A renormalisation-group approach to two-body scattering with long-range forces

We apply the renormalisation-group to two-body scattering by a combination of known long-range and unknown short-range forces. A crucial feature is that the low-energy effective theory is regulated by applying a cut-off in the basis of distorted waves for the long range potential. We illustrate the method by applying it to scattering in the presence of a repulsive 1/r^2 potential. We find a trivial fixed point, describing systems with weak short-range interactions, and a unstable fixed point. The expansion around the latter corresponds to a distorted-wave effective-range expansion.Comment: 4 pages (AIP style), talk presented at Mesons and Light Nuclei, Prague, 200

Cyclin A2 degradation during the spindle assembly checkpoint requires multiple binding modes to the APC/C.

The anaphase-promoting complex/cyclosome (APC/C) orchestrates cell cycle progression by controlling the temporal degradation of specific cell cycle regulators. Although cyclin A2 and cyclin B1 are both targeted for degradation by the APC/C, during the spindle assembly checkpoint (SAC), the mitotic checkpoint complex (MCC) represses APC/C's activity towards cyclin B1, but not cyclin A2. Through structural, biochemical and in vivo analysis, we identify a non-canonical D box (D2) that is critical for cyclin A2 ubiquitination in vitro and degradation in vivo. During the SAC, cyclin A2 is ubiquitinated by the repressed APC/C-MCC, mediated by the cooperative engagement of its KEN and D2 boxes, ABBA motif, and the cofactor Cks. Once the SAC is satisfied, cyclin A2 binds APC/C-Cdc20 through two mutually exclusive binding modes, resulting in differential ubiquitination efficiency. Our findings reveal that a single substrate can engage an E3 ligase through multiple binding modes, affecting its degradation timing and efficiency

Effective theories of scattering with an attractive inverse-square potential and the three-body problem

A distorted-wave version of the renormalisation group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wave function satisfies a Schroedinger equation with an attractive inverse-square potential, as shown by Efimov. The resulting oscillatory behaviour controls the renormalisation of the three-body interactions, with the renormalisation-group flow tending to a limit cycle as the cut-off is lowered. The approach used here leads to single-valued potentials with discontinuities as the bound states are cut off. The perturbations around the cycle start with a marginal term whose effect is simply to change the phase of the short-distance oscillations, or the self-adjoint extension of the singular Hamiltonian. The full power counting in terms of the energy and two-body scattering length is constructed for short-range three-body forces.Comment: 19 pages (RevTeX), 2 figure

Precise numerical results for limit cycles in the quantum three-body problem

The study of the three-body problem with short-range attractive two-body forces has a rich history going back to the 1930's. Recent applications of effective field theory methods to atomic and nuclear physics have produced a much improved understanding of this problem, and we elucidate some of the issues using renormalization group ideas applied to precise nonperturbative calculations. These calculations provide 11-12 digits of precision for the binding energies in the infinite cutoff limit. The method starts with this limit as an approximation to an effective theory and allows cutoff dependence to be systematically computed as an expansion in powers of inverse cutoffs and logarithms of the cutoff. Renormalization of three-body bound states requires a short range three-body interaction, with a coupling that is governed by a precisely mapped limit cycle of the renormalization group. Additional three-body irrelevant interactions must be determined to control subleading dependence on the cutoff and this control is essential for an effective field theory since the continuum limit is not likely to match physical systems ({\it e.g.}, few-nucleon bound and scattering states at low energy). Leading order calculations precise to 11-12 digits allow clear identification of subleading corrections, but these corrections have not been computed.Comment: 37 pages, 8 figures, LaTeX, uses graphic

Naive Dimensional Analysis for Three-Body Forces Without Pions

For systems of three identical particles in which short-range forces produce shallow two-particle bound states, and in particular for the ``pion-less'' Effective Field Theory of Nuclear Physics, I extend and systematise the power-counting of three-body forces to all partial-waves and orders, including external currents. With low-energy observables independent of the details of short-distance dynamics, the typical strength of a three-body force is determined from the superficial degree of divergence of the three-body diagrams which contain only two-body forces. This na\"ive dimensional analysis must be amended as the asymptotic solution to the leading-order Faddeev equation depends for large off-shell momenta crucially on the partial wave and spin-combination of the system. It is shown by analytic construction to be weaker in most channels with angular momentum smaller than 3 than expected. This demotes many three-nucleon forces to high orders. Observables like the quartet-S-scattering length are less sensitive to three-nucleon forces than guessed. I also comment on the Efimov effect and limit-cycle for non-zero angular momentum.Comment: 31 pages LaTeX2e, including 8 figures in 13 .eps files, embedded with includegraphicx; linguistic corrections only, version to appear in Nucl Phys

Simultaneous and extensive removal of the East Asian lithospheric root

Much evidence points to a dramatic thinning of East Asian lithosphere during the Mesozoic, but with little precision on when, or over what time scale. Using geochemical constraints, we examine an extensive compilation of dated volcanic samples from Russia, Mongolia and North China to determine when the lithosphere thinned and how long that process took. Geochemical results suggest that magmatism before 107 Ma derived from metasomatised subcontinental lithospheric mantle (SCLM), whereas after 107 Ma, melt predominantly derived from an asthenospheric source. The switch to an asthenospheric magma source at ~107 Ma occurred in both Mongolia and North China (>1600 km apart), whereas in eastern Russia the switch occurred a little later (~85 Ma). Such a dramatic change to an asthenospheric contribution appears to have taken, from beginning to end, just ~30 Myrs, suggesting this is the duration for lithospheric mantle weakening and removal. Subsequent volcanism, through the Cenozoic in Mongolia and North China does not appear to include any contribution from the removed SCLM, despite melts predominantly deriving from the asthenosphere

Evidence for southward subduction of the Mongol-Okhotsk oceanic plate: Implications from Mesozoic adakitic lavas from Mongolia

A combination of new 40Ar/39Ar dating results, major- and trace-element data, plus Sr-Nd-Pb-Hf isotope data, are used to investigate the petrogenesis of Triassic high-Si adakite (HSA), Cretaceous low-Si adakite-like (LSA) lavas, and Cretaceous high-K and shoshonitic trachyandesite lavas, from eastern and south-central Mongolia. All samples are light rare-earth element and large-ion lithophile element enriched but depleted in some high-field strength elements (notably Nb, Ta and Ti). Two alternative models are proposed to explain the petrogenesis of the HSA samples. (1) A southward-subducting Mongol-Okhotsk slab underwent partial melting in the Triassic during the closure of the Mongol-Okhotsk Ocean, with the resultant melts assimilating mantle and crustal material. Alternatively (2), a basaltic underplate of thickened (>50 km; >1.5 GPa), eclogitic lower crust foundered into the underlying mantle, and underwent partial melting with minor contamination from mantle material and some shallow-level crustal contamination. The LSA samples are interpreted as melts derived from a lithospheric mantle wedge that was previously metasomatised by slab melts. Similarly, the trachyandesite lavas are interpreted as melts deriving from a subduction-enriched subcontinental lithospheric mantle. The spatial distribution of these samples implies that metasomatism likely occurred due to a southward-subducting Mongol-Okhotsk slab associated with the closure of the Mongol-Okhotsk Ocean. When this interpretation is combined with previous evidence for a northward-subducting Mongol-Okhotsk slab it advocates that the Mongol-Okhotsk Ocean closed with double-sided subduction

Data collection with a tailored X-ray beam size at 2.69 angstrom wavelength (4.6 keV):sulfur SAD phasing of Cdc23(Nterm)

The capability to reach wavelengths of up to 3.1 Å at the newly established EMBL P13 beamline at PETRA III, the new third-generation synchrotron at DESY in Hamburg, provides the opportunity to explore very long wavelengths to harness the sulfur anomalous signal for phase determination. Data collection at $\lambda$ = 2.69 Å (4.6 keV) allowed the crystal structure determination by sulfur SAD phasing of Cdc23$^{Nterm}$, a subunit of the multimeric anaphase-promoting complex (APC/C). At this energy, Cdc23$^{Nterm}$ has an expected Bijvoet ratio <|F$_{anom}$|>/<F> of 2.2%, with 282 residues, including six cysteines and five methionine residues, and two molecules in the asymmetric unit (65.4 kDa; 12 Cys and ten Met residues). Selectively illuminating two separate portions of the same crystal with an X-ray beam of 50 µm in diameter allowed crystal twinning to be overcome. The crystals diffracted to 3.1 Å resolution, with unit-cell parameters a = b = 61.2, c = 151.5 Å, and belonged to space group $P4_3$. The refined structure to 3.1 Å resolution has an R factor of 18.7% and an R$_{free}$ of 25.9%. This paper reports the structure solution, related methods and a discussion of the instrumentation

A renormalisation group approach to two-body scattering in the presence of long-range forces

We apply renormalisation-group methods to two-body scattering by a combination of known long-range and unknown short-range potentials. We impose a cut-off in the basis of distorted waves of the long-range potential and identify possible fixed points of the short-range potential as this cut-off is lowered to zero. The expansions around these fixed points define the power countings for the corresponding effective field theories. Expansions around nontrivial fixed points are shown to correspond to distorted-wave versions of the effective-range expansion. These methods are applied to scattering in the presence of Coulomb, Yukawa and repulsive inverse-square potentials.Comment: 22 pages (RevTeX), 4 figure

Connecting Quorum Sensing, c-di-GMP, Pel Polysaccharide, and Biofilm Formation in Pseudomonas aeruginosa through Tyrosine Phosphatase TpbA (PA3885)

With the opportunistic pathogen Pseudomonas aeruginosa, quorum sensing based on homoserine lactones was found to influence biofilm formation. Here we discern a mechanism by which quorum sensing controls biofilm formation by screening 5850 transposon mutants of P. aeruginosa PA14 for altered biofilm formation. This screen identified the PA3885 mutant, which had 147-fold more biofilm than the wild-type strain. Loss of PA3885 decreased swimming, abolished swarming, and increased attachment, although this did not affect production of rhamnolipids. The PA3885 mutant also had a wrinkly colony phenotype, formed pronounced pellicles, had substantially more aggregation, and had 28-fold more exopolysaccharide production. Expression of PA3885 in trans reduced biofilm formation and abolished aggregation. Whole transcriptome analysis showed that loss of PA3885 activated expression of the pel locus, an operon that encodes for the synthesis of extracellular matrix polysaccharide. Genetic screening identified that loss of PelABDEG and the PA1120 protein (which contains a GGDEF-motif) suppressed the phenotypes of the PA3885 mutant, suggesting that the function of the PA3885 protein is to regulate 3,5-cyclic diguanylic acid (c-di-GMP) concentrations as a phosphatase since c-di-GMP enhances biofilm formation by activating PelD, and c-di-GMP inhibits swarming. Loss of PA3885 protein increased cellular c-di-GMP concentrations; hence, PA3885 protein is a negative regulator of c-di-GMP production. Purified PA3885 protein has phosphatase activity against phosphotyrosine peptides and is translocated to the periplasm. Las-mediated quorum sensing positively regulates expression of the PA3885 gene. These results show that the PA3885 protein responds to AHL signals and likely dephosphorylates PA1120, which leads to reduced c-di-GMP production. This inhibits matrix exopolysaccharide formation, which leads to reduced biofilm formation; hence, we provide a mechanism for quorum sensing control of biofilm formation through the pel locus and suggest PA3885 should be named TpbA for tyrosine phosphatase related to biofilm formation and PA1120 should be TpbB