Lyubeznik numbers, F-modules and modules of generalized fractions

This paper presents an algorithm for calculation of the Lyubeznik numbers of a local ring which is a homomorphic image of a regular local ring R of prime characteristic. The methods used employ Lyubeznik's F-modules over R, particularly his F-finite F-modules, and also the modules of generalized fractions of Sharp and Zakeri. It is shown that many modules of generalized fractions over R have natural structures as F-modules; these lead to F-module structures on certain local cohomology modules over R, which are exploited, in conjunction with F-module structures on injective R-modules that result from work of Huneke and Sharp, to compute Lyubeznik numbers. The resulting algorithm has been implemented in Macaulay2

Criteria for flatness and injectivity

Let $R$ be a commutative Noetherian ring. We give criteria for flatness of $R$-modules in terms of associated primes and torsion-freeness of certain tensor products. This allows us to develop a criterion for regularity if $R$ has characteristic $p$, or more generally if it has a locally contracting endomorphism. Dualizing, we give criteria for injectivity of $R$-modules in terms of coassociated primes and (h-)divisibility of certain \Hom-modules. Along the way, we develop tools to achieve such a dual result. These include a careful analysis of the notions of divisibility and h-divisibility (including a localization result), a theorem on coassociated primes across a \Hom-module base change, and a local criterion for injectivity.Comment: 19 page

Intercalibration of the barrel electromagnetic calorimeter of the CMS experiment at start-up

Calibration of the relative response of the individual channels of the barrel electromagnetic calorimeter of the CMS detector was accomplished, before installation, with cosmic ray muons and test beams. One fourth of the calorimeter was exposed to a beam of high energy electrons and the relative calibration of the channels, the intercalibration, was found to be reproducible to a precision of about 0.3%. Additionally, data were collected with cosmic rays for the entire ECAL barrel during the commissioning phase. By comparing the intercalibration constants obtained with the electron beam data with those from the cosmic ray data, it is demonstrated that the latter provide an intercalibration precision of 1.5% over most of the barrel ECAL. The best intercalibration precision is expected to come from the analysis of events collected in situ during the LHC operation. Using data collected with both electrons and pion beams, several aspects of the intercalibration procedures based on electrons or neutral pions were investigated

Measurement of the mass difference between top quark and antiquark in pp collisions at root s=8 TeV

Peer reviewe

Measurements of the ϒ(1S), ϒ(2S), and ϒ(3S) differential cross sections in pp collisions at s=7TeV

Differential cross sections as a function of transverse momentum pTpT are presented for the production of ϒ(nS)ϒ(nS) (n = 1, 2, 3) states decaying into a pair of muons. Data corresponding to an integrated luminosity of 4.9View the MathML sourcefb−1 in pp collisions at View the MathML sources=7TeV were collected with the CMS detector at the LHC. The analysis selects events with dimuon rapidity |y|<1.2|y|<1.2 and dimuon transverse momentum in the range View the MathML source10<pT<100GeV. The measurements show a transition from an exponential to a power-law behavior at View the MathML sourcepT≈20GeV for the three ϒ states. Above that transition, the ϒ(3S)ϒ(3S) spectrum is significantly harder than that of the ϒ(1S)ϒ(1S). The ratios of the ϒ(3S)ϒ(3S) and ϒ(2S)ϒ(2S) differential cross sections to the ϒ(1S)ϒ(1S) cross section show a rise as pTpT increases at low pTpT, then become flatter at higher pTpT

Search for W ' -> tb in proton-proton collisions at root s=8 TeV

Peer reviewe

Search for stealth supersymmetry in events with jets, either photons or leptons, and low missing transverse momentum in pp collisions at 8 TeV

The results of a search for new physics in final states with jets, either photons or leptons, and low missing transverse momentum are reported. The study is based on a sample of proton-proton collisions collected at a center-of-mass energy s=8 TeV with the CMS detector in 2012. The integrated luminosity of the sample is 19.7 fb-1. Many models of new physics predict the production of events with jets, electroweak gauge bosons, and little or no missing transverse momentum. Examples include stealth models of supersymmetry (SUSY), which predict a hidden sector at the electroweak energy scale in which SUSY is approximately conserved. The data are used to search for stealth SUSY signatures in final states with either two photons or an oppositely charged electron and muon. No excess is observed with respect to the standard model expectation, and the results are used to set limits on squark pair production in the stealth SUSY framework

Measurement of the t-channel single-top-quark production cross section and of the |Vtb| CKM matrix element in pp collisions at SQR = 8 TeV

Measurements are presented of the t -channel single-top-quark production cross section in proton-proton collisions at s&#8730; = 8 TeV. The results are based on a data sample corresponding to an integrated luminosity of 19.7 fb &#8722;1 recorded with the CMS detector at the LHC. The cross section is measured inclusively, as well as separately for top (t) and antitop (t¯) , in final states with a muon or an electron. The measured inclusive t -channel cross section is &#963; t -ch. = 83 . 6 ± 2 . 3 (stat.) ± 7 . 4 (syst.) pb. The single t and t¯ cross sections are measured to be &#963; t -ch. ( t ) = 53 . 8 ± 1 . 5 (stat.) ± 4 . 4 (syst.) pb and &#963; t -ch. (t¯) = 27 . 6 ± 1 . 3 (stat.) ± 3 . 7 (syst.) pb, respectively. The measured ratio of cross sections is R t -ch. = &#963; t -ch. (t) /&#963; t -ch. (t¯) = 1 . 95 ± 0 . 10 (stat.) ± 0 . 19 (syst.), in agreement with the standard model prediction. The modulus of the Cabibbo-Kobayashi-Maskawa matrix element V tb is extracted and, in combination with a previous CMS result at s&#8730; = 7 TeV, a value | V tb | = 0 . 998 ± 0 . 038 (exp.) ± 0 . 016 (theo.) is obtained