16849310
Extra Dimensions: A View from the Top
In models with compact extra dimensions, where the Standard Model fields are confined to a 3+1 dimensional hyperplane, the tt̄ production cross-section at a hadron collider can receive significant contributions from multiple exchange of KK modes of the graviton. These are carefully computed in the well-known ADD and RS scenarios, taking the energy dependence of the sum over graviton propagators into account. Using data from Run-I of the Tevatron, 95% C.L. bounds on the parameter space of both models are derived. For Run-II of the Tevatron and LHC, discovery limits are estimated. ∗Magda.Lola@cern.ch †mathews@it.unesp.br ‡sreerup@iitk.ac.in, sreerup@mail.cern.ch §sridhar@theory.tifr.res.in In recent years, there has been tremendous interest in higher dimensional theories where the extra dimensions are compactified in such a way as to have physically interesting consequences[1]. These have been inspired by recent developments in our understanding of some non-perturbative aspects of string theories. The weak-coupling spectrum of such a theory reveals only one-dimensional strings but, in the strong coupling regime, p+1 dimensional defects embedded in the higher-dimensional spacetime — called Dp-branes — arise. These are dynamical objects analogous to solitons in field theory and are particularly interesting because it is possible to localize gauge fields on them. We then have the exciting possibility that the observable universe is a D3-brane (or 3-brane) with the Standard Model (SM) fields localized on it, leaving gravity free to propagate in the extra dimensions or bulk. In such a scenario, it becomes possible to lower the gravity/string scale to the order of a TeV, without running into contradiction with experiment. This new TeV-scale physics then provides fresh perspectives on the hierarchy problem arising in the standard electroweak theory. The first realization of these ideas is the ADD scenario proposed by Arkani-Hamed, Dimopoulos and Dvali[2], where the SM fields are localized on a 3-brane embedded in a 10-dimensional spacetime consisting of 4 non-compact Minkowski dimensions, d dimensions compactified with a large radius Rc and the remaining 6 − d dimensions compactified to the Planck length. The Planck scale MP is then related[2] to the scale MS of gravitational interactions by MP ∼ R cM S . Choosing the scale MS to be of the order of a TeV (which eliminates the usual hierarchy problem) it follows that Rc ∼ 1032/d−19 m. This immediately precludes d = 1, but for any value d > 1, we find that MS can be arranged to be a TeV for compactification radii as large as a millimetre, without confliciting with gravity experiments[3]. Effects of non-Newtonian (quantum) gravity can then become apparent at these surprisingly low values of energy. While it is possible[4] to construct a physically viable scenario with large Rc which can survive the existing astrophysical and cosmological constraints, such a scenario inevitably predicts large deviations from the SM in several low-energy effects [5]. Thus, laboratory data can be used to derive [5] bounds on MS in the TeV range — though some astrophysical bounds can, in fact, be considerably stronger [6]. The main criticism of the ADD scenario is the reappearance of a large hierarchy between the string scale MS ∼ 1 TeV and the compactification radius Rc ∼ (10−16 TeV)−1, which makes it difficult to stabilize the size of the large extra dimensions. This has inspired the RS scheme — proposed by Randall and Sundrum [7] — where only a single extra dimension is invoked. This fifth dimension φ is strongly curved and is compactified on a S/Z orbifold with a radius Rc, which is assumed to be somewhat larger than the Planck length. Two 3-branes are located at the orbifold fixed points: a ‘Planck brane’ at φ = 0 and a ‘TeV brane’ at φ = π. The tension on the branes and the cosmological constant in the bulk are fine-tuned to give a flat (Minkowski) geometry on the 3-branes. The bulk metric that guarantees this
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.
121827797
Finite tension strings in SU(2) gauge theory
Abstract The second-order field equations of the SU(2) Higgs model are studied and a new class of string solutions is obtained. The tension is finite and scale-dependent and the strings are of minus one unit flux.
15386012
Searching for signals of minimal length in extra dimensional models using dilepton production at hadron colliders
Theories of quantum gravity suggest the existence of a minimal length scale. It is interesting to speculate what the consequences of the existence of such a length scale would be for models of large extra dimensions, in particular, the ADD model. When ADD model is conflated with the minimal length scale scenario, processes involving virtual exchange of gravitons cease to be ulraviolet divergent. We study the production of dileptons at hadron colliders as an example of a process mediated by virtual gravitons. We find that the bounds we derive on the effective string scale are significantly different (in fact, less stringent) from those derived in the conventional ADD model, both at the upgraded Tevatron and the large hadron collider.
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.
9952561
Testing TeV scale quantum gravity using Dijet production at the Tevatron
Dijet production at the Tevatron including effects of virtual exchanges of spin-2 Kaluza-Klein modes in theories with large extra dimensions is considered. The experimental dijet mass and angular distribution are exploited to obtain stringent limits ( > 1.2 TeV) on the effective string scale MS.
120881483
Relativistic Schrodinger Equations for Particles of Arbitrary Spin
Relativistic wave equations in the Schrodinger form i∂ψ/∂t=Hψ for particles of nonzero mass and arbitrary spin are investigated. The wave function ψ is taken to transform according to the representation D(0,s)⊕D(s,0) of the homogeneous Lorentz group, a unique spin s for the particle being thereby assured without the aid of any supplementary condition. It is shown that the requirement that the Schrodinger equation be invariant under the operations of the Poincare group, as well as under space and time inversions and charge conjugation, restricts the possible choices of H (as a function of the operators representing the above symmetry operations) to a well-defined class which shrinks to a unique possibility (coinciding with the Hamiltonian derived by Weaver, Hammer, and Good) when a further regularity condition of a physical nature is imposed: namely, that the Hamiltonian have a unique finite limit in the rest system of the particle. In this process, an ambiguity which exists initially in the definition of operators representing time reversal and charge conjugation gets eliminated. The Hamiltonian itself is obtained in explicit form for particles of any spin.
120859611
Inconsistencies in the symmetric tensor field description of spin-2 particles in an external homogeneous magnetic field
We present a systematic investigation of the problem of a spin-2 particle, described by a symmetric tensor wave function, moving in a homogeneous magnetic field (h.m.f.). An interaction involving a multiple of the Federbush term, besides the minimal interaction, is considered. By explicit solution of the wave equation with an external h.m.f., we show that the energy spectrum of the spin-2 particle, like that of the spin-3/2 particle (Rarita-Schwinger theory with minimal coupling) spills over into the complex plane. This happens even for arbitrarily small magnetic fields if the coupling is minimal, while the onset of the trouble is delayed till the field strength rises to 2m/sup 2//3e if the Federbush term is included. Our results also throw new light on the problem of the number of constraints, and bring into focus the associated breakdown of Lorentz invariance. We demonstrate that the correct number of constraints exists (irrespective of whether the Federbush term is present or not) if the electromagnetic field is a pure h.m.f.; but the number of constraints is too few for any other electromagnetic field (even one obtainable from a pure h.m.f. by a Lorentz transformation) unless the standard Federbush term is included. The results of ourmore » analysis are discussed in relation to a similar analysis for lower spins as well as their implications for higher-spin theories. (AIP)« less
122825959
Rarita-Schwinger particles in homogeneous magnetic fields, and inconsistencies of spin-3/2 theories
The Rarita-Schwinger equation for a spin-$\frac{3}{2}$ particle with minimal electromagnetic coupling is solved completely in the case when a constant homogeneous external magnetic field $\mathcal{H}$ is present. It is shown that the spectrum of energy eigenvalues includes complex values if $\mathcal{H}$ is such that $\ensuremath{\eta}\ensuremath{\equiv}(\frac{2e\mathcal{H}}{3{m}^{3}})g1$, and further that the norm of the Rarita-Schwinger wave function (i.e., the total "charge" integral defined from the Lagrangian) which is positive definite for $\ensuremath{\eta}l1$ becomes indefinite (even after taking account of the constraints) when $\ensuremath{\eta}$ exceeds unity. These results confirm that the difficulties in quantization first discovered by Johnson and Sudarshan are a reflection of the indefiniteness of the norm which appears already at the $c$-number level, and suggest that the nature of the energy spectrum (whether or not complex values are present) in the presence of very large magnetic fields would provide a quick means of predicting whether such difficulties would arise in quantization.
118914003
Wave equations for zero-mass particle with invariant helicities
SummaryWe present a brief discussion of the difficulties associated with taking the limitm→0 in massive-particle equations of the formi(∂ψ/∂t)=Hψ, in which ψ transforms according to theD(0,s)⊕D(s,0) representation of the homogeneous Lorentz group. It is pointed out that, though the HamiltonianH tends to a well-defined form asm→0, the resulting wave equation is still unsatisfactory as the invariant scalar product (in the space of solutions of the wave equation) has an unacceptable form. We observe that this difficulty is due to the indecomposability of the representation of the Poincaré group over wave functions transforming asD(0,s)⊕D(s,0) in the massless case. Making due allowance for this fact we obtain, in close parallel to the treatment for massive particles, wave equations for zero-mass particles with invariant helicities ±s. The relevant invariant scalar products are also determined.RiassuntoSi presenta una breve discussione associata con il limitem→0 in equazioni per particelle con massa della formai(∂ψ/∂t)=Hψ, in cuiψ si trasforma secondo la rappresentazioneD(0,s)⊕C(s,0) del gruppo di Lorentz omogeneo. Si mette in rilievo che, sebbene l’hamiltonianoH tenda ad una forma ben definita quandom→0, l’equazione d’onda risultante non è ancora soddisfacente in quanto il prodotto scalare invariante (nello spazio delle soluzioni dell’equazione d’onda) ha una forma inaccettabile. Si osserva che questa difficoltà è dovuta alla indecomponibilità della rappresentazione del gruppo di Poincaré rispetto alle funzioni d’onda che si trasformano comeD(0,s)⊕D(s, 0) nel caso senza massa. Tenendo dovuto conto di questo fatto si ottengono, in stretta analogia con il trattamento per particelle con massa, equazioni per particelle con massa nulla con elicità invarianti ±s. Si determinano anche i relativi prodotti scalari invarianti.РеэюмеВкратце обсуждаются трудности, воэникаюшие при переходе к пределуm→;0 в уравнениях видаi(∂ψ/∂t)=H у с отличной от нуля массой частиц, в которых ψ преобраэуется согласно представлениюD(0,s)⊕D(s, 0) однородной группы Лорентца. Отмечается, что хотя Гамильтониан Я стремится к хорощо иэвестному выражению приm→0, но окончательное волновое уравнение является неудовлетворит ельным, так как инвариантное скалярное проиэведение (в пространстве рещений волнового уравнения) имеет неприемлемый вид. Мы обнаруживаем, что зта трудность обусловлена неприводимостью представления группы Пуанкаре череэ волновые функции, преобраэуюшиеся, какD(0,s)⊕D(s,0) в случае нулевой массы. Учитывая зтот факт, мы, по аналогии с рассмотрением для частиц с отличной от нуля массой, получаем волновое уравнение для частиц нулевой массы с инвариантными спиральностями ±s. Также определяются соответствуюшие инвариантные скалярные проиэведения.
119688870
Poincaré and TCP invariance in the determination of wave equations for particles of arbitrary spin
A brief outline is given of different types of approaches to the derivation of relativistic wave equations for free particles of arbitrary mass m and spin s. It is pointed out that all such equations can be subsumed in a standard form involving wavefunctions transforming according to the representation D (0,s) ⊕ D (s,0) of the Lorentz group. Generalizing earlier work employing this standard form, we determine all such equations (in a standard form) which are invariant under the Poincare group and the combined operation Θ ≡ TCP. It is shown that the resulting equations are automatically invariant under T, C, and P separately.