Faheem Hussain

Heavy - light hadrons and current induced transitions among them

Abstract We discuss several dynamical schemes that allow one to calculate current induced transitions among heavy-light hadrons. Among these are a Bethe-Salpeter wavefunction calculation, a Bloch-Nordsiek approximation and a QCD Green function approach. In the limit where the mass of the heavy quark (or hadron) becomes large but its four velocity ν μ = p μ / M remains fixed all these schemes lead to the same results. Namely they give a product of a trace over U(12) wavefunctions with the current sandwiched in between and a (to be determined) form factor function which is normalised to unity at maximum momentum transfer. The various approaches sketched here are useful in that they allow one to identify and calculate 1/ M corrections to the heavy mass limit.

GENERAL-ANALYSIS OF WEAK DECAY FORM-FACTORS IN HEAVY TO HEAVY AND HEAVY TO LIGHT BARYON TRANSITIONS

We present a complete analysis of the heavy to heavy and heavy to light baryon semi-leptonic decays in the heavy quark effective theory within the framework of a Bethe-Salpeter (BS) approach and demonstrate the equivalence of this approach to other work in the field. We present in a compact form the baryon BS amplitudes which incorporate the symmetries manifest in the heavy quark limit and which also show clearly the light quark dynamics. A similar form of the BS amplitude is presented for light baryons. Using the BS amplitudes, the heavy to heavy and heavy to light semi-leptonic baryon decays are considered. As expected there is a dramatic reduction in the number of form factors. An advantage of our BS approach is demonstrated where the form factors are written as loop integrals which in principle can be calculated.

Axion production from gravitons off interacting 0-branes

We study axion-graviton scattering from a system of two DO-branes in a Type II superstring theory, a process which does not occur on a single brane. The two DO-branes interact via the exchange of closed string states which form a cylinder joining them. By compactifying on the Z3 orbifold we find a non vanishing amplitude coming from the odd spin structure sector, thus from the exchanged RR states. We compute, in particular, the leading term of the amplitude at large distance from the branes, which corresponds to taking a field theory limit. This seems to suggest that the process takes place through the coupling of an axion to the RR states exchanged between the 0-branes.

Interaction of moving D-branes on orbifolds

We use the boundary state formalism to study the interaction of two moving identical D-branes in the Type II superstring theory compactified on orbifolds. By computing the velocity dependence of the amplitude in the limit of large separation we can identify the nature of the different forces between the branes. In particular, in the Z(3) orbifold case we find a boundary state which is coupled only to the N = 2 graviton multiplet containing just a graviton and a vector like in the extremal Reissner-Nordstrom configuration. We also discuss other cases including T-4/Z(2)

CLOSED STRING RADIATION FROM MOVING D-BRANES

We compute the amplitude for the radiation of massless NS-NS closed string states from the interaction of two moving D-branes. We consider particle-like D-branes with reference to four-dimensional spacetime, in toroidal and orbifold compactifications, and we calculate the relevant world sheet propagators within the moving boundary state formalism. We find no on-shell axion emission. For large inter-brane separation, we compute the spacetime graviton emission amplitude and estimate the average energy radiated, whereas the spacetime dilaton amplitude is found to vanish in this limit. The possibility of emission of other massless states depends on the nature of the branes and of the compactification scheme

Some general aspects of coset models and topological Kazama-Suzuki models

Abstract We study global aspects of N = 2 Kazama-Suzuki coset models by investigating topological G / H Kazama-Suzuki models in a Lagrangian framework based on gauged Wess-Zumino-Witten models. To that end, we first generalize Wittens analysis of the holomorphic factorization of bosonic G / H models to models with N = 1 and N = 2 supersymmetry, in the course of which we also find some new anomaly-free and supersymmetric models based on non-diagonal embeddings of the gauge group. We then explain the basic properties (action, symmetries, metric independence, etc.) of the topologically twisted G / H Kazama-Suzuki models. As non-trivial gauge bundles unavoidably occur, we explain how all of the above generalizes to that case. We employ the path integral methods of localization and abelianization (shown to be valid also for non-trivial bundles) to establish that the twisted G / H models can be localized to bosonic H / H models (with certain quantum corrections), and can hence be reduced to an abelian bosonic T / T model, T a maximal torus of H . We also present the action and the symmetries of the coupling of these models to topological gravity. We determine the bosonic observables for all the models based on classical flag manifolds and the bosonic observables and their fermionic descendants for models based on complex Grassmannians. These results will be used in subsequent publications to calculate explicitly the chiral primary ring of Kazama-Suzuki models.

On the D → K̄∗e + νe form factors

Abstract The infinite mass effective theory, when a heavy quark mass goes to infinity, and chiral perturbation theory at the quark level, based on the extended Nambu-Jona-Lasinio model, are applied for the calculation of the D → K ∗ e + ν e decay form factors. The theoretical results agree with experimental data.

Current s-quark mass corrections to the form factors of D-meson semileptonic decays

Abstract The infinite mass effective theory, when a heavy quark mass tends to infinity, and Chiral perturbation theory at the quark level, based on the extended Nambu-Jona-Lasinio model with linear realization of chiraal U(3) × U(3) symmetry, are applied to the calculation of current s-quark mass corrections to the form factors of the D → K e + ν e and D → K ∗ e + ν e decays. These corrections turn out to be quite significant, of the order of 7–20%. The theoretical results are compared with experimental data.

Non-commutative geometry and supersymmetry II

Abstract Extending results of a previous work [Phys. Lett. B 260 (1991) 359], we establis that anothe non-commutative model proposed by Balakrishna, Gursey and Wali may be expressed as a Yang-Mills theory of a graded Lie group.

Grassmannian topological Kazama-Suzuki models and cohomology

Abstract We investigate in detail the topological gauged Wess-Zumino-Witten models describing topological Kazama-Suzuki models based on complex Grassmannians. We show that there is a topological sector in which the ring of observables (constructed from the Grassmann-odd scalars of the theory) coincides with the classical cohomology ring of the Grassmannian for all values of the level k. We perform a detailed analysis of the non-trivial topological sectors arising from the adjoint gauging, and investigate the general ring structure of bosonic correlation functions, uncovering a whole hierarchy of level-rank relations (including the standard level-rank duality) among models based on different Grassmannians. Using the previously established localization of the topological Kazama-Suzuki model to an abelian topological field theory, we reduce the correlators to finite-dimensional purely algebraic expressions. As an application, these are evaluated explicitly for the |C P(2) model at level k and shown for all k to coincide with the cohomological intersection numbers of the two-plane Grassmannian G(2,k+2), thus realizing the level-rank duality between this model and the G(2,k+2) model at level one.