120399594
A simple accurate formula for the energy levels of oscillators with a quartic potential
Abstract In this note we present a simple analytical formula which reproduces the energy eigenvalues Ek(λ) of the pure quartic and quartic anharmonic oscillators with high accuracy for all values of the anharmonicity parameter λ and the level number k.
123558201
On inequivalent classes of unique‐mass–spin relativistic wave equations involving repeated irreducible representations with arbitrary multiplicities
Considering all representations S(Λ) of the proper Lorentz group which are equivalent to the direct sum of three unspecified inequivalent irreducible representations, each occurring with arbitrary multiplicity, the question is investigated as to what representations of the above class can support first‐order relativistic wave equations for unique‐spin, unique‐mass particles. An important requirement made from the outset is that the equation shall not be equivalent to any simpler one in the presence of arbitrary interactions. Strong restrictions which result on the irreducible representation content of S(Λ) are identified by a consideration of the Jordan canonical form of the matrix β0 entering such equations. With parity invariance as an additional requirement, it is shown that only 0 and 1 can be physical spins; classes of S(Λ) which can lead to new equations for these spins are determined. Finally, the restrictions which are needed to hold down the minimal degree of β0 to low values (≤6) are also determ...
121389983
A reduction of the Kemmer equation and the singular behaviour of integer-spin relativistic Hamiltonians
Abstract A reduced form of the Kemmer equation for spin one particles is derived, wherein the wave function, which has no redundant components, transforms locally (unlike in earlier reductions). The reduced Hamiltonian is identical to the spin one specialisation of the general integer-spin Hamiltonian obtained from recent investigations on second quantizable relativistic wave equations having the Hamiltonian form. It is an observation from the present analysis that while the reduced equation is well defined for the non-zero helicity projections of the wave function, the first time derivative of the zero helicity part of the reduced wave function is essentially undefined (much as if this part described a scalar particle). This helps to explain the “improper” nature of the general Hamiltonian for integer spin.
120479737
Arbitrary‐Spin Wave Equations and Lorentz Invariance
In an earlier paper it was shown that invariance of the arbitrary‐spin wave equation i(∂ψ/∂t) = Hψ [with ψ transforming according to the representation D(0,s)⊕D(s,0) under rotations, T, C, and P, and boosts in the direction of the momentum, permits four infinite classes of solutions for H. Here we show that when invariance under boosts transverse to the momentum also is imposed, just two possible forms for H survive (in the c‐number formalism). When we go over to the q‐number theory, one of these forms leads to a consistent theory for half‐integer spins only and the other for integer spins.
124611352
Quantization of wave equations for zero-mass particles with invariant helicities
SummaryIn a recent paper we constructed relativistic wave equations in the standard formi∂ψ/∂t=Hψ (ψ∼D(0,s) ⊕D(s, 0)) for zeromass particles with invariant helicities. Outlining the essential steps only, we present in this short paper the details of second quantization of these equations.RiassuntoIn un recente articolo abbiamo costruito le equazioni d’onda relativistiche nella forma normalei∂ψ/∂t=Hψ (ψ∼D(0,s) ⊕D(s, 0)) per particelle di massa nulla con elicità invarianti. Delineando solo i passaggi principali presentiamo in questo breve articolo i dettagli della seconda quantizzazione di queste equazioni.РеэюмеВ недавней работе мы сконструировали релятивистские уравнения в стандартной форме i∂ψ/∂t = Нψ (ψ∼D(0, в) ⊕ D(s, 0)) для частиц нулевой массы с инвариантными спиральностями. Намечая лищь основные зтапы, мы в зтой короткой статье приводим детали только вторичного квантования зтих уравнений.
123041317
Indecomposability of poincare-group representations over massless fields, and the quantization problem for electromagnetic potentials
Considering the little group of the Poincare group associated with a lightlike four-vector, we determine explicitly, in global form, the representation of this little group over the space of covariant massless fields transforming according to some irreducible representation D (m,n) of the homogeneous Lorentz group. The little-group representation is indecomposable and nonunitary. Exploiting the knowledge of this representation for D (½, ½) (i.e., vector fields), we prove that the vector transformation property of the electromagnetic potentials A μ together with the invariance of their two-point Wightman functions (in momentum space) make it impossible to have any nontrivial scheme of quantization in which the metric is positive-definite or even semidefinite. The proof does not involve any axioms beyond those required for the definition and invariance of the Wightman functions; in particular, we do not assume the spectral condition, local commutativity, or any equations of motion or constraint.
119301953
Graviton plus vector boson production to NLO in QCD at the LHC
Abstract We present the next-to-leading order QCD corrections to the associated production of the vector gauge boson ( Z / W ± ) and the graviton in the large extra dimension model at the LHC. We estimate the impact of the QCD corrections on the total cross sections as well as the differential distributions of the gauge bosons and find that they are significant. We also study the dependence of the cross sections on the arbitrary factorization scale and show the reduction in the scale uncertainties at NLO level. Further, we discuss the ultraviolet sensitivity of the theoretical predictions.
21626154
Three photon production to NLO+PS accuracy at the LHC
In this paper, we present the next-to-leading order predictions for three photon production in the standard model, matched to the parton shower using the MC@NLO formalism. We have studied the role of the parton shower on various observables and we show a selection of results for the $$14$$14 TeV Large Hadron Collider.
14631557
Direct Signals for Large Extra Dimensions in the Production of Fermion Pairs at Linear Colliders
We analyze the potential of the next generation of ${e}^{+}{e}^{\ensuremath{-}}$ linear colliders to search for large extra dimensions via the production of fermion pairs in association with Kaluza-Klein gravitons $(G),$ i.e., ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}f\overline{f}G.$ This process leads to a final state exhibiting a significant amount of missing energy in addition to acoplanar lepton or jet pairs. We study in detail this reaction using the full tree level contributions due to the graviton emission and the standard model backgrounds. After choosing the cuts to enhance the signal, we show that a linear collider with a center-of-mass energy of 500 GeV will be able to probe quantum gravity scales from 0.96 (0.86) up to 4.1 (3.3) TeV at a 2 $(5)\ensuremath{\sigma}$ level, depending on the number of extra dimensions.
119298265
${\cal {O}}(\alpha_s^2)$ QCD corrections to the resonant sneutrino / slepton production at LHC
We present a complete next to next to leading order QCD corrections to the resonant production of sneutrino and charged slepton at the Tevatron and the Large Hadron Collider within the context of R-parity violating supersymmetric model. We have demonstrated the role of NNLO QCD corrections in reducing uncertainties resulting from renormalisation and factorisation scales and thereby making our predictions reliable.
125974090
Tri-vector boson production at NLO with parton shower
We have studied the production of three photons at the LHC taking into account realistic experimental cuts. We have used NLO corrected QCD results for the production mechanism along with parton showering through HERWIG and Pythia. This is achieved using aMC@NLO framework which uses FKS subtracton method through MadFKS to handle infrared singularities present in the intermediate stages of NLO computation. We find that the results at NLO level in QCD with parton showering show less PDF and factorisation scale dependence.