Numerical Algebraic Geometry: A New Perspective on String and Gauge Theories

The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these short-comings. Its so-called 'embarrassing parallelizability' allows us to solve many problems and extract physical information which elude the symbolic methods. We describe the method and then use it to solve various problems arising from physics which could not be otherwise solved.Comment: 36 page

Search for supersymmetric particles in scenarios with a gravitino LSP and stau NLSP

Sleptons, neutralinos and charginos were searched for in the context of scenarios where the lightest supersymmetric particle is the gravitino. It was assumed that the stau is the next-to-lightest supersymmetric particle. Data collected with the DELPHI detector at a centre-of-mass energy near 189 GeV were analysed combining the methods developed in previous searches at lower energies. No evidence for the production of these supersymmetric particles was found. Hence, limits were derived at 95% confidence level.Comment: 31 pages, 14 figure

Measurement of Trilinear Gauge Couplings in e+e−e^+ e^- Collisions at 161 GeV and 172 GeV

Trilinear gauge boson couplings are measured using data taken by DELPHI at 161~GeV and 172~GeV. Values for $WWV$ couplings ($V=Z, \gamma$) are determined from a study of the reactions \eeWW\ and \eeWev, using differential distributions from the $WW$ final state in which one $W$ decays hadronically and the other leptonically, and total cross-section data from other channels. Limits are also derived on neutral $ZV\gamma$ couplings from an analysis of the reaction \eegi

Study of B0_s anti-B0_s oscillations and B0_s lifetimes using hadronic decays of B0_s mesons

Oscillations of B0s mesons have been studied in samples selected from about 3.5 million hadronic Z decays detected by DELPHI between 1992 and 1995. One analysis uses events in the exclusive decay channels: B0s -> Ds- pi+ or Ds- a1+ and B0s -> anti-D0 K- pi+ or anti-D0 K- a1+, where the D decays are completely reconstructed. In addition, B0s anti-B0s oscillations have been studied in events with an exclusively reconstructed Ds accompanied in the same hemisphere by a high momentum hadron of opposite charge. Combining the two analyses, a limit on the mass difference between the physical B0s states has been obtained: Delta(m_B0s) > 4.0 ps^{-1} at the 95% C.L. with a sensitivity of Delta(m_B0s) = 3.2 ps^{-1}. Using the latter sample of events, the B0s lifetime has been measured and an upper limit on the decay width difference between the two physical B0s states has been obtained: tau(B0s) = 1.53^{+0.16}_{-0.15}(stat.) +/- {0.07}(syst.) ps \Delta\Gamma(B0s)/\Gamma(B0s) < 0.69 at the 95% C.L. The combination of these results with those obtained using Ds+- lepton-+ sample gives: Delta(m_B0s) > 4.9 ps^{-1} at the 95% C.L. with a sensitivity of Delta(m_B0s) = 8.7 ps^{-1}. tau(B0s) = 1.46 +/- 0.11 ps and \Delta\Gamma(B0s)/\Gamma(B0s) < 0.45 at the 95% C.L.Comment: 42 pages, 13 figure

A Precise measurement of the partial decay width ratio R(b)**0 = Gamma(b anti-b) / Gamma(had)

The partial decay width of the Z to b (b) over bar quark pairs has been measured by the DELPHI detector at LEP using data taken in the years 1992 to 1995. Decays of b-hadrons were tagged by several methods using tracks with large impact parameters and/or reconstructed secondary vertices; complemented by event shape variables. Combining these methods in a multivariate analysis the value Gamma(Z --> b (b) over bar)/Gamma(Z --> had) = 0.21634 +/- 0.00067(stat) +/- 0.00060(syst) was obtained, where the c (c) over bar production fraction was fixed to its Standard Model value. RI De Angelis, Alessandro/B-5372-2009; Ragazzi, Stefano/D-2463-2009; Gonzalez Caballero, Isidro/E-7354-2010; Krammer, Manfred/A-6508-2010; Muresan, Raluca-Anca/C-3725-2011; Katsanevas, Stavros/A-4297-2011; Ruiz, Alberto/E-4473-2011; Marti-Garcia, Salvador/F-3085-2011; Verzi, Valerio/B-1149-2012; branchini, paolo/A-4857-2011; Shellard, Ronald/G-4825-2012; Monge, Maria Roberta/G-9127-2012; Petrolini, Alessandro/H-3782-2011; Fruhwirth, Rudolf/H-2529-201

Search for Leptoquarks and FCNC in e(+)(e)(-) annihilations root s = 183 GeV

A search fur events with one jet and at most one isolated lepton used data taken at LEP-2 by the DELPHI detector. These data were accumulated at a center-of-mass energy of 183 GeV and correspond to an integrated luminosity of 47.7 pb(-1) Production of single scalar and vector leptoquarks was searched for. Limits at 95% confidence level were derived on the masses (ranging from 134GcV/c(2) to 171GeV/c(2) for electromagnetic type couplings) and couplings of the leptoquark rates. A search for top-charm flavour changing neutral currents (e(+)e(-) --&gt; (t) over bar c or charge conjugate) used the semileptonic decay channel. A limit on the flavour changing cross-section via neutral currents was set at 0.55pb (95%: confidence level). (C) 1999 Elsevier Science B.V. All rights reserved. RI De Angelis, Alessandro/B-5372-2009; Gonzalez Caballero, Isidro/E-7354-2010; Krammer, Manfred/A-6508-2010; Muresan, Raluca-Anca/C-3725-2011; Katsanevas, Stavros/A-4297-2011; Peralta, Luis/C-8369-2011; Ruiz, Alberto/E-4473-2011; Marti-Garcia, Salvador/F-3085-2011; Verzi, Valerio/B-1149-2012; branchini, paolo/A-4857-2011; Shellard, Ronald/G-4825-2012; Petrolini, Alessandro/H-3782-2011; Fruhwirth, Rudolf/H-2529-2012; Monge, Maria Roberta/G-9127-201