Current status of the Standard Model CKM fit and constraints on $Delta F=2$ New Physics

This letter summarises the status of the global fit of the CKM parameters within the Standard Model performed by the CKMfitter group. Special attention is paid to the inputs for the CKM angles $alpha$ and $gamma$ and the status of $B_stomumu$ and $B_dto mumu$ decays. We illustrate the current situation for other unitarity triangles. We also discuss the constraints on generic $Delta F=2$ New Physics. All results have been obtained with the CKMfitter analysis package, featuring the frequentist statistical approach and using Rfit to handle theoretical uncertainties.

Isospin breaking in the phases of the Ke4 form factors

Isospin breaking in the Kl4 form factors induced by the difference between charged and neutral pion masses is studied. Starting from suitably subtracted dispersion representations, the form factors are constructed in an iterative way up to two loops in the low-energy expansion by implementing analyticity, crossing, and unitarity due to two-meson intermediate states. Analytical expressions for the phases of the two-loop form factors of the Kpm -> pi^+ pi^- e^pm nu_e channel are given, allowing one to connect the difference of form-factor phase shifts measured experimentally (out of the isospin limit) and the difference of S- and P-wave pi-pi phase shifts studied theoretically (in the isospin limit). The isospin-breaking correction consists of the sum of a universal part, involving only pi-pi rescattering, and a process-dependent contribution, involving the form factors in the coupled channels. The dependence on the two S-wave scattering lengths a_0^0 and a_0^2 in the isospin limit is worked out in a general way, in contrast to previous analyses based on one-loop chiral perturbation theory. The latter is used only to assess the subtraction constants involved in the dispersive approach. The two-loop universal and process-dependent contributions are estimated and cancel partially to yield an isospin-breaking correction close to the one-loop case. The recent results on the phases of K^pm -> pi^+ pi^- e^pm nu_e form factors obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including this isospin-breaking correction to extract values for the scattering lengths a_0^0 and a_0^2, as well as for low-energy constants and order parameters of two-flavour ChPT.

Determining the chiral condensate from the distribution of the winding number beyond topological susceptibility

The first two non-trivial moments of the distribution of the topological charge (or gluonic winding number), i.e., the topological susceptibility and the fourth cumulant, can be computed in lattice QCD simulations and exploited to constrain the pattern of chiral symmetry breaking. We compute these two topological observables at next-to-leading order in three-flavour Chiral Perturbation Theory, and we discuss the role played by the eta propagation in these expressions. For hierarchies of light-quark masses close to the physical situation, we show that the fourth cumulant has a much better sensitivity than the topological susceptibility to the three-flavour quark condensate, and thus constitutes a relevant tool to determine the pattern of chiral symmetry breaking in the limit of three massless flavours. We provide the complete formulae for the two topological observables in the isospin limit, and predict their values in the particular setting of the recent analysis of the RBC/UKQCD collaboration. We show that a combination of the topological susceptibility and the fourth cumulant is able to pin down the three-flavour condensate in a particularly clean way in the case of three degenerate quarks.

Combined constraints on CP-violation in the Standard Model and beyond

I review the status of CP violation in the Standard Model from the combination of flavour constraints within the CKMfitter frequentist approach and I describe studies of New Physics restricted to the Delta F=2 sector to explain recent results on neutral-meson mixing. All results have been obtained using data available for the Winter 2012 conferences.

Topological susceptibility on the lattice and the three-flavour quark condensate

We reanalyse the topological susceptibility assuming the possibility of a significant paramagnetic suppression of the three-flavour quark condensate and a correlated enhancement of vacuum fluctuations of $sbar{s}$ pairs. Using the framework of resummed ChPT, we point out that simulations performed near the physical point, with a significant mass hierarchy between u,d and s dynamical quarks, are not able to disentangle the contributions from the quark condensate and sea $sbar{s}$-pair fluctuations, and that simulations with three light quark masses of the same order are better suited for this purpose. We perform a combined fit of recent RBC/UKQCD data on pseudoscalar masses and decay constants as well as the topological susceptibility, and we reconsider the determination of lattice spacings in our framework, working out the consequences on the parameters of the chiral Lagrangian. We obtain Sigma(3;2 GeV)^1/3=243 pm 12 MeV for the three-flavour quark condensate in the chiral limit. We notice a significant suppression compared to the two-flavour quark condensate Sigma(2;2 GeV)/Sigma(3;2 GeV)=1.51pm 0.11 and we confirm previous findings of a competition between leading order and next-to-leading order contributions in three-flavour chiral series.

New Physics in B-Bbar mixing in the light of recent LHCb data

We perform model-independent statistical analyses of three scenarios accommodating New Physics (NP) in Delta F=2 flavour-changing neutral current amplitudes. In a scenario in which NP in B_d-B_d-bar and B_s-B_s-bar is uncorrelated, we find the parameter point representing the Standard-Model disfavoured by 2.4 standard deviations. However, recent LHCb data on B_s neutral-meson mixing forbid a good accommodation of the D0 data on the semileptonic CP asymmetry A_SL. We introduce a fourth scenario with NP in both M_12^d,s and Gamma_12^d,s, which can accommodate all data. We discuss the viability of this possibility and emphasise the importance of separate measurements of the CP asymmetries in semileptonic B_d and B_s decays. All results have been obtained with the CKMfitter analysis package, featuring the frequentist statistical approach and using Rfit to handle theoretical uncertainties.

Anatomy of New Physics in B-Bbar mixing

We analyse three different New Physics scenarios for Delta F=2 flavour-changing neutral currents in the quark sector in the light of recent data on neutral-meson mixing. We parametrise generic New Physics contributions to B_q-Bbar_q mixing (q=d,s), in terms of one complex quantity Delta_q, while three parameters Delta_K^tt, Delta_K^ct and Delta_K^cc are needed to describe K-Kbar mixing. In Scenario I, we consider uncorrelated New Physics contributions in the B_d, B_s, and K sectors. In this scenario, it is only possible to constrain the parameters Delta_d and Delta_s whereas there are no non-trivial constraints on the kaon parameters. In Scenario II, we study the case of Minimal Flavour Violation (MFV) and small bottom Yukawa coupling and Scenario III is the generic MFV case with large bottom Yukawa couplings. Our quantitative analyses consist of global CKM fits within the Rfit frequentist statistical approach, determining the Standard Model parameters and the new physics parameters of the studied scenarios simultaneously. We find that the recent measurements indicating discrepancies with the Standard Model are well accomodated in Scenarios I and III with new mixing phases, with a slight preference for Scenario I that permits different new CP phases in the B_d and B_s systems. Within our statistical framework, we find evidence of New Physics in both B_d and B_s systems. The Standard-Model hypothesis Delta_d=Delta_s=1 is disfavoured with p-values of 3.6 sigma and 3.3 sigma in Scenarios I and III, respectively. We also present an exhaustive list of numerical predictions in each scenario. In particular, we predict the CP phase in B_s -> J psi phi and the difference between the B_s and B_d semileptonic asymmetries, which will be both measured by the LHCb experiment.

Extracting CP violation and strong phase in D decays by using quantum correlations in psi(3770)-> D0bar{D}0 -> (V1V2)(V3V4) and psi(3770)->D0bar{D}0 -> (V1V2)(K pi)

The charm quark offers interesting opportunities to cross-check the mechanism of CP violation precisely tested in the strange and beauty sectors. In this paper, we exploit the angular and quantum correlations in the Dbar{D} pairs produced through the decay of the psi(3770) resonance in a charm factory to investigate CP-violation in two different ways. We build CP-violating observables in psi(3770) -> Dbar{D} -> (V_1V_2)(V_3 V_4) to isolate specific New Physics effects in the charm sector. We also consider the case of psi(3770) -> Dbar{D} -> (V_1V_2)(Kpi) decays, which provide a new way to measure the strong phase difference delta between Cabibbo-favored and doubly-Cabibbo suppressed D decays required in the determination of the CKM angle gamma. Neglecting the systematics, we give a first rough estimate of the sensitivities of these measurements at BES-III with an integrated luminosity of 20 fb^-1 at psi(3770) peak and at a future Super tau-charm factory with a luminosity of 10^35 cm^-2.s^-1.

Parametrisations of the D -> K l nu form factor and the determination of hat{g}

The vector form factor f_+(t) of the semileptonic decay D -> K l nu, measured recently with a high accuracy, can be used to determine the strong coupling constant g_{D_s^* D K}. The latter is related to the normalised coupling hat{g} releveant in heavy-meson chiral perturbation theory. This determination relies on the estimation of the residue of the form factor at the D_s^* pole and thus on an extrapolation of the form factor in the unphysical region (m_D-m_K)^2<t<(m_D+m_K)^2. We test this extrapolation for several parametrisations of the form factors by determining the value of hat{g}, whose value can be compared to other (experimental and theoretical) estimates. Several unsophisticated parametrisations, differing by the amount of physical information that they embed, are shown to pass this test. An apparently more elaborated parametrisation of form factors, the so-called z-expansion, is at variance with the other models, and we point out some significant shortcomings of this parametrisation for the problem under consideration.