Noncommutative Standard Model Research Articles

Lepton Pair Production in the Non-Commutative Standard Model with Polarized $${{e}^{ + }}{{e}^{ - }}$$ Beams

Lepton Pair Production in the Non-Commutative Standard Model with Polarized $${{e}^{ + }}{{e}^{ - }}$$ Beams

Study of hadron production through pair annihilation in the noncommutative standard model

Study of hadron production through pair annihilation in the noncommutative standard model

Higgs pt distribution in Higgs + jet production at hadron colliders within the noncommutative effective standard model

We use the noncommutative Higgs effective standard model to make a phenomenological prediction for the transverse momentum distribution of the Higgs boson produced in association with a jet at hadron colliders. We calculate at leading order in the noncommutative parameter [Formula: see text] as well as leading order in the strong coupling [Formula: see text], the one-loop [Formula: see text] distribution of the Higgs boson. As in the standard model, the fixed-order distribution suffers from large logarithms at small [Formula: see text] which require an all-orders resummation. We find that the large-[Formula: see text] region of the distribution is strongly affected by the non-commutativity, while small-[Formula: see text] region is not. Following this observation, we propose a simple matching method that allows us to compute a result that is also valid at small [Formula: see text] obtained with standard-model parton showers such as Pythia 8. We also compare our results with the next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) distributions in the standard model, in order to assess the importance of higher-order effects in the search for non-commutativity at colliders.

Vector heavy quarkonia production in gluon fragmentation in the ordinary and noncommutative standard model

Study of the mechanism of heavy quarkonia production is a powerful tool for a better understanding of the dynamics of strong interactions and probably to search for new physics. It is well-known that the fragmentation mechanism is dominant for heavy quarkonia production and forms the nonperturbative aspect of hadron production. Since the main contribution of [Formula: see text] production in high energy processes results from the gluon fragmentation, through this work, we study the fragmentation mechanism of gluon into S-wave vector heavy charmonium [Formula: see text] at lowest order perturbative QCD and extend our work to the noncommutative standard model. To investigate the effects of space–time noncommutativity, we employ the Seiberg–Witten maps. Our results show that the noncommutative effects are considerable, specifically when the gluon transverse momentum is small; [Formula: see text][Formula: see text]GeV.

Extensions of the noncommutative Standard Model and the weak order one condition

In the derivation of the Standard Model from the axioms of noncommutative geometry the scalar sector is given by a finite Dirac operator which has to satisfy the first-order condition. However, the general solution to this constraint still has unphysical terms which must be fine-tuned to zero. Some of them can be removed by the so-called second-order condition. However, the first-order condition generally does not survive in extensions to models with gauge groups larger that U(1) × SU(2) × SU(3). In this paper we show that in the U(1)B–L-extension one can implement a weaker form of the first-order condition which, we argue, is necessary in order for noncommutative Gauge theory to make sense at all, and that this condition reduces the amount of fine-tuning to the off-diagonal terms in the Yukawa mass matrices for the leptons and quarks. It follows that the weak order one condition imposed on a the B–L-extended model yields exactly the same constraint as the much more restrictive, and, we believe, less well motivated, second-order condition imposed on the Standard Model alone.

Bounds on the scale of noncommutativity from mono photon production in ATLAS Runs -1 and -2 experiments at LHC energies

Leading order study of direct photon production from proton–proton collisions, in the framework of Minimal (Seiberg–Witten) Non-Commutative Standard Model (NCSM), taking into account the Earth-rotation effects. We found that relative non-commutative contributions increase significantly at very high photon transverse momentum. Therefore, using Run-1 ([Formula: see text] TeV) and Run-2 ([Formula: see text] TeV) ATLAS experimental data of inclusive isolated prompt photon cross-section, TeV-Scale bounds of the non-commutativity (NC) parameter are obtained. For space-space non-commutativity, we obtain: [Formula: see text][Formula: see text]TeV, and for space-time non-commutativity, we obtain : [Formula: see text][Formula: see text]TeV.

Noncommutative geometry, the Lorentzian standard model, and its B−L extension

We explore the 1-loop renormalization group flow of two models coming from a generalization of the Connes-Lott version of Noncommutative Geometry in Lorentzian signature: the Noncommutative Standard Model and its B-L extension. Both make predictions on coupling constants at high energy, but only the latter is found to be compatible with the top quark and Higgs boson masses at the electroweak scale. We took into account corrections introduced by threshold effects and the relative positions of the Dirac and Majorana neutrino mass matrices and found them to be important. Some effects of 2-loop corrections are briefly discussed. The model is consistent with experiments only for a very small part of its parameter space and is thus predictive. The masses of the $Z'$ and B-L breaking scalar are found to be of the order $10^{14}$ GeV.

Renormalizing Yukawa interactions in the standard model with matrices and noncommutative geometry

We show that gauge-independent terms in the one-loop and multi-loops β-functions of the standard model can be exactly computed from the Wetterich functional renormalization of a matrix model. Our framework is associated to the finite spectral triple underlying the computation of the standard model Lagrangian from the spectral action of noncommutative geometry. This matrix-Yukawa duality for the β-function is a first hint towards understanding the renormalization of the noncommutative standard model conceptually, and provides a novel computational approach for multi-loop β-functions of particle physics models.

Top Quark Pair-Production in Noncommutative Standard Model

The differential cross-section of the top quark pair production via the quark-antiquark annihilation subprocess in hadron collision is calculated within the noncommutative standard model. A pure NC analytical expression for the forward-backward asymmetry at the tree level is obtained. Moreover, using recent Tevatron results from the full RUN2 data, a new lower bound on the noncommutative geometry parameter is deduced.

Probing Space-time Noncommutativity in the Bhabha Scattering

We investigate Bhabha scattering with the Seiberg-Witten expended noncommutative standard model scenario to first order of the noncommutativity parameter $\Theta_{\mu \nu }$. This study is based on the definition of the noncommutativity parameter that we have assumed. We explore the noncommutative scale $\Lambda_{_{NC}}\geq0.8$ TeV considering different machine energy ranging from $0.5$ TeV to $1.5$ TeV.

Spectral Noncommutative Geometry Standard Model and all that

We review the approach to the Standard Model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and phenomenological aspects. In particular, the bosonic spectral action and the fermionic action are discussed in detail, and how they lead to phenomenology. We also discuss the Euclidean versus Lorentz issues and how to go beyond the Standard Model in this framework.

Inferring the covariant \u0398-exact noncommutative coupling in the top quark pair production at linear colliders

A novel non-minimal interaction of neutral right-handed fermion and abelian gauge field in the covariant Θ-exact noncommutative standard model (NCSM) which is invariant under Very Special Relativity (VSR) Lorentz subgroup, opens an avenue to study the top quark pair production at linear colliders. Here the non-minimal coupling is denoted as κ and the noncommutative (NC) scale Λ. In this work, we consider two types of analysis, one is without considering helicity basis technique and another, considering helicity of the initial and final state particles. Further, the realistic electron and positron beam polarization are taken into account to measure the NC parameters. In the first case, when κ is positive and certain values of Λ, we found that a specific threshold value of machine energy (optimal energy in the units of GeV) sqrt{s_0}left(simeq 2.52 varLambda +39right) may be quite useful to look for the signature of the spacetime noncommutativity with unpolarized beam. The statistical χ2 analysis of the azimuthal anisotropy which is due to broken rotational invariance about the beam axis, is quite possible when κ takes negative value 0 > κ > −0.596 which persuade a lower limit on NC scale Λ (1.0 to 2.4 TeV) at κmax = −0.296 with 95% C.L according to luminosity ranging from 100 fb−1 to 1000 fb−1 at machine energy sqrt{s}=1.4 TeV and 3.0 TeV. In another case, we perform detailed analysis for the polarized and unpolarized electron-positron beam to probe spacetime noncommutativity in light of following observables like azimuthal anisotropy, helicity correlation, and top quark helicity left-right asymmetry. The polarization of the initial beam {Pe− , Pe+ } = {−0.8, 0.3}({−0.8, 0.6}) enhances the ranges of lower limit on Λ, i.e. 1.13 to 2.80 TeV at κmax alongside the κmax enhanced into −0.5445 (−0.607) 95%C.L accord with luminosity and machine energy. Finally, we studied the intriguing mixing of the UV and the IR by invoking a specific structure of noncommutative anti-symmetric tensor Θμν which is invariant under translational T (2) VSR Lorentz subgroup.

Azimuthal correlation function of polarized top quark in noncommutative space–time

The azimuthal correlation belongs to a class of polarization observables which vanishes at the Born term level in the standard model for the semileptonic rest frame decay of a polarized top quark t(↑)→bW+→bℓ+υℓ. In this frame, the azimuthal correlation is defined between the planes formed by the vectors (p→ℓ,p→Xb) and (p→ℓ,P→t). We calculate the azimuthal correlation function of polarized top quark in the framework of the noncommutative standard model for the first time. We find that this observable is nonzero in the leading order of noncommutative space–time. Further the appearance of the oscillatory azimuthal distribution of decay rate provides a practical possibility to test the noncommutativity in particle colliders.

Anapole Dark matter in the standard model extension and non-commutative standard model

Anapole Dark matter in the standard model extension and non-commutative standard model

Noncommutative universe and chameleon field dynamics

We consider a noncommutative standard model with a minimal coupling scalar field and a dynamical deformation between the canonical momenta of its scale factor and scalar field, and a chameleon model with a non-minimally coupling scalar field. We indicate that there is a correspondence between these two models, more specific, actually between the noncommutative parameter and the chameleon coupling strength, and also between the matter density of the chameleon model and the noncommutative geometry. In addition, the analogy constrains the type of the matter field in the chameleon model to be nearly a cosmic string-like during the inflation. Thus, the scenario enables the evolution of the universe being described by one single scalar field. That is, the effects of the chameleon and the inflaton can be described by one single scalar field which plays the role of inflaton in the very early universe and then, acts as a chameleon field. Moreover, the proposed correspondence procedure not only sets some constraints on the noncommutative parameter and the chameleon coupling constant, but also nearly specifies functions of the scalar field and its potential.

Lorentz violation parameters and noncommutative scale

We consider the noncommutative Standard Model that contains Lorentz symmetry violation as a subset of the Standard Model extension. We introduce a constant electromagnetic field as a background to derive mutual relations between the free parameters of both theories. As the Lorentz violation parameters of the Standard Model extension are extensively explored in different experiments and many stringent bounds on these parameters are available, we can find new bounds on the scale of noncommutativity of the order of a few to tens of teraelectron volts.

Minimal NCSM Direct Photon Production in Proton-antiproton Collisions

In this paper, we present the results of our calculations for the direct photons with proton-antiproton collision in Minimal Non-Commutative Standard Model at a center-of-mass energy √ s = 1.96 Tev. The analytical expression of the differential cross section of the two subprocesses is deduced after applying a series of rotation from the equatorial coordinates system to the laboratory frame. Subsequently, we have calculated the inclusive cross section in both space-space and space-time cases independently, by averaging over all unknown angles except the scattering angle and the colatitudes γ of electric-like vector $\vec {\theta }_{E}$ and magnetic-like vector $\vec {\theta }_{B}$ . Thus, comparison with the experimental CDF data of Tevatron allowed us to deduce two larges bounds on the non-commutativity parameter: $$ {\Lambda}_{bound}^{space-space} =449.93\pm 29.20\text{GeV} $$ and ${\Lambda }_{bound}^{space-time} =459.83\pm 16.40\text { GeV}$ . Moreover, the analysis between the difference experiment-theory and the purely non-commutative contribution, for γ varying between 0 ∘ to 90 ∘, allowed us to deduce a Pearson correlation coefficient: 0,58 ≤ ρ s p a c e−s p a c e ≤0,64 and 0,55 ≤ ρ s p a c e−t i m e ≤0,61. We deduce that the perpendicular to the earth rotation axis, given by γ = 90∘, is the preferred orientation of $\vec {\theta }_{E}$ and $\vec {\theta }_{B}$ .

Phenomenological study of the γγ → W+W− scattering in the minimal noncommutative standard model

We study the diboson production through scattering in the context of the noncommutative standard model and find the 95% confidence level sensitivity of the scattering cross section to the noncommutative effects. We obtained the bound for the noncommutative scale. The analysis of the differential cross sections shows that noncommutativity breaks the rotational invariance of the scattering. It was also found that the scattering is always forward-backward symmetric as in the standard model. We evaluate the diboson production cross section for some input values of the noncommutative scale and compare the numerical results with those expected from the standard model.

O(θ)Feynman rules for quadrilinear gauge boson couplings in the noncommutative standard model

We examine the electroweak gauge sector of noncommutative standard model and in particular, obtain the $\mathcal{O} \,(\theta)$ Feynman rules for all quadrilinear gauge boson couplings. Surprisingly, an electroweak-chromodynamics mixing appears in the gauge sector of noncommutative standard model, where photon as well as the neutral weak boson are coupled directly to three gluons. The phenomenological perspectives of the model in $W^-W^+ \rightarrow Z Z$ scattering are studied and it is shown that there is a characteristic oscillatory behaviour in azimuthal distribution of scattering cross sections which can be interpreted as a direct signal of noncommutative standard model. Assuming the integrated luminosity 100 $\mathrm{fb}^{-1}$, the number of $W^-W^+ \rightarrow Z Z$ subprocesses are estimated for some values of noncommutative scale $\Lambda_{\mathrm{NC}}$ at different center of mass energies and the results are compared with predictions of the standard model.

Electric dipole moment induced by CP-violating deformations in the noncommutative Standard Model

The possibility to detect the noncommutative (NC) spacetime in the electric dipole moments (EDM) experiments is studied in the effective field theory of noncommutative Standard Model (NCSM) with many additional deformations. The EDM given by the previous literatures do not have any observable effect since they are spin-independent. In this work, it is found that three of the deformed terms provide extra sources of CP violation contributed to EDM. We show that these EDMs are sensitive to the spin and thus have potential to be measured in the highly precise experiments. In particular, the EDM induced by NC spacetime may not be parallel to the direction of spin, which demonstrates the intrinsic feature of NC field theory.