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.
122212810
Carruthers’ theorem for any spin and parastatistics
SummaryIt is shown that Carruthers’ theorem (that particle multiplets of half-integral isospin cannot be self-conjugate) holds even for particles which obey the general parastatistics instead of the usual Bose or Fermi statistics.RiassuntoSi dimostra che il teorema di Carruther (sull’impossibilità di autoconiugazione per multipletti di particelle con isospin semintero) value anche per particelle che obbediscono solo alla parastatistica generale invece che alla statistica consueta di Bose o Fermi.
118727721
Semi-coherent states of the quantum harmonic oscillator
SummaryIt is shown that there exists for the quantum harmonic oscillator a large class of « semi-coherent » states, which represent harmonically oscillating wave packets whose « spread » or « size » remains constant. These states are different from the coherent states in not having the minimum value 1/2ħ for the uncertainty product Δx·Δp.RiassuntoSi dimostra che esiste per l’oscillatore armonico quantistico una grande varietà di stati « semicoerenti », che rappresentano pacchetti d’onde oscillanti armonicamente, la cui « diffusione » o « dimensione » rimane costante. Questi stati differiscono dagli stati coerenti per non avere il valore minimo 1/2ħ per il prodotto d’indeterminazione Δx·Δp.РезюмеПоказывается, что для квантового гармонического осци ллятора существует б ольшой класс « полукоreр ентньIх» состояний, кот орые предст « полукоreрентньIх» состо яний, которые предста вляют гармони чески осциллирующие волновые пакеты, «разброс » или «разме ры » которых остаются постояннымгармонич ески осциллирующие волновые пакеты, «раз брос » или «размеры » которых остаются постоянными. Эти сост ояния отличаются от к огерентных состояни й тем, что не имеют мини мальной величины Р дл я произве или «размеры » которых остаются постоянными. Эти состояния отлича ются от когерентных с остояний тем, что не им еют минимальной вели чины Р для произведен ия неопределенносте й состояния отличаютс я от когерентных сост ояний тем, что не имеют минимальной величин ы Р для произведения н еопределенностей что не имеют минималь ной величины Р для про изведения неопредел енностей неопределенностей Ах Ар.
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).
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}
18381800
Can polarized Drell-Yan shed more light on the proton spin
We analyze polarized Drell-Yan process using the factorization method and derive operator definitions for polarized parton distribution functions. We demonstrate that a factorization analogous to that in the unpolarized Drell-Yan case holds in this process. We study the leading order gluonic contribution to the first moment of polarized Drell-Yan function and show that it is consistent with the results obtained from polarized deep inelastic scattering.
54538817
Quark and gluon spin-2 form factors to two-loops in QCD
A bstractWe present complete two-loop radiative corrections to the graviton-quark-antiquark form factor G∗ → q$ \overline{q} $ and graviton-gluon-gluon form factor G∗ → g g in SU(N) gauge theory with nf light flavours using d-dimensional regularisation to all orders in ε = d − 4. Thisisanimportantingredienttonext-to-next-to-leadingorderQCDcorrections to hadronic scattering processes in models with large extra-dimensions where Kaluza-Klein graviton modes couple to Standard Model fields. We show that these form factors obey Sudakov integro-differential equation and the resulting cusp, collinear and soft anomalous dimensions coincide with those of electroweak vector boson and gluon form factors. We also find the universal behaviour of the infrared singularities in accordance with the proposal by Catani.
119270253
NNLO QCD corrections to the resonant sneutrino/slepton production at hadron colliders
We present a complete next to next to leading order QCD corrections to the resonant sneutrino and charged slepton production cross sections at hadronic colliders such as the Tevatron and the Large Hadron Collider within the context of R-parity violating supersymmetric model. We have demonstrated the role of these corrections in reducing uncertainties resulting from renormalisation and factorisation scales and thereby making our predictions reliable. We have incorporated soft gluon effects at N 3 LO level in order to study the stability of our results under perturbation. The NNLO corrections are found to be large and significant. The results obtained in this article are also applicable to resonance production of any color-neutral scalar.
121500354
Gluonic corrections to spin dependent weak structure functions
We compute gluonic corrections to the spin dependent weak structure functions g1, g3 and g4. g1WP is found o be directly proportional to the singlet part of g1μP and is ∑i(Δqi + Δqi−αsΔg/2π). In the gluon sector, g3 and g4 are both free from infrared and collinear divergences since they do not receive any gluonic corrections. Hence the Callan-Gross relation in the weak sector is nor corrected by the g→q, q subprocess. g3WP measures Δuv + Δdv. The distribution functions are identified with corresponding OPE matrix elements.