119760786
Covariant wave functions with invariant helicity for massless particles
Considering a wave functionψ for a massless particle, transforming according to an arbitrary irreducible representation (IR) of the homogeneous Lorentz group, we determine the basic conditions forψ to be an eigenfunction with a specified valueλ of the helicity inall Lorentz frames. The method used is direct and elementary, requiring no knowledge of the IR's of the Poincaré group. It is shown that there existsno invariant helicity state in unitary representations of the Lorentz group, and one such state in any non-unitary representation (with one extra in special cases).
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.
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...
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.
120740147
Relativistic wave equations: proper Lorentz invariance and invariance under discrete transformations
Considering the standard form i∂ψ/∂t=Hψ [with ψ transforming according to D(0,s)⊕D(s,0)] of wave equations for free particles of arbitrary spin, we determined in a recent paper the admissible forms of H consistent with invariance of the equation under the Poincare group and under T, C, and P. Here we show that even if T and C invariance is not imposed, the admissible Hamiltonians are the same (apart from one extra possibility H = E). Expressed differently, except for the trivial case H = E, invariance of free‐particle equations under the connected Poincare group and P implies T and C also.
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.
118428442
Associated production of vector gauge boson & graviton to NLO QCD
In this talk, we discuss the next-to-leading order (NLO) QCD corrections to the associated production of the vector gauge boson (Z/W ± ) and the graviton in the large extra dimension model, namely the ADD model, at the LHC. After a brief review of the ADD model, we present the importance of QCD correction to these preferred processes and the impact of the QCD corrections on the total cross sections as well as the differential distr ibutions of the gauge bosons. The dependence of the cross sections on the arbitrary factorization s cale is studied and the reduction in the scale uncertainties at NLO level is shown. The ultraviolet sensitivity of the theoretical prediction is also presented.
121522381
GLUONIC CONTRIBUTIONS TO SPIN-DEPENDENT WEAK STRUCTURE FUNCTIONS: METHOD OF FACTORIZATION
We compute the gluonic contributions to the spin-dependent weak structure functions (i=1, 3, 4), using the factorization theorem in the minimal subtraction scheme, . We have considered the most general case where the quark flavor masses are distinguished and the gluons are off mass shell. The gluonic contribution to the first moment of is found to vanish and do not receive leading order gluonic contribution. These results are shown to be free of mass singularities.
14620818
Unparticle physics at hadron collider via dilepton production
The scale invariant unparticle physics recently proposed by Georgi could manifest at low energies as non-integral number dU of invisible particles. Unparticles if existing, could couple to the Standard Model fields and consequently affect the collider phenomenology. We consider the DY process to explore effects of the peculiar propagator of the scalar and tensor unparticle operators. To probe these effects at hadron collider one needs to go beyond LO in QCD and hence the quantitative impact of QCD corrections for unparticle physics at LHC is investigated. We present the K-factors at LHC. Inclusion of QCD corrections to NLO stabilises the cross section with respect to scale variations.
11061527
{chi}{sub 1} and polarization asymmetries for quarkonia at high orders in nonrelativistic QCD
We study doubly polarized asymmetries of {bar c}c and {bar b}b mesons in hadroproduction and photoproduction at low transverse momentum in nonrelativistic QCD to high orders in the relative velocity of the pair, v. We give the complete set of expressions required for the asymmetries up to order v{sup 9}. The asymmetries in the production of {eta}{sub c,b} states are a stable measure of the polarized gluon densities. The asymmetries for {chi}{sub c,b}, J/{psi}, {psi}{sup {prime}}, and the various {Upsilon} states are stringent tests of the NRQCD scaling relations. {copyright} {ital 1997} {ital The American Physical Society}
255052
Diphoton signals in theories with large extra dimensions to NLO QCD at hadron colliders
We present a full next-to-leading order (NLO) QCD corrections to diphoton production at the hadron colliders in both standard model and ADD model. The invariant mass and rapidity distributions of the diphotons are obtained using a semi-analytical two cut-off phase space slicing method which allows for a successful numerical implementation of various kinematical cuts used in the experiments. The fragmentation photons are systematically removed using smooth-cone-isolation cuts on the photons. The NLO QCD corrections not only stabilise the perturbative predictions but also enhance the production cross section significantly.