[MUSIC] Hello everyone, this week we are going to continue our experimental physics journey. The primary focus this time will be comparison of two hypothesis through the measurement of some real-world parameters. We'll follow analysis strategy that LHCb experiment, for example, uses for hunting for rare decays. We'll see how machine learning can be used to improve sensitivity of research, and examine some essential boundary conditions that restrict the use of an arbitrary predictive model. One of the most extraordinary scientists of all the times, Richard Feynman. I hope you've already had a chance to appreciate his way of transforming doodles into a powerful communication tool find on diagrams. He used to say that present situation in physics as if we know chess, but we don't know one or two rules. In fact, the situation is a bit more complicated. Now, we understand that there are a whole lot of things going on with dark matter and dark energy, and we don't have a clue how many rules we are actually missing. However, as long as we're talking about chess as a metaphor for a scientific research, it works quite nice. We have to play various games scenarios to figure out what kind of rules apply to our figures. In our case, instead of chess figures, we have standard model particles. Just let's recap. The standard model of particle physics describes what universe is made of, and how it holds together. It rests on two central ideas. The first one, all matter is made of particles, and these particles interact with each other by exchanging other particles associated with fundamental forces. The essential grains of matter are fermions, and the force carriers are bosons. Fermions are represented by quarks, building blocks that stick together, and form higher order of matter like neutrons and protons. And leptons that are thought of as a fundamental independent bits of matter. If you consider a decay like one we've looked at the first lecture, a decay of a muon into an electron neutrino and antineutrino, you can count specific numbers like mass, charge, on the left and on the right part of the equation. There is also a quantum number that is called lepton charge, or lepton number, which is representing the difference between the number of leptons and number of anti-leptons in an elementary particle reaction. So, on the left and on the right part of the equation, you have this difference equal to one. Let's introduce one more quantity. Every matter of particle occupies a particular column in the table, you see on the screen, it is called generation. So electron belongs to the first generation, and muon belongs to the second generation. So for every decay we can count the number of leptons of the first generation, of the second generation, and of the third generation. So we have a tuple of free elements that is called lepton flavor. Let's remember it for a minute and it we'll come back to that factor in a couple of slides, we know that standard model although quite powerful, it is not all mighty. There is no gravity, no dark matter particles, etc. There are alternative models like I've mentioned in the first lecture, extra dimension model, or micro black holes. Among those there is a real princess of such models called super symmetry, or SUSY for short. It assumes the existence of super particles symmetrical to all particle of standard model, you can see it on the slide. There was quite a bit of hope to discover at least some of those at LHC. Introduction of those super partners could explain various things we have no reasonable explanation for. Dark matter phenomena for example. Another thing, introduction of this method is unification of all the forces that suppose to happen at specific energy level. So, if we want to compare to different models. So we have our basic model or, standard model in our case or, or a null hypothesis, and we have an alternative model hypothesis X. That, for example, explains some unknown phenomena, and at the same time, this alternative model has different prediction for specific measurable quantity. For example, a branch inflation will explain what it is a little bit later in the next slide for specific decay D. So we can estimate theoretical predictions of standard model and of theory X for this quantity. Let them call BSM and BX. So, we make an experimental observation of D and measure the actual value for the quantity B observable, and we measure some uncertainty, sigma. So, if this value that we measure in the experiment is too far from BSM, and close to the prediction of alternative model, hail to the alternative model. If it is too far from prediction of the alternative model, we can forget about it. Otherwise, we wait for more data. And here, by the distance, we mean the for example P value. So by convention of particle physics if a measured quantity sits outside of five sigma interval, so, which has probability of random equation is less than decimal number, then the prediction and then the absorbed value is considered to be far enough. So, as for branching fraction. So, we can consider all different types of the decay that happen with certain kind of particles, for example, a Tau particle can decay into different modes. So here, you see some examples. So, and there are different probabilities for those modes, for example for electron and electron antineutrino, the probability is rougly 17%. For muon and muon antineutrino is 70%,, it will look less, etc. And if you want to know all possible decay outcomes, or so called final states, you can follow the link that leads to one of the most important resource in particle physics, which is called particle data group. That has all measure decays of Tau particle. [SOUND]