Derivation of Friedman Equations

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2014, Tutor: Eduard Salvador SoléIn this report we make a detailed derivation of Friedman Equations, which are the dy- namical equations of a homogeneous and isotropic universe. First, we derive them in the framework of the General Relativity keeping the relativistic expressions as a reference for the rest of the report. Then, using the Newtonian formalism and solving some fundamental problems, we reach some dy- namical equations for the universe and compare the results with the relativistic ones, focusing our attention on the meaning of the expressions and on the cosmological constant

Measurement of the forward Z boson production cross-section in pp collisions at s=13\sqrt{s} = 13 TeV

A measurement of the production cross-section of Z bosons in pp collisions at $\sqrt{s} = 13$ TeV is presented using dimuon and dielectron final states in LHCb data. The cross-section is measured for leptons with pseudorapidities in the range $2.0 \eta 4.5$, transverse momenta $p_\text{T} 20$ GeV and dilepton invariant mass in the range $60 m(\ell\ell) 120$ GeV. The integrated cross-section from averaging the two final states is \begin{equation*}\sigma_{\text{Z}}^{\ell\ell} = 194.3 \pm 0.9 \pm 3.3 \pm 7.6\text{ pb,}\end{equation*} where the first uncertainty is statistical, the second is due to systematic effects, and the third is due to the luminosity determination. In addition, differential cross-sections are measured as functions of the Z boson rapidity, transverse momentum and the angular variable $\phi^*_\eta$

Les droits disciplinaires des fonctions publiques : « unification », « harmonisation » ou « distanciation ». A propos de la loi du 26 avril 2016 relative à la déontologie et aux droits et obligations des fonctionnaires

The production of tt‾ , W+bb‾ and W+cc‾ is studied in the forward region of proton–proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98±0.02 fb−1 . The W bosons are reconstructed in the decays W→ℓν , where ℓ denotes muon or electron, while the b and c quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions.The production of $t\overline{t}$, $W+b\overline{b}$ and $W+c\overline{c}$ is studied in the forward region of proton-proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98 $\pm$ 0.02 \mbox{fb}^{-1}. The $W$ bosons are reconstructed in the decays $W\rightarrow\ell\nu$, where $\ell$ denotes muon or electron, while the $b$ and $c$ quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions

Physics case for an LHCb Upgrade II - Opportunities in flavour physics, and beyond, in the HL-LHC era

The LHCb Upgrade II will fully exploit the flavour-physics opportunities of the HL-LHC, and study additional physics topics that take advantage of the forward acceptance of the LHCb spectrometer. The LHCb Upgrade I will begin operation in 2020. Consolidation will occur, and modest enhancements of the Upgrade I detector will be installed, in Long Shutdown 3 of the LHC (2025) and these are discussed here. The main Upgrade II detector will be installed in long shutdown 4 of the LHC (2030) and will build on the strengths of the current LHCb experiment and the Upgrade I. It will operate at a luminosity up to 2×1034 cm−2s−1, ten times that of the Upgrade I detector. New detector components will improve the intrinsic performance of the experiment in certain key areas. An Expression Of Interest proposing Upgrade II was submitted in February 2017. The physics case for the Upgrade II is presented here in more depth. CP-violating phases will be measured with precisions unattainable at any other envisaged facility. The experiment will probe b → sl+l−and b → dl+l− transitions in both muon and electron decays in modes not accessible at Upgrade I. Minimal flavour violation will be tested with a precision measurement of the ratio of B(B0 → μ+μ−)/B(Bs → μ+μ−). Probing charm CP violation at the 10−5 level may result in its long sought discovery. Major advances in hadron spectroscopy will be possible, which will be powerful probes of low energy QCD. Upgrade II potentially will have the highest sensitivity of all the LHC experiments on the Higgs to charm-quark couplings. Generically, the new physics mass scale probed, for fixed couplings, will almost double compared with the pre-HL-LHC era; this extended reach for flavour physics is similar to that which would be achieved by the HE-LHC proposal for the energy frontier

LHCb upgrade software and computing : technical design report

This document reports the Research and Development activities that are carried out in the software and computing domains in view of the upgrade of the LHCb experiment. The implementation of a full software trigger implies major changes in the core software framework, in the event data model, and in the reconstruction algorithms. The increase of the data volumes for both real and simulated datasets requires a corresponding scaling of the distributed computing infrastructure. An implementation plan in both domains is presented, together with a risk assessment analysis

Observation of the Doubly Charmed Baryon Xi(++)(cc)

International audienceA highly significant structure is observed in the Λc+K-π+π+ mass spectrum, where the Λc+ baryon is reconstructed in the decay mode pK-π+. The structure is consistent with originating from a weakly decaying particle, identified as the doubly charmed baryon Ξcc++. The difference between the masses of the Ξcc++ and Λc+ states is measured to be 1334.94±0.72(stat.)±0.27(syst.)  MeV/c2, and the Ξcc++ mass is then determined to be 3621.40±0.72(stat.)±0.27(syst.)±0.14(Λc+)  MeV/c2, where the last uncertainty is due to the limited knowledge of the Λc+ mass. The state is observed in a sample of proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 1.7  fb-1, and confirmed in an additional sample of data collected at 8 TeV

Measurement of branching fractions of charmless four-body Λ⁰_b and Ξ⁰_b decays

A search for charmless four-body decays of Λ b 0 and Ξ b 0 baryons with a proton and three charged mesons (either kaons or pions) in the final state is performed. The data sample used was recorded in 2011 and 2012 with the LHCb experiment and corresponds to an integrated luminosity of 3 fb−1. Six decay modes are observed, among which Λ b 0  → pK−π+π−, Λ b 0  → pK−K+K−, Ξ b 0  → pK−π+π− and Ξ b 0  → pK−π+K− are established for the first time. Their branching fractions (including the ratio of hadronisation fractions in the case of the Ξ b 0 baryon) are determined relative to the Λ b 0  → Λ c + π− decay

Measurement of forward W→eνW\to e\nu production in pppp collisions at s=8 \sqrt{s}=8\,TeV

A measurement of the cross-section for $W \to e\nu$ production in $pp$ collisions is presented using data corresponding to an integrated luminosity of $2\,$fb$^{-1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8\,$TeV. The electrons are required to have more than $20\,$GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive $W$ production cross-sections, where the $W$ decays to $e\nu$, are measured to be \begin{align*} \begin{split} \sigma_{W^{+} \to e^{+}\nu_{e}}&=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\,\mathrm{pb},\\ \sigma_{W^{-} \to e^{-}\bar{\nu}_{e}}&=\,\,\,809.0\pm 1.9\pm 18.1\pm\,\,\,7.0\pm \phantom{0}9.4\,\mathrm{pb}, \end{split} \end{align*} where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination. Differential cross-sections as a function of the electron pseudorapidity are measured. The $W^{+}/W^{-}$ cross-section ratio and production charge asymmetry are also reported. Results are compared with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. Finally, in a precise test of lepton universality, the ratio of $W$ boson branching fractions is determined to be \begin{align*} \begin{split} \mathcal{B}(W \to e\nu)/\mathcal{B}(W \to \mu\nu)=1.020\pm 0.002\pm 0.019, \end{split} \end{align*} where the first uncertainty is statistical and the second is systematic.A measurement of the cross-section for $W \to e\nu$ production in $pp$ collisions is presented using data corresponding to an integrated luminosity of $2\,$fb$^{-1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8\,$TeV. The electrons are required to have more than $20\,$GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive $W$ production cross-sections, where the $W$ decays to $e\nu$, are measured to be \begin{equation*} \sigma_{W^{+} \to e^{+}\nu_{e}}=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\,\mathrm{pb}, \end{equation*} \begin{equation*} \sigma_{W^{-} \to e^{-}\bar{\nu}_{e}}=\,\,\,809.0\pm 1.9\pm 18.1\pm\,\,\,7.0\pm \phantom{0}9.4\,\mathrm{pb}, \end{equation*} where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination. Differential cross-sections as a function of the electron pseudorapidity are measured. The $W^{+}/W^{-}$ cross-section ratio and production charge asymmetry are also reported. Results are compared with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. Finally, in a precise test of lepton universality, the ratio of $W$ boson branching fractions is determined to be \begin{equation*} \mathcal{B}(W \to e\nu)/\mathcal{B}(W \to \mu\nu)=1.020\pm 0.002\pm 0.019, \end{equation*} where the first uncertainty is statistical and the second is systematic.A measurement of the cross-section for W → eν production in pp collisions is presented using data corresponding to an integrated luminosity of 2 fb$^{−1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8$ TeV. The electrons are required to have more than 20 GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive W production cross-sections, where the W decays to eν, are measured to be ${\sigma}_{W^{+}\to {e}^{+}{\nu}_e}=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\kern0.5em \mathrm{p}\mathrm{b},$ ${\sigma}_{W^{-}\to {e}^{-}{\overline{\nu}}_e}=809.0\pm 1.9\pm 18.1\pm \kern0.5em 7.0\pm \kern0.5em 9.4\,\mathrm{p}\mathrm{b},$ where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination

Measurements of prompt charm production cross-sections in pp collisions at s=5 \sqrt{s}=5 TeV

Production cross-sections of prompt charm mesons are measured using data from $pp$ collisions at the LHC at a centre-of-mass energy of $5\,$TeV. The data sample corresponds to an integrated luminosity of $8.60\pm0.33\,$pb$^{-1}$ collected by the LHCb experiment. The production cross-sections of $D^0$, $D^+$, $D_s^+$, and $D^{*+}$ mesons are measured in bins of charm meson transverse momentum, $p_{\text{T}}$, and rapidity, $y$. They cover the rapidity range $2.0 < y < 4.5$ and transverse momentum ranges $0 < p_{\text{T}} < 10\, \text{GeV}/c$ for $D^0$ and $D^+$ and $1 < p_{\text{T}} < 10\, \text{GeV}/c$ for $D_s^+$ and $D^{*+}$ mesons. The inclusive cross-sections for the four mesons, including charge-conjugate states, within the range of $1 < p_{\text{T}} < 8\, \text{GeV}/c$ are determined to be \begin{equation*} \sigma(pp\rightarrow D^0 X) = 1190 \pm 3 \pm 64\,\mu\text{b} \end{equation*} \begin{equation*} \sigma(pp\rightarrow D^+ X) = 456 \pm 3 \pm 34\,\mu\text{b} \end{equation*} \begin{equation*} \sigma(pp\rightarrow D_s^+ X) = 195 \pm 4 \pm 19\,\mu\text{b} \end{equation*} \begin{equation*} \sigma(pp\rightarrow D^{*+} X)= 467 \pm 6 \pm 40\,\mu\text{b} \end{equation*} where the uncertainties are statistical and systematic, respectively.Production cross-sections of prompt charm mesons are measured using data from pp collisions at the LHC at a centre-of-mass energy of 5 TeV. The data sample corresponds to an integrated luminosity of 8.60 ± 0.33 pb$^{−1}$ collected by the LHCb experiment. The production cross-sections of D$^{0}$, D$^{+}$, D$_{s}^{+}$ , and D$^{∗+}$ mesons are measured in bins of charm meson transverse momentum, p$_{T}$, and rapidity, y. They cover the rapidity range 2.0 < y < 4.5 and transverse momentum ranges 0 < p$_{T}$ < 10 GeV/c for D$^{0}$ and D$^{+}$ and 1 < p$_{T}$ < 10 GeV/c for D$_{s}^{+}$ and D$^{∗+}$ mesons. The inclusive cross-sections for the four mesons, including charge-conjugate states, within the range of 1 < p$_{T}$ < 8 GeV/c are determined to be $\begin{array}{l}\sigma \left( pp\to {D}^0X\right)=1004\pm 3\pm 54\mu \mathrm{b},\\ {}\sigma \left( pp\to {D}^{+}X\right)=402\pm 2\pm 30\mu \mathrm{b},\\ {}\sigma \left( pp\to {D}_s^{+}X\right)=170\pm 4\pm 16\mu \mathrm{b},\\ {}\sigma \left( pp\to {D}^{\ast +}X\right)=421\pm 5\pm 36\mu \mathrm{b},\end{array}$ where the uncertainties are statistical and systematic, respectively.Production cross-sections of prompt charm mesons are measured using data from $pp$ collisions at the LHC at a centre-of-mass energy of $5\,$TeV. The data sample corresponds to an integrated luminosity of $8.60\pm0.33\,$pb$^{-1}$ collected by the LHCb experiment. The production cross-sections of $D^0$, $D^+$, $D_s^+$, and $D^{*+}$ mesons are measured in bins of charm meson transverse momentum, $p_{\text{T}}$, and rapidity, $y$. They cover the rapidity range $2.0<y<4.5$ and transverse momentum ranges $0 < p_{\text{T}} < 10\, \text{GeV}/c$ for $D^0$ and $D^+$ and $1 < p_{\text{T}} < 10\, \text{GeV}/c$ for $D_s^+$ and $D^{*+}$ mesons. The inclusive cross-sections for the four mesons, including charge-conjugate states, within the range of $1 < p_{\text{T}} < 8\, \text{GeV}/c$ are determined to be \sigma(pp\rightarrow D^0 X) = 1004 \pm 3 \pm 54\,\mu\text{b} \sigma(pp\rightarrow D^+ X) = 402 \pm 2 \pm 30\,\mu\text{b} \sigma(pp\rightarrow D_s^+ X) = 170 \pm 4 \pm 16\,\mu\text{b} \sigma(pp\rightarrow D^{*+} X)= 421 \pm 5 \pm 36\,\mu\text{b} where the uncertainties are statistical and systematic, respectively

Measurement of the J/ψ pair production cross-section in pp collisions at s=13 \sqrt{s}=13 TeV

The production cross-section of J/ψ pairs is measured using a data sample of pp collisions collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of 279 ±11 pb$^{−1}$. The measurement is performed for J/ψ mesons with a transverse momentum of less than 10 GeV/c in the rapidity range 2.0 < y < 4.5. The production cross-section is measured to be 15.2 ± 1.0 ± 0.9 nb. The first uncertainty is statistical, and the second is systematic. The differential cross-sections as functions of several kinematic variables of the J/ψ pair are measured and compared to theoretical predictions.The production cross-section of $J/\psi$ pairs is measured using a data sample of $pp$ collisions collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s} = 13 \,{\mathrm{TeV}}$, corresponding to an integrated luminosity of $279 \pm 11 \,{\mathrm{pb^{-1}}}$. The measurement is performed for $J/\psi$ mesons with a transverse momentum of less than $10 \,{\mathrm{GeV}}/c$ in the rapidity range $2.0<y<4.5$. The production cross-section is measured to be $15.2 \pm 1.0 \pm 0.9 \,{\mathrm{nb}}$. The first uncertainty is statistical, and the second is systematic. The differential cross-sections as functions of several kinematic variables of the $J/\psi$ pair are measured and compared to theoretical predictions