Counting Form Factors of Twist-Two Operators

We present a simple method to count the number of hadronic form factors based on the partial wave formalism and crossing symmetry. In particular, we show that the number of independent nucleon form factors of spin-n, twist-2 operators (the vector current and energy-momentum tensor being special examples) is n+1. These generalized form factors define the generalized (off-forward) parton distributions that have been studied extensively in the recent literature. In proving this result, we also show how the J^{PC} rules for onium states arise in the helicity formalism.Comment: 7 pages, LaTeX (revtex

Comment on "Does Gluons Carry Half of the Nucleon Momentum?" by X. S. Chen et. al. (PRL103, 062001 (2009))

The authors claim to have found a "proper", "gauge-invariant" definition of a charged-particle's momentum in gauge theory, which is more "superior" than the textbook version. I show that their result arises from a misunderstanding of gauge symmetry by generalizing the Coulomb gauge result indiscriminately and is not physical

Implications of Color Gauge Symmetry For Nucleon Spin Structure

We study the chromodynamical gauge symmetry in relation to the internal spin structure of the nucleon. We show that 1) even in the helicity eigenstates the gauge-dependent spin and orbital angular momentum operators do not have gauge-independent matrix element; 2) the evolution equations for the gluon spin take very different forms in the Feynman and axial gauges, but yield the same leading behavior in the asymptotic limit; 3) the complete evolution of the gauge-dependent orbital angular momenta appears intractable in the light-cone gauge. We define a new gluon orbital angular momentum distribution $L_g(x)$ which {\it is} an experimental observable and has a simple scale evolution. However, its physical interpretation makes sense only in the light-cone gauge just like the gluon helicity distribution $\Delta g(x)$y.Comment: Minor corrections are made in the tex

Reciprocatory magnetic reconnection in a coronal bright point

Coronal bright points (CBPs) are small-scale and long-duration brightenings in the lower solar corona. They are often explained in terms of magnetic reconnection. We aim to study the sub-structures of a CBP and clarify the relationship among the brightenings of different patches inside the CBP. The event was observed by the X-ray Telescope (XRT) aboard the Hinode spacecraft on 2009 August 22$-$23. The CBP showed repetitive brightenings (or CBP flashes). During each of the two successive CBP flashes, i.e., weak and strong flashes which are separated by $\sim$2 hr, the XRT images revealed that the CBP was composed of two chambers, i.e., patches A and B. During the weak flash, patch A brightened first, and patch B brightened $\sim$2 min later. During the transition, the right leg of a large-scale coronal loop drifted from the right side of the CBP to the left side. During the strong flash, patch B brightened first, and patch A brightened $\sim$2 min later. During the transition, the right leg of the large-scale coronal loop drifted from the left side of the CBP to the right side. In each flash, the rapid change of the connectivity of the large-scale coronal loop is strongly suggestive of the interchange reconnection. For the first time we found reciprocatory reconnection in the CBP, i.e., reconnected loops in the outflow region of the first reconnection process serve as the inflow of the second reconnection process.Comment: 13 pages, 8 figure

Log-concavity and lower bounds for arithmetic circuits

One question that we investigate in this paper is, how can we build log-concave polynomials using sparse polynomials as building blocks? More precisely, let $f = \sum\_{i = 0}^d a\_i X^i \in \mathbb{R}^+[X]$ be a polynomial satisfying the log-concavity condition a\_i^2 \textgreater{} \tau a\_{i-1}a\_{i+1} for every $i \in \{1,\ldots,d-1\},$ where \tau \textgreater{} 0. Whenever $f$ can be written under the form $f = \sum\_{i = 1}^k \prod\_{j = 1}^m f\_{i,j}$ where the polynomials $f\_{i,j}$ have at most $t$ monomials, it is clear that $d \leq k t^m$. Assuming that the $f\_{i,j}$ have only non-negative coefficients, we improve this degree bound to $d = \mathcal O(k m^{2/3} t^{2m/3} {\rm log^{2/3}}(kt))$ if \tau \textgreater{} 1, and to $d \leq kmt$ if $\tau = d^{2d}$. This investigation has a complexity-theoretic motivation: we show that a suitable strengthening of the above results would imply a separation of the algebraic complexity classes VP and VNP. As they currently stand, these results are strong enough to provide a new example of a family of polynomials in VNP which cannot be computed by monotone arithmetic circuits of polynomial size

Spin-lattice order in frustrated ZnCr2O4

Using synchrotron X-rays and neutron diffraction we disentangle spin-lattice order in highly frustrated ZnCr$_2$O$_4$ where magnetic chromium ions occupy the vertices of regular tetrahedra. Upon cooling below 12.5 K the quandary of anti-aligning spins surrounding the triangular faces of tetrahedra is resolved by establishing weak interactions on each triangle through an intricate lattice distortion. The resulting spin order is however, not simply a N\'{e}el state on strong bonds. A complex co-planar spin structure indicates that antisymmetric and/or further neighbor exchange interactions also play a role as ZnCr$_2$O$_4$ resolves conflicting magnetic interactions

Parametric survey of longitudinal prominence oscillation simulations

It is found that both microflare-sized impulsive heating at one leg of the loop and a suddenly imposed velocity perturbation can propel the prominence to oscillate along the magnetic dip. An extensive parameter survey results in a scaling law, showing that the period of the oscillation, which weakly depends on the length and height of the prominence, and the amplitude of the perturbations, scales with $\sqrt{R/g_\odot}$, where $R$ represents the curvature radius of the dip, and $g_\odot$ is the gravitational acceleration of the Sun. This is consistent with the linear theory of a pendulum, which implies that the field-aligned component of gravity is the main restoring force for the prominence longitudinal oscillations, as confirmed by the force analysis. However, the gas pressure gradient becomes non-negligible for short prominences. The oscillation damps with time in the presence of non-adiabatic processes. Compared to heat conduction, the radiative cooling is the dominant factor leading to the damping. A scaling law for the damping timescale is derived, i.e., $\tau\sim l^{1.63} D^{0.66}w^{-1.21}v_{0}^{-0.30}$, showing strong dependence on the prominence length $l$, the geometry of the magnetic dip (characterized by the depth $D$ and the width $w$), and the velocity perturbation amplitude $v_0$. The larger the amplitude, the faster the oscillation damps. It is also found that mass drainage significantly reduces the damping timescale when the perturbation is too strong.Comment: 17 PAGES, 8FIGURE

Virtual meson cloud of the nucleon and generalized parton distributions

We present the general formalism required to derive generalized parton distributions within a convolution model where the bare nucleon is dressed by its virtual meson cloud. In the one-meson approximation the Fock states of the physical nucleon are expanded in a series involving a bare nucleon and two-particle, meson-baryon, states. The baryon is assumed here to be either a nucleon or a $\Delta$ described within the constituent quark model in terms of three valence quarks; correspondingly, the meson, assumed to be a pion, is described as a quark-antiquark pair. Explicit expressions for the unpolarized generalized parton distributions are obtained and evaluated in different kinematics.Comment: 37 pages, 9 figures, minor corrections, and figure 3 replaced; version to appear in Phys. Rev.

Investigation of the energy dependence of the orbital light curve in LS 5039

LS 5039 is so far the best studied $\gamma$-ray binary system at multi-wavelength energies. A time resolved study of its spectral energy distribution (SED) shows that above 1 keV its power output is changing along its binary orbit as well as being a function of energy. To disentangle the energy dependence of the power output as a function of orbital phase, we investigated in detail the orbital light curves as derived with different telescopes at different energy bands. We analysed the data from all existing \textit{INTEGRAL}/IBIS/ISGRI observations of the source and generated the most up-to-date orbital light curves at hard X-ray energies. In the $\gamma$-ray band, we carried out orbital phase-resolved analysis of \textit{Fermi}-LAT data between 30 MeV and 10 GeV in 5 different energy bands. We found that, at $\lesssim$100 MeV and $\gtrsim$1 TeV the peak of the $\gamma$-ray emission is near orbital phase 0.7, while between $\sim$100 MeV and $\sim$1 GeV it moves close to orbital phase 1.0 in an orbital anti-clockwise manner. This result suggests that the transition region in the SED at soft $\gamma$-rays (below a hundred MeV) is related to the orbital phase interval of 0.5--1.0 but not to the one of 0.0--0.5, when the compact object is "behind" its companion. Another interesting result is that between 3 and 20 GeV no orbital modulation is found, although \textit{Fermi}-LAT significantly ($\sim$18$\sigma$) detects LS 5039. This is consistent with the fact that at these energies, the contributions to the overall emission from the inferior conjunction phase region (INFC, orbital phase 0.45 to 0.9) and from the superior conjunction phase region (SUPC, orbital phase 0.9 to 0.45) are equal in strength. At TeV energies the power output is again dominant in the INFC region and the flux peak occurs at phase $\sim$0.7.Comment: 7 pages, 6 figures, accepted for publication in MNRA