## Final Activity Report Summary - LQCDBPHYSICS (B Physics from lattice QCD)

A topic of key importance in current physics is that of whether the Standard Model of particle physics can adequately describe the difference between matter and antimatter in Nature. This violation of matter-antimatter symmetry is known as CP violation. In the Standard Model it arises through complex couplings that can be collected in a unitary matrix (the CKM matrix). By studying quark weak decays, it will be possible to determine these couplings in several different ways, over constraining them, to show up any internal inconsistency due to the existence of new physics beyond the Standard Model. That must be done by combining experimental measurements and theoretical calculations. The aim of this project is to provide the theoretical input needed.

To study such quantities it is necessary to describe the strong forces that bind the fundamental particles, the quarks, into hadrons, the particles whose decay rates and masses are measured in the experiment. The theory used for it is Quantum Chromodynamics (QCD), and the only way to do this ab initio is using numerical simulations of QCD.

Although the methodology of such simulations has been known for the past twenty five years, only recently has it been possible to address the main difficulty in these calculations: the inclusion of 'sea' quark anti-quark pairs created by short-lived energy fluctuations of the vacuum.

At a first stage of the project we have focussed on the calculation of the bag parameter B_K which measures indirect CP violation in the system of kaon mesons. This parameter is one of the main sources of uncertainty in the studies of the CKM matrix. We have calculated it using lattice QCD and including the effects of quark anti-quark fluctuations of the vacuum. Although in this result we have eliminated the uncertainty associated with the quark vacuum polarization effects, it still suffers from large uncertainties coming from the method used to relate the results obtained from the numerical simulations to the quantities needed by phenomenology. We will need to use a more precise method in order to have a prediction with an error of a few percent, as required to match the experimental precision.

We have also started an analogous calculation of the parameter B_B, which will allow us to study the ratio f_B^2B_B for the B_s over that for the B_d. Using experimental results for the oscillations of and mesons over the next few years, a ratio of couplings in the CKM matrix can be also derived which will provide one of the key constraints on the internal consistency of CP violation in the Standard Model of particle physics.

To study such quantities it is necessary to describe the strong forces that bind the fundamental particles, the quarks, into hadrons, the particles whose decay rates and masses are measured in the experiment. The theory used for it is Quantum Chromodynamics (QCD), and the only way to do this ab initio is using numerical simulations of QCD.

Although the methodology of such simulations has been known for the past twenty five years, only recently has it been possible to address the main difficulty in these calculations: the inclusion of 'sea' quark anti-quark pairs created by short-lived energy fluctuations of the vacuum.

At a first stage of the project we have focussed on the calculation of the bag parameter B_K which measures indirect CP violation in the system of kaon mesons. This parameter is one of the main sources of uncertainty in the studies of the CKM matrix. We have calculated it using lattice QCD and including the effects of quark anti-quark fluctuations of the vacuum. Although in this result we have eliminated the uncertainty associated with the quark vacuum polarization effects, it still suffers from large uncertainties coming from the method used to relate the results obtained from the numerical simulations to the quantities needed by phenomenology. We will need to use a more precise method in order to have a prediction with an error of a few percent, as required to match the experimental precision.

We have also started an analogous calculation of the parameter B_B, which will allow us to study the ratio f_B^2B_B for the B_s over that for the B_d. Using experimental results for the oscillations of and mesons over the next few years, a ratio of couplings in the CKM matrix can be also derived which will provide one of the key constraints on the internal consistency of CP violation in the Standard Model of particle physics.