A Feynman integral via higher normal functions

We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a classical Picard-Fuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of K3 surfaces. We show that the integral is given by a sum of elliptic trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm value is related to the regulator of a class in the motivic cohomology of the K3 family. We prove a conjecture by David Broadhurst that at a special kinematical point the Feynman integral is given by a critical value of the Hasse-Weil L-function of the K3 surface. This result is shown to be a particular case of Deligne's conjectures relating values of L-functions inside the critical strip to periods.Comment: Latex. 70 pages. 3 figures. v3: minor changes and clarifications. Version to appear in Compositio Mathematic

A genetic assessment of parentage in the blackspot sergeant damselfish, Abudefduf sordidus (Pisces: Pomacentridae)

Microsatellite markers were used to investigate the reproductive behavior of the damselfish Abudefduf sordidus at Johnston Atoll, Central Pacific Ocean. Genetic results indicated that ten males maintained guardianship over their nest territories for up to nine nest cycles during a 3.5 month period. Genotypes of 1025 offspring sampled from 68 nests (composed of 129 clutches) were consistent with 95% of the offspring being sired by the guardian male. Offspring lacking paternal alleles at two or more loci were found in 19 clutches, indicating that reproductive parasitism and subsequent alloparental care occurred. Reconstructed maternal genotypes allowed the identification of a minimum of 74 different females that spawned with these ten territorial males. Males were polygynous, mating with multiple females within and between cycles. Genetic data from nests, which consisted of up to four clutches during a reproductive cycle, indicated that each clutch usually had only one maternal contributor and that different clutches each had different dams. Females displayed sequential polyandry spawning with one male within a cycle but switched males in subsequent spawning cycles. These results highlight new findings regarding male parasitic spawning, polygyny, and sequential polyandry in a marine fish with exclusive male paternal care.Published versio

Magneto-optics in pure and defective Ga_{1-x}Mn_xAs from first-principles

The magneto-optical properties of Ga$_{1-x}$Mn$_{x}$As including their most common defects were investigated with precise first--principles density-functional FLAPW calculations in order to: {\em i}) elucidate the origin of the features in the Kerr spectra in terms of the underlying electronic structure; {\em ii}) perform an accurate comparison with experiments; and {\em iii}) understand the role of the Mn concentration and occupied sites in shaping the spectra. In the substitutional case, our results show that most of the features have an interband origin and are only slightly affected by Drude--like contributions, even at low photon energies. While not strongly affected by the Mn concentration for the intermediately diluted range ($x\sim$ 10%), the Kerr factor shows a marked minimum (up to 1.5$^o$) occurring at a photon energy of $\sim$ 0.5 eV. For interstitial Mn, the calculated results bear a striking resemblance to the experimental spectra, pointing to the comparison between simulated and experimental Kerr angles as a valid tool to distinguish different defects in the diluted magnetic semiconductors framework.Comment: 10 pages including 2 figures, submitted to Phys. Rev.

X-Ray Observations of Black Widow Pulsars

We describe the first X-ray observations of five short orbital period ($P_B < 1$ day), $\gamma$-ray emitting, binary millisecond pulsars. Four of these, PSRs J0023+0923, J1124$-$3653, J1810+1744, and J2256$-$1024 are `black-widow' pulsars, with degenerate companions of mass $\ll0.1 M_{\odot}$, three of which exhibit radio eclipses. The fifth source, PSR J2215+5135, is an eclipsing `redback' with a near Roche-lobe filling $\sim$0.2 solar mass non-degenerate companion. Data were taken using the \textit{Chandra X-Ray Observatory} and covered a full binary orbit for each pulsar. Two pulsars, PSRs J2215+5135 and J2256$-$1024, show significant orbital variability while PSR J1124$-$3653 shows marginal orbital variability. The lightcurves for these three pulsars have X-ray flux minima coinciding with the phases of the radio eclipses. This phenomenon is consistent with an intrabinary shock emission interpretation for the X-rays. The other two pulsars, PSRs J0023+0923 and J1810+1744, are fainter and do not demonstrate variability at a level we can detect in these data. All five spectra are fit with three separate models: a power-law model, a blackbody model, and a combined model with both power-law and blackbody components. The preferred spectral fits yield power-law indices that range from 1.3 to 3.2 and blackbody temperatures in the hundreds of eV. The spectrum for PSR J2215+5135 shows a significant hard X-ray component, with a large number of counts above 2 keV, which is additional evidence for the presence of intrabinary shock emission and is similar to what has been detected in the low-mass X-ray binary to millisecond pulsar transition object PSR J1023+0038.Comment: 8 pages, 6 figures, 2 tables, submitted to Ap

Peculiar Spin Frequency and Radio Profile Evolution of PSR J1119−-6127 Following Magnetar-like X-ray Bursts

We present the spin frequency and profile evolution of the radio pulsar J1119$-$6127 following magnetar-like X-ray bursts from the system in 2016 July. Using data from the Parkes radio telescope, we observe a smooth and fast spin-down process subsequent to the X-ray bursts resulting in a net change in the pulsar rotational frequency of $\Delta\nu\approx-4\times10^{-4}$\,Hz. During the transition, a net spin-down rate increase of $\Delta\dot\nu\approx-1\times10^{-10}$\,Hz\,s$^{-1}$ is observed, followed by a return of $\dot{\nu}$ to its original value. In addition, the radio pulsations disappeared after the X-ray bursts and reappeared about two weeks later with the flux density at 1.4\,GHz increased by a factor of five. The flux density then decreased and undershot the normal flux density followed by a slow recovery back to normal. The pulsar's integrated profile underwent dramatic and short-term changes in total intensity, polarization and position angle. Despite the complex evolution, we observe correlations between the spin-down rate, pulse profile shape and radio flux density. Strong single pulses have been detected after the X-ray bursts with their energy distributions evolving with time. The peculiar but smooth spin frequency evolution of PSR~J1119$-$6127 accompanied by systematic pulse profile and flux density changes are most likely to be a result of either reconfiguration of the surface magnetic fields or particle winds triggered by the X-ray bursts. The recovery of spin-down rate and pulse profile to normal provides us the best case to study the connection between high magnetic-field pulsars and magnetars.Comment: Accepted for publication in MNRAS on 2018 July 2

Six New Millisecond Pulsars from Arecibo Searches of Fermi Gamma-Ray Sources

We have discovered six radio millisecond pulsars (MSPs) in a search with the Arecibo telescope of 34 unidentified gamma-ray sources from the Fermi Large Area Telescope (LAT) 4-year point source catalog. Among the 34 sources, we also detected two MSPs previously discovered elsewhere. Each source was observed at a center frequency of 327 MHz, typically at three epochs with individual integration times of 15 minutes. The new MSP spin periods range from 1.99 to 4.66 ms. Five of the six pulsars are in interacting compact binaries (period < 8.1 hr), while the sixth is a more typical neutron star-white dwarf binary with an 83-day orbital period. This is a higher proportion of interacting binaries than for equivalent Fermi-LAT searches elsewhere. The reason is that Arecibo's large gain afforded us the opportunity to limit integration times to 15 minutes, which significantly increased our sensitivity to these highly accelerated systems. Seventeen of the remaining 26 gamma-ray sources are still categorized as strong MSP candidates, and will be re-searched.Comment: Accepted for publication in ApJ; 8 pages, 3 figures, 5 table

HST Astrometry of M4 and the Galactic Constant V_0/R_0

From multi-epoch WFPC2/HST observations we present astrometric measurements of stars in the Galactic globular cluster M4 (NGC 6121) and in the foreground/background. The presence of an extragalactic point source allows us to determine the absolute proper motion of the cluster, and, through use of the field stars in this region only 18 degree from the Galactic center, to measure the difference between the Oort constants, A-B. We find: (mu_alpha cos dec, mu_dec)_J2000 = (-13.21 +/- 0.35, -19.28 +/- 0.35) mas/yr, and A-B = V_0/R_0 = 27.6 +/- 1.7 km / s / kpc.Comment: 20 pages, 6 figures, A.J.__ACCEPTED__, 1 April, 2003, (...!