Radiative corrections to hard spectator scattering in B→ππB\to \pi\pi decays

We present the calculation of the next-to-leading corrections to the tree amplitudes which appear in the description of non-leptonic B-decays in the factorization approach. These corrections, together with radiative corrections to the jet functions, represent the full next-to-leading contributions to the dominant hard spectator scattering term generated by operators $O_{1,2}$ in the decay amplitudes. Using obtained analytical results we estimate $B\to\pi\pi$ branchings fractions in the physical (or BBNS) factorization scheme. We have also found that the imaginary part generated in the hard spectator scattering term is rather large compared to the imaginary part of the vertex contribution.Comment: text is improved and typos are corrected, accepted for publication in JHE

Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

We present exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set of possible spin values, $Z(G,q,s,v,w)$, where $v$ and $w$ are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial $Ph(G,q,s,w)$ that counts the number of colorings of the vertices of $G$ subject to the condition that colors of adjacent vertices are different, with a weighting $w$ that favors or disfavors colors in the interval $I_s$. We derive powerful new upper and lower bounds on $Z(G,q,s,v,w)$ for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for $Z(G,q,s,v,w)$ on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.Comment: 39 pages, 1 figur

Potts model on recursive lattices: some new exact results

We compute the partition function of the Potts model with arbitrary values of $q$ and temperature on some strip lattices. We consider strips of width $L_y=2$, for three different lattices: square, diced and `shortest-path' (to be defined in the text). We also get the exact solution for strips of the Kagome lattice for widths $L_y=2,3,4,5$. As further examples we consider two lattices with different type of regular symmetry: a strip with alternating layers of width $L_y=3$ and $L_y=m+2$, and a strip with variable width. Finally we make some remarks on the Fisher zeros for the Kagome lattice and their large q-limit.Comment: 17 pages, 19 figures. v2 typos corrected, title changed and references, acknowledgements and two further original examples added. v3 one further example added. v4 final versio

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phy

Soil biochemistry and microbial activity in vineyards under conventional and organic management at Northeast Brazil.

The São Francisco Submedium Valley is located at the Brazilian semiarid region and is an important center for irrigated fruit growing. This region is responsible for 97% of the national exportation of table grapes, including seedless grapes. Based on the fact that orgThe São Francisco Submedium Valley is located at the Brazilian semiarid region and is an important center for irrigated fruit growing. This region is responsible for 97% of the national exportation of table grapes, including seedless grapes. Based on the fact that organic fertilization can improve soil quality, we compared the effects of conventional and organic soil management on microbial activity and mycorrhization of seedless grape crops. We measured glomerospores number, most probable number (MPN) of propagules, richness of arbuscular mycorrhizal fungi (AMF) species, AMF root colonization, EE-BRSP production, carbon microbial biomass (C-MB), microbial respiration, fluorescein diacetate hydrolytic activity (FDA) and metabolic coefficient (qCO2). The organic management led to an increase in all variables with the exception of EE-BRSP and qCO2. Mycorrhizal colonization increased from 4.7% in conventional crops to 15.9% in organic crops. Spore number ranged from 4.1 to 12.4 per 50 g-1 soil in both management systems. The most probable number of AMF propagules increased from 79 cm-3 soil in the conventional system to 110 cm-3 soil in the organic system. Microbial carbon, CO2 emission, and FDA activity were increased by 100 to 200% in the organic crop. Thirteen species of AMF were identified, the majority in the organic cultivation system. Acaulospora excavata, Entrophospora infrequens, Glomus sp.3 and Scutellospora sp. were found only in the organically managed crop. S. gregaria was found only in the conventional crop. Organically managed vineyards increased mycorrhization and general soil microbial activity

Transversity Form Factors and Generalized Parton Distributions of the pion in chiral quark models

The transversity Generalized Parton Distributions (tGPDs) and related transversity form factors of the pion are evaluated in chiral quark models, both local (Nambu--Jona-Lasinio) and nonlocal, involving a momentum-dependent quark mass. The obtained tGPDs satisfy all a priori formal requirements, such as the proper support, normalization, and polynomiality. We evaluate generalized transversity form factors accessible from the recent lattice QCD calculations. These form factors, after the necessary QCD evolution, agree very well with the lattice data, confirming the fact that the spontaneously broken chiral symmetry governs the structure of the pion also in the case of the transversity observables.Comment: 6 pages, 3 figures, presented by WB at LIGHTCONE 2011, 23 - 27 May, 2011, Dalla

Fitting the integrated Spectral Energy Distributions of Galaxies

Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details ofdust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (sedfitting.org), where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.Comment: 54 pages, 26 figures, Accepted for publication in Astrophysics & Space Scienc

Coupled free-carrier and exciton relaxation in optically excited semiconductors

The energy relaxation of coupled free-carrier and exciton populations in semiconductors after low-density ultrafast optical excitation is studied through a kinetic approach. The set of semiclassical Boltzmann equations, usually written for electron and hole populations only, is complemented by an additional equation for the exciton distribution. The equations are coupled by reaction terms describing phonon-mediated exciton binding and dissociation. All the other relevant scattering mechanisms, such as carrier-carrier, carrier-phonon, and exciton-phonon interactions, are also included. The resulting system of rate equations in reciprocal space is solved by an extended ensemble Monte Carlo method. As a first application, we show results for the dynamics of bulk GaAs in the range from 1 to ∼200 ps after photoexcitation. The build-up of an exciton population and its sensitivity to the excitation conditions are discussed in detail. As a consequence of the pronounced energy dependence of the LO-phonon-assisted transition probabilities between free-pair states and excitons, it is found that the efficiency of the exciton-formation process and the temporal evolution of the resulting population are sensitive to the excitation energy. We discuss the effects on luminescence experiments