aa r X i v : . [ h e p - ph ] S e p Flavour Theory and the LHC Era
Andrzej J. Buras
Physik-Department, Technische Universit¨at M¨unchen, D-85748 Garching, GermanyTUM Institute of Advanced Study, Lichtenbergstr. 2a, D-85748 Garching, Germany
DOI: w ill be assigned This decade should make a significant progress towards the Theory of Flavour and themain goal of this talk is to transfer this believe to my colleagues in the particle physicscommunity. Indeed a significant part of this decade could turn out to be the Flavour Erawith participation of the LHC, Belle II, Super-Flavour-Facility and dedicated Kaon andlepton flavour violation experiments. Selected superstars of flavour physics listed belowwill play a prominent role in these events. In this writeup the leading role is played by the prima donna of 2010: CP violation in B s system. In our search for a fundamental theory of elementary particles we need to improve our under-standing of flavour [1, 2]. This is clearly a very ambitious goal that requires the advances indifferent directions as well as continuos efforts of many experts day and night, as depicted withthe help of a ”Flavour Clock” in Figure 1.Figure 1: Working towards the Theory of Flavour around the Flavour Clock.
PLHC2010 flavour violating
CP-violating (CPV) phases that could explaincertain anomalies present in the flavour data and simultaneously play a role in the expla-nation of the observed baryon-antibaryon asymmetry in the universe (BAU)?5. Are there any flavour conserving
CPV phases that could also help in explaining the flavouranomalies in question and would be signalled in this decade through enhanced electricdipole moments (EDMs) of the neutron, the electron and of other particles?6. Are there any new sequential heavy quarks and leptons of the 4th generation and/or newfermions with exotic quantum numbers like vectorial fermions?7. Are there any elementary neutral and charged scalar particles with masses below 1 TeVand having a significant impact on flavour physics?8. Are there any new heavy gauge bosons representing an enlarged gauge symmetry group?9. Are there any relevant right-handed (RH) weak currents that would help us to make ourfundamental theory parity conserving at short distance scales well below those exploredby the LHC?10. How would one successfully address all these question if the breakdown of the electroweaksymmetry would turn out to be of a non-perturbative origin?An important question is the following one: will some of these questions be answered throughthe interplay of high energy processes explored by the LHC with low energy precision experi-ments or are the relevant scales of fundamental flavour well beyond the energies explored by theLHC and future colliders in this century? The existing tensions in some of the corners of theSM and still a rather big room for new physics (NP) contributions in rare decays of mesons andleptons and CP-violating observables including in particular EDMs give us hopes that indeedseveral phenomena required to answer at least some of these questions could be discovered inthis decade.2
PLHC2010
Superstars of Flavour Physics in 2010-2015
In this decade we will be able to resolve the short distance scales by more than an order ofmagnitude, extending the picture of fundamental physics down to scales 5 · − m with the helpof the LHC. Further resolution down to scales as short as 10 − m or even shorter scales shouldbe possible with the help of high precision experiments in which flavour violating processes willplay a prominent role.As far as high precision experiments are concerned a number of selected processes andobservables will in my opinion play the leading role in learning about the NP in this newterritory. This selection is based on the sensitivity to NP and theoretical cleanness. The formercan be increased with the increased precision of experiments and the latter can improve withthe progress in theoretical calculations, in particular the non-perturbative ones like the latticesimulations.My superstars for the coming years are as follows: • The mixing induced CP-asymmetry S ψφ ( B s ) that is tiny in the SM: S ψφ ≈ .
04. Theasymmetry S φφ ( B s ) is also important. It is also very strongly suppressed in the SM andis sensitive to NP similar to the one explored through the departure of S φK S ( B d ) from S ψK S ( B d ) [5]. • The rare decays B s,d → µ + µ − that could be enhanced in certain NP scenarios by an orderof magnitude with respect to the SM values. • The angle γ of the unitarity triangle (UT) that can be precisely measured through treelevel decays. • B + → τ + ν τ that is sensitive to charged Higgs particles. • The rare decays K + → π + ν ¯ ν and K L → π ν ¯ ν that belong to the theoretically cleanestdecays in flavour physics. • Numerous angular symmetries and asymmetries in B → K ∗ l − l − . • Lepton flavour violating decays like µ → eγ , τ → eγ , τ → µγ , decays with three leptonsin the final state and µ − e conversion in nuclei. • Electric dipole moments of the neutron, the electron, atoms and leptons. • Anomalous magnetic moment of the muon ( g − µ that indeed seems to be ”anomalous”within the SM even after the inclusion of radiative corrections. • The ratio ε ′ /ε in K L → ππ decays which is known experimentally within 10% and whichshould gain in importance in this decade due to improved lattice calculations.Clearly, there are other stars in flavour physics but I believe that the ones above will play thecrucial role in our search for the theory of flavour. Having experimental results on these decaysand observables with sufficient precision accompanied by improved theoretical calculations willexclude several presently studied models reducing thereby our exploration of short distancescales to a few avenues.In the rest of this presentation I will discuss some of these decays in the context of thebasic questions in flavour physics listed previously. In particular we will collect a number of PLHC2010 B s,d -mixing and related NP see a very detailed recentanalysis in [6]. During the last 35 years several extensions of the SM have been proposed and analyzed inthe rich literature. In particular in the last 10 years, after the data on B d,s decays, B d,s − ¯ B d,s mixing and related CP violation improved considerably and the bounds on lepton flavourviolating decays became stronger, useful model independent analyses of FCNC processes couldbe performed. Moreover several extensive analyses of the full spectrum of flavour violatingprocesses in the context of specific BSM scenarios have been published. Among the model independent approaches in flavour physics the most prominent role is playedby MFV [7, 8] in which flavour violation including CP violation originates entirely from the SMYukawa couplings. This approach naturally suppresses FCNC processes to the level observedexperimentally even in the presence of new particles with masses of a few hundreds GeV. Italso implies specific correlations between various observables, which are most stringent in theso-called constrained MFV (CMFV) [8] in which only the SM operators are assumed to berelevant. Basically MFV reduces to CMFV when only one Higgs doublet is present.A particularly interesting set-up is obtained introducing flavour-blind CPV phases compat-ible with the MFV symmetry principle [9, 10, 11, 12, 13].As recently shown in [14], the general formulation of the MFV hypothesis with flavour-blind CPV phases (FBPh) applied to a general two Higgs doublet model is very effective insuppressing FCNCs to a level consistent with experiments, leaving open the possibility of sizablenon-standard effects also in CPV observables. In what follows we will call this model 2HDM
MFV with the ”bar” on MFV indicating the presence of FBPhs. As discussed in [14], the 2HDM
MFV can accommodate a large CP-violating phase in B s mixing, as hinted by CDF and D0 data [15,16, 17], while ameliorating simultaneously the observed anomaly in the relation between ǫ K and S ψK S [18, 19].On general grounds, it is natural to expect that FBPhs contribute also to CPV flavour-conserving processes, such as the EDMs. Indeed, the choice adopted in [7] to assume theYukawa couplings as the unique breaking terms of both the flavour symmetry and the CPsymmetry, was motivated by possibly too large effects in EDMs with generic FBPhs. Thispotential problem has indeed been confirmed by the recent model-independent analysis in [20].In [21] the correlations between EDMs and CP violation in B s,d mixing in 2HDM MFV including FBPhs in Yukawa interactions and the Higgs potential have been studied in detail. Ithas been shown that in both cases the upper bounds on EDMs of the neutron and the atoms donot forbid sizable non-standard CPV effects in B s mixing. However, if a large CPV phase in B s mixing will be confirmed, this will imply hadronic EDMs very close to their present experimentalbounds, within the reach of the next generation of experiments, as well as Br ( B s,d → µ + µ − )4 PLHC2010 ypically largely enhanced over its SM expectation. The two flavour-blind CPV mechanismscan be distinguished through the correlation between S ψK S and S ψφ that is strikingly differentif only one of them is relevant. Which of these two CPV mechanisms dominates depends onthe precise values of S ψφ and S ψK S , as well as on the CKM phase (as determined by tree-levelprocesses). Current data seems to show a mild preference for a hybrid scenario where boththese mechanisms are at work. I will be a bit more explicit about this result below. There is a number of explicit BSM models that introduce new sources of flavour violationand CP violation beyond those present in the MFV framework discussed above. Among themthe Littlest Higgs Model with T-parity (LHT), the Randall-Sundrum model without and withcustodial protection (RSc), various supersymmetric flavour models, Z ′ -models, models withvectorial new quarks, the SM extended by the fourth sequential generation of quarks andleptons (SM4) and multi-Higgs doublet models are the ones in which most extensive flavouranalyses have been performed. Most of them have been reviewed in some details in [1], wherethe relevant references can be found. I will concentrate in this presentation on very recentdevelopments and will only recall some of the most interesting results of these older analyses ifnecessary.During the second half of 2009 and also in 2010 the flavour analyses in the framework ofthe 2HDM with and without MFV and also the SM4 became popular. The 2HDM MFV hasbeen already briefly discussed above. The SM4 introduces three new mixing angles s , s , s and two new phases in the quark sector and can still have a significant impact on flavourphenomenology. Most recent extensive analyses of FCNC processes in the SM4 can be foundin [22, 23, 24, 25]. More about it later.Next, let me mention an effective theory approach in which the impact of RH currents inboth charged- and neutral-current flavour-violating processes has been analysed [26]. WhileRH currents are present in several supersymmetric flavour models, in RS models and of coursein left-right symmetric models based on the gauge group SU (2) L × SU (2) R × U (1) B − L (see[27, 28] for most recent papers), the recent phenomenological interest in these models originatedin tensions between inclusive and exclusive determinations of the elements of the CKM matrix | V ub | and | V cb | . It could be that these tensions are due to the underestimate of theoreticaland/or experimental uncertainties. Yet, it is a fact, as pointed out and analyzed recently inparticular in [29, 30, 31], that the presence of RH currents could either remove or significantlyweaken some of these tensions, especially in the case of | V ub | . Implications of this setup for otherobservables, in particular FCNC processes without specifying the fundamental theory in detailbut only assuming its global symmetry and the pattern of its breakdown have been analyzedin [26]. As we will see this approach can be considered as a minimal flavour violating scenarioin the RH sector and will be called RHMFV in what follows. I will return to the results of thiswork below.Finally, recent studies of flavour violating processes in models for fermion masses and mixings[32, 33, 34], indicate that a full theory of flavour has to involve at a certain level non-MFVinteractions. PLHC2010 Waiting for Signals of NP in FCNC Processes
The last decade has established that flavour-changing and CPV processes in B s,d and K systemsare on the whole well described by the SM. The same applies to electroweak precision tests. Thisimplies automatically tight constraints on flavour-changing phenomena beyond the SM and apotential problem for a natural solution of the hierarchy problem and other problems listed inthe Introduction, several of which require the presence of NP not far from the electroweak scale.It is evident from various model-independent studies that NP at the TeV scale must havea non-generic flavour structure in order to satisfy existing constraints. Moreover, in order toavoid fine tuning of parameters, natural protection mechanisms suppressing FCNCs generatedby NP are required. In addition to MFV and GIM, RS-GIM, T-parity in Littlest Higgs models,alignment and degeneracy, most familiar from supersymmetric models and generally flavoursymmetries (abelian and non-abelian) have been invented for this purpose. Last but certainlynot least, custodial symmetries, like the ones related to the Higgs system and relevant forelectroweak precision tests, can be used to suppress specific flavour-violating neutral gaugeboson couplings.It should be emphasized that only protection mechanisms that are stable under radiativecorrections can be considered as solutions to flavour problems and considerations of protectionmechanisms only at tree level are insufficient. In this context let us recall that the standardassignment of the SU (2) L × U (1) Y quark charges, identified long ago by Glashow, Iliopoulos, andMaiani (GIM) [4], forbids tree-level flavour-changing couplings of the quarks to the SM neutralgauge bosons. This mechanism is only violated at the loop level and the FCNC processes arestrongly suppressed by the products of CKM elements and mass splittings of quarks or leptonscarrying the same electric charge. Only in processes involving the top quark exchanges is GIMstrongly broken but in a calculable manner and the pattern of this breakdown seems to agreewith experiment although the tests of this pattern have to be still very much improved.In the case of only one Higgs doublet, namely within the SM, this structure is effectivealso in eliminating possible dimension-four FCNC couplings of the quarks to the Higgs field.While the SU (2) L × U (1) Y assignment of quarks and leptons can be considered as being wellestablished, much less is known about the Higgs sector of the theory. In the presence of morethan one Higgs field the appearance of tree-level FCNC is not automatically forbidden by thestandard assignment of the SU (2) L × U (1) Y fermion charges: additional conditions have to beimposed on the model in order to guarantee a sufficient suppression of FCNC processes [35, 36].The absence of renormalizable couplings contributing at the tree level to FCNC processes, inmulti-Higgs models, goes under the name of Natural Flavour Conservation (NFC) hypothesis.It has been pointed out recently [14] that the MFV hypothesis is more stable in suppressingFCNCs than the hypothesis of NFC alone when quantum corrections are taken into account.Indeed the NFC hypothesis is usually based on a U (1) P Q symmetry that has to be broken inorder to avoid massless scalars. NFC can also be enforced by a Z symmetry. However, itturns out that also this symmetry is insufficient to protect FCNCs when radiative correctionsare considered. On the other hand MFV hypothesis based on continuous flavour symmetriesis more powerful. Thus 30 years after the seminal papers of Glashow, Weinberg and Paschos,the hypothesis of NFC can be replaced by the more powerful and more general hypothesis ofMFV. Other recent interesting analyzes of 2HDMs can be found in [37, 38, 39, 40].6 PLHC2010 .2 Three Strategies in Waiting for NP in Flavour Physics
Particle physicists are waiting eagerly for a solid evidence of NP for the last 30 years. Exceptfor neutrino masses, the BAU and dark matter, no clear signal emerged so far. While waitingseveral strategies for finding NP have been developed. They can be divided roughly into threeclasses.
Here basically the goal is to calculate the background to NP coming from the known dynamicsof the SM. At first sight this approach is not very exciting. Yet, in particular in flavour physics,where the signals of NP are generally indirect, this approach is very important. From my pointof view, being involved more than one decade in calculations of higher order QCD corrections[41], I would claim that for most interesting decays these perturbative and renormalizationgroup improved calculations reached already the desired level. The most advanced NNLOQCD calculations have been done for B → X s γ , K + → π + ν ¯ ν , B → X s l + l − and recently for ε K [42]. See also the two loop electroweak contributions to K → πν ¯ ν [43].The main progress is now required from lattice groups. Here the main goals for the comingyears are more accurate values of weak decay constants F B d,s and various ˆ B i parameters relevantfor B d,s physics. For K − ¯ K mixing the relevant parameter ˆ B K is now known with an accuracyof 4% [44]. An impressive achievement. Let us hope that also the parameters B and B ,relevant for ε ′ /ε will be known with a similar accuracy within this decade.Clearly further improvements on the hadronic part of two-body non-leptonic decays ismandatory in order to understand more precisely the direct CP violation in B s,d decays. In this approach one constructs effective field theories involving only light degrees of freedomincluding the top quark in which the structure of the effective Lagrangians is governed bythe symmetries of the SM and often other hypothetical symmetries. This approach is ratherpowerful in the case of electroweak precision studies and definitely teaches us something about∆ F = 2 transitions. However, except for the case of MFV and closely related approaches basedon flavour symmetries, the bottom-up approach ceases, in my view, to be useful in ∆ F = 1decays, because of very many operators that are allowed to appear in the effective Lagrangianswith coefficients that are basically unknown [45]. In this approach then the correlations betweenvarious ∆ F = 2 and ∆ F = 1 observables in K , D , B d and B s systems are either not visible orvery weak, again except MFV, CMFV or closely related approaches. Moreover the correlationsbetween flavour violation in low energy processes and flavour violation in high energy processesto be studied soon at the LHC is lost. Again MFV belongs to a few exceptions. My personal view shared by some of my colleagues is that the top-down approach is more usefulin flavour physics. Here one constructs first a specific model with heavy degrees of freedom. Forhigh energy processes, where the energy scales are of the order of the masses of heavy particlesone can directly use this “full theory” to calculate various processes in terms of the fundamentalparameters of a given theory. For low energy processes one again constructs the low energytheory by integrating out heavy particles. The advantage over the previous approach is that
PLHC2010
Having the last strategy in mind my group at the Technical University Munich, consistingdominantly of diploma students, PhD students and young post–docs investigated in the lastdecade flavour violating processes with the emphasis put on FCNC processes, in the followingmodels: CMFV, MFV, MFV-MSSM, Z ′ -models, general MSSM, a model with a universal flat5th dimension, the Littlest Higgs model (LH), the Littlest Higgs model with T-parity (LHT),SUSY-GUTs, Randall-Sundrum model with custodial protection (RSc), flavour blind MSSM(FBMSSM), three classes of supersymmetric flavour models with the dominance of left-handedcurrents ( δ LL model), the dominance of right-handed currents (AC model) and models withequal strength of left- and right-handed currents (RVV2 and AKM models), the last commentsapplying only to the NP part. This year we have analyzed the SM4, the 2HDM
MFV andfinally quark flavour mixing with RH currents in an effective theory approach RHMFV. Theseanalyses where dominated by quark flavour physics, but in the case of the LHT, FBMSSM,supersymmetric flavour models and the SM4 lepton flavour violation has also been studied indetail.As a partial review of this work appeared already in [1] with various correlations presentedin Figures 5 - 11 of that paper I will not discuss them in detail here. In [1] numerous references(301) to our papers and studies by other groups can be found. The detailed discussion of thesupersymmetric flavour models ( δ LL, AC, RVV2, AKM) can be found in [32].The “DNA” of flavour physics effects for the most interesting observables constructed in [32]and extended by the recent results obtained in the SM4 is presented in Table 1. This table onlyindicates whether large, moderate or small NP effects in a given observable are still allowed ina given model but does not exhibit correlations between various observables characteristic fora given model. Such correlations can be found in [1] and original papers quoted there. I willsummarize the most striking ones later on. ε K -anomaly and related tensions It has been pointed out in [19] that the SM prediction for ε K implied by the measured valueof S ψK S = sin 2 β , the ratio ∆ M d / ∆ M s and the value of | V cb | turns out to be too small toagree well with experiment. This tension between ε K and S ψK S has been pointed out from adifferent perspective in [18]. These findings have been confirmed by a UTfitters analysis [46].The CKMfitters having a different treatment of uncertainties find less significant effects [6].The main reasons for this tension are on the one hand a decreased value of the relevant non-perturbative parameter ˆ B K = 0 . ± . ± .
028 [44] resulting from unquenched lattice calcu-lations and on the other hand the decreased value of ε K in the SM arising from a multiplicativefactor, estimated first to be κ ε = 0 . ± .
02 [19]. This factor took into account the departureof φ ε from π/ in the K − ¯ K mixing. The recentinclusion of LD effects in Im M modified this estimate to κ ε = 0 . ± .
02 [47]. Very recently8
PLHC2010
C RVV2 AKM δ LL FBMSSM LHT RSc 4G D − ¯ D ⋆⋆⋆ ⋆ ⋆ ⋆ ⋆ ⋆⋆⋆ ? ⋆⋆ ǫ K ⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆ ⋆ ⋆⋆ ⋆⋆⋆ ⋆⋆ S ψφ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆ ⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ S φK S ⋆⋆⋆ ⋆⋆ ⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆ ? ⋆⋆ A CP ( B → X s γ ) ⋆ ⋆ ⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆ ? ⋆ A , ( K ∗ µ + µ − ) ⋆ ⋆ ⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆ ? ⋆⋆ B s → µ + µ − ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆ ⋆ ⋆⋆⋆ K + → π + ν ¯ ν ⋆ ⋆ ⋆ ⋆ ⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ K L → π ν ¯ ν ⋆ ⋆ ⋆ ⋆ ⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ µ → eγ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ τ → µγ ⋆⋆⋆ ⋆⋆⋆ ⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ µ + N → e + N ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ d n ⋆⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆ ⋆⋆⋆ ⋆ ⋆⋆⋆ ⋆ d e ⋆⋆⋆ ⋆⋆⋆ ⋆⋆ ⋆ ⋆⋆⋆ ⋆ ⋆⋆⋆ ⋆ ( g − µ ⋆⋆⋆ ⋆⋆⋆ ⋆⋆ ⋆⋆⋆ ⋆⋆⋆ ⋆ ? ⋆ Table 1: “DNA” of flavour physics effects for the most interesting observables in a selection of SUSYand non-SUSY models. ⋆⋆⋆ signals large NP effects, ⋆⋆ visible but small NP effects and ⋆ impliesthat the given model does not predict sizable NP effects in that observable. From [32]. also NNLO-QCD corrections to the QCD factor η ct in ε K [42] have been calculated enhancingthe value of ε K by 3%. Thus while in [19] the value | ε K | SM = (1 . ± . · − has been quotedand with the new estimate of LD effects and new input one finds | ε K | SM = (1 . ± . · − ,including NNLO corrections gives the new value | ε K | SM = (1 . ± . · − , (1)significantly closer to the experimental value | ε K | exp = (2 . ± . · − . This result iscompatible with [42, 6] although the central value in (1) is sensitive to the input parameters,in particular the value of sin 2 β .Consequently, the ε K -anomaly softened considerably but it is still alive. Indeed, the sin 2 β =0 . ± .
02 from UT fits is visibly larger than the experimental value S ψK S = 0 . ± . ε K exactly: sin 2 β ≈ .
80 [18, 19].One should also recall the tension between inclusive and exclusive determinations with theexclusive ones in the ballpark of 3 . · − and the inclusive ones typically above 4 . · − .As discussed in [18, 19] a small negative NP phase ϕ B d in B d − ¯ B d mixing would solve some PLHC2010
9f these problems. Indeed we have then S ψK S ( B d ) = sin(2 β + 2 ϕ B d ) , S ψφ ( B s ) = sin(2 | β s | − ϕ B s ) , (2)where the corresponding formula for S ψφ in the presence of a NP phase ϕ B s in B s − ¯ B s mixinghas also been given. With a negative ϕ B d the true sin 2 β is larger than S ψK S , implying a highervalue on | ε K | , in reasonable agreement with data and a better UT-fit. This solution wouldfavour the inclusive value of | V ub | .Now with a universality hypothesis of ϕ B s = ϕ B d [48, 19], a negative ϕ B d would automat-ically imply an enhanced value of S ψφ which in view of | β s | ≈ ◦ amounts to roughly 0.04 inthe SM. However, in order to be in agreement with the experimental value of S ψK S this typeof NP would imply S ψφ ≤ . ϕ B s = ϕ B d in [48, 19] was clearly ad hoc. Recently, in viewof the enhanced value of S ψφ at CDF and D0 a more dynamical origin of this relation has beendiscussed by other authors and different relations between these two phases corresponding stillto a different dynamics have been discussed in the literature. Let us elaborate on this topic inmore detail. B s mixing Possibly the most important highlight in flavour physics in 2008, 2009 [15] and even more in2010 was the enhanced value of S ψφ measured by the CDF and D0 collaborations, seen eitherdirectly or indirectly through the correlations with various semi-leptonic asymmetries. Whilein 2009 and in the Spring of 2010 [16], the messages from Fermilab indicated good prospects for S ψφ above 0.5, the recent messages from ICHEP 2010 in Paris, softened such hopes significantly[17]. Both CDF and D0 find the enhancement by only one σ . Yet, this does not yet preclude S ψφ above 0.5, which would really be a fantastic signal of NP. But S ψφ below 0.5 appears morelikely at present. Still even a value of 0.2 would be exciting. Let us hope that the future datafrom Tevatron and in particular from the LHCb, will measure this asymmetry with sufficientprecision so that we will know to which extent NP is at work here. One should also hope thatthe large CPV in dimuon CP asymmetry from D0, that triggered new activities, will be betterunderstood. I have nothing to add here at present and can only refer to numerous papers[39, 49, 50, 6, 51].Leaving the possibility of S ψφ ≥ . S ψφ ≤ . S ψφ ≥ . Such large values can be obtained in the RSc model due to KK gluon exchanges and also heavyneutral KK electroweak gauge boson exchanges. In the supersymmetric flavour model with thedominance of right-handed currents like the AC model, double Higgs penguins constitute thedominant NP contributions responsible for S ψφ ≥ .
5, while in the RVV2 model where NPleft-handed current contributions are equally important, also gluino boxes are relevant. On theoperator level, it is LR scalar operator which is primarly responsible for this enhancement.Interestingly the SM4 having only ( V − A ) ∗ ( V − A ) operators is also capable in obtaininghigh values of S ψφ [22, 23, 25] but not as easily as the RSc, AC and RVV2 models. Thelower scales of NP in the SM4 relative to the latter models and the non-decoupling effects of t ′ PLHC2010 ompensate to some extent the absene of LR scalar operators. In the LHT model where only( V − A ) ∗ ( V − A ) operators are present and the NP enters at higher scales than in the SM4, S ψφ above 0.5 is out of reach [52].All these models contain new sources of flavour and CP violation and it is not surprising thatin view of many parameters involved large values of S ψφ can be obtained. The question thenarises whether strongly enhanced values of this asymmetry would uniquely imply new sourcesof flavour violation beyond the MFV hypothesis. The answer to this question is as follows: • In models with MFV and FBPhs set to zero, S ψφ remains indeed SM-like. • In supersymmetric models with MFV and non-vanishing FBPhs and in the FBMSSM,at both small and large tan β , the supersymmetry constraints do not allow values of S ψφ visibly different from the SM value [32, 50] • In the 2HDM
MFV in which at one-loop both Higgs doublets couple to up- and down-quarks, the interplay of FBPh with the CKM matrix allows to obtain S ψφ ≥ . S ψφ the latter model allows also for a simple and unique softening ofthe ε K -anomaly and of the tensions in the UT analysis if the FBPh in the Yukawa interactionsare the dominant source of new CPV. In this case the NP phases ϕ B s and ϕ B d are relatedthrough ϕ B d ≈ m d m s ϕ B s ≈ ϕ B s , (3)in visible contrast to the hypothesis ϕ B s = ϕ B d of [48, 19]. Thus in this scenario large ϕ B s required to obtain values of S ψφ above 0.5 imply a unique small shift in S ψK S that allows tolower S ψK S from 0.74 down to 0.70, that is closer to the experimental value 0 . ± . β = 0 .
74 and not S ψK S = 0 .
67 that should be used in calculating ε K resulting in a value of ε K ≈ . · − within one σ from the experimental value. The directHiggs contribution to ε K is negligible because of small masses m d,s . We should emphasize thatonce ϕ B s is determined from the data on S ψφ by means of (2), the implications for ε K and S ψK S are unique. It is remarkable that such a simple set up allows basically to solve all thesetensions provided S ψφ is sufficiently above 0.5. The plots of ε K and S ψK S versus S ψφ in [14]show this very transparently. S ψφ ≈ . Yet, as signalled recently by CDF and D0 data [17], S ψφ could be smaller. In this case allnon-MFV models listed above can reproduce such values and in particular this time also theLHT model [52] and another supersymmetric flavour model (AKM) analysed by us stay alive[32].Again MSSM-MFV cannot reproduce such values. On the other hand the 2HDM MFV canstill provide interesting results. Yet as evident from the plots in [14] the FBPh in Yukawainteractions cannot now solve the UT tensions. Indeed the relation in (3) precludes now anyinteresting effects in ε K and S ψK S : S ψφ and the NP phase ϕ B s are simply too small. Evidently,this time the relation ϕ B d = ϕ B s (4)would be more appropriate. PLHC2010
MFV . This time the FBPh in the Higgs potential are at work, the relation in (4) followsand the plots of ε K and S ψK S versus S ψφ are strikingly modified: the dependence is muchstronger and even moderate values of S ψφ can solve all tensions. This time not scalar LRoperators but scalar LL operators are responsible for this behaviour.Presently it is not clear which relation between ϕ B s and ϕ B d fits best the data but themodel independent analysis of [49] indicates that ϕ B s should be significantly larger than ϕ B d ,but this hierarchy appears to be smaller than in (3). Therefore as pointed out in [21] in the2HDM MFV the best agreement with the data is obtained by having these phases both in Yukawainteractions and the Higgs potential, which is to be expected in any case. Which of the twoflavour-blind CPV mechanisms dominates depends on the value of S ψφ , which is still affectedby a sizable experimental error, and also by the precise amount of NP allowed in S ψK S .Let us summarize the dynamical picture behind an enhanced value of S ψφ within 2HDM MFV .For S φφ ≥ . S φφ ≤ .
25 the FBPh in the Higgs potential are expected to dominate the scene. If S ψφ will eventually be found somewhere between 0.3 and 0.6, a hybrid scenario analyzed in [21]would be most efficient although not as predictive as the cases in which only one of these twomechanism is at work. S ψφ Let us then assume that indeed S ψφ will be found to be significantly enhanced over the SMvalue. The studies of different observables in different models allow then immediately to makesome concrete predictions on a number of observables which makes it possible to distinguishdifferent models. This is important as S ψφ alone is insufficient for this purpose.In view of space limitations I will discuss here only the implications for B s,d → µ + µ − and K → πν ¯ ν decays, which we declared to be the superstars of the coming years. SubsequentlyI will make brief comments on a number of other superstars: EDMs, ( g − µ , lepton flavourviolation and ε ′ /ε . S ψφ ≥ . The detailed studies of several models in which such high values of S ψφ can be attained implythe following pattern: • In the AC model and the 2HDM
MFV , Br ( B s,d → µ + µ − ) will be automatically enhancedup to the present upper limit of roughly 3 · − from CDF and D0. The double Higgspenguins are responsible for this correlation [14, 21, 32]. • In the SM4 this enhancement will be more moderate: up to (6 − · − , that is a factorof 2-3 above the SM value [23, 25]. • In the non-abelian supersymmetric flavour model RVV2, Br ( B s,d → µ + µ − ) can be en-hanced up to a few 10 − but it is not uniquely implied due to the pollution of double-Higgscontributions through gluino boxes, that disturbs the correlation present in the AC model[32].12 PLHC2010
In the RSc, Br ( B s,d → µ + µ − ) is SM-like independently of the value of S ψφ [53]. Ifthe custodial protection for Z flavour violating couplings is removed values of 10 − arepossible [53, 54].The question then arises what kind of implications does one have for Br ( B d → µ + µ − ). Ourstudies show that • The 2HDM
MFV implies automatically an enhancement of Br ( B d → µ + µ − ) with the ratioof these two branching ratios governed solely by | V td /V ts | and weak decay constants. • This familiar MFV relation between the two branching ratios Br ( B s,d → µ + µ − ) isstrongly violated in non-MFV scenarios like AC and RVV2 models and as seen in Fig. 5of [1] taken from [32] for a given Br ( B s → µ + µ − ) the range for Br ( B d → µ + µ − ) can belarge with the values of the latter branching ratios being as high as 5 · − . • Interestingly, in the SM4, large S ψφ accompanied by large Br ( B s → µ + µ − ) precludes alarge departure of Br ( B d → µ + µ − ) from the SM value 1 · − [25].We observe that simultaneous consideration of S ψφ and Br ( B s,d → µ + µ − ) can already helpus in eliminating some NP scenarios. Even more insight will be gained when Br ( K + → π + ν ¯ ν )and Br ( K L → π ν ¯ ν ) will be measured: • First of all the supersymmetric flavour models mentioned above predict by constructiontiny NP contributions to K → πν ¯ ν decays. This is also the case of the 2HDM MFV . • In the RSc model significant enhancements of both branching ratios are generally possible[53, 54] but not if S ψφ is large. Similar comments would apply to the LHT model wherethe NP effects in K → πν ¯ ν can be larger than in the RSc [52]. However, the LHT modelhas difficulties to reproduce a very large S ψφ and does not belong to this scenario. • Interestingly, in the SM4 large S ψφ , Br ( K + → π + ν ¯ ν ) and Br ( K L → π ν ¯ ν ) can coexistwith each other [25]. S ψφ ≈ .
25 Scenario
In this scenario many effects found in the large S ψφ scenario are significantly weakend. Promi-nent exceptions are • In the SM4, Br ( B s → µ + µ − ) is not longer enhanced and can even be suppressed, while Br ( B d → µ + µ − ) can be significantly enhanced [25]. • The branching ratios Br ( K + → π + ν ¯ ν ) and Br ( K L → π ν ¯ ν ) can now be strongly en-hanced in the LHT model [52] and RSc model [53, 54] with respect to the SM but this isnot guaranteed.These patterns of flavour violations demonstrate very clearly the power of flavour physicsin distinguishing different NP scenarios. PLHC2010 .7 EDMs, ( g − µ and µ → eγ These three observables are governed by dipole operators but describe different physics as far asCP violation and flavour violation is concerned. EDMs are flavour conserving but CP-violating, µ → eγ is CP-conserving but lepton flavour violating and finally ( g − µ is lepton flavourconserving and CP-conserving. A nice paper discussing all these observables simultaneously is[55].In concrete models there exist correlations between these three observables of which EDMsand µ → eγ are very strongly suppressed within the SM and have not been seen to date. ( g − µ on the other hand has been very precisely measured and exhibits a 3 . σ departure from thevery precise SM value (see [56] and references therein). Examples of these correlations can befound in [32, 57]. In certain supersymmetric flavour models with non-MFV interactions thesolution of the ( g − µ anomaly implies simultaneously d e and Br ( µ → eγ ) in the reach ofexperiments in this decade.Here I would like only to report on correlations between S ψφ and the EDMs of the neutron,Thallium and Mercury atoms within the 2HDM MFV . The significant FBPhs required to repro-duce the enhanced value of S ψφ in this model, necessarily imply large EDMs in question. As arecent detailed analysis in [21] shows the present upper bounds on the EDMs do not forbid siz-able non-standard CPV effects in B s mixing. However, if a large CPV phase in B s mixing willbe confirmed, this will imply hadronic EDMs very close to their present experimental bounds,within the reach of the next generation of experiments. One of the main properties of the Standard Model regarding flavour violating processes is theleft-handed structure of the charged currents that is in accordance with the maximal violationof parity observed in low energy processes. Yet, the SM is expected to be only the low-energylimit of a more fundamental theory in which parity could be a good symmetry implying theexistence of RH charged currents. Prominent examples of such fundamental theories are left-right symmetric models on which a rich literature exists. We have also seen that several NPmodels that we discussed contain RH currents.The recent phenomenological interest in the RH currents in general, and not necessarily inthe context of a given left-right symmetric model as done recently in [27, 28], originated intensions between inclusive and exclusive determinations of the elements of the CKM matrix | V ub | and | V cb | . In particular it has been pointed out [29, 30, 31], that the presence of RHcurrents could either remove or significantly weaken some of these tensions, especially in thecase of | V ub | .Assuming that RH currents provide the solution to the problem at hand, there is an impor-tant question whether the strength of the RH currents required for this purpose is consistentwith other flavour observables and whether it implies new effects somewhere else that could beused to test this idea more globally.In order to answer this question an effective theory approach for the study of RH currentshas been proposed in [26]. In this approach the central role is played by a left-right symmetricflavour group SU (3) L × SU (3) R , commuting with an underlying SU (2) L × SU (2) R × U (1) B − L global symmetry and broken only by two Yukawa couplings. The model contains a new unitarymatrix V R controlling flavour-mixing in the RH sector and can be considered as the minimallyflavour violating generalization to the RH sector. Thus bearing in mind that this model contains14 PLHC2010 on-MFV interactions from the point of view of the standard MFV hypothesis that includesonly LH charged currents, we will call this model RHMFV.A detailed analysis of this setup in [26] shows that the general structure of V R can bedetermined, under plausible assumptions, from the existing tree level decays in the K and B d systems and FCNC processes. The presence of ( V − A ) ∗ ( V + A ) operators, whose contributionsare strongly enhanced through renormalization group effects and in the case of ε K also throughchiral enhancement of their matrix elements, plays here an important role. The resulting V R differs significantly from the CKM matrix.As already stated above the RHMFV model goes beyond the MFV framework and new CPVphases in the RH sector allow for sizable enhancement of S ψφ and solution of the ε K -anomalyas well as of the | V ub | -problem. The resulting “true” value of sin 2 β = 0 . ± .
05 is muchlarger than the measured value of S ψK S = 0 . ± . ϕ B d , however the ε K constraint does not allow in this modelfor a non-negligible value of this phase. It appears then that the simultaneous explanation ofthe | V ub | -problem, of large S ψφ and of the data on S ψK S is problematic through RH currentsalone. Similarly in this simple setup the B s,d → µ + µ − constraints eliminate the possibility ofremoving the known anomaly in Z → b ¯ b .On top of it, the constraint from B → X s l + l − precludes B s → µ + µ − to be close to itspresent experimental bound. Moreover NP effects in B d → ℓ + ℓ − are found generally smallerthan in B s → ℓ + ℓ − . Contributions from RH currents to B → { X s , K, K ∗ } ν ¯ ν and K → πν ¯ ν decays can still be significant. Most important, the deviations from the SM in these decayswould exhibit a well-defined pattern of correlations. ε ′ /ε The flavour studies of the last decade have shown that provided the hadronic matrix elementsof QCD-penguin and electroweak penguin operators will be known with sufficient precision, ε ′ /ε will play a very important role in constraining NP models. We have witnessed recently animpressive progress in the lattice evaluation of ˆ B K that elevated ε K to the group of observablesrelevant for precision studies of flavour physics. Hopefully this could also be the case of ε ′ /ε already in this decade. We are at the beginning of a new decade which certainly will bring us first more detailed insightsinto the physics at short distance scales 10 − − − m. The interplay of high energy colliderresults with the flavour precision experiments will allow us to make important steps towards aNew Standard Model of which Flavour Theory will be a prominent part. For the time being wehave to wait for the first big discoveries at the LHC and at other machines around the world.In particular we look forward to the full performance of the flavour superstars. These noteshopefully demonstrate that we will have a lot of fun with flavour physics in this decade. Acknowledgements
I would like to thank the organizers for inviting me to such a pleasant conference and all mycollaborators for exciting time we spent together exploring the short distance scales with the
PLHC2010
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