Flavor physics within and beyond the Standard Model
aa r X i v : . [ h e p - ph ] J un TTP10-27 SFB/CPP-10-46
Flavour physics within and beyond the Standard Model U. Nierste ( ) ( ) Karlsruhe Institute of TechnologyUniversit¨at KarlsruheInstitut f¨ur Theoretische Teilchenphysik76128 Karlsruhe, Germany
Summary. — I review recent progress in theoretical calculations related to theCKM unitarity triangle. After briefly discussing hints for new physics in B d − B d andB s − B s mixing I present three topics of MSSM flavour physics: First I discuss newtan β -enhanced radiative corrections to flavour-changing neutral current (FCNC)amplitudes which go beyond the familiar Higgs-mediated FCNC diagrams and mayenhance the mixing-induced CP asymmetry in B d → φK S . The second topic is areappraisal of the idea that flavour violation originates from the soft supersymmetry-breaking terms. Finally I discuss how µ → eγ can be used to constrain the flavourstructure of the dimension-5 Yukawa interactions which appear in realistic grandunified theories.12.60.Jv,13.20.He,12.10.-g
1. – Introduction
Flavour physics addresses the transitions between fermions of different generations.Within the Standard Model these transitions originate from the Yukawa couplings ofthe Higgs field to the fermion fields. In the case of quarks the responsible term of theLagrangian reads − X j,k =1 Y ujk u Lj u Rk ( v + H ) − X j,k =1 Y djk d Lj d Rk ( v + H ) + h.c. H . (1) ( ) Invited talk at Les Rencontres de Physique de la Vall´ee d’Aoste , La Thuile, Italy, Feb 28 –Mar 6, 2010. 1
U. NIERSTE
Here H denotes the field of the yet-to-be-discovered physical Higgs boson and v =174 GeV is the corresponding vacuum expectation value. The indices j and k labelthe generations and L and R refer to the chirality of the quark fields. The Yukawa cou-plings for up-type and down-type quarks are 3 × Y u and Y d , respectively. Eq. (1) entails the mass matrices m u = Y u v and m d = Y d v. (2)The diagonalisations of m u and m d involve four unitary rotations in flavour space, oneeach for u L , u R , d L , and d R . Since the left-handed fields u Lk and d Lk , which were originallymembers of a common SU(2) doublet, undergo different rotations, the electroweak SU(2)symmetry is no more manifest in the physical basis in which mass matrices are diagonal.The mismatch between the rotations of the left-handed fields defines the unitary Cabibbo-Kobayashi-Maskawa (CKM) matrix [1, 2], V = V ud V us V ub V cd V cs V cb V td V ts V tb . (3)The CKM elements occur in the couplings of the W boson, because the W e.g. couplesthe c L field to the linear combination V cd d L + V cs s L + V cb b L as a consequence of theunitary rotations in flavour space. V can be parametrised in terms of three angles andone phase, the CP-violating Kobayashi-Maskawa phase γ [2]. With a history of morethan 50 years, research in quark flavour has been essential for the construction of theStandard Model, having guided us to phenomena which were “new physics” at theirtime: Highlights were the breakdown of the discrete symmetries P [3] and CP [4, 2],the prediction of the charm quark [5] and its mass [6], and a heavy top quark predictedfrom the size of B d − B d mixing [7]. In the decade behind us the asymmetric B factoriesBELLE and BaBar have consolidated the CKM picture of quark flavour physics. Withthe advent of the LHC era, the focus of flavour physics has shifted from CKM metrologyto physics beyond the Standard Model. In the Standard Model flavour-changing neutralcurrent (FCNC) processes (such as meson-antimeson mixing, B → X s γ or K → πνν )are forbidden at tree-level and only occur through highly suppressed one-loop diagrams.FCNC processes are therefore excellent probes of new physics. This is a strong rationaleto complement the high- p T physics programs at ATLAS and CMS with precision flavourphysics at LHCb, NA62, BELLE-II, Super-B, BES-III, J-PARC and the future intenseproton source Project X at Fermilab.With the discovery of neutrino flavour oscillations, the much younger field of leptonflavour physics has emerged. The Standard Model in its original formulation [8] lacks aright-handed neutrino field and can neither accommodate neutrino masses nor neutrinooscillations. The simplest remedy for this is the introduction of a dimension-5 Yukawaterm composed of two lepton doublets L = ( ν Lℓ , ℓ L ) and two Higgs doublets leadingto Majorana masses for the neutrinos and generating the desired lepton flavour mixing.Alternatively one can mimic the quark sector by introducing right-handed neutrino fields(and imposing B − L , the difference between baryon and lepton numbers, as an exactsymmetry). With both variants FCNC transitions among charged leptons (such as µ → eγ ) are unobservably small, so that any observation of such a process will imply theexistence of further new particles. Charged-lepton FCNC decays are currently searched TP10-27 SFB/CPP-10-46 [5MM] FLAVOUR PHYSICS WITHIN AND BEYOND THE STANDARD MODEL γα α d m ∆ K ε K ε s m ∆ & d m ∆ SLub V ν τ ub V β sin 2 (excl. at CL > 0.95) < 0 β sol. w/ cos 2 α βγ ρ −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 η e xc l uded a r ea ha s C L > . Beauty 09
CKM f i t t e r
Fig. 1. – Experimental constraints on the unitarity triangle, from ref. [12]. for in the dedicated MEG experiment (studying µ → eγ ), in B factory data (on e.g. τ → µγ ) and at three of the four major LHC experiments (searching e.g. for τ → µµµ ).In the following section I briefly review recent theoretical progress on the Standard-Model predictions for FCNC processes. Subsequently I discuss new developments inflavour physics beyond the Standard Model. I limit myself to supersymmetric theories,which reflects my personal research interests. For a recent broader overview, which alsocovers extra dimensions and Little-Higgs models, see ref. [10]. Exhaustive studies of theflavour sector in a four-generation Standard Model can be found in refs. [11].
2. – Standard Model
The standard unitarity triangle (UT) is a triangle with unit baseline and apex ( ρ, η ),which is defined through ρ + iη ≡ − V ∗ ub V ud V ∗ cb V cd . (4)The two non-trivial sides of the triangle are R u ≡ p ρ + η and R t ≡ p (1 − ρ ) + η .The triangle’s three angles α = arg (cid:20) − V td V ∗ tb V ud V ∗ ub (cid:21) , β = arg (cid:20) − V cd V ∗ cb V td V ∗ tb (cid:21) , γ = arg (cid:20) − V ud V ∗ ub V cd V ∗ cb (cid:21) . (5)are associated with CP-violating quantities. Measurements of flavour-changing quantitiesimply constraints on ( ρ, η ). Last year’s global analysis of the UT performed by theCKMfitter collaboration is shown in fig. 1. For the results of the UTFit collaboration,which uses a different statistical approach see ref. [13]. The figure shows the consistency ofthe various measurements, which single out the small yellow area as the allowed regionfor the apex of the triangle. Clearly, the CKM mechanism is the dominant source offlavour violation in the quark sector. U. NIERSTE
From the quantities entering the global UT analysis in fig. 1 the meson-antimesonmixing amplitudes are the ones most sensitive to generic new physics. While the ex-traction of the UT angle β from the CP phase in B d − B d mixing is theoretically veryclean, all other quantities related to meson-antimeson mixing are plagued by theoreticaluncertainties. Namely, the uncertainties in the mass differences ∆ m q and ∆ m s of thetwo B − B mixing complexes and in ǫ K , which quantifies CP violation in K − K mixing,completely dominate over the irrelevantly small experimental errors. Note that ∆ m s ispractically independent of ρ and η and is only useful for the UT fit because the ratio∆ m d / ∆ m s has a smaller uncertainty than ∆ m d . The K − K mixing mixing amplitude M involves the matrix element h K | H ∆ S =2 | K i of the ∆ S = 2 hamiltonian H ∆ S =2 [18]. H ∆ S =2 is proportional to the four-quark operator d L γ ν s L d L γ ν s L with the relevantmatrix element h K | d L γ ν s L d L γ ν s L ( µ ) | K i = 23 M K f K b B K b ( µ ) . (6)This equation merely defines the parameter b B K which is commonly used to parametrisethe matrix element of interest. In eq. (6) M K = 497 . f K = 160 MeV aremass and decay constant of the neutral Kaon and b K ( µ ) is introduced to render b B K independent of the unphysical renormalisation scale µ and the renormalisation schemechosen for the definition of the operator d L γ ν s L d L γ ν s L ( µ ). In the commonly used MSscheme one has b K ( µ = 1 GeV) = 1 . ± .
02. The matrix element in eq. (6) must becalculated with lattice gauge theory. A new computation by Aubin, Laiho and Van deWater finds [14] b B K = 0 . b B K = 0 . | ǫ K | = (2 . ± . × − further progress on b B K is certainly highly desirable. Theincreasing precision in b B K has also stimulated more precise analyses of other ingredientsof M . Recently a reanalysis of the long-distance contribution to Im M has resultedin an upward shift of 2% in ǫ K [19]. A similar contribution constituting the element Γ of the decay matrix, affects ǫ K at the few-percent level [16, 17].In the case of B − B mixing all long-distance contributions are highly GIM-suppressedand only the local contribution from the box diagram with internal top quarks and W bosons matters. The two mass eigenstates of the neutral B q − B q system differ in theirmasses and widths. The mass difference ∆ m q , q = d, s , which equals the B q − B q oscilla-tion frequency, is given by ∆ m q ≃ | M q | = 2 |h B q | H ∆ B =2 | B q i| . Lattice calculations areneeded to compute f B q b B B q , which is defined in analogy to eq. (6). Here I focus on the ra-tio ∆ m d / ∆ m s yielding the orange (medium gray) annulus centred around ( ρ, η ) = (1 , ξ = f B s q b B B s f B d q b B B d = 1 . ± . . (8)The numerical value in eq. (8) is my bold average of the values summarised by Aubinat the Lattice’09 conference [20]. With this number and the measured values ∆ m B d = TP10-27 SFB/CPP-10-46 [5MM] FLAVOUR PHYSICS WITHIN AND BEYOND THE STANDARD MODEL (0 . ± . − [21] and ∆ m B s = (17 . ± . ± .
07) ps − [22] one finds (cid:12)(cid:12)(cid:12)(cid:12) V td V ts (cid:12)(cid:12)(cid:12)(cid:12) = s ∆ m B d ∆ m B s s M B s M B d ξ = 0 . ± . . (9)With | V td /V ts | = 0 . R t one finds R t = 0 . ± .
03 for the side of the UT opposite to γ .For a pedagogical introduction into meson-antimeson mixing and CKM phenomenologycf. ref. [23].
3. – Beyond the Standard Model3 .1.
Phenomenology of new physics in B − B mixing . – The plot of the UT in fig. 1 isnot the best way to show possible deviations from the Standard Model, because it concealscertain correlations between different quantities. In the LHC era we will more often seeplots of quantities which directly quantify the size of new physics contributions. In thecase of meson-antimeson mixing new physics can be parametrised model-independentlyby a single complex parameter [24]. For B q − B q mixing, q = d, s , one defines∆ q = M q M q, SM12 . (10)The CKMfitter collaboration has found that the Standard-Model point ∆ d = 1 is ruledout at 95% CL (left plot in fig. 2), if all other quantities entering the global UT analysisare assumed free of new physics contributions. This discrepancy is largely driven by B ( B + → τ + ν ) and, if interpreted in terms of new physics, may well indicate non-standard physics in quantities other than B d − B d mixing. A tension on the global UTfit was also noted by Lunghi and Soni [27] and by Buras and Guadagnoli [17]. Thesituation is much simpler in the case of B s − B s mixing, which shows a deviation fromthe Standard Model expectation of similar size (right plot in fig. 2). The allowed regionfor ∆ s is essentially independent from input other than the B s − B s mixing amplitude M s . The quantities entering the analysis are primarily ∆ m s , the width difference ∆Γ s [28, 24], the time-dependent angular distribution in B s → J/ψφ (with access to themixing-induced CP asymmetry A mixCP ( B s → J/ψφ ) if the B s flavour is tagged), and theCP asymmetry in flavour-specific decays a s fs [28, 24]. The first global analysis of thesequantities, which used improved Standard-Model predictions, was performed in 2006[24] showing a 2 σ deviation from the Standard-Model value ∆ s = 1. At the time of thistalk the discrepancy from the combined DØ and CDF data on B s → J/ψφ alone wasbetween 2.0 σ and 2.3 σ , depending on details of the statistical analysis [29]. After thisconference the discrepancy in a s fs has increased due to a new DØ measurement of thedimuon asymmetry in a mixed B d , B s data sample [30]. On the other hand, new CDFdata on A mixCP ( B s → J/ψφ ) have pulled the result towards the Standard Model [31]. Stillall measurements favour arg ∆ s < .2. Supersymmetry with large tan β . – Extensions of the Standard Model typicallycome with new sources of flavour violation, beyond the Yukawa couplings in eq. (1). Inthe Minimal Supersymmetric Standard Model (MSSM) the soft supersymmetry breakingterms a priori possess a flavour structures which is unrelated to Y u and Y d . To avoidexcessive FCNCs violating experimental bounds the MSSM is often supplemented with U. NIERSTE α sSL & A SL & A dSL A s m ∆ & d m ∆ >0 β ; cos 2 β sin 2SM point d ∆ Re -2 -1 0 1 2 3 d ∆ I m -2-1012 excluded area has CL > 0.68Moriond 09 CKM f i t t e r mixing d B - d New Physics in B sSL & A SL & A dSL A FSs τ & d Γ / d Γ∆ , s Γ ∆ s m ∆ & d m ∆ s φ SM point s ∆ Re -2 -1 0 1 2 3 s ∆ I m -2-1012 excluded area has CL > 0.68Moriond 09 CKM f i t t e r mixing s B - s New Physics in B
Fig. 2. – Complex ∆ d and ∆ s planes, plots taken from the web site in ref. [12]. (See ref. [25] fordetails of the analysis.) Similar analyses by the UTfit collaboration can be found in refs. [13, 26]. the assumption of Minimal Flavour Violation (MFV), which amounts to a flavour-blindsupersymmetry-breaking sector. In the MFV-MSSM supersymmetric FCNC transitionsare typically smaller than the error bars of today’s experiments, unless the parame-ter tan β is large. Probing values around tan β = 60 tests the unification of top andbottom Yukawa couplings. Importantly, loop suppression factors can be offset by a fac-tor of tan β and may yield contributions of order one, with most spectacular effectsin B ( B s → µ + µ − ) [32]. The tan β -enhanced loop corrections must be summed to allorders in perturbation theory. In the limit that the masses of the SUSY particles inthe loop are heavier than the electroweak vev and the masses of the five Higgs bosons, M SUSY ≫ v, M A , M H + . . . , one can achieve this resummation easily: After integrat-ing out the heavy SUSY particles one obtains an effective two-Higgs doublet model withnovel loop-induced couplings [33]. In supersymmetric theories, however, it is natural that M SUSY is not much different from v and further M SUSY ≫ M A involves an unnaturalfine-tuning in the Higgs sector. Phenomenologically, large-tan β scenarios comply withthe experimental bound from B ( B s → µ + µ − ) more easily if M A is large, which mayeasily conflict with M SUSY ≫ M A . To derive resummation formulae valid for arbitraryvalues of M SUSY one cannot resort to the method of an effective field theory. Insteadone should work strictly diagrammatically in the full MSSM to identify tan β -enhancedcorrections. This procedure requires full control of the renormalisation scheme: Theanalytical results for the resummed expressions differ for different schemes and not allrenormalisation schemes permit an analytic solution to the resummation problem. Thediagrammatic resummation has been obtained for the flavour-diagonal case in ref. [34]and recently for flavour-changing interactions in ref. [35]. This opens the possibility tostudy tan β -enhanced corrections also to supersymmetric loop processes which decouplefor M SUSY ≫ v and to collider processes involving supersymmetric particles. In ref. [35]a novel large effect, which does not involve Higgs bosons, in the Wilson coefficient C hasbeen found, with interesting implications for the mixing-induced CP asymmetry S φK S in B d → φK S (see fig. 3). TP10-27 SFB/CPP-10-46 [5MM] FLAVOUR PHYSICS WITHIN AND BEYOND THE STANDARD MODEL
400 500 600 700 800 900 1000 È A t È H
GeV L S Φ K S SM + chargino + gluinoSM + charginoSM Fig. 3. – S φK S as a function of | A t | for a parameter point compatible with other experimentalconstraints (see ref. [35] for details). Solid: full result including the new contribution, dashed:SM plus one-loop chargino diagram, dotted: SM value. Shaded area: experimental 1 σ range. .3. Radiative flavour violation . – A symmetry-based definition of MFV starts fromthe observation that the MSSM sector is invariant under arbitrary unitary rotations of the(s)quark multiplets in flavour space. This [U(3)] flavour symmetry ([U(3)] if (s)leptonsare included) is broken by the Yukawa couplings, and MFV can be defined through thepostulate that the Yukawa couplings are the only spurion fields breaking the [U(3)] flavour symmetry [36]. Interestingly, there is a viable alternative to MFV to solve thesupersymmetric flavour problem: We may start with a Yukawa sector in which all Yukawacouplings of the first and second generation are zero. That is, the MSSM superpotentialpossesses an exact [ U (2)] × U (1) symmetry. Then we postulate that the trilinear SUSYbreaking terms A uij and A dij are the spurion fields breaking this symmetry. The observedoff-diagonal CKM elements and the light quark masses are generated radiatively throughsquark-gluino loops, explaining their smallness in a natural way. In ref. [37] it has beenfound that this setup of Radiative Flavour Violation (RFV) complies with all FCNCbounds, if the squark masses are larger than roughly 500 GeV. By contrast, the bilin-ear SUSY breaking terms cannot be the spurion fields breaking [ U (2)] × U (1) withoutviolating the constraints from FCNC processes. The idea that SUSY breaking could bethe origin of flavour violation is not new [38, 39], remarkably the absence of tree-levellight-fermion Yukawa couplings substantially alleviates the supersymmetric CP problemassociated with electric dipole moments [39].The finding that loop contributions involving A qij , q = u, d , can be large has alsoconsequences for the generic MSSM: In FCNC analyses aiming at constraints on flavour-violating SUSY-breaking terms one must include chirally enhanced higher-order correc-tions involving A qij and, if tan β is large, also corrections with bilinear SUSY-breakingterms [40]. The trilinear terms further imply important loop corrections to quark andlepton masses [41] and can induce right-handed W couplings [42]. .4. MSSM with GUT constraints . – In grand unified theories (GUTs) quarks andleptons are combined into symmetry multiplets. As a consequence, it may be possibleto see imprints of lepton mixing in the quark sector and vice versa. In particular, thelarge atmospheric neutrino mixing angle may influence b → s transitions through themixing of right-handed ˜ b and ˜ s squarks [43]. Yet the usual small dimension-4 Yukawainteractions of the first two generations are sensitive to corrections from dimension-5terms which are suppressed by M GUT /M Planck [44]. These contributions are welcometo fix the unification of the Yukawa couplings, but may come with an arbitrary flavour
U. NIERSTE structure, spoiling the predictiveness of the quark-lepton flavour connection. SU(5) andSO(10) models with dimension-5 Yukawa couplings have been studied in great detail [45].Phenomenologically one can constrain the troublesome flavour misalignment using dataon FCNC transitions between the first two generations. Here I present a recent SU(5)analysis exploiting the experimental bound on B ( µ → eγ ) [46]. At the GUT scale theYukawa matrices for down-type quarks, Y d and Y l , read Y d = Y GUT + k d σM Planck Y σ , Y ⊤ l = Y GUT + k e σM Planck Y σ . (11)Here Y GUT is the unified dimension-4 Yukawa matrix, σ = O ( M GUT ) is a linear com-bination of Higgs vevs and the prefactors k d and k e differ from each other due to GUTbreaking. If the universality condition A l = A d = a Y GUT is invoked at the GUT scale,any misalignment between Y GUT and Y σ will lead to a non-MFV low-energy theory,because A l ∝ / Y l and A d ∝ / Y d . We may parametrise this effect as A l ≃ A cos θ − sin θ θ cos θ
00 0 1 Y l . (12)Now the experimental upper bound on B ( µ → eγ ) determines the maximally allowed | θ | as a function of A . In ref. [46] it is found that | θ | can hardly exceed 10 degrees once | A | exceeds 50 GeV. An analysis in the quark sector (studying SO(10) models [43]) findssimilar strong constraints from ǫ K [47]. As a consequence, the dimension-5 terms canbarely spoil the GUT prediction derived from the dimension-4 relation Y d = Y ⊤ l = Y GUT ,unless | A | is small. This result may indicate that dimension-4 and dimension-5 Yukawacouplings are governed by the same flavour symmetries. Acknowledgements
I thank the organisers for the invitation to this wonderful conference and for finan-cial support. The presented work is supported by the DFG Research Unit SFB–TR 9,by BMBF grant no. 05H09VKF and by the EU Contract No. MRTN-CT-2006-035482,“FLAVIAnet”.
REFERENCES[1]
N. Cabibbo , Phys. Rev. Lett. , (1963) 531.[2] M. Kobayashi and T. Maskawa , Progr. Theor. Phys. , (1973) 652.[3] T. D. Lee and C. N. Yang , Phys. Rev. , (1956) 254.[4] J. H. Christenson, J. W. Cronin, V. L. Fitch and R. Turlay , Phys. Rev. Lett. , (1964) 138.[5] S. L. Glashow, J. Iliopoulos and L. Maiani, Phys. Rev. D2 (1970) 1285.[6] M. K. Gaillard and B. W. Lee, Phys. Rev. D10 (1974) 897.[7]
H. Albrecht et al. [ARGUS Collaboration] , Phys. Lett. B , (1987) 245.[8] S. L. Glashow , Nucl. Phys. , (1961) 579. S. Weinberg , Phys. Rev. Lett. , (1967) 1264. A. Salam , in:
Elementary Particle Physics (Nobel Symp. 8) , ed. N. Svartholm, Almquistand Wilsell, Stockholm, 1968.[9]
S. Weinberg , Phys. Rev. Lett. , (1979) 1566.TP10-27 SFB/CPP-10-46 [5MM] FLAVOUR PHYSICS WITHIN AND BEYOND THE STANDARD MODEL [10] A. J. Buras , to appear in
Proc. of Europhysics Conference on High Energy Physics, EPS-HEP 2009, July 16–22, 2009, Krakow, Poland ; arXiv:0910.1032 [hep-ph].[11]
M. Bobrowski, A. Lenz, J. Riedl and J. Rohrwild , Phys. Rev. D , (2009)113006. A. J. Buras, B. Duling, T. Feldmann, T. Heidsieck, C. Promberger andS. Recksiegel , arXiv:1002.2126 [hep-ph].
O. Eberhardt, A. Lenz and J. Rohrwild ,arXiv:1005.3505 [hep-ph].[12]
A. H¨ocker, H. Lacker, S. Laplace and F. Le Diberder , Eur. Phys. J. C , (2001)225 J. Charles et al. [CKMfitter Group] , Eur. Phys. J. C , (2005) 1. Figures takenfrom the web site: http://ckmfitter.in2p3.fr [13] M. Ciuchini et al. , JHEP , (2001) 013. M. Bona et al. [UTfit Collaboration] ,arXiv:hep-ph/0509219. For updated analyses see: http://utfit.roma1.infn.it [14]
C. Aubin, J. Laiho and R. S. Van de Water , Phys. Rev. D , (2010) 014507.[15] S. D. Cohen and D. Antonio [RBC and UKQCD Collaborations] , PoS , LAT2007 (2007) 347.[16]
U. Nierste , in: K. Anikeev et al. , B physics at the Tevatron: Run II and beyond [hep-ph/0201071].[17] A. J. Buras and D. Guadagnoli , Phys. Rev. D , (2008) 033005[18] A. J. Buras, M. Jamin and P. H. Weisz , Nucl. Phys. B , (1990) 491. S. Herrlichand U. Nierste , Nucl. Phys. B , (1994) 292, Phys. Rev. D , (1995) 6505, Nucl. Phys.B , (1996) 27.[19] A. J. Buras, D. Guadagnoli and G. Isidori , Phys. Lett. B , (2010) 309.[20] C. Aubin , contribution to
Lattice 2009 , Beijing, China, 25-31 Jul 2009, arXiv:0909.2686[hep-lat].[21]
C. Amsler et al. [Particle Data Group] , Phys. Lett. B , (2008) 1.[22] V. M. Abazov et al. [DØ Collaboration] , Phys. Rev. Lett. , (2006) 021802; DØ Note5618-CONF. A. Abulencia et al. [CDF Collaboration] , Phys. Rev. Lett. , (2006)242003[23] U. Nierste , Three Lectures on Meson Mixing and CKM Phenomenology , in:
Heavy Quarkphysics , ed. A.Ali and M.Ivanov, ISBN 978-3-935702-40-9, arXiv:0904.1869 [hep-ph].[24]
A. Lenz and U. Nierste , JHEP , (2007) 072[25] O. Deschamps , CKM global fit and constraints on New Physics in the B meson mixing ,arXiv:0810.3139 [hep-ph].[26] M. Bona et al. [UTfit Collaboration] , JHEP , (2008) 049[27] E. Lunghi and A. Soni , Phys. Lett. B , (2008) 162[28] M. Beneke, G. Buchalla, C. Greub, A. Lenz and U. Nierste , Phys. Lett. B , (1999) 631. M. Beneke, G. Buchalla, A. Lenz and U. Nierste , Phys. Lett. B , (2003) 173. M. Ciuchini, E. Franco, V. Lubicz, F. Mescia and C. Tarantino , JHEP , (2003) 031.[29] CDF and DØ collaborations , Public Note
CDF/PHYS/BOTTOM/CDFR/9787 (DØNote 5928-CONF) .[30]
V. M. Abazov et al. [The D0 Collaboration] , Evidence for an anomalous like-signdimuon charge asymmetry , arXiv:1005.2757 [hep-ex].[31]
Louise Oakes , Talk at FPCP 2010, May 25-29, 2010, Torino, Italy ,http://agenda.infn.it/materialDisplay.py?contribId=12& materialId=slides& confId=2635[32]
K. S. Babu and C. F. Kolda , Phys. Rev. Lett. (2000) 228 [arXiv:hep-ph/9909476]. C. S. Huang, W. Liao, Q. S. Yan and S. H. Zhu , Phys. Rev. D (2001) 114021[Erratum-ibid. D (2001) 059902] [arXiv:hep-ph/0006250]. A. Dedes, H. K. Dreinerand U. Nierste , Phys. Rev. Lett. (2001) 251804 [arXiv:hep-ph/0108037].[33] L. J. Hall, R. Rattazzi and U. Sarid , Phys. Rev. D (1994) 7048 [arXiv:hep-ph/9306309]. R. Hempfling , Phys. Rev. D (1994) 6168. M. Carena, M. Olechowski,S. Pokorski and C. E. M. Wagner , Nucl. Phys. B (1994) 269 [arXiv:hep-ph/9402253].
T. Blazek, S. Raby and S. Pokorski , Phys. Rev. D (1995) 4151[arXiv:hep-ph/9504364]. C. Hamzaoui, M. Pospelov and M. Toharia , Phys. Rev. D (1999) 095005 [arXiv:hep-ph/9807350]. A. J. Buras, P. H. Chankowski, J. Rosiek, andL. Slawianowska , Nucl. Phys.
B619 (2001) 434–466.
A. J. Buras, P. H. Chankowski, U. NIERSTE
J. Rosiek and L. Slawianowska , Phys. Lett. B (2002) 96 [arXiv:hep-ph/0207241].
A. J. Buras, P. H. Chankowski, J. Rosiek and L. Slawianowska , Nucl. Phys. B (2003) 3 [arXiv:hep-ph/0210145].
M. Gorbahn, S. J¨ager, U. Nierste, and S. Trine ,arXiv:0901.2065 [hep-ph].[34]
M. Carena, D. Garcia, U. Nierste and C. E. M. Wagner , Nucl. Phys. B (2000)88 [arXiv:hep-ph/9912516].
S. Marchetti, S. Mertens, U. Nierste and D. Stockinger ,Phys. Rev. D (2009) 013010 [arXiv:0808.1530 [hep-ph]].[35] L. Hofer, U. Nierste and D. Scherer , JHEP (2009) 081 [arXiv:0907.5408 [hep-ph]].
L. Hofer, U. Nierste and D. Scherer , to appear in
Proc. of the 2009 EurophysicsConference on High Energy Physics (EPS-HEP 2009), Cracow, Poland, 16-22 Jul 2009 ,arXiv:0909.4749 [hep-ph].[36]
G. D’Ambrosio, G. F. Giudice, G. Isidori and A. Strumia , Nucl. Phys. B , (2002)155[37] A. Crivellin and U. Nierste , Phys. Rev. D , (2009) 035018[38] W. Buchmuller and D. Wyler , Phys. Lett. B , (1983) 321. J. Ferrandis andN. Haba , Phys. Rev. D , (055003) 2004.[39] F. Borzumati, G. R. Farrar, N. Polonsky and S. D. Thomas , arXiv:hep-ph/9805314.
F. Borzumati, G. R. Farrar, N. Polonsky and S. D. Thomas , Nucl. Phys. B , (1999) 53.[40] A. Crivellin and U. Nierste , Phys. Rev. D , (2010) 095007[41] F. Gabbiani, E. Gabrielli, A. Masiero and L. Silvestrini , Nucl. Phys. B , (1996)321. A. Crivellin and J. Girrbach , Phys. Rev. D , (2010) 076001[42] A. Crivellin , Phys. Rev. D , (2010) 031301.[43] T. Moroi , Phys. Lett. B , (2000) 366. D. Chang, A. Masiero and H. Murayama , Phys. Rev. D , (2003) 075013.[44] J. R. Ellis and M. K. Gaillard , Phys. Lett. B , (1979) 315.[45] S. Baek, T. Goto, Y. Okada and K. i. Okumura , Phys. Rev. D , (2001) 095001[arXiv:hep-ph/0104146]. F. Borzumati and T. Yamashita , arXiv:0903.2793 [hep-ph].
F. Borzumati and T. Yamashita , AIP Conf. Proc. , (2010) 916.[46] J. Girrbach, S. Mertens, U. Nierste and S. Wiesenfeldt , JHEP , (2010) 026.[47] S. Trine, S. Westhoff, and S. Wiesenfeldt , JHEP ,08