arXiv subjects

Andrzej J. Buras

Publications and source records attributed to Andrzej J. Buras.

At least 73 records · Page 4Linked to original sources

arXiv2016

Kaon Flavour Physics Strikes Back

In this short presentation I emphasize the increased importance of kaon flavour physics in the search for new physics (NP) that we should witness in the rest of this decade and in the next decade. The main actors will be the branching ratios for the rare decays $K^+\rightarrowπ^+ν\barν$ and $K_{L}\rightarrowπ^0ν\barν$, to be measured by NA62 and KOTO, and their correlations with the ratio $\varepsilon'/\varepsilon$ on which recently progress by lattice QCD and large $N$ dual QCD approach has been made implying a new flavour anomaly. Further correlations of $K^+\rightarrowπ^+ν\barν$, $K_{L}\rightarrowπ^0ν\barν$ and $\varepsilon'/\varepsilon$ with $\varepsilon_K$, $ΔM_K$, $K_L\toμ^+μ^-$ and $K_L\toπ^0\ell^+\ell^-$ will help us to identify indirectly possible NP at short distance scales. This talk summarizes the present highlights of this fascinating field including some results from concrete NP scenarios.

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arXiv2016

The Revival of Kaon Flavour Physics

After years of silence we should witness in the rest of this decade and in the next decade the revival of kaon flavour physics. This is not only because of the crucial measurements of the branching ratios for the rare decays $K^+\toπ^+ν\barν$ and $K_{L}\to π^0ν\barν$ by NA62 and KOTO that being theoretically clean and very sensitive to new physics (NP) could hint for new phenomena even beyond the reach of the LHC without any significant theoretical uncertainties. Indeed simultaneously the advances in the calculations of perturbative and in particular non-perturbative QCD effects in $\varepsilon'/\varepsilon$, $\varepsilon_K$, $ΔM_K$, $K_L\toμ^+μ^-$ and $K_L\toπ^0\ell^+\ell^-$ will increase the role of these observables in searching for NP. In fact the hints for NP contributing to $\varepsilon'/\varepsilon$ have been already signalled last year through improved estimates of hadronic matrix elements of QCD and electroweak penguin operators $Q_6$ and $Q_8$ by lattice QCD and large $N$ dual QCD approach. This talk summarizes in addition to this new flavour anomaly the present highlights of this field including some results from concrete NP scenarios.

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arXiv2016

The Renaissance of Kaon Flavour Physics

There is no doubt that in the coming years we will witness the renaissance of kaon flavour physics with crucial measurements of the branching ratios for the rare decays $K^+\rightarrowπ^+ν\barν$ and $K_{L}\rightarrowπ^0ν\barν$ that are very sensitive to new physics (NP) and are theoretically very clean. Simultaneously the role of $\varepsilon'/\varepsilon$, $\varepsilon_K$, $ΔM_K$, $K_L\toμ^+μ^-$ and $K_L\toπ^0\ell^+\ell^-$ in searching for NP will significantly increase through their improved estimates within the SM. In fact the hints for NP contributing to $\varepsilon'/\varepsilon$ have been signalled last year through improved estimates of hadronic matrix elements of QCD and electroweak penguin operators $Q_6$ and $Q_8$ by lattice QCD and large $N$ dual QCD approach. Also recent increased tensions between $\varepsilon_K$ and $ΔM_{s,d}$ mass differences in $B_{s,d}^0-\bar B_{s,d}^0$ mixing within the SM and models with constrained MFV tell us that we should have tremendous fun in chasing NP through all these observables. The present talk discusses the hinted anomalies in $\varepsilon'/\varepsilon$,and $ΔF=2$ transitions and summarizes possible implications of simultaneous anomalies in $\varepsilon'/\varepsilon$ and $\varepsilon_K$ for $K^+\rightarrowπ^+ν\barν$ and $K_{L}\rightarrowπ^0ν\barν$ and $ΔM_K$ in models with tree-level $Z$ and $Z^\prime$ exchanges. The anomalies in $\varepsilon'/\varepsilon$ and $\varepsilon_K$, if confirmed, would signal new sources of CP violation. This is in contrast to the recent anomalies in $B$ physics that signal lepton flavour non-universalities and NP in CP-conserving observables. Highlights from recent flavour analyses of 331 models are briefly described.

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arXiv2016

331 Models Facing the Tensions in $ΔF=2$ Processes with the Impact on $\varepsilon^\prime/\varepsilon$, $B_s\toμ^+μ^-$ and $B\to K^*μ^+μ^-$

Motivated by the recently improved lattice QCD results on the hadronic matrix elements entering $ΔM_{s,d}$ in $B_{s,d}^0-\bar B_{s,d}^0$ mixings and the resulting increased tensions between $ΔM_{s,d}$ and $\varepsilon_K$ in the Standard Model and CMFV models, we demonstrate that these tensions can be removed in 331 models based on the gauge group $SU(3)_C\times SU(3)_L\times U(1)_X$ both for $M_{Z^\prime}$ in the LHC reach and well beyond it. But the implied new physics (NP) patterns in $ΔF=1$ observables depend sensitively on the value of $|V_{cb}|$. Concentrating the analysis on three 331 models that have been selected by us previously on the basis of their performance in electroweak precision tests and $\varepsilon^\prime/\varepsilon$ we illustrate this for $|V_{cb}|=0.042$ and $|V_{cb}|=0.040$. We find that these new lattice data still allow for positive shifts in $\varepsilon^\prime/\varepsilon$ up to $6\times 10^{-4}$ for $M_{Z^\prime}=3~TeV$ for both values of $$|V_{cb}|$ but for $M_{Z^\prime}=10~TeV$ only for $|V_{cb}|=0.040$ such shifts can be obtained. NP effects in $B_s\toμ^+μ^-$ and in the Wilson coefficient $C_9$ are significantly larger in all three models for the case of $|V_{cb}|=0.040$. In particular in two models the rate for $B_s\toμ^+μ^-$ can be reduced by NP by $20\%$ for $M_{Z^\prime}=3~TeV$ resulting in values in the ballpark of central values from CMS and LHCb. In the third model a shift in $C_9$ up to $C_9^\text{NP}=-0.5$ is possible. We also consider the simplest 331 model, analyzed recently in the literature, in which $X=Y$, the usual hypercharge. We find that in this model NP effects in flavour observables are much smaller than in the three models with $X\not=Y$, in particular NP contributions to the ratio $\varepsilon^\prime/\varepsilon$ are very strongly suppressed.

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arXiv2016

Charm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading Order

We calculate the complete NNLO QCD corrections to the charm contribution of the rare decay K+ -> pi+ nu nu-bar. We encounter several new features, which were absent in lower orders. We discuss them in detail and present the results for the 2-loop matching conditions of the Wilson coefficients, the 3-loop anomalous dimensions, and the 2-loop matrix elements of the relevant operators that enter the NNLO renormalization group analysis of the Z-penguin and the electroweak box contribution. The inclusion of the NNLO QCD corrections leads to a significant reduction of the theoretical uncertainty from 9.8% down to 2.4% in the relevant parameter Pc, implying the leftover scale uncertainties in BR(K+ -> pi+ nu nu-bar) and in the determination of |V_td|, sin(2 beta), and gamma from the K -> pi nu nu system to be 1.3%, 1.0%, 0.006, and 1.2 degrees, respectively. For the charm quark MSbar mass mc=(1.30+-0.05) GeV and |V_us|= 0.2248 the NLO value Pc=0.37+-0.06 is modified to Pc=0.38+-0.04 at the NNLO level with the latter error fully dominated by the uncertainty in mc. We present tables for Pc as a function of mc and alphas(MZ) and a very accurate analytic formula that summarizes these two dependences as well as the dominant theoretical uncertainties. Adding the recently calculated long-distance contributions we find BR(K+ -> pi+ nu nu-bar)=(8.0+-1.1)*10^-11 with the present uncertainties in mc and the Cabibbo-Kobayashi-Maskawa elements being the dominant individual sources in the quoted error. We also emphasize that improved calculations of the long-distance contributions to K+ -> pi+ nu nu-bar and of the isospin breaking corrections in the evaluation of the weak current matrix elements from K+ -> pi0 e+ nu would be valuable in order to increase the potential of the two golden K -> pi nu nu decays in the search for new physics.

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arXiv2016

Universal Unitarity Triangle 2016 and the Tension Between $ΔM_{s,d}$ and $\varepsilon_K$ in CMFV Models

Motivated by the recently improved results from the Fermilab Lattice and MILC Collaborations on the hadronic matrix elements entering $ΔM_{s,d}$ in $B_{s,d}^0-\bar B_{s,d}^0$ mixing, we determine the Universal Unitarity Triangle (UUT) in models with Constrained Minimal Flavour Violation (CMFV). Of particular importance are the very precise determinations of the ratio $|V_{ub}|/|V_{cb}|=0.0864\pm0.0025$ and of the angle $γ=(63.0\pm 2.1)^\circ$. They follow in this framework from the experimental values of $ΔM_{d}/ΔM_s$ and of the CP-asymmetry $S_{ψK_S}$. As in CMFV models the new contributions to meson mixings can be described by a single flavour-universal variable $S(v)$, we next determine the CKM matrix elements $|V_{ts}|$, $|V_{td}|$, $|V_{cb}|$ and $|V_{ub}|$ as functions of $S(v)$ using the experimental value of $ΔM_s$ as input. The lower bound on $S(v)$ in these models, derived by us in 2006, implies then upper bounds on these four CKM elements and on the CP-violating parameter $\varepsilon_K$, which turns out to be significantly below its experimental value. This strategy avoids the use of tree-level determinations of $|V_{ub}|$ and $|V_{cb}|$ that are presently subject to considerable uncertainties. On the other hand if $\varepsilon_K$ is used instead of $ΔM_s$ as input, $ΔM_{s,d}$ are found significantly above the data. In this manner we point out that the new lattice data have significantly sharpened the tension between $ΔM_{s,d}$ and $\varepsilon_K$ within the CMFV framework. This implies the presence of new physics contributions beyond this framework that are responsible for the breakdown of the flavour universality of the function $S(v)$. We also present the implications of these results for $K^+\toπ^+ν\barν$, $K_L\toπ^0ν\barν$ and $B_{s,d}\toμ^+μ^-$ within the Standard Model.

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arXiv2016

Quark flavour observables in the Littlest Higgs model with T-parity after LHC Run 1

The Littlest Higgs Model with T-parity (LHT) belongs to the simplest new physics scenarios with new sources of flavour and CP violation. We present a new analysis of quark observables in the LHT model in view of the oncoming flavour precision era. We use all available information on the CKM parameters, lattice QCD input and experimental data on quark flavour observables and corresponding theoretical calculations, taking into account new lower bounds on the symmetry breaking scale and the mirror quark masses from the LHC. We investigate by how much the branching ratios for a number of rare $K$ and $B$ decays are still allowed to depart from their SM values. This includes $K^+\toπ^+ν\barν$, $K_L\toπ^0ν\barν$, $K_L\to μ^+μ^-$, $ε'/ε$, $B\to X_sγ$, $B_{s,d}\toμ^+μ^-$, $B\to K^{(*)}\ell^+\ell^-$, $B\to K^{(*)}ν\barν$. Taking into account the constraints from $ΔF=2$ processes, significant departures from the SM predictions for $K^+\toπ^+ν\barν$ and $K_L\toπ^0ν\barν$ are possible while the effects in $B$ decays are much smaller. In particular, the LHT model favours $\mathcal{B}(B_{s}\toμ^+μ^-) \ge \mathcal{B}(B_{s}\toμ^+μ^-)_{\rm SM}$, which is not supported by the data, and the present anomalies in $B\to K^{(*)}\ell^+\ell^-$ decays cannot be explained in this model. With the recent lattice and large $N$ input the imposition of the $ε'/ε$ constraint implies a significant suppression of the branching ratio for $K_L\toπ^0ν\barν$ with respect to its SM value while allowing only for small modifications for $K^+\toπ^+ν\barν$. Finally, we investigate how the LHT physics could be distinguished from other models by means of indirect measurements and discuss the consequences for quark flavour observables of not finding any LHT state in the coming years.

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arXiv2016

New Physics Patterns in $\varepsilon^\prime/\varepsilon$ and $\varepsilon_K$ with Implications for Rare Kaon Decays and $ΔM_K$

The SM prediction for the ratio $\varepsilon^\prime/\varepsilon$ appears to be significantly below the experimental data. Also $\varepsilon_K$ in the SM tends to be below the data. Any NP removing these anomalies will first of all have impact on flavour observables in the $K$ meson system, in particular on rare $K$ decays and $ΔM_K$. Restricting the operators contributing to $\varepsilon^\prime/\varepsilon$ to the SM ones and to the corresponding primed operators, NP contributions are quite generally dominated either by QCD penguin (QCDP) operators $Q_6(Q_6^\prime)$ or electroweak penguin (EWP) operators $Q_8(Q_8^\prime)$ with rather different implications for other flavour observables. We discuss general models with tree-level $Z$ and $Z^\prime$ flavour violating exchanges and few specific models. We find that simultaneous enhancements of $\varepsilon^\prime/\varepsilon$, $\varepsilon_K$, $\mathcal{B}(K_L\toπ^0ν\barν)$ and $\mathcal{B}(K^+\toπ^+ν\barν)$ in $Z$ scenarios are only possible in the presence of both LH and RH flavour-violating couplings. In $Z^\prime$ scenarios this is not required but the size of NP effects and the correlation between $\mathcal{B}(K_L\toπ^0ν\barν)$ and $\mathcal{B}(K^+\toπ^+ν\barν)$ depends strongly on whether QCDP or EWP dominate NP contributions to $\varepsilon^\prime/\varepsilon$. In the QCDP case possible enhancements of both branching ratios are much larger than for EWP scenario and take place only on the branch parallel to the Grossman-Nir bound, which is in the case of EWP dominance only possible in the absence of NP in $\varepsilon_K$. QCDP and EWP scenarios of NP in $\varepsilon^\prime/\varepsilon$ can also be uniquely distinguished by the size and the sign of NP contribution to $ΔM_K$, elevating the importance of the precise calculation of $ΔM_K$ in the SM.

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arXiv2016

$\varepsilon'/\varepsilon$ in 331 Models

Motivated by the recent findings that the ratio $\varepsilon'/\varepsilon$ in the Standard Model (SM) appears to be significantly below the data we investigate whether the necessary enhancement of this ratio can be obtained in 331 models, in which new physics (NP) contributions to $\varepsilon'/\varepsilon$ and other flavour observables are dominated by tree-level exchanges of a $Z^\prime$. NP contributions to $\varepsilon'/\varepsilon$ in these models are governed by the electroweak operator $Q_8$ for which the hadronic matrix element is rather well known so that our analysis of NP contributions is subject to much smaller uncertainties than within the SM. We consider seven 331 models selected in our earlier analysis on the basis of electroweak precision data. Imposing the constraints from $ΔF=2$ transitions we find that only three of these models can provide a significant positive shift in $\varepsilon'/\varepsilon$ up to $6\times 10^{-4}$ for $M_{Z^\prime}=3$ TeV. Two of them allow simultaneously a supression of ${\cal B}(B_{s}\to μ^+μ^-)$ by $20\%$, bringing the theory closer to the data without any significant impact on the Wilson coefficient $C_9$. The third one provides also the shift $ΔC_9=-0.6$, softening the anomalies in $B\to K^*μ^+μ^-$, without any significant impact on $B_{s}\to μ^+μ^-$. NP effects in rare $K$ decays and in $B\to K(K^*)ν\barν$ turn out to be small. The flavour structure of 331 models implies that even for $M_{Z^\prime}=30$ Tev a shift of $\varepsilon'/\varepsilon$ up to $8\times 10^{-4}$ and a significant shift in $\varepsilon_K$ can be obtained, while the effects in other flavour observables are small.

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arXiv2015

$K\toπν\barν$ and $ε'/ε$ in Simplified New Physics Models

The decays $K^+\toπ^+ν\barν$ and $K_L\toπ^0ν\barν$, being the theoretically cleanest rare decays of mesons, are very sensitive probes of New Physics. In view of the excellent prospects of reaching the Standard Model sensitivity for $K^+\toπ^+ν\barν$ by the NA62 experiment at CERN and for $K_L\toπ^0ν\barν$ by the KOTO experiment at J-PARC, we study them in the simplest extensions of the SM in which stringent correlations between these two decays and other flavour observables are present. We first consider simple models with tree-level Z and Z' contributions in which either MFV or a $U(2)^3$ symmetry is imposed on the quark flavour-violating couplings. We then compare the resulting correlations with those present in generic models in which the latter couplings are arbitrary, subject to constraints from $ΔF=2$ processes, electroweak and collider data. Of particular interest are the correlations with $ε'/ε$ and $K_L\toμ^+μ^-$ which limit the size of NP contributions to $K^+\toπ^+ν\barν$ and $K_L\toπ^0ν\barν$, depending on the Dirac structure of couplings and the relevant operators. But in MFV also the constraint from $B_s\toμ^+μ^-$ turns out to be important. We take into account the recent results from lattice QCD and large N approach that indicate $ε'/ε$ in the SM to be significantly below the data. While in many models the enhancement of $ε'/ε$ implies a suppression of $K_L\toπ^0ν\barν$, we present two models in which these observables can be simultaneously enhanced relative to SM predictions. A correlation between $K^+\toπ^+ν\barν$ and $B\to K(K^*)μ^+μ^-$, found by us in the simple models considered here, should be of interest for NA62 and LHCb experimentalists at CERN in the coming years. The one with $B\to K(K^*)ν\barν$ will be tested at Belle II.

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arXiv2015

Improved anatomy of epsilon'/epsilon in the Standard Model

We present a new analysis of the ratio epsilon'/epsilon within the Standard Model (SM) using a formalism that is manifestly independent of the values of leading (V-A)x(V-A) QCD penguin, and EW penguin hadronic matrix elements of the operators Q_4, Q_9, and Q_10, and applies to the SM as well as extensions with the same operator structure. It is valid under the assumption that the SM exactly describes the data on CP-conserving K -> pi pi amplitudes. As a result of this and the high precision now available for CKM and quark mass parameters, to high accuracy epsilon'/epsilon depends only on two non-perturbative parameters, B_6^(1/2) and B_8^(3/2), and perturbatively calculable Wilson coefficients. Within the SM, we are separately able to determine the hadronic matrix element _0 from CP-conserving data, significantly more precisely than presently possible with lattice QCD. Employing B_6^(1/2) = 0.57+-0.19 and B_8^(3/2) = 0.76+-0.05, extracted from recent results by the RBC-UKQCD collaboration, we obtain epsilon'/epsilon = (1.9+-4.5) 10^-4, substantially more precise than the recent RBC-UKQCD prediction and 2.9 sigma below the experimental value (16.6+-2.3) 10^-4, with the error being fully dominated by that on B_6^(1/2). Even discarding lattice input completely, but employing the recently obtained bound B_6^(1/2) <= B_8^(3/2) <= 1 from the large-N approach, the SM value is found more than 2 sigma below the experimental value. At B_6^(1/2) = B_8^(3/2) = 1, varying all other parameters within one sigma, we find epsilon'/epsilon = (8.6+-3.2) 10^-4. We present a detailed anatomy of the various SM uncertainties, including all sub-leading hadronic matrix elements, briefly commenting on the possibility of underestimated SM contributions as well as on the impact of our results on new physics models.

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arXiv2015

Upper Bounds on epsilon'/epsilon Parameters B_6^{(1/2)} and B_8^{(3/2)} from Large N QCD and other News

We demonstrate that in the large N approach developed by the authors in collaboration with Bardeen, the parameters B_6^{(1/2)} and B_8^{(3/2)} parametrizing the K\toππmatrix elements _0 and _2 of the dominant QCD and electroweak operators receive both negative O(1/N) corrections such that B_6^{(1/2)} < B_8^{(3/2)}<1 in agreement with the recent lattice results of the RBC-UKQCD collaboration. We also point out that the pattern of the size of the hadronic matrix elements of all QCD and electroweak penguin operators Q_i contributing to the K\to ππamplitudes A_0 and A_2, obtained by this lattice collaboration, provides further support to our large N approach. In particular, a very precise lattice result for the matrix element _0 implies for the corresponding parameter B_8^{(1/2)}=1.0\pm 0.2 to be compared with large N value B_8^{(1/2)}=1.1\pm 0.1. We discuss briefly the implications of these findings for the ratio epsilon'/epsilon. In fact, with the precise value for B_8^{(3/2)} from RBC-UKQCD collaboration, our upper bound on B_6^{(1/2)} implies epsilon'/epsilon in the SM roughly by a factor of two below its experimental value (16.6\pm 2.3)\times 10^{-4}. We also briefly comment on the parameter \hat B_K and the ΔI=1/2$ rule.

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arXiv2015

$K^+\toπ^+ν\barν$ and $K_L\toπ^0ν\barν$ in the Standard Model: Status and Perspectives

In view of the recent start of the NA62 experiment at CERN that is expected to measure the $K^+\toπ^+ν\barν$ branching ratio with a precision of 10%, we summarise the present status of this promising decay within the Standard Model (SM). We do likewise for the closely related $K_L\toπ^0ν\barν$, which will be measured by the KOTO experiment around 2020. As the perturbative QCD and electroweak corrections in both decays are under full control, the dominant uncertainties within the SM presently originate from the CKM parameters $V_{cb}$, $V_{ub}$ and $γ$. We show this dependence with the help of analytic expressions as well as accurate interpolating formulae. Unfortunately a clarification of the discrepancies between inclusive and exclusive determinations of $V_{cb}$ and $V_{ub}$ from tree-level decays will likely require results from the Belle II experiment available at the end of this decade. Thus we investigate whether higher precision on both branching ratios is achievable by determining $V_{cb}$, $V_{ub}$ and $γ$ by means of other observables that are already precisely measured. In this context $\varepsilon_K$ and $ΔM_{s,d}$, together with the expected progress in QCD lattice calculations will play a prominent role. We find $\mathcal{B}(K^+\toπ^+ν\barν) = (9.11\pm 0.72) \times 10^{-11}$ and $\mathcal{B}(K_L\toπ^0ν\barν) = (3.00\pm 0.30) \times 10^{-11}$, which is more precise than using averages of the present tree-level values of $V_{cb}$, $V_{ub}$ and $γ$. Furthermore, we point out the correlation between $\mathcal{B}(K^+\toπ^+ν\barν)$, $\overline{\mathcal{B}}(B_s\toμ^+μ^-)$ and $γ$ within the SM, that is only very weakly dependent on other CKM parameters. Finally, we also update the ratio $\varepsilon'/\varepsilon$ in the SM and present its correlation with $K_L\toπ^0ν\barν$.

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arXiv2015

Kaon Theory News

During the last fifteen years B_{s,d} decays, B_{s,d}^0-\bar B^0_{s,d} mixings, CP-violating asymmetries S_{ψK_S} and S_{ψϕ} provided the dominant information about the pattern of flavour violation within the SM and its extensions. We emphasize that in the coming years K meson physics will certainly strike back through the measurements of the branching ratios of theoretically very clean decays K^+->pi^+ν\barνand K_L->π^0ν\barνand improved calculations of the ratio epsilon'/epsilon=\epe. We summarize the status of K^+->pi^+ν\barνand K_L->π^0ν\barνwithin the SM and simplified NP models and update the picture of flavour violation in the Littlest Higgs model with T-parity taking all available constraints into account. But the highlight of this talk are new results on \epe from lattice QCD and large N approach that give a strong indication for a new anomaly in flavour physics, this time coming from K mesons. Indeed, \epe within the SM is found to be significantly below the data of NA48 and KTeV collaborations. Combining lattice results on the non-perturbative parameters B6 and B8 with the assumption that the SM dynamics dominates the Delta I=1/2 rule a 3 sigma anomaly in \epe emerges. Moreover, the recently derived upper bounds on B6 and B8 from large N approach increase the confidence that the found anomaly could be an important signal of NP at work. Of particular importance are the correlations between K^+->pi^+ν\barν, K_L->π^0ν\barνand \epe. With future precise measurements of K^+->pi^+ν\barνand K_L->π^0ν\barνand improved calculations of \epe they will surely provide powerful tools for selecting the favourite NP models. We illustrate this with the help of the LHT model and simplified models in which NP in K\toπν\barνand \epe is governed by Z with flavour violating couplings or by a heavy Z'.

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arXiv2015

Flavour Expedition to the Zeptouniverse

After the completion of the Standard Model (SM) through the Higgs discovery particle physicists are waiting for the discovery of new particles either directly with the help of the Large Hadron Collider (LHC) or indirectly through quantum fluctuations causing certain rare processes to occur at different rates than predicted by the SM. While the later route is very challenging, requiring very precise theory and experiment, it allows a much higher resolution of short distance scales than it is possible with the help of the LHC. In fact in the coming flavour precision era, in which the accuracy of the measurements of rare processes and of the relevant lattice QCD calculations will be significantly increased, there is a good chance that we may get an insight into the scales as short as 10^{-21} m (Zeptouniverse) corresponding to energy scale of 200 TeV or even shorter distance scales. We discuss the requirements that have to be met for such a flavour expedition to the Zeptouniverse to be successful. In particular we emphasize the power of correlations between flavour observables in the search for New Physics and identify a number of correlations that could allow to discover NP even if it would appear at the level of 20% of the SM contributions. The correlation between K^+\toπ^+ν\barν, B_s\toμ^+μ^- and γextracted from tree-level decays within the SM is one of them. We address the recent data on B_{s,d}\toμ^+μ^- and the anomalies in B_d\to K(K^*)μ^+μ^-, including breakdown of lepton flavour universality. We emphasize the correlations of B_d\to K(K^*)μ^+μ^- with B_d\to K(K^*)ν\barν. We summarize the recent study of K\toπν\barνand B_{d,s}\toμ^+μ^- decays which demonstrates that these decays play important roles in finding out what happens in the Zeptouniverse.

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arXiv2014

$B\to K^{(*)}ν\barν$ decays in the Standard Model and beyond

We present an analysis of the rare exclusive $B$ decays $B\to Kν\barν$ and $B\to K^{*}ν\barν$ within the Standard Model (SM), in a model-independent manner, and in a number of new physics (NP) models. Combining new form factor determinations from lattice QCD with light-cone sum rule results and including complete two-loop electroweak corrections to the SM Wilson coefficient, we obtain the SM predictions $\text{BR}(B^+\to K^+ν\barν) = (4.0 \pm 0.5) \times 10^{-6}$ and $\text{BR}(B^0\to K^{* 0}ν\barν) = (9.2\pm1.0) \times 10^{-6}$, more precise and more robust than previous estimates. Beyond the SM, we make use of an effective theory with dimension-six operators invariant under the SM gauge symmetries to relate NP effects in $b\to sν\barν$ transitions to $b\to s\ell^+\ell^-$ transitions and use the wealth of experimental data on $B\to K^{(*)}\ell^+\ell^-$ and related modes to constrain NP effects in $B\to K^{(*)}ν\barν$. We then consider several specific NP models, including $Z'$ models, the MSSM, models with partial compositeness, and leptoquark models, demonstrating that the correlations between $b\to sν\barν$ observables among themselves and with $B_s\toμ^+μ^-$ and $b\to s\ell^+\ell^-$ transitions offer powerful tests of NP with new right-handed couplings and non-MFV interactions.

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arXiv2014

Can we reach the Zeptouniverse with rare K and B_{s,d} decays?

The Large Hadron Collider will directly probe distance scales as short as 10^{-19}m, corresponding to energy scales at the level of a few TeV. In order to reach even higher resolutions before the advent of future high-energy colliders, it is necessary to consider indirect probes of New Physics (NP), a prime example being Delta F=2 neutral meson mixing processes, which are sensitive to much shorter distance scales. However Delta F=2 processes alone cannot tell us much about the structure of NP beyond the LHC scales. To identify for instance the presence of new quark flavour-changing dynamics of a left-handed (LH) or right-handed (RH) nature, complementary results from Delta F=1 rare decay processes are vital. We therefore address the important question of whether NP could be seen up to energy scales as high as 200 TeV, corresponding to distances as small as 10^{-21}m -- the Zeptouniverse -- in rare K and B_{s,d} decays, subject to present Delta F=2 constraints and perturbativity. We focus in particular on a heavy Z' gauge boson. If restricted to purely LH or RH Z' couplings to quarks, we find that rare K decays, in particular KL-> pi^0 nu nubar and K^+->pi^+ nu nubar, allow us to probe the Zeptouniverse. On the other hand rare B_s and B_d decays, which receive stronger Delta F=2 constraints, allow us to reach about 15 TeV. Allowing for both LH and RH couplings a loosening of the Delta F=2 constraints is possible, and we find that the maximal values of M_Z' at which NP effects that are consistent with perturbative couplings could be found are approximately 2000 TeV for K decays and 160 TeV for rare B_{s,d} decays. Finally we present a simple idea for an indirect determination of M_Z' that could be realised at the next linear e^+e^- or mu^+ mu^- collider and with future precise flavour data.

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arXiv2014

$ΔI=1/2$ Rule and $\hat B_K$ : 2014

I summarize the status of the $ΔI=1/2$ rule in $K\toππ$ decays within an {\it analytic} approach based on the dual representation of QCD as a theory of weakly interacting mesons for large $N$, where $N$ is the number of colours. This approximate approach, developed in the 1980s by William Bardeen, Jean-Marc Gérard and myself, allowed us already 28 years ago to identify the dominant dynamics behind the $ΔI=1/2$ rule. However, the recent inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones to hadronic matrix elements of current-current operators and the calculation of the corresponding Wilson coefficients in a momentum scheme at the NLO improved significantly the matching between quark-gluon short distance contributions and meson long distance contributions over our results in 1986. We obtain satisfactory description of the ${\rm Re}A_2$ amplitude and ${\rm Re}A_0/{\rm Re}A_2=16.0\pm 1.5$ to be compared with its experimental value of $22.3$. While this difference could be the result of present theoretical uncertainties in our approach, it cannot be excluded that New Physics (NP) is here at work. The analysis by Fulvia De Fazio, Jennifer Girrbach-Noe and myself shows that indeed a tree-level $Z^\prime$ or $G^\prime$ exchanges with masses in the reach of the LHC and special couplings to quarks can significantly improve the theoretical status of the $ΔI=1/2$ rule. I stress that our approach allows to understand the physics behind recent numerical results obtained in lattice QCD not only for the $ΔI=1/2$ rule but also for the parameter $\hat B_K$ that enters the evaluation of $\varepsilon_K$. In contrast to the $ΔI=1/2$ rule the chapter on $\hat B_K$ in QCD appears to be basically closed.

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