Exploring the timelike region for the elastic form factor in the light-front quantization

Even though the Drell-Yan-West formulation is the most rigorous and well-established framework to compute the exclusive processes, its utility has been limited only to the spacelike region because of the intrinsic kinematic constraint $q^+=0$. We present an explicit example demonstrating how one may obtain the necessary information (i.e. nonvalence or so called Z-graph contribution) in the timelike region of exclusive process without encountering a formidable task of direct calculation that has hindered so far the progress in this area. In the analysis of $q\bar{Q}$ bound state form factors using an exactly solvable model of $(3+1)$ dimensional scalar field theory interacting with gauge fields, the results analytically continued from the spacelike region coincide exactly with the direct results in the timelike region. This example verifies that the method of analytic continuation is capable of yielding the effect of complicate nonvalence contributions. The meson peaks analogous to the vector meson dominance(VMD) phenomena are also generated at the usual VMD positions.Comment: 21 pages, 8 figures, we changed the title, added some references and included some paragraphs in the introduction and conclusions; version to appear in Nucl. Phys.

Frame-Independence of Exclusive Amplitudes in the Light-Front Quantization

While the particle-number-conserving convolution formalism established in the Drell-Yan-West reference frame is frequently used to compute exclusive amplitudes in the light-front quantization, this formalism is limited to only those frames where the light-front helicities are not changed and the good (plus) component of the current remains unmixed. For an explicit demonstration of such criteria, we present the relations between the current matrix elements in the two typical reference frames used for calculations of the exclusive amplitudes, i.e. the Drell-Yan-West and Breit frames and investigate both pseudoscalar and vector electromagnetic currents in detail. We find that the light-front helicities are unchanged and the good component of the current does not mix with the other components of the current under the transformation between these two frames. Thus, the pseudoscalar and vector form factors obtained by the diagonal convolution formalism in both frames must indeed be identical. However, such coincidence between the Drell-Yan-West and Breit frames does not hold in general. We give an explicit example in which the light-front helicities are changed and the plus component of the current is mixed with other components under the change of reference frame. In such a case, the relationship between the frames should be carefully analyzed before the established convolution formalism in the Drell-Yan-West frame is used.Comment: 14 pages, 4 figure

Scalable Task-Based Algorithm for Multiplication of Block-Rank-Sparse Matrices

A task-based formulation of Scalable Universal Matrix Multiplication Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is applied to the multiplication of hierarchy-free, rank-structured matrices that appear in the domain of quantum chemistry (QC). The novel features of our formulation are: (1) concurrent scheduling of multiple SUMMA iterations, and (2) fine-grained task-based composition. These features make it tolerant of the load imbalance due to the irregular matrix structure and eliminate all artifactual sources of global synchronization.Scalability of iterative computation of square-root inverse of block-rank-sparse QC matrices is demonstrated; for full-rank (dense) matrices the performance of our SUMMA formulation usually exceeds that of the state-of-the-art dense MM implementations (ScaLAPACK and Cyclops Tensor Framework).Comment: 8 pages, 6 figures, accepted to IA3 2015. arXiv admin note: text overlap with arXiv:1504.0504

Effective Potentials for Light Moduli

We examine recent work on compactifications of string theory with fluxes, where effective potentials for light moduli have been derived after integrating out moduli that are assumed to be heavy at the classical level, and then adding non-perturbative (NP) corrections to the superpotential. We find that this two stage procedure is not valid and that the correct potential has additional terms. Althought this does not affect the conclusion of Kachru et al (KKLT) that the Kaehler moduli may be stabilized by NP effects, it can affect the detailed physics. In particular it is possible to get metastable dS minima without adding uplifting terms.Comment: Minor revisions, References added, Version to be published in PLB, 14 pages 3 figure

Moduli-mixing racetrack model

We study supersymmetric models with double gaugino condensations in the hidden sector, where the gauge couplings depend on two light moduli of superstring theory. We perform a detailed analysis of this class of model and show that there is no stable supersymmetric minimum with finite vacuum values of moduli fields. Instead, we find that the supersymmetry breaking occurs with moduli stabilized and negative vacuum energy. That yields moduli-dominated soft supersymmetry breaking terms. To realize slightly positive (or vanishing) vacuum energy, we add uplifting potential. We discuss uplifting does not change qualitatively the vacuum expectation values of moduli and the above feature of supersymmetry breaking.Comment: 23 pages, 4 eps figure

The degenerate gravitino scenario

In this work, we explore the "degenerate gravitino" scenario where the mass difference between the gravitino and the lightest MSSM particle is much smaller than the gravitino mass itself. In this case, the energy released in the decay of the next to lightest sypersymmetric particle (NLSP) is reduced. Consequently the cosmological and astrophysical constraints on the gravitino abundance, and hence on the reheating temperature, become softer than in the usual case. On the other hand, such small mass splittings generically imply a much longer lifetime for the NLSP. We find that, in the constrained MSSM (CMSSM), for neutralino LSP or NLSP, reheating temperatures compatible with thermal leptogenesis are reached for small splittings of order 10^{-2} GeV. While for stau NLSP, temperatures of 4x10^9 GeV can be obtained even for splittings of order of tens of GeVs. This "degenerate gravitino" scenario offers a possible way out to the gravitino problem for thermal leptogenesis in supersymmetric theories.Comment: 27 pages, 10 figures and 1 table. Minor typos and references fixed. Matches published version in JCAP

Interference and binding effects in decays of possible molecular component of X(3872)

It is pointed out that the internal structure of the narrow resonance X(3872) at the D^0 {\bar D}^{*0} threshold can be studied in some detail by measuring the rate and the spectra in the decays X(3872) \to D^0 {\bar D}^0 \pi^0 and X(3872) \to D^0 {\bar D}^0 \gamma. In particular, if this resonance contains a dominant `molecular' component D {\bar D^*} \pm {\bar D} D^*, this component can be revealed and studied by a distinct pattern of interference between the underlying decays of D^{*0} and {\bar D}^{*0} whose coherence is ensured by fixed (but yet unknown) C parity of the X(3872).Comment: 7 pages, 1 figur

New Developments in Treacherous Points of Light-Front Dynamics

Light-front dynamics(LFD) plays an important role in hadron phenomenology. Last few years, however, it has been emphasized that treacherous points such as zero-mode contributions should be taken into account for successful LFD applications to hadron phenomenology. We discuss examples of treacherous points and present new progresses made last few years to handle them correctly.Comment: 5 pages, espcrc1.sty. proceedings of FB XVIII (August 2006, Brazil), to be published in Nucl. Phys.

Numerical shadows: measures and densities on the numerical range

For any operator $M$ acting on an $N$-dimensional Hilbert space $H_N$ we introduce its numerical shadow, which is a probability measure on the complex plane supported by the numerical range of $M$. The shadow of $M$ at point $z$ is defined as the probability that the inner product $(Mu,u)$ is equal to $z$, where $u$ stands for a random complex vector from $H_N$, satisfying $||u||=1$. In the case of N=2 the numerical shadow of a non-normal operator can be interpreted as a shadow of a hollow sphere projected on a plane. A similar interpretation is provided also for higher dimensions. For a hermitian $M$ its numerical shadow forms a probability distribution on the real axis which is shown to be a one dimensional $B$-spline. In the case of a normal $M$ the numerical shadow corresponds to a shadow of a transparent solid simplex in $R^{N-1}$ onto the complex plane. Numerical shadow is found explicitly for Jordan matrices $J_N$, direct sums of matrices and in all cases where the shadow is rotation invariant. Results concerning the moments of shadow measures play an important role. A general technique to study numerical shadow via the Cartesian decomposition is described, and a link of the numerical shadow of an operator to its higher-rank numerical range is emphasized.Comment: 37 pages, 8 figure