Non-commutative standard model: model building

A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by _U* (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just . We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherent CP violation and new neutrino interactions. Received: 23 January 2003, Published online: 18 June 2003     

Four-fermion production at $\gamma\gamma$ colliders: 2. Radiative corrections in double-pole approximation

The electroweak radiative corrections to within the electroweak standard model are calculated in double-pole approximation (DPA). Virtual corrections are treated in DPA, leading to a classification into factorizable and non-factorizable contributions, and real-photonic corrections are based on complete lowest-order matrix elements for . Soft and collinear singularities appearing in the virtual and real corrections are combined alternatively in two different ways, namely by using the dipole subtraction method or by applying phase-space slicing. The radiative corrections are implemented in a Monte Carlo generator called Coffer - the computer code can be obtained from the authors upon request - which optionally includes anomalous triple and quartic gauge-boson couplings in addition and performs a convolution over realistic spectra of the photon beams. A detailed survey of numerical results comprises corrections to integrated cross sections as well as to angular, energy, and invariant-mass distributions. Particular attention is paid to the issue of collinear safety in the observables.Received: 3 June 2005, Published online: 5 August 2005     

The $Z \rightarrow \gamma \gamma,\;gg$ decays in the non-commutative standard model

On non-commutative spacetime, the standard model (SM) allows new, usually SM forbidden, triple gauge boson interactions to occur. In this letter we propose the SM strictly forbidden and decay modes coming from the gauge sector of the non-commutative standard model (NCSM) as a place where non-commutativity could be experimentally discovered. Received: 2 July 2002, Revised: 28 February 2003, Published online: 18 June 2003     

Strong and electroweak interactions and their unification with non-commutative space-time

Quantum field theories based on non-commutative space-time (NCQFT) have been extensively studied recently. However no NCQFT model which can uniquely describe the strong and electroweak interactions has been constructed. This prevents one to make a consistent and systematic study of non-commutative space-time. In this work we construct a NCQFT model based on the trinification gauge group . A unique feature of this model, that all matter fields (fermions and Higgs bosons) are assigned to (anti-) fundamental representations of the factor SU(3) groups, allows us to construct a NCQFT model for strong and electroweak interactions and their unification without ambiguities. This model provides an example which allows one to make a consistent and systematic study of non-commutative space-time phenomenology. We also comment on some related issues regarding extensions to E₆ and models. Received: 18 September 2002 / Revised version: 21 February 2003 / Published online: 5 May 2003     

Exclusive radiative and electroweak b\to d and b\to s penguin decays at NLO

We provide standard model expectations for the rare radiative decays , and , and the electroweak penguin decays and at the next-to-leading order (NLO), extending our previous results to transitions. We consider branching fractions, isospin asymmetries and direct CP asymmetries. For the electroweak penguin decays, the lepton-invariant mass spectrum and forward-backward asymmetry is also included. Radiative and electroweak penguin transitions in are mainly interesting in the search for new flavor-changing neutral current interactions, but in addition the decays provide constraints on the CKM parameters . The potential impact of these constraints is discussed.Received: 16 January 2005, Published online: 16 March 2005 Corresponding author: Th. Feldmann     

Electroweak precision constraints on vector-like fermions

We calculate the oblique electroweak corrections and confront them with the experiments in an extension of the standard model. The new fields added are a vector-like weak doublet and a singlet fermion. After electroweak symmetry breaking there is a mixing between the components of the new fields, but there is no mixing allowed with the standard fermions. Four electroweak parameters, , , W and Y, are presented in the formalism of Barbieri et al.; these are the generalization of the Peskin–Takeuchi S, T and U. The vector-like extension is slightly constrained. requires the new neutral fermion masses not to be very far from each other, allowing for higher mass differences for higher masses and smaller mixing. , W and Y give practically no constraints on the masses. This extension can give a positive contribution to , allowing for a heavy Higgs boson in electroweak precision tests of the standard model.     

Dilaton field induces a commutative D<Emphasis Type="Italic">p</Emphasis>-brane coordinate

It is well known that the space-time coordinates and the corresponding Dp-brane world-volume become non-commutative when the ends of the open string are attached to a Dp-brane with the Neveu-Schwarz background field . In this paper, we extend these considerations by including an additional dilaton field , linear in . In that case, the conformal part of the world-sheet metric becomes a new non-commutative variable, while the coordinate in the direction orthogonal to the hyper plane becomes commutative. Received: 15 November 2004, Revised: 11 May 2005, Published online: 6 October 2005 PACS: . Work supported in part by the Serbian Ministry of Science and Environmental Protection, under contract No. 1486.     

Anomalous gauge-boson couplings and the Higgs-boson mass

We study anomalous gauge-boson couplings induced by a locally SU(2) × U(1) invariant effective Lagrangian containing ten operators of dimension six built from boson fields of the standard model (SM) before spontaneous symmetry breaking (SSB). After SSB some operators lead to new three- and four-gauge-boson interactions, some contribute to the diagonal and off-diagonal kinetic terms of the gauge bosons, to the kinetic term of the Higgs boson and to the mass terms of the W and Z bosons. This requires a renormalisation of the gauge-boson fields, which, in turn, modifies the charged- and neutral-current interactions, although none of the additional operators contain fermion fields. Also the Higgs field must be renormalised. Bounds on the anomalous couplings from electroweak precision measurements at LEP and SLC are correlated with the Higgs-boson mass m_H. Rather moderate values of anomalous couplings allow m_H up to 500 GeV. At a future linear collider the triple-gauge-boson couplings and ZWW can be measured in the reaction . We compare three approaches to anomalous gauge-boson couplings: the form-factor approach, the addition of anomalous-coupling terms to the SM Lagrangian after and, as outlined above, before SSB. The translation of the bounds on the couplings from one approach to another is not straightforward. We show that it can be done for the process by defining new effective and ZWW couplings.Received: 8 June 2004, Revised: 26 January 2005, Published online: 8 June 2005     

Electroweak precision observables in the MSSM with non-minimal flavor violation

The leading corrections to electroweak precision observables in the MSSM with non-minimal flavor violation (NMFV) are calculated and the effects on M _W and are analyzed. The corrections are obtained by evaluating the full one-loop contributions from the third and second generation scalar quarks, including the mixing in the scalar top and charm, as well as in the scalar bottom and strange sector. Furthermore the leading corrections to the mass of the lightest MSSM Higgs-boson, m _h , is obtained. The electroweak one-loop contribution to M _W can amount up to 140 MeV and up to 70 x 10^-5 for , allowing one to set limits on the NMFV parameters. The corrections for m _h are not significant for moderate generation mixing.Received: 1 July 2004, Published online: 13 October 2004     

Seesaw induced electroweak scale, the hierarchy problemand sub-eV neutrino masses

We describe a model for the scalar sector where all interactions occur either at an ultra-high scale, Λ_U~10¹⁶-10¹⁹ GeV, or at an intermediate scale, Λ_I = 10⁹-10¹¹ GeV. The interaction of physics on these two scales results in an SU(2) Higgs condensate at the electroweak (EW) scale, Λ_EW, through a seesaw-like Higgs mechanism, , while the breaking of the SM SU(2) x U(1) gauge symmetry occurs at the intermediate scale Λ_I . The EW scale is, therefore, not fundamental but is naturally generated in terms of ultra-high energy phenomena and so the hierarchy problem is alleviated. We show that the class of such "seesaw Higgs" models predict the existence of sub-eV neutrino masses which are generated through a "two-step" seesaw mechanism in terms of the same two ultra-high scales: . The neutrinos can be either Dirac or Majorana, depending on the structure of the scalar potential. We also show that our seesaw Higgs model can be naturally embedded in theories with tiny extra dimensions of size fm, where the seesaw induced EW scale arises from a violation of a symmetry at a distant brane; in particular, in the scenario presented there are seven tiny extra dimensions. Received: 19 August 2004, Revised: 27 July 2005, Published online: 14 October 2005     

Flavor changing neutral currents from lepton and <Emphasis Type="Italic">B</Emphasis> decays in the two Higgs doublet model

Constraints on the whole spectrum of lepton flavor violating vertices are shown in the context of the standard two Higgs doublet model. The vertex involving the e- mixing is much more constrained than the others, and the decays proportional to such a vertex are usually very suppressed. On the other hand, bounds on the quark sector are obtained from leptonic decays of the B_d,s⁰ mesons and from . We emphasize that although the B_d⁰- mixing restricts severely the d-b mixing vertex, the upper bound for this vertex could still give a sizable contribution to the decay with respect to the standard model contribution, from which we see that such a vertex could still play a role in the phenomenology.Received: 16 September 2004, Published online: 26 April 2005PACS: 12.60.Fr, 12.15.Mm, 12.15.Ff, 11.30.Hv     

Non-hermitian quantum mechanics in non-commutative space

A recent investigation of the possibility of having a -symmetric periodic potential in an optical lattice stimulated the urge to generalize non-hermitian quantum mechanics beyond the case of commutative space. We thus study non-hermitian quantum systems in non-commutative space as well as a -symmetric deformation of this space. Specifically, a -symmetric harmonic oscillator together with an iC(x ₁+x ₂) interaction are discussed in this space, and solutions are obtained. We show that in the deformed non-commutative space the Hamiltonian may or may not possess real eigenvalues, depending on the choice of the non-commutative parameters. However, it is shown that in standard non-commutative space, the iC(x ₁+x ₂) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not -symmetric. A complex interacting anisotropic oscillator system also is discussed.     

Comment on triple gauge boson interactionsin the non-commutative electroweak sector

In this comment we present an analysis of electroweak neutral triple gauge boson couplings projected out of the gauge sector of the extended non-commutative standard model. A brief overview of the current experimental situation is given.Received: 31 July 2003, Published online: 20 November 2003     

One-loop electroweak factorizable correctionsfor the Higgsstrahlung at a linear collider

We present standard model predictions for the four-fermion reaction being one of the best detection channels of a low-mass Higgs boson produced through the Higgsstrahlung mechanism at a linear collider. We include leading virtual and real QED corrections due to initial state radiation and a modification of the Higgs- Yukawa coupling, caused by the running of the b-quark mass, for . The complete electroweak corrections to Z-Higgs production and to the Z-boson decay width, as well as the remaining QCD and EW corrections to the Higgs decay width, as can be calculated with the program HDECAY, are taken into account in the double-pole approximation. Received: 17 March 2005, Revised: 30 March 2005, Published online: 30 August 2005 Work supported in part by the Polish State Committee for Scientific Research in years 2004-2006 as a research grant, by the European Community's Human Potential Program under contracts HPRN-CT-2000-00149 Physics at Colliders and CT-2002-00311 EURIDICE, and by DFG under Contract SFB/TR 9-03.     

The experimental status of Higgs Sector of the Standard Electroweak Model at the end of the LEP-SLC era

A method is proposed to calculate the confidence level for agreement of data with the Higgs sector of the Standard Model (SM). This is done by combining information from direct and indirect Higgs Boson searches. Good agreement with the SM is found for GeV using the observables most sensitive to m_H: A_l and m_W. In particular, quantum corrections, as predicted by the SM, are observed with a statistical significance of forty-four standard deviations. However, apparent deviations from the SM of 3.7 and 2.8 are found for the Z and right-handed Zb couplings respectively. The maximum confidence level for agreement with the SM of the entire data set considered is for GeV. The reason why confidence levels about an order of magnitude higher than this have been claimed for global fits to similar data sets is explained.Received: 8 September 2004, Revised: 22 March 2005, Published online: 18 May 2005     

No UV/IR mixing in unitary space-time non-commutative field theory

In this article we calculate several divergent amplitudes in -theory on non-commutative space-time ( ) in the framework of interaction-point time-ordered perturbation theory (IPTOPT), continuing work done in hep-th/0209253. On the ground of these results we find corresponding Feynman rules that allow for a much easier diagrammatic calculation of amplitudes. The most important feature of the present theory is the absence of the UV/IR mixing problem in all amplitudes calculated so far. Although we are not yet able to give a rigorous proof, we provide a strong argument for this result to hold in general. Together with the Feynman rules we found, this opens promising vistas onto the systematic renormalization of non-commutative field theories.Received: 26 August 2003, Published online: 20 November 2003V. Putz: Work supported by the Fonds zur Förderung der Wissenschaften (FWF) under contract P15015-TPH.     

Analysis of $B^{0}_{d} \to \phi K^{{*0}} $ decay mode with supersymmetry

Motivated by the recent measurement of a low longitudinal polarization fraction in the decay mode , which appears not to be in agreement with the standard model expectation, we analyze this mode in the minimal supersymmetric standard model with the mass insertion approximation. Within the standard model, with the factorization approximation, the longitudinal polarization is expected to be . We find that this anomaly can be explained in the minimal supersymmetric standard model with either the LR or the RL mass insertion approximation. PACS. 13.25.Hw, 11.30.Er, 12.60.Jv Received: 9 May 2005, Revised: 26 July 2005, Published online: 30 August 2005     

Probing signals of the littlest Higgs model via the WW fusion processes at the high energy e + e- collider

In the framework of the littlest Higgs (LH) model, we consider the processes and , and we calculate the contributions of new particles to the cross sections of these processes in the future high energy e ⁺ e^- collider (ILC) with TeV. We find that, with reasonable values of the free parameters, the deviations of the cross sections for the processes from their SM values might be comparable to the future ILC measurement precision. The contributions of the light Higgs boson H⁰ to the process are significantly large in all of the parameter space preferred by the electroweak precision data, which might be detected in the future ILC experiments. However, the contributions of the new gauge bosons B_H and Z_H to this process are very small.Received: 22 February 2005, Revised: 27 April 2005, Published online: 6 July 2005PACS: 12.60.Cn, 14.70.Pw, 14.80.Cp     

Electroweak corrections uncertainty on the <Emphasis Type="Bold">W</Emphasis> mass measurement at LEP

The systematic uncertainty on the W mass and width measurement resulting from the imperfect knowledge of electroweak radiative corrections is discussed. The intrinsic uncertainty in the 4-f generator used by the DELPHI Collaboration is studied following the guidelines of the authors of YFSWW, on which its radiative corrections part is based. The full DELPHI simulation, reconstruction and analysis chain is used for the uncertainty assessment. A comparison with the other available 4-f calculation implementing DPA corrections, RacoonWW, is also presented. The uncertainty on the W mass is found to be below 10 MeV for all the WW decay channels used in the measurement. Received: 15 June 2005, Revised: 22 August 2005, Published online: 6 October 2005     

General formulation for proton decay rate in minimal supersymmetric SO(10) GUT

We give an explicit formula for the proton decay rate in the minimal renormalizable supersymmetric (SUSY) SO(10) model. In this model, the Higgs fields consist of the 10 and SO(10) representations in the Yukawa interactions with matter and of the 10, , 126, and 210 representations in the Higgs potential. We present all the mass matrices for the Higgs fields contained in this minimal SUSY SO(10) model. Finally, we discuss the threshold effects of these Higgs fields on the gauge coupling unification.Received: 8 March 2005, Published online: 8 June 2005PACS: 12.10.-g, 12.10.Dm, 12.10.Kt