scholarly journals THE SU(2) ⊗ U(1) ELECTROWEAK MODEL BASED ON THE NONLINEARLY REALIZED GAUGE GROUP

2009 ◽  
Vol 24 (14) ◽  
pp. 2639-2654 ◽  
Author(s):  
D. BETTINELLI ◽  
R. FERRARI ◽  
A. QUADRI
Keyword(s):  
Gauge Group ◽  
Dimensional Regularization ◽  
Higgs Field ◽  
Landau Gauge ◽  
Tree Level ◽  
Subtraction Procedure ◽  
Local Functional ◽  
Weinberg Angle ◽  
Electroweak Model ◽  
Intermediate Vector

The electroweak model is formulated on the nonlinearly realized gauge group SU (2) ⊗ U (1). This implies that in perturbation theory no Higgs field is present. This paper provides the effective action at the tree level, the Slavnov–Taylor identity (necessary for the proof of physical unitarity), the local functional equation (used for the control of the amplitudes involving the Goldstone bosons) and the subtraction procedure (nonstandard, since the theory is not power-counting renormalizable). Particular attention is devoted to the number of independent parameters relevant for the vector mesons; in fact, there is the possibility of introducing two mass parameters. With this choice the relation between the ratio of the intermediate vector meson masses and the Weinberg angle depends on an extra free parameter. We briefly outline a method for dealing with γ5 in dimensional regularization. The model is formulated in the Landau gauge for sake of simplicity and conciseness. The QED Ward identity has a simple and intriguing form.

scholarly journals FURTHER COMMENTS ON THE SYMMETRIC SUBTRACTION OF THE NONLINEAR SIGMA MODEL

2008 ◽  
Vol 23 (02) ◽  
pp. 211-232 ◽  
Author(s):  
DANIELE BETTINELLI ◽  
RUGGERO FERRARI ◽  
ANDREA QUADRI
Keyword(s):  
Sigma Model ◽  
Dimensional Regularization ◽  
Formal Proof ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Flat Connection ◽  
Subtraction Procedure ◽  
Feynman Rules ◽  
Local Functional ◽  
Two Parameters

Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled to the nonlinear sigma model constraint (flat connection formalism). The construction is based on a local functional equation, which overcomes the problems due to the presence (already at one loop) of nonchiral symmetric divergences. The subtraction procedure of the divergences in the loop expansion is performed by means of minimal subtraction of properly normalized amplitudes in dimensional regularization. In this paper we complete the study of this subtraction procedure by giving the formal proof that it is symmetric to all orders in the loopwise expansion. We provide further arguments on the issue that, within our subtraction strategy, only two parameters can be consistently used as physical constants.

GENERALIZATION OF MANTON’S CONSTRUCTION OF THE WEINBERG-SALAM MODEL WITH A GAUSS-BONNET TERM

1992 ◽  
Vol 07 (31) ◽  
pp. 7741-7752 ◽  
Author(s):  
CHRISTINE BERTRAND ◽  
RICHARD KERNER ◽  
SALVATORE MIGNEMI
Keyword(s):  
Gauge Group ◽  
Higgs Mass ◽  
Dimensional Space ◽  
Internal Space ◽  
Yang Mills ◽  
Weinberg Angle ◽  
Definition Of ◽  
The Masses ◽  
Electroweak Model ◽  
Bonnet Term

In a paper1 published in 1979 Manton has derived the bosonic sector of the Weinberg-Salam electroweak model by considering the Yang-Mills Lagrangian on a six-dimensional space M4×S2. The model turned out to be very rigid and identified the Weinberg angle with the angle between two neighbor roots in the Cartan diagram of the gauge group. leading to θW=60° for SU(3), θW=45° for O(5) and θW=30° for G2 and to the equality of the masses of the Z particle and of the Higgs boson. We generalize this model by identifying the Yang-Mills Lagrangian with a part of the Einstein-Hilbert Lagrangian on the fibre bundle P(M4×S2), and by adding to it a Gauss-Bonnet invariant. which produces new terms, quartic and cubic in Fμν. This in turn modifies the definition of the Weinberg angle and the Higgs mass. The new free parameter is the dimensional factor in front of the Gauss-Bonnet term. We discuss the values of MW, MZ and MH in function of this parameter and the radii of the internal space S2 of the gauge group G. Realistic values can be obtained if the Gauss-Bonnet term contributes to the Lagrangian with a negative sign.

scholarly journals Color-kinematic duality in ABJM theory without amplitude relations

2017 ◽  
Vol 32 (02n03) ◽  
pp. 1750002
Author(s):  
Allic Sivaramakrishnan
Keyword(s):  
Gauge Group ◽  
Explicit Form ◽  
Tree Level ◽  
Abjm Theory ◽  
Gauge Freedom

We explicitly show that the Bern–Carrasco–Johansson color-kinematic duality holds at tree level through at least eight points in Aharony–Bergman–Jafferis–Maldacena theory with gauge group [Formula: see text]. At six points we give the explicit form of numerators in terms of amplitudes, displaying the generalized gauge freedom that leads to amplitude relations. However, at eight points no amplitude relations follow from the duality, so the diagram numerators are fixed unique functions of partial amplitudes. We provide the explicit amplitude-numerator decomposition and the numerator relations for eight-point amplitudes.

scholarly journals Gauge-fixed Lattice QCD and the dispersion relation of Wilson fermions

2022 ◽  
Vol 258 ◽  
pp. 02003
Author(s):  
Giuseppe Burgio ◽  
Hannes Vogt
Keyword(s):  
Dispersion Relation ◽  
Lattice Qcd ◽  
Correlation Functions ◽  
Landau Gauge ◽  
Coulomb Gauge ◽  
Tree Level ◽  
Wilson Fermions

We show that, when investigating Wilson-fermions correlation functions on the lattice, one is bound to encounter major difficulties in defining their dispersion relation, even at tree level. The problem is indeed quite general and, although we stumbled upon it while studying Coulomb-gauge applications, it also affects gauge fixed studies in covariant gauges, including their most popular version, Landau gauge. In this paper we will discuss a solution to this problems based on a redefinition of the kinematic momentum of the fermion.

scholarly journals Zeros of amplitude in the associated production of photon and leptoquark at $$\varvec{e}$$-$$\varvec{p}$$ collider

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Priyotosh Bandyopadhyay ◽  
Saunak Dutta ◽  
Anirban Karan
Keyword(s):  
Standard Model ◽  
Gauge Group ◽  
Single Photon ◽  
Tree Level ◽  
Associated Production ◽  
The Standard Model ◽  
Radiation Amplitude ◽  
Complementary Set

AbstractThough various extensions of the Standard Model with higher gauge group predict the existence of leptoquarks, none of them has been observed yet at any of the colliders. In this paper, we study the prospect of several past and future $$e$$ e -$$p$$ p colliders like HERA, LHeC and FCC-he to detect them through radiation amplitude zero. We find that the leptoquarks showing zeros in the tree-level single-photon amplitudes at $$e$$ e -$$p$$ p collider lie within the complementary set of those exhibiting zeros at e-$$\gamma $$ γ collider. We present a PYTHIA-based analysis for HERA, LHeC and FCC-he (run II) to detect the leptoquarks with masses 70 GeV, 900 GeV and 1.5 TeV (2.0 TeV) respectively through radiation amplitude zero.

scholarly journals Matching and running sensitivity in non-renormalizable inflationary models

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jacopo Fumagalli ◽  
Marieke Postma ◽  
Melvin van den Bout
Keyword(s):  
Particle Physics ◽  
Higgs Field ◽  
Effective Field ◽  
Large Field ◽  
Tree Level ◽  
Planck Data ◽  
The Standard Model ◽  
Set Up ◽  
The One ◽  
Inflationary Models

Abstract Most of the inflationary models that are in agreement with the Planck data rely on the presence of non-renormalizable operators. If the connection to low energy particle physics is made, the renormalization group (RG) introduces a sensitivity to ultraviolet (UV) physics that can be crucial in determining the inflationary predictions. We analyse this effect for the Standard Model (SM) augmented with non-minimal derivative couplings to gravity. Our set-up reduces to the SM for small values of the Higgs field, and allows for inflation in the opposite large field regime. The one-loop beta functions in the inflationary region are calculated using a covariant approach that properly accounts for the non-trivial structure of the field space manifold. We run the SM parameters from the electroweak to the inflationary scale, matching the couplings of the different effective field theories at the boundary between the two regimes, where we also include threshold corrections that parametrize effects from UV physics. We then compute the spectral index and tensor-to-scalar ratio and find that RG flow corrections can be determinant: a scenario that is ruled out at tree level can be resurrected and vice versa.

scholarly journals ASYMPTOTICALLY SAFE WEAK INTERACTIONS

2011 ◽  
Vol 26 (21) ◽  
pp. 1571-1576 ◽  
Author(s):  
XAVIER CALMET
Keyword(s):  
General Relativity ◽  
Fixed Point ◽  
Higgs Boson ◽  
Weak Interactions ◽  
Higgs Field ◽  
Tree Level ◽  
Electroweak Interactions ◽  
Weak Scale

We emphasize that the electroweak interactions without a Higgs boson are very similar to quantum general relativity. The Higgs field could just be a dressing field and might not exist as a propagating particle. In that interpretation, the electroweak interactions without a Higgs boson could be renormalizable at the nonperturbative level because of a nontrivial fixed point. Tree-level unitarity in electroweak bosons scattering is restored by the running of the weak scale.

CP Violation in SU(3) × U(1) Electroweak Model

1997 ◽  
Vol 12 (24) ◽  
pp. 4411-4424 ◽  
Author(s):  
Tae Hoon Lee ◽  
Dae Sung Hwang
Keyword(s):  
Cp Violation ◽  
Mass Matrix ◽  
Neutral Current ◽  
Tree Level ◽  
Additional Contribution ◽  
Matrix Elements ◽  
Mixing Angle ◽  
Mixing Matrix ◽  
Electroweak Model ◽  
New Phase

We study the charged and the neutral current interactions of quarks in an SU (3)L × U (1)X electroweak model. Based on the assumption that u-type quarks coincide with their mass eigenstates, we obtain a new mixing angle θ′ and another CP violating phase δ′ in the extra heavy quark sector besides the usual Kobayashi–Maskawa mixing matrix. This new phase δ′ does not effect a change in the mass matrix elements of the [Formula: see text] systems when θ′ is small, but extra heavy quarks and gauge bosons give rise to additional contribution to the real part of the off-diagonal mass matrix elements and then the CP violation parameter ε is modified. By requiring that the tree level FCNC does not have an important effect on the [Formula: see text] and [Formula: see text] mixings in this model, we obtain a new lower bound on the mass of the extra heavy neutral gauge boson as 1.8 TeV.

IS THE INVISIBLE HADRONIC AXION ALWAYS HARMLESS?

1987 ◽  
Vol 02 (06) ◽  
pp. 409-415 ◽  
Author(s):  
HAI-YANG CHENG
Keyword(s):  
Goldstone Boson ◽  
Higgs Field ◽  
Tree Level ◽  
Hadronic Axion ◽  
Invisible Axion ◽  
The Invisible

In the Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion model, if the invisible axion is hadronized (i.e. if the axion is made to decouple from leptons at tree level), it will be accompanied by a visible real Goldstone boson which interacts with both leptons and quarks. Consequently, the Higgs field coupled to right-handed leptons must also couple to right-handed d- or u-type quark singlets. Astrophysical bounds on viable hadronic axions are discussed.

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