Theory of CP violation in B decays

The study of CP violation in $B$-meson decays has already reached a high level of precision, which will be pushed even higher in the future era of Belle-II and the LHCb upgrade. %Important probes of CP violation are the $B_d^0$ and $B_s^0$ mixing phases and the CKM angle $\gamma$. Here, the theoretical challenge is to control the uncertainties from strong interactions to distinguish between the Standard Model and possible New Physics effects. In this talk, I will present a selected overview of recent theoretical developments in this field. This includes, in particular, the semileptonic asymmetry $a_{\text{sl}}^s$ and extractions of the CKM angle $\gamma$ and the $B_d^0$ and $B_s^0$ mixing phases. I focus on recently proposed strategies in which the theory uncertainties can be controlled through data using flavour symmetries of the strong interaction. A newly found puzzle in the $B \to \pi K$ system is highlighted and a theoretically clean way to determine the underlying electroweak penguin parameters is discussed. Finally, the recent progress to describe three-body $B$ decays in QCD factorization is discussed.Comment: To be published in the proceedings of The International Conference on B-Physics at Frontier Machines - BEAUTY2018, La Biodola, Elba Island, Italy, 6-11 May, 2018 and in the proceedings of the XIV International Conference on Heavy Quarks and Leptons (HQL2018), Yamagata, Japan, May 27- June 1, 201

Towards New Frontiers with B→πKB\to\pi K Decays

Exploring correlations between the CP asymmetries of $B^0_d\to\pi^0K_{\rm S}$ following from an isospin relation, we uncover new tensions with the Standard Model in data for neutral $B\to\pi K$ decays. Should this intriguing picture originate from New Physics, a modified electroweak penguin sector provides a key scenario. It includes models with extra $Z'$ bosons, which offer attractive ways to resolve anomalies in $B\to K^{(*)}\ell^+\ell^-$ measurements. We present a new strategy to reveal the underlying physics, apply it to current $B\to\pi K$ data, and discuss the excellent prospects for Belle II.Comment: 7 pages, 3 figure

VcbV_{cb} determination from inclusive b→cb \to c decays: an alternative method

The determination of $V_{cb}$ relies on the Heavy-Quark Expansion and the extraction of the non-perturbative matrix elements from inclusive $b\to c$ decays. The proliferation of these matrix elements complicates their extraction at $1/m_b^4$ and higher, thereby limiting the $V_{cb}$ extraction. Reparametrization invariance links different operators in the Heavy-Quark expansion thus reducing the number of independent operators at $1/m_b^4$ to eight for the total rate. We show that this reduction also holds for spectral moments as long as they are defined by reparametrization invariant weight-functions. This is valid in particular for the leptonic invariant mass spectrum ($q^2$), i.e. the differential rate and its moments. Currently, $V_{cb}$ is determined by fitting the energy and hadronic mass moments, which do not manifest this parameter reduction and depend on the full set of 13 matrix elements up to $1/m_b^4$. In light of this, we propose an experimental analysis of the $q^2$ moments to open the possibility of a model-independent $V_{cb}$ extraction from semileptonic decays including the $1/m_b^4$ terms in a fully data-driven way.Comment: 16 pages, 2 figures. v2: version published in JHEP, references added plus minor change

Reparametrization Invariance and Partial Re-Summations of the Heavy Quark Expansion

We extend existing work on reparametrization invariance (RPI) of the heavy-quark expansion. We discuss the total rates of inclusive processes and obtain results which have a manifest RPI and can be expressed through matrix elements of operators and states defined in full QCD. This approach leads to a partial re-summation of higher-order terms in the heavy-quark expansion and has the advantage that the number of independent parameters is reduced.Comment: 22 page

The heavy quark expansion for inclusive semileptonic charm decays revisited

The Heavy Quark Expansion (HQE) has become an extremely powerful tool in flavor physics. For charm decays, where the expansion parameters α$_{s}$(m$_{c}$) and Λ$_{QCD}$/m$_{c}$ are bigger than for bottom decays, it remains to be seen if the HQE can be applied with similar success. Nevertheless, to make optimal use of the plethora of data already available and coming in the near future, a better understanding of HQE for charm decays is crucial. This paper discusses in detail how the HQE for charm decays is set up, what is the role of four-quark (weak annihilation) operators and how this compares to the well understood bottom decays. Subtleties concerning radiative corrections and the charm mass scheme are briefly discussed. An experimental study of the relevant HQE hadronic matrix elements will then show if the HQE expansion for charm converges well enough. Besides serving as an important cross check for inclusive B decays, in the end, this study might open the road for inclusive |V$_{cs}$| and |V$_{cd}$| extractions

Alternative Treatment of the Quark Mass in the Heavy Quark Expansion

The treatment of the quark mass plays an important role when it comes to increasing the precision of the predictions of the heavy quark expansion for inclusive heavy hadron decays. Various short-distance mass schemes have been invented to minimize the uncertainties induced by the quark mass, which needs to be extracted from other, independent observables. We suggest to replace the quark mass directly by an observable such as e.g. the inverse moments of the cross section for $e^+ e^- \to$ hadrons. We investigate this alternative strategy and study its impact on the perturbative series.Comment: 20 page

Five-particle contributions to the inclusive rare Bˉ→Xs(d) ℓ+ℓ−\bar B \to X_{s(d)} \, \ell^+\ell^- decays

We calculate tree-level contributions to the inclusive rare $\bar B \to X_{s(d)} \, \ell^+\ell^-$ decays. At the partonic level they stem from the five-particle process $b \to s(d) \, q \bar q \, \ell^+\ell^-$, with $q \in \{u,d,s\}$. While for $b \to d$ transitions such five-body final states contribute at the same order in the Wolfenstein expansion compared to the three-body partonic decay, they are CKM suppressed in $b \to s$ decays. In the perturbative expansion, we include all leading-order contributions, as well as partial next-to-leading order QCD and QED effects. In the case of the differential branching ratio, we present all results completely analytically in terms of polylogarithmic functions of at most weight three. We also consider the differential forward-backward asymmetry, where all except one interference could be obtained analytically. From a phenomenological point of view the newly calculated contributions are at the percent level or below.Comment: 23 pages, 3 figures (Matches published version