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In this paper we compute the NLO QCD corrections for the inclusive nonleptonic decay rates of $B$-hadrons at subleading power of the heavy quark expansion. In particular, we discuss the coefficient of the chromomagnetic moment parameter $\mu_G$ which has a large uncertainty at leading order due to its dependence on the renormalization scale. We find that the renormalization-scale dependence of this coefficient is significantly reduced, thereby reducing the theoretical uncertainty of the coefficient and consequently of the rates. The sign of the coefficient becomes stable, and we estimate that the NLO corrections will increase the decay rates by around $2\%$., Comment: 23 pages, 8 figures and 1 ancillary file

In this work we are concerned with the crossover between strong disorder (SD) and weak disorder (WD) behaviors in three well-known problems that involve minimal paths: directed polymers (directed paths with fixed starting point and length), optimal paths (undirected paths with fixed end-to-end/spanning distance) and undirected polymers (undirected paths with fixed starting point and length). We present a unified theoretical framework from which we can easily deduce the scaling of the crossover point of each problem. Our theory is based on the fact that the SD limit behavior of these systems is closely related to the corresponding percolation problem. As a result, the properties of those minimal paths are completely controlled by the so-called red bonds of percolation theory. Our model is first addressed numerically and then approximated by a ``two-term'' approach. This approach provides us with an analytical expression that seems to be reasonably accurate. The results are in perfect agreement with our simulations and with most of the results reported in related works. Our research also lead us to propose this crossover point as a universal measure of the disorder strength in each case. Interestingly, that measure depends on both the statistical properties of the disorder and the topological properties of the network., Comment: 17 pages, 17 figures

In this paper we compute $\alpha_s$ corrections to the matching coefficients of the dimension six operators in the Heavy Quark Expansion of the inclusive semileptonic heavy hadron decay rate and leptonic invariant mass spectrum with a massless quark and both a massive or massless lepton in the final state, analytically. The obtained results can be applied to the inclusive semileptonic $B\rightarrow X_u \ell \bar{\nu}_\ell$ ($\ell = e,\,\mu,\,\tau$) and $D\rightarrow X \ell \bar{\nu}_\ell$ ($\ell = e,\,\mu$) decays. The main application of our results is the background subtraction of the $B\rightarrow X_u \ell \bar{\nu}_\ell$ decay in the measurement of the $B\rightarrow X_c\ell \bar{\nu}_\ell$ decay, which is important for the precise extraction of $V_{cb}$ and $R(D^{(*)})$. They also play a role in the computation of lifetimes of heavy hadrons., Comment: 29 pages, 3 figures, 1 ancillary file

We consider the Heavy Quark Expansion (HQE) for the nonleptonic decay rates of heavy hadrons, and compute the NLO QCD corrections to power terms up to order $1/m_Q^2$. We neglect the masses of the final-state quarks, so the application of our result is mainly for charmed hadrons. Our result can be applied also to bottomed hadrons as they constitute the main effect to this order up to corrections of $\mathcal{O}(m_c/m_b)$ and contributions due to penguin operators. We discuss the impact of our result for the lifetimes of heavy hadrons., Comment: 17 pages, 8 figures

Feedback control uses the state information of the system to actuate on it. The information used implies an effective entropy reduction of the controlled system, potentially increasing its performance. How to compute this entropy reduction has been formally shown for a general system, and has been explicitly computed for spatially discrete systems. Here, we address a relevant example of how to compute the entropy reduction by information in a spatially continuous feedback-controlled system. Specifically, we consider a feedback flashing ratchet, which constitutes a paradigmatic example for the role of information and feedback in the dynamics and thermodynamics of transport induced by the rectification of Brownian motion. A Brownian particle moves in a periodic potential that is switched on and off by a controller, with the latter performing the switching depending on the system state. We show how the entropy reduction can be computed from the entropy of a sequence of control actions, and also discuss the required sampling effort for its accurate computation. Moreover, the output power developed by the particle against an external force is investigated, which -- for some values of the system parameters -- is shown to become larger than the input power due to the switching of the potential: the apparent efficiency of the ratchet thus becomes higher than one, if the entropy reduction contribution is not considered. This result highlights the relevance of including the entropy reduction by information in the thermodynamic balance of feedback controlled devices, specifically when writing the second principle: the inclusion of the entropy reduction by information leads to a well-behaved efficiency over all the range of parameters investigated., Comment: 17 pages, 13 figures

This paper presents $\alpha_s$ corrections to the inclusive semitauonic $B \to X_c \tau \bar{\nu}_\tau$ decay width and leptonic invariant mass spectrum up to order $1/m_b^3$ in the heavy quark expansion. Analytical results with full dependence on the final-state quark and tau lepton masses are obtained. The results up to $1/m_b^2$ can be extrapolated to the $B \to X_u \tau \bar{\nu}_\tau$ decay by taking the limit of vanishing final-state quark mass., Comment: 30 pages and 11 figures

This work details worked solutions to the various problems set by the lecturers during the course of the Les Houches summer school 2017 on effective field theories in particle physics and cosmology., Comment: 92 pages, 14 figures; Contribution to the Proceedings of the 2017 Les Houches Summer School on Effective Field Theory in Particle Physics and Cosmology (Les Houches, France, July 3-28, 2017)

We complete the calculation of the contributions from the dimension six operators in the heavy quark expansion for the total lifetime of heavy hadrons. We give the expressions for the Wilson coefficients of the Darwin term $\rho_D$ and the spin-orbit term $\rho_{\rm LS}$ at tree level., Comment: 26 pages and 3 figures

The present paper incorporates the effects induced by massless spectator quarks in the renormalization group improved Wilson coefficients associated to the ${\cal O}(1/m^3)$ spin-dependent heavy quark effective theory Lagrangian operators. The computation is carried out in Coulomb gauge with leading logarithmic precision. The result completes the Lagrangian to $\mathcal{O}(1/m^3)$ with that accuracy., Comment: 27 pages, 5 figures

We obtain the renormalization group improved expressions of the Wilson coefficients associated to the ${\cal O}(1/m^3)$ spin-dependent heavy quark effective theory Lagrangian operators, with leading logarithmic approximation, in the case of zero light quarks. We have employed the Coulomb gauge., Comment: 26 pages and 4 figures (but 7 images)