Next-to-leading order QCD calculations with parton showers II: soft singularities

Programs that calculate observables in quantum chromodynamics at next-to-leading order typically generate events that consist of partons rather than hadrons -- and just a few partons at that. These programs would be much more useful if the few partons were turned into parton showers, which could be given to one of the Monte Carlo event generators to produce hadron showers. In a previous paper, we have seen how to generate parton showers related to the final state collinear singularities of the perturbative calculation for the example of e+ + e- --> 3 jets. This paper discusses the treatment of the soft singularities.Comment: 26 pages with 5 figures. This version is close to the version to be publishe

Structure of a new dense amorphous ice

The detailed structure of a new dense amorphous ice, VHDA, is determined by isotope substitution neutron diffraction. Its structure is characterized by a doubled occupancy of the stabilizing interstitial location that was found in high density amorphous ice, HDA. As would be expected for a thermally activated unlocking of the stabilizing "interstitial," the transition from VHDA to LDA (low-density amorphous ice) is very sharp. Although its higher density makes VHDA a better candidate than HDA for a physical manifestation of the second putative liquid phase of water, as for the HDA case, the VHDA to LDA transition also appears to be kinetically controlled

General subtraction method for numerical calculation of one-loop QCD matrix elements

We present a subtraction scheme for eliminating the ultraviolet, soft, and collinear divergences in the numerical calculation of an arbitrary one-loop QCD amplitude with an arbitrary number of external legs. The subtractions consist of local counter terms in the space of the four-dimensional loop momentum. The ultraviolet subtraction terms reproduce MSbar renormalization. The key point in the method for the soft and collinear subtractions is that, although the subtraction terms are defined graph-by-graph and the matrix element is also calculated graph-by-graph, the sum over graphs of the integral of each the subtraction term can be evaluated analytically and provides the well known simple pole structure that arises from subtractions from real emission graphs, but with the opposite sign.Comment: 38 pages, 10 figures, axodraw styl

Market Risk and Market-Implied Inflation Expectations

We examine interactions between market risk and market-implied inflation expectations. We argue that these interactions are asymmetric and varied in time. Specifically, market risk becomes elevated by expectations of either very low or high expected inflation. Market risk does not react to expectations of moderate, stable inflation. In our analysis, market risk is proxied by VIX and market-implied inflation expectations are reflected by five- and ten-year breakeven inflation. We use daily data for 5 and 10 year breakeven inflation and VIX for the sample period January 3, 2003 – January 24, 2019 for empirical testing. We employ asymptotic VAR, multiple breakpoint regression and Markov switching tests to examine changeable patterns in these interactions. Our tests indicate prevalence of responses of expected low inflation or deflation to higher market risk, mainly for the 5-year breakeven inflation series. These responses are particularly significant during the run-up and aftermath of the 2008 financial crisis

X-ray Diffraction and Molecular Dynamics Study of Medium-range Order in Ambient and Hot Water

We have developed x-ray diffraction measurements with high energy-resolution and accuracy to study water structure at three different temperatures (7, 25 and 66 C) under normal pressure. Using a spherically curved Ge crystal an energy resolution better than 15 eV has been achieved which eliminates influence from Compton scattering. The high quality of the data allows a precise oxygen-oxygen pair correlation function (PCF) to be directly derived from the Fourier transform of the experimental data resolving shell structure out to ~12 {\AA}, i.e. 5 hydration shells. Large-scale molecular dynamics (MD) simulations using the TIP4P/2005 force-field reproduce excellently the experimental shell-structure in the range 4-12 {\AA} although less agreement is seen for the first peak in the PCF. The Local Structure Index [J. Chem. Phys. 104, 7671 (1996)] identifies a tetrahedral minority giving the intermediate-range oscillations in the PCF and a disordered majority providing a more featureless background in this range. The current study supports the proposal that the structure of liquid water, even at high temperatures, can be described in terms of a two-state fluctuation model involving local structures related to the high-density and low-density forms of liquid water postulated in the liquid-liquid phase transition hypothesis.Comment: Submitted to Phys. Chem. Chem. Phy

Microscopic Structure of Liquid Nitric Oxide

The microscopic structure of nitric oxide is investigated using neutron scattering experiments. The measurements are performed at various temperatures between 120 and 144 K and at pressures between 1.1 and 9 bar. Using the technique of empirical potential structure refinement (EPSR), our results show that the dimer is the main form, around 80%, of nitric oxide in the liquid phase at 120 K, but the degree of dissociation to monomers increases with increasing temperature. The reported degree of dissociation of dimers, and its trend with increasing temperature, is consistent with earlier measurements and studies. It is also shown that nonplanar dimers are not inconsistent with the diffraction data and that the possibility of nitric oxide molecules forming longer oligomers, consisting of bonded nitrogen atoms along the backbone, cannot be ruled out in the liquid. A molecular dynamics simulation is used to compare the present EPSR simulations with an earlier proposed intermolecular potential for the liquid

Reducing full one-loop amplitudes to scalar integrals at the integrand level

We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no information on the analytical structure of the amplitude is required, making our method appealing for an efficient numerical implementationComment: updated versio

Efficiency improvements for the numerical computation of NLO corrections

In this paper we discuss techniques, which lead to a significant improvement of the efficiency of the Monte Carlo integration, when one-loop QCD amplitudes are calculated numerically with the help of the subtraction method and contour deformation. The techniques discussed are: holomorphic and non-holomorphic division into sub-channels, optimisation of the integration contour, improvement of the ultraviolet subtraction terms, importance sampling and antithetic variates in loop momentum space, recurrence relations.Comment: 34 pages, version to be publishe

Quark Mass Effects in Fermionic Decays of the Higgs Boson in O(αs2)O(\alpha_s^2) Perturbative QCD

The results of analytical evaluation of $O(\alpha_s^2)$ QCD contributions due to the nonvanishing quark masses to $\Gamma_{H\rightarrow q_f\overline{q}_f}$ are presented. The ``triangle anomaly'' type contributions are included. As a byproduct the $O(\alpha_s^3)$ logarithmic contributions are evaluated. The results are presented both in terms of running and pole quark masses. The partial decay modes $H \rightarrow b\overline{b}$ and $H \rightarrow c\overline{c}$ are considered. The calculated corrections decrease the absolute value of large and negative $O(\alpha_s^2)$ massless limit coefficient by $\leq 1\%$ in the intermediate mass region and by 1\%$-$20\% in the low mass region which, however, is experimentally ruled out. The results are relevant for $H \rightarrow t\overline{t}$ decay mode for the higher Higgs mass region where the mass effects are large and important. The high order corrections remove a very large discrepancy between the results for $\Gamma_{H\rightarrow q_f\overline{q}_f}$ in terms of running and pole quark masses almost completely and reduce the scale dependence from about 40\% to nearly 5\%.Comment: 16 pages, LATeX, +5 figures available upon request, preprint OITS-543 (University of Oregon, USA, May 1994). ( Additions are made: Previous general result for the H-->qq is applied to the H-->tt decay mode where the calculated corrections are significant.