FormLink/FeynCalcFormLink : Embedding FORM in Mathematica and FeynCalc
FORM, a symbolic manipulation system, has been widely used in a lot of calculations for High Energy Physics due to its high performance and fficient design. Mathematica, another computational software program, has also widely been used, but more for reasons of generality and user-friendliness than for speed. Especially calculations involving tensors and noncommutative operations like calculating Dirac traces can be rather slow in Mathematica, compared to FORM. In this article we describe FormLink and FeynCalcFormLink, two Mathematica packages to link Mathematica and FeynCalc with FORM. FormLink can be used without FeynCalc and FeynCalcFormLink, which is an extension loading FormLink and FeynCalc automatically. With these two packages the impressive speed and other special features of FORM get embedded into the generality of Mathematica and FeynCalc in a simple manner. FeynCalcFormLink provides a FORM-based turbo for FeynCalc, making it much more efficient. FormLink turns Mathematica into an editor and code organizer for FORM.

title: A Note on the $k_T$-Factorization for Exclusive Processes
abstract: We show in detail that the $k_T$-factorization for exclusive processes is gauge-dependent and inconsistent.

title: Resummation of Large Logarithms in the Electromagnetic Form factor of pion
abstract: In the collinear factorization of the form factor for the transition $\gamma^* \pi^0 \to \pi$ the hard part contains double log terms. These terms will spoil the perturbative expansion of the hard part. A simple exponentiation for resummation leads to divergent results. We study the resummation of these double log's. We make an analysis to show the origin of the double log's. With the understanding of the origin one can introduce soft factors and Nonstandard Light-Cone Wave Functions(NLCWF) to derive a factorized form for the form factor, where the hard part does not contain the double log's. There is a perturbative relation between NLCWF and the standard Light-Cone Wave Function(LCWF). Beside the renormalization scale $\mu$ the introduced NLCWF's and soft factors have extra scales to characterize the double log's. Using the evolutions of the extra scales and the relation we can do the resummation of the double log's perturbatively in sense that LCWF's are the only nonpertubative objects in the resumed formula. Our results with some models of LCWF show that there is a significant difference between numerical predictions with or without the resummation.

title: $O(\alpha_s)$ corrections to $J/\psi+\chi_{cJ}$ production at $B$ factories
abstract: We investigate the ${\cal O}(\alpha_s)$ corrections to $e^+e^-\to J/\psi(\psi')+\chi_{cJ}$ ($J=0,1,2$) in the NRQCD factorization approach. These next-to-leading order (NLO) corrections are calculated at the level of helicity amplitude. We have made a detailed analysis for both polarized and unpolarized cross sections, and compared our predictions with the measurements at the $B$ factories. We also derive the asymptotic expressions for each of the NLO helicity amplitudes, and confirm the earlier speculation that at NLO in $\alpha_s$, the double logarithm of type $\ln^2 (s/m_c^2)$ appearing in the NRQCD short-distance coefficient is always associated with the helicity-suppressed channels.

title: Automated One-loop Computation in Quarkonium Process within NRQCD Framework
abstract: In last decades, it has been realized that the next-to-leading order corrections may become very important, and sometimes requisite, for some processes involving quarkoinum production or decay, e.g., e+e− → J/ψ + ηc and J/ψ → 3γ. In this article, we review some basic steps to perform automated one-loop computations in quarkonium process within the Non-relativistic Quantum Chromodynamics (NRQCD) factorization framework1 and we give an introduction to some related public tools or packages and their usages in each step. We start from generating Feynman diagrams and amplitudes with FEYNARTS for the quarkonium process, performing Dirac- and Color- algebras simplifications using FEYNCALC and FEYNCALCFORMLINK, and then to doing partial fractions on the linear-dependent propagators by APART, and finally to reducing the Tensor Integrals (TI) into Scalar Integrals (SI) or Master Integrals (MI) using Integration-By-Parts (IBP) method with the help of FIRE. We will use a simple concrete example to demonstrate the basic usages of the corresponding packages or tools in each step.

title: ${\mathcal O}(\alpha_s)$ corrections to $e^+e^-\rightarrow J/\psi+\eta_{c2}(\chi_{c1}^\prime)$ at $B$ factories
abstract: We investigate the O(alpha(s)) correction to e(+)e(-) -> J/psi + eta(c2) in the NRQCD factorization approach. A detailed comparative study between e(+)e(-) -> J/psi + eta(c2), and e(+)e(-) -> J/psi + chi(c1)', at the B factory energy is also carried out. After incorporating the O(alpha(s)) correction, we predict the cross section for the former process to be around 0.3 fb, while that of the latter is about 6 times greater. The outgoing J/psi is found to be dominantly transversely polarized in the former process, while longitudinally polarized in the latter. These features may provide valuable guidance for the Belle 2 experiment to establish the chi(c1)', or eta(c2) states. In the Appendix, we also identify the coefficients of the double logarithms of form 1n(2)(s/m(c)(2)) associated with all the relevant next -to -leading -order Feynman diagrams, for the helicity-suppressed double-charmonium production channels e(+)e(-) -> J/psi + eta(c2) and e(+)e(-) -> J/psi + chi(c0,1,2).

title: A history of the gamma-ray burst flux at the Earth from Galactic globular clusters
abstract: Nearby gamma-ray bursts (GRBs) are likely to have represented a significant threat to life on the Earth. Recent observations suggest that a significant source of such bursts is compact binary mergers in globular clusters. This link between globular clusters and GRBs o ers the possibility to find time intervals in the past with higher probabilities of a nearby burst, by tracing globular cluster orbits back in time. Here we show that the expected flux from such bursts is not flat over the past 550 Myr but rather exhibits three broad peaks, at 70, 180 and 340 Myr ago. The main source for nearby GRBs for all three time intervals is the globular cluster 47 Tuc, a consequence of its large mass and high stellar encounter rate, as well as the fact that it is one of the globular clusters which comes quite close to the Sun. Mass extinction events indeed coincide with all three time intervals found in this study, although a chance coincidence is quite likely. Nevertheless, the identified time intervals can be used as a guide to search for specific signatures of GRBs in the geological record around these times.

title: Evidence for periodicities in the extinction record? Response to Melott & Bambach [arXiv:1307.1884]
abstract: In a recent paper, we applied time series analysis methods to study the possible influence of the solar motion through the Galaxy on terrestrial extinction (Feng & Bailer-Jones 2013). We drew conclusions about the relative probabilities of how well different models explain the geological extinction record. We found no strong evidence for either a periodicity in the extinction record or for a link between the solar orbit and this extinction record. In response to this, Melott & Bambach (2013) dedicate the majority of their article to criticizing our analysis. Their main objection is to evidence-based model comparison. Here we deal with their criticisms one by one, and show that they are largely misplaced, leaving our conclusions unaffected. The bottom line is that although one can get a periodic model at some period to fit the extinction data, there are other models which explain the data better.

title: Radio jets and galaxies as cosmic string probes
abstract: The lensing effect of a cosmic string is studied, and some new methods are proposed to detect the cosmic string. The technique for using jets as extended gravitational lensing probes was first explored by Kronberg. We use the “alignment-breaking parameter” ηG as a sensitive indicator of gravitational distortion by a wiggly cosmic string. Then, we applied the non-constant deflection angle to jets, and ηG of a specific jet is just related to the projected slope of the jet. At least three jets in the sample of Square Kilometer Array (SKA) would have significant signals (ηG > 10°) if the wiggly infinite cosmic string existed. The distortion of elliptical object is also studied and used to do a statistical research on the directions of axes and ellipticities of galaxies. In the direction of the string, we find that galaxies appear to be more elliptical for an observer and the distribution of apparent ellipticity changes correspondingly. The ellipticity distribution of current SDSS spiral sample has the signal-to-noise ratio up to 8.48 which is large enough for astronomical observations. The future survey, such as Large Synoptic Survey Telescope (LSST) and Dark Energy Survey (DES) would weaken the requirement of special geometry in the data processing. As a result, all kinds of distributions, including ellipticity axis distribution, would serve as probes to detect wiggly strings in the near future. In brief, if a wiggly cosmic string existed, these signals would be convenient to be observed with the future weak lensing survey or other surveys in the deep space. If there was no lensing signal in these distributions, it would give the upper limit of the abundance of infinite strings.

title: Assessing the Influence of the Solar Orbit on Terrestrial Biodiversity
abstract: The terrestrial fossil record shows a significant variation in the extinction and origination rates of species during the past half-billion years. Numerous studies have claimed an association between this variation and the motion of the Sun around the Galaxy, invoking the modulation of cosmic rays, gamma rays, and comet impact frequency as a cause of this biodiversity variation. However, some of these studies exhibit methodological problems, or were based on coarse assumptions (such as a strict periodicity of the solar orbit). Here we investigate this link in more detail, using a model of the Galaxy to reconstruct the solar orbit and thus a predictive model of the temporal variation of the extinction rate due to astronomical mechanisms. We compare these predictions as well as those of various reference models with paleontological data. Our approach involves Bayesian model comparison, which takes into account the uncertainties in the paleontological data as well as the distribution of solar orbits consistent with the uncertainties in the astronomical data. We find that various versions of the orbital model are not favored beyond simpler reference models. In particular, the distribution of mass extinction events can be explained just as well by a uniform random distribution as by any other model tested. Although our negative results on the orbital model are robust to changes in the Galaxy model, the Sun's coordinates, and the errors in the data, we also find that it would be very difficult to positively identify the orbital model even if it were the true one. (In contrast, we do find evidence against simpler periodic models.) Thus, while we cannot rule out there being some connection between solar motion and biodiversity variations on the Earth, we conclude that it is difficult to give convincing positive conclusions of such a connection using current data.