Conceptual introduction to quantum mechanics: some keys ideas

Grao en FísicaPódese consultar a versión en castelán en: http://hdl.handle.net/10347/12470[EN]The course work presented here is a mathematically precise introduction to the conceptual body, and calculation tools, of Quantum Mechanics, as a basis for the study of Quantum Physics. It is addressed to those that, having a mathematical background in differential and integral calculus, and being familiar with Classical Mechanics and waves, would like to have an insight into the foundations of Quantum Mechanics, and acquire in a short period of time the power of calculation to resolve physical problems in this field. In particular, to students following a course of Quantum Physics in a graduate program, either in Science or Engineering. Feynman's propagation is used as an axiomatic basis for Quantum Mechanics, completed with the generally admitted ideas about the measurement problem. A simple notion is provided of the immersion that Quantum Mechanics undergoes in Quantum Field Theory, illustrated with the emission of quanta. This course has been conducted at the University of Santiago de Compostela in recent years, as part of the graduate program in Physics. It is continued with a second part containing the analytic resolution of a number of normalized cases of the Schrödinger equation, within the subject of Quantum Physics I.[ES]El material didáctico que se presenta aquí es una introducción, matemáticamente precisa, al cuerpo conceptual y herramientas de cálculo de la Mecánica Cuántica, como base para el estudio de la Física Cuántica. Está dirigido a personas que, teniendo una base matemática en el cálculo diferencial e integral, y estando familiarizados con la Mecánica Clásica y las ondas, deseen conocer de cerca los fundamentos de la Mecánica Cuántica, y adquirir en poco tiempo capacidad operativa para la resolución de problemas físicos en esta disciplina. En particular, a alumnos que cursen una asignatura de Física Cuántica, en cualquier programa universitario, ya sea en Ciencias o Ingeniería. Se utiliza la propagación de Feynman como base axiomática de la Mecánica Cuántica, completada con las ideas generalmente admitidas sobre el problema de la medida. Se proporciona una idea simple de la inmersión que sufre dicha Mecánica Cuántica en la Teoría Cuántica de Campos, ilustrado con la emisión de cuanta. Este curso se ha llevado a cabo durante los últimos años en la Universidad de Santiago de Compostela, dentro del programa de grado en Física, y se continúa con la resolución analítica de una serie de casos normalizados de la ecuación de Schrödinger, como parte de la asignatura de Física Cuántica I

Measurement of forward Z → e+e− production s√s=8 TeV

A measurement of the cross-section for Z-boson production in the forward region of pp collisions at 8 TeV centre-of-mass energy is presented. The measurement is based on a sample of Z → e+e− decays reconstructed using the LHCb detector, corresponding to an integrated luminosity of 2.0 fb−1. The acceptance is defined by the requirements 2.0 20 GeV for the pseudorapidities and transverse momenta of the leptons. Their invariant mass is required to lie in the range 60-120 GeV. The cross-section is determined to beS

Measurement of indirect CP asymmetries in D0 → K−K+ and D0 → π−π+ decays using semileptonic B decays

Time-dependent CP asymmetries in the decay rates of the singly Cabibbo-suppressed decays D0 → K−K+ and D0 → π−π+ are measured in pp collision data corresponding to an integrated luminosity of 3.0 fb−1 collected by the LHCb experiment. The D0 mesons are produced in semileptonic b-hadron decays, where the charge of the accompanying muon is used to determine the initial state as D0 or D¯0. The asymmetries in effective lifetimes between D0 and D¯0 decays, which are sensitive to indirect CP violation, are determined to be AΓ(K−K+)=(−0.134±0.077−0.026−0.034)%,AΓ(π−π+)=(−0.092±0.145−0.025−0.033)%, where the first uncertainties are statistical and the second systematic. This result is in agreement with previous measurements and with the hypothesis of no indirect CP violation in D0 decays.S

Precise measurements of the properties of the B1(5721)0,+ and B *2(5747)0,+ states and observation of B+,0π−,+ mass structures

Invariant mass distributions of B+π− and B0π+ combinations are investigated in order to study excited B mesons. The analysis is based on a data sample corresponding to 3.0 fb−1 of pp collision data, recorded by the LHCb detector at centre-of-mass energies of 7 and 8 TeV. Precise measurements of the masses and widths of the B1(5721)0,+ and B2(5747)0,+ states are reported. Clear enhancements, particularly prominent at high pion transverse momentum, are seen over background in the mass range 5850-6000 MeV in both B+π− and B0π+ combinations. The structures are consistent with the presence of four excited B mesons, labelled B J (5840)0,+ and B J (5960)0,+, whose masses and widths are obtained under different hypotheses for their quantum numbersS

Observation of the B0→ρ0ρ0 decay from an amplitude analysis of B0→(π+π−)(π+π−)decays

Proton–proton collision data recorded in 2011 and 2012 by the LHCb experiment, corresponding to an integrated luminosity of 3.0fb−1, are analysed to search for the charmless B0→ρ0ρ0decay. More than 600 B0→(π+π−)(π+π−)signal decays are selected and used to perform an amplitude analysis, under the assumption of no CP violation in the decay, from which the B0→ρ0ρ0decay is observed for the first time with 7.1 standard deviations significance. The fraction of B0→ρ0ρ0decays yielding a longitudinally polarised final state is measured to be fL=0.745+0.048−0.058(stat) ±0.034(syst). The B0→ρ0ρ0branching fraction, using the B0→φK∗(892)0decay as reference, is also reported as B(B0→ρ0ρ0)=(0.94±0.17(stat)±0.09(syst)±0.06(BF))×10−6S

Study of the rare B0s and B0s decays into the π+π−μ+μ−final state

A search for the rare decays B0s→π+π−μ+μ−and B0→π+π−μ+μ−is performed in a data set corresponding to an integrated luminosity of 3.0fb−1collected by the LHCb detector in proton–proton collisions at centre-of-mass energies of 7 and 8TeV. Decay candidates with pion pairs that have invariant mass in the range 0.5–1.3GeV/c2and with muon pairs that do not originate from a resonance are considered. The first observation of the decay B0s→π+π−μ+μ−and the first evidence of the decay B0→π+π−μ+μ−are obtained and the branching fractions, restricted to the dipion-mass range considered, are measured to be B(B0s→π+π−μ+μ−) =(8.6 ±1.5(stat) ±0.7(syst) ±0.7 (norm)) ×10−8and B(B0→π+π−μ+μ−) =(2.11±0.51(stat)±0.15(syst)±0.16(norm))×10−8, where the third uncertainty is due to the branching fraction of the decay B0→J/ψ(→μ+μ−)K∗(892)0(→K+π−), used as a normalisation.S

Measurement of the CP-violating phase βin B0→J/ψπ+π−decays and limits on penguin effects

Time-dependent CPviolation is measured in the (—)B0→J/ψπ+π−channel for each π+π−resonant final state using data collected with an integrated luminosity of 3.0fb−1in ppcollisions using the LHCb detector. The final state with the largest rate, J/ψρ0(770), is used to measure the CP-violating angle 2βeffto be (41.7 ±9.6+2.8−6.3)◦.This result can be used to limit the size of penguin amplitude contributions to CPviolation measurements in, for example, (—)B0s→J/ψφdecays. Assuming approximate SU(3) flavour symmetry and neglecting higher order diagrams, the shift in the CP-violating phase φsis limited to be within the interval [−1.05◦, +1.18◦] at 95% confidence level. Changes to the limit due to SU(3) symmetry breaking effects are also discussed.S

Search for CP violation in D0→π−π+π0 decays with the energy test

A search for time-integrated CPviolation in the Cabibbo-suppressed decay D0→π−π+π0is performed using for the first time an unbinned model-independent technique known as the energy test. Using proton–proton collision data, corresponding to an integrated luminosity of 2.0fb−1collected by the LHCbdetector at a centre-of-mass energy of √s=8TeV, the world’s best sensitivity to CPviolation in this decay is obtained. The data are found to be consistent with the hypothesis of CPsymmetry with a p-value of (2.6 ±0.5)%S

Measurement of CP asymmetries and polarisation fractions in B0s→K∗0K¯∗0 decays

An angular analysis of the decay B0s→K∗0K¯∗0 is performed using pp collisions corresponding to an integrated luminosity of 1.0 fb−1 collected by the LHCb experiment at a centre-of-mass energy s√=7 TeV. A combined angular and mass analysis separates six helicity amplitudes and allows the measurement of the longitudinal polarisation fraction f L = 0.201 ± 0.057 (stat.) ± 0.040 (syst.) for the B0s→K∗(892)0K¯∗(892)0 decay. A large scalar contribution from the K ∗0(1430) and K ∗0(800) resonances is found, allowing the determination of additional CP asymmetries. Triple product and direct CP asymmetries are determined to be compatible with the Standard Model expectations. The branching fraction B(Bs→K∗(892)0K¯∗(892)0) is measured to be (10.8 ± 2.1 (stat.) ± 1.4 (syst.) ± 0.6 (f d /f s )) × 10−6.S

Measurement of the Z+b-jet cross-section in pp collisions at √s = 7 TeV in the forward region

The associated production of a Z boson or an off-shell photon γ * with a bottom quark in the forward region is studied using proton-proton collisions at a centre-of-mass energy of 7 TeV. The Z bosons are reconstructed in the Z/γ * → μ + μ − final state from muons with a transverse momentum larger than 20 GeV, while two transverse momentum thresholds are considered for jets (10 GeV and 20 GeV). Both muons and jets are reconstructed in the pseudorapidity range 2.0 < η < 4.5. The results are based on data corresponding to 1.0 fb−1 recorded in 2011 with the LHCb detector. The measurement of the Z+b-jet cross-section is normalized to the Z+jet cross-section. The measured cross-sections are σ( Z/γ∗(μ+μ−)+b-jet)=295±60 (stat)±51 (syst)±10 (lumi) fb (0.1) for p T(jet) > 10 GeV, and σ(Z/γ∗(μ+μ−)+b-jet)=128±36 (stat)±22 (syst)±5 (lumi) fb (0.2) for p T(jet) > 20 GeVS