz Cillero, Juan José
Nuclear and particle physics proceedings,
March 2023, 2023-03-00, Volume:
324-329
Journal Article
Peer reviewed
We present an implementation of the Electroweak Chiral Lagrangian (also denoted as Higgs Effective Theory) in several high energy physics Mathematica packages. In particular, we implement the bosonic ...part of the electoweak Lagrangian up to next-to-leading order for FeynRules, FeynArts and FeynCalc. These tools are publicly available and can be used to readily calculate the Feynman rules and amplitudes in the theory.
Padé approximants and resonance poles Masjuan, Pere; Sanz-Cillero, Juan José
The European physical journal. C, Particles and fields,
10/2013, Volume:
73, Issue:
10
Journal Article
Peer reviewed
Open access
Based on the mathematically well defined Padé theory, a theoretically safe new procedure for the extraction of the pole mass and width of a resonance is proposed. In particular, thanks to the ...Montessus de Ballore theorem we are able to unfold the second Riemann sheet of an amplitude to search for the position of the resonance pole in the complex plane. The method is systematic and provides a model-independent treatment of the prediction and the corresponding errors of the approximation. Likewise, it can be used in combination with other well-established approaches to improve future determinations of resonance parameters.
A
bstract
We study the
η
-
η
′ mixing up to next-to-next-to-leading-order in U(3) chiral perturbation theory in the light of recent lattice simulations and phenomenological inputs. A general ...treatment for the
η
-
η
′ mixing at higher orders, with the higher-derivative, kinematic and mass mixing terms, is addressed. The connections between the four mixing parameters in the two-mixing-angle scheme and the low energy constants in the U(3) chiral effective theory are provided both for the singlet-octet and the quark-flavor bases. The axial-vector decay constants of pion and kaon are studied in the same order and confronted with the lattice simulation data as well. The quark-mass dependences of
m
η
,
m
η
′
and
m
K
are found to be well described at next-to-leading order. Nonetheless, in order to simultaneously describe the lattice data and phenomenological determinations for the properties of light pseudoscalars
π, K, η
and
η
′, the next-to-next-to-leading order study is essential. Furthermore, the lattice and phenomenological inputs are well reproduced for reasonable values of low the energy constants, compatible with previous bibliography.
Using the Resonance Chiral Theory Lagrangian, we perform a calculation of the vector form factor of the pion at the next-to-leading order (NLO) in the 1/
N
C
expansion. Imposing the correct QCD ...short-distance constraints, one fixes the amplitude in terms of the pion decay constant
F
and resonance masses. Its low momentum expansion determines then the corresponding
and
low-energy chiral couplings at NLO, keeping control of their renormalization scale dependence. At
μ
0
= 0.77 GeV, we obtain
L
9
(
μ
0
) = (7.9 ± 0.4) ∙ 10
−3
and
C
88
(
μ
0
) −
C
90
(
μ
0
) = (−4.6 ± 0.4) ∙ 10
−5
.
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