More synergies from beauty, top, Z and Drell-Yan measurements in SMEFT

We perform a global analysis of Beauty, Top, Z and Drell-Yan measurements in the framework of the Standard Model effective theory (SMEFT). We work within the minimal flavor violation (MFV) hypothesis, which relates different sectors and generations beyond the SU(2)L-link between left-handed top and beauty quarks. We find that the constraints on the SMEFT Wilson coefficients from the combined analysis are stronger than the constraints from a fit to the individual sectors, highlighting synergies in the global approach. We also show that constraints within MFV are strengthened compared to single-generation fits. The strongest bounds are obtained for the semileptonic four-fermion triplet operator Clq3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {C}_{lq}^{(3)} $$\end{document}, probing scales as high as 18 TeV, followed by the gluon dipole operator CuG with 7 TeV, and other four-fermion and penguin operators in the multi-TeV range. Operators with left-handed quark bilinears receive order one contributions from higher orders in the MFV expansion induced by the top Yukawa coupling as a result of the FCNC b → sμμ anomalies combined with the other sectors. We predict the 68% credible intervals of the dineutrino branching ratios within MFV as 4.25⋅10−6≤BB0→K∗0νν¯≤11.13⋅10−6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 4.25\cdot {10}^{-6}\le \mathcal{B}\left({B}^0\to {K}^{\ast 0}\nu \overline{\nu}\right)\le 11.13\cdot {10}^{-6} $$\end{document} and 2.26⋅10−6≤BB+→K+νν¯≤5.78⋅10−6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 2.26\cdot {10}^{-6}\le \mathcal{B}\left({B}^{+}\to {K}^{+}\nu \overline{\nu}\right)\le 5.78\cdot {10}^{-6} $$\end{document}, which include the respective Standard Model predictions, and are in reach of the Belle II experiment. We show how future measurements of the dineutrino branching ratios can provide insights into the structure of new physics in the global fit.

left-handed quark bilinears receive order one contributions from higher orders in the MFV expansion induced by the top Yukawa coupling as a result of the FCNC b → sµµ anomalies combined with the other sectors.We predict the 68% credible intervals of the dineutrino branching ratios within MFV as 4.25 • 10 −6 ≤ B(B 0 → K * 0 ν ν) ≤ 11.13 • 10 −6 and 2.26 • 10 −6 ≤ B(B + → K + ν ν) ≤ 5.78 • 10 −6 , which include the respective Standard Model predictions, and are in reach of the Belle II experiment.We show how future measurements of the dineutrino branching ratios can provide insights into the structure of new physics in the global fit.

I. INTRODUCTION
The Standard Model (SM) continues to rule as the theory of the strong, weak and electromagnetic interactions, despite its shortcomings in addressing various observations and puzzles, including the origin of neutrino masses, the matter-antimatter asymmetry, flavor and dark matter, and the persisting tension with the b → sµµ-data.This implies that new physics (NP) is very weakly coupled, or the scale of physics beyond the Standard Model (BSM) is considerably larger than the scale of electroweak symmetry breaking.If such a separation of scales exist, a powerful tool to describe the low-energy effects of possible BSM physics are effective field theories (EFTs).In this regard, the Standard Model effective theory (SMEFT) has become increasingly important for phenomenology by delivering a framework to globally analyze data from various experiments, energies, and flavor sectors.In other words, SMEFT allows to "join forces" of the high energy and precision frontiers and therefore intensifies the search for NP.As SMEFT respects the SU (3) C × SU (2) L × U (1) Y -symmetry, it directly links fermion flavors within weak isospin multiplets, notably top-and b-quarks, [1][2][3][4], but also different generations due to mixing [5,6], as well as charged leptons and neutrinos.The latter as a means to test lepton flavor structures, such as universality or lepton flavor conservation, has been systematically explored recently in [7].
The number of SMEFT operators in the Warsaw basis [8] at dimensions six, 59, is large, and goes up to 2499 once fermion flavor structure is taken into account.Even though only a subset of operators contributes to a given process, including those via renormalization group mixing, the number of independent Wilson coefficients is in general too large for a fully model-independent analysis.
Flavor patterns linking various components of a given Wilson coefficient help here in two ways: different sectors, flavor changing neutral currents (FCNCs), charged currents and flavor diagonal observables, become correlated and thus can be combined in one global analysis, and the number of degrees of freedom in the global fit is reduced.Several flavor patterns have been considered in the literature, such as minimal flavor violation (MFV) [9][10][11][12], the top-philic approach [13,14] or U (2) or U (3) symmetries [15][16][17].
Here we employ MFV to explore flavorful synergies within SMEFT, building upon and extending existing works [13], which was based on the top-philic approach.Previous SMEFT fits based on MFV do not include top observables [11], or focus on four-quark operators, including top [10] and dijet searches [12].For earlier works, see [1,18].None of these works include LHC Drell-Yan data, which are powerful for flavor analyses and semileptonic four-fermion operators [19][20][21][22].Our goal is to fill this gap and combine b → s FCNCs, top, Z and Drell Yan measurements.This paper is organized as follows: The effective field theory setup is introduced in Sec.II.
The flavor structure of the Wilson coefficients based on MFV is given in Sec.III.In Sec.IV, we discuss the computation of observables and the sensitivities to the Wilson coefficients.Details of the fitting procedure and the results of the fit are presented in Sec.V, as well as the interplay with b → sν ν branching ratios.We conclude in Sec.VI.Auxiliary information is provided in appendices VII A-VII C.

II. EFFECTIVE FIELD THEORY FRAMEWORKS
We briefly review SMEFT in Sec.II A and give the operators and Wilson coefficients that contribute to the processes considered in this analysis.In Sec.II B, we review the weak effective theory that is used to evaluate B physics observables.

A. Standard Model Effective Field Theory
The SMEFT Lagrangian can be written as [23]  L SM stands for the Lagrangian of the SM.Odd-dimensional operators violate lepton or baryon number [24].As we only consider processes that conserve these quantum numbers, we neglect such operators, hence also those with the lowest dimension, d = 5.We consider operators with dimension six, and drop in the following the corresponding superscript from operators and coefficients.
We employ the Warsaw basis [8], a non-redundant basis of dimension-six operators.Wilson coefficients carry in general quark and lepton flavor indices, inflating the number of operators.To relate different processes and reduce the degrees of freedom, we assume MFV.We discuss the flavor structure in detail in Sec.III.We restrict the Wilson coefficients to be real-valued, implying that we allow for no CP violation from beyond the SM.In our analysis, we consider the following operators: lq = lL γ µ l L (q L γ µ q L ) , O Here, q L and l L denote the left-handed SU (2) L quark and lepton doublets, u R and d R the righthanded SU (2) L up-type and down-type quark singlets and e R the right-handed charged leptons.
Each fermion field further carries a flavor index, which is suppressed here for brevity.The gauge field strength tensors of SU (3) C , SU (2) L and U (1) Y are denoted by G A µν , W I µν and B µν , respectively, with A = 1, ..., 8 and I = 1, 2, 3. T A = λ A /2 and τ I /2 are the generators of SU (3) C and SU (2) L in the fundamental representation, with the Gell-Mann matrices λ A and the Pauli matrices τ I .We denote by φ the Higgs field and by φ = iτ 2 φ * its conjugate.The covariant derivative is defined as penguins, whereas the remaining ones in (1) are semileptonic four-fermion operators.
Further dimension-six operators beyond those given in (1) could contribute to the observables considered in this analysis.However, many of these are suppressed in MFV by lepton Yukawa couplings, or down-type quark Yukawas, which we neglect in our analysis, as detailed in Sec.III.This concerns, for instance, four-fermion tensor operators O ledq and O (1,3) lequ , down-type quark and leptonic dipole operators.Furthermore, we neglect leptonic penguins, which are strongly constrained in purely leptonic transitions [18].Moreover, we also neglect possible shifts of the SM couplings from bosonic operators after the diagonalization of the mass matrices [25].
The Wilson coefficients evolve with energy scale governed by the renormalization group equations (RGEs).These are computed at the one-loop level for the SMEFT [26][27][28].For the numerical computation of the running, we employ the python package wilson [29].We note that through RG-running operators in addition to (1) are induced such as four-quark or four-lepton operators.
Those contributions are neglected in this work as the RG-induced effects are at most of the order of a few percent.We recall that MFV is radiatively stable [30], so RG-effects cannot switch on operators beyond MFV.

B. Matching onto the Weak Effective Theory
While NP contributions to collider observables such as top-quark and Drell-Yan production can be described by SMEFT, the energy scale of b-hadron observables is considerably lower, below the electroweak scale.The appropriate theory in this region is the Weak Effective Theory (WET), in which the W, Z, h bosons as well as the top quark have been integrated out, and the SM gauge symmetry is broken to SU (3) C × U (1) em .For b → s decays, the effective Lagrangian reads with Fermi's constant G F = 1/( √ 2v 2 ), V ij are elements of the Cabibbo Kobayashi Maskawa (CKM) matrix, and the effective operators The dipole operators Q In the fit we also consider the B s − Bs mass-difference ∆m s , described by the Lagrangian where m W denotes the mass of the W -boson, with the operator and the corresponding Wilson coefficient C mix V,LL .Further operators including right-handed quarks are not relevant for our EFT analysis, since right-handed FCNCs are induced at a higher order in the MFV expansion.
We match the SMEFT onto the WET at the one-loop level at the scale µ = m W .The analytic matching conditions are taken from Ref. [31].They are stated in the appendix VII A for completeness.The numerical matching conditions are presented in the appendix VII B.

III. MINIMAL FLAVOR VIOLATION IN SMEFT
In this section, we give the flavor ansatz we employ to connect the different sectors, and discuss the phenomenological implications that arise in SMEFT.We start with the MFV ansatz in Sec.III A and the implementation in SMEFT.In Sec.III B we discuss the rotation to the mass-basis and the resulting phenomenology.We give the parameterization of the flavor structure of Wilson coefficients in Sec.III C.

A. The MFV ansatz
MFV has been widely used in flavor studies to reduce the number of free parameters and establish connections between various observables.MFV imposes the flavor structure of the SM onto NP, ensuring that FCNCs are controlled by SM parameters, CKM elements and quark masses.
Therefore, the scale of NP can be as low as a few TeV, despite the tight constraints from FCNC measurements that would otherwise require NP to be much further away.Formally, MFV requires the SMEFT Lagrangian to respect a U (3) 5 symmetry In the SM, this symmetry is broken by the SM Yukawa matrices.In MFV, the latter are promoted to spurions, i.e., fictitious fields transforming non-trivially under G F , such that the flavor symmetry is formally restored.The SM fermion fields are charged under G F as while the Higgs is a singlet, and the Yukawa spurion fields transform under G F as With this prescription, all terms in the SM Lagrangian are formally invariant under G F .Specifically, the Yukawa terms  Such a universal flavor structure originates from flavor symmetry, under which all operators of type qqX with any flavor singlet X have the same transformation properties.This allows for a significant reduction in the number of fit parameters.On the other hand, universality is not exact.
It receives radiative corrections from electroweak loops and Yukawa-induced mixing with other operators [27,28], noting also that Froggatt-Nielsen flavor symmetries generically only provide patterns accurate up to numbers of order one, effects of which are not considered in our analysis.
Models with multi-messengers2 , which transform non-trivially under G F can be constructed that also break universality.An example is a Z ′ that couples flavor-blind to qL q L and both ēR e R and lL l L , together with a leptoquark that couples to qL l L transforming as u R lL , that is, as ( hence with a Yukawa coupling proportional to Y u .The leptoquark induces a 2 in C lq only, whereas the Z ′ feeds into a 1 of both C lq and C qe .We do find, however, from the actual analysis that our simplified ansatz employed for qL q L and ūR u R and confronted to present experimental sensitivities leads to a convergent fit 3 .We hope to come back to fits with more parameters (from flavor, or further operators) and improved data in the future.
The lepton flavor structure can be analogously expressed in terms of Y e as lL l L : ) It has been pointed out that the a priori infinite series in Eq. ( 9) can be resummed by using the Cayley-Hamilton identity [30,32]

B. Mass basis
To apply the MFV ansatz to the fit, the flavor-basis expansion in Eq. ( 9) has to be given in the mass basis of the fermions.We write the transformation from flavor to mass eigenstates (primed fields) for the quarks as where the unitary matrices S u,d L,R are obtained from the diagonalization of Yukawa matrices, with the diagonal (mass basis) matrices given by the quark masses As we neglect lepton masses there is no corresponding transformation in this sector.
In contrast to the top-philic approach, the choice of a mass basis -up mass or down mass basis -does not affect the phenomenology in the MFV scenario.This is similar to the SM, where only the CKM-matrix defined as is physical, while the individual rotation matrices S u/d L and S u/d R cannot be probed.To demonstrate this point, let us consider an operator containing two left-handed quark doublets in the flavor basis After the rotation to the mass basis, we obtain for the up-type quarks and for the down-type quarks Using unitarity and Eq. ( 14), these expressions can be simplified to which are independent of whether flavor originates from the up or the down sector.
In this work, we neglect all Yukawa couplings except for the one of the top we use With these assumptions, a rotation of the quark bilinears in (9) to the mass basis yields Neglecting the down-Yukawa switches off chirality-flipping interactions in the down-quark sector.
While left-handed down-type FCNCs d Lj → d Li proportional to a 2 y 2 t V * ti V tj are induced in this setup, no up-type or right-handed down-type FCNCs arise.Neglecting the masses of the leptons switches off chirality-flipping interactions among leptons, and the chirality-conserving lepton bilinears are flavor diagonal and universal Let us comment on (19), that is, neglecting the lepton and down-type quark Yukawas in SMEFT.
While these couplings are subdominant in single-Higgs models (13), they can be parametrically enhanced in multi-Higgs models, for example, the Minimal Supersymmetric Standard Model by ratios of vacuum expectation values.In any case, for Y d ̸ = 0 and Y e ̸ = 0 chirality flipping operators arise which contribute at tree-level to the anomalous moments of the leptons, and radiative Bdecays.Since presently no new physics in these observables has been established, we focus on the set-up (1), targeting semileptonic B-decays and top-observables, among others.In principle further SMEFT operators can and ideally should be taken into account in future works to make the analysis more model-independent.However, this comes at the price of a significant step in complexity regarding the number of degrees of freedom, their correlation and the measurements, which is beyond the scope of this analysis.

C. Parameterization in the fit
As customary in SMEFT studies, we rescale the Wilson coefficients by v 2 /Λ 2 , generically, Concerning the MFV flavor structure, inspecting the qL q L bilinears in Eq. ( 20), relevant for the operators O (1) lq , and O lq , we see that those involving top quarks are multiplied by a 1 + a 2 y 2 t .In contrast, the flavor-conserving operators containing up-type quarks of the first or second generation receive a contribution from the leading term of the MFV expansion only, a 1 .
We absorb the latter into the rescaled Wilson coefficient for left-handed up-type first and second generation bilinears as The Wilson coefficient for processes involving left-handed top quarks is then given by with Note that all higher orders of the top-Yukawa with terms a 2n (Y u Y † u ) n in the spurion expansion can be absorbed into γ a as they lead to the same flavor structure as the leading correction The ratio γ a is universal for all operators containing a qL q L structure.In our setup, this parameter represents the relative strength of the NP coupling to left-handed third-generation quark-doublets compared to the flavor-diagonal coupling.As such, it provides an indirect probe of the flavor structure of BSM physics.
We can test γ a in a combined fit to b → s FCNC processes, Drell-Yan production, and t t observables with sensitivity to the same Wilson coefficients, but different combinations of Cqq and γ a .For instance, the left-handed down-type FCNC coupling di d j , i ̸ = j is directly proportional to γ a and parameterized by Cqq γ a V * ti V tj .On the other hand, Drell-Yan production with flavor-diagonal up-type quarks in the initial state multiplies probes Cqq , while left-handed down-type diagonal For right-handed tops we employ a parameterization analogous to (28) using (21) with and the coefficient for the first and second generation currents ūRi Λ 2 e 1 contributes as an additional degree of freedom in the fit.The lepton flavor bilinears that enter the semileptonic four-fermion operators comprise only lepton flavor-diagonal couplings due to the vanishing lepton Yukawas in our setup (19).Hence, the respective MFV coefficients f i and g i can simply be absorbed into the Wilson coefficients, resulting in a lepton-flavor universal scenario.
To summarize, we end up with in total 16 degrees of freedom in the full fit -14 Wilson coefficients Ci and two flavor ratios γ a,b .

IV. SIMULATION AND MEASUREMENTS
In this section, we describe the computation of the theory predictions for the different observables and discuss their sensitivity to the SMEFT Wilson coefficients.In general, a cross section in the SMEFT framework can be parameterized in terms of the Wilson coefficients as with the SM cross section σ SM , the interference terms σ int in the expansion as the dimension-six terms squared, are neglected in this work.Quantifying the impact of dimension-eight operators on fits in general requires a case by case study as it depends on the processes and operators considered as well as the scale separation [33][34][35][36][37]: The larger the separation between Λ and the energy of the process, the smaller the impact.The impact also drops if dimension-six and dimension-eight operators are correlated [22].As the number of operators at higher dimension quickly rises, to make progress we restrict ourselves in our analysis to the leading operators in the SMEFT.
Alternatively, one could stop in (33) at order 1/Λ 2 at the level of the cross section, that is, discard the pure BSM contribution σ BSM ij .Analyses of single-top production data from the LHC reveal that the constraints on dimension-six operators with or without quadratic 1/Λ 4 terms are in very good agreement, indicating that the impact of partial higher order EFT corrections is subleading here [38].On the other hand, the quadratic terms are important for Drell-Yan production, since for the FCNC quark flavor combinations the interference terms with the SM are negligible.
The SMEFT contributions σ int i and σ BSM ij for the top, Drell-Yan and Z-decay observables employed in the global fit are generated with the predefined UFO model SMEFTsim 3.0 [25,43], whereas the top-quark observables "Before 2021" in Sec.V A are computed with the dim6top_LO UFO model [14].As a first step, we validate our setup by reproducing the SM predictions.We find an agreement within 20% for all collider observables, which is reasonable since we do not consider higher-order corrections and have only limited statistics for the Monte Carlo data.In the high-p T and invariant-mass tails of the distributions, which are most relevant due to the energy enhancement, the precision is comparable to the experimental uncertainty.In the fits we include the recent SM predictions [44][45][46][47][48][49][50][51][52][53].We further consider only the most precise measurement of each individual process, as correlations among different experiments can have a significant impact on the fit [38].

A. Top quark observables
We consider inclusive cross sections of t tH and t tW production as well as the differential t t, t tZ and t tγ cross section measurements.In addition, we also include the decay width of the top quark, Γ t , and the W -boson helicity fractions f 0 and f L .The decay width and the helicity fractions are computed following Ref.[54] including quadratic SMEFT contributions.For the computation of the inclusive t tH and t tW cross sections, we generate 50 000 events at leading order (LO) for each operator.In order to compute the differential cross sections of the t t, t tZ and t tγ processes, we generate an inclusive sample with 200 000 events for each observable.These samples are subsequently binned with regard to the differential observable of interest, which is the mass of the t t pair, the p T of the Z boson, and the p T of the photon, respectively.The binning is performed with MadAnalysis 5 [55] according to the binning employed in the experimental analyses.
In general, a linear combination of several Wilson coefficients contributes to a given observable.
In the case of associated top-quark pair production, these linear combinations are given by with the weak mixing angle θ w .The observables, sensitivities and corresponding measurements of the top-quark sector are summarized in Tab.I.The Drell-Yan process at LO is sensitive to all Wilson coefficients in (1) except for the dipole operators.These do not contribute to the LO Drell-Yan process in our parameterization, because the only non-vanishing Yukawa coupling in our setup is the top-Yukawa (19).The strongest Drell-Yan constraints arise for semileptonic four-fermion operators, since they grow with energy as O(s/Λ 2 ) [36] and thus generate large contributions in the high-p T tails where the SM contribution is small.The vertex-correcting penguin operators, on the other hand, only alter the coupling of the W and Z boson to quarks with respect to the SM coupling.As the energy exceeds the electroweak scale, the contributions from both these operators decrease.
Due to the high momenta of particles at the LHC, different chirality states can be regarded as independent particles.Therefore, the interference terms between operators comprising different chiralities of quarks and leptons vanish and only interference terms between the left-handed singlet and triplet operators O With the Drell-Yan process, five different initial state quarks can be accessed in the proton, whose composition is described by the parton distribution functions (PDFs).We define the parton-parton luminosity L q i qj for a collision of a quark q i with an antiquark qj , where τ = ŝ/s [21].Here, f q i denotes the PDF of the quark q i , µ F is the factorization scale and √ s and √ ŝ refer to the proton-proton and partonic center-of-mass energy, respectively.The parton-parton luminosities in Eq. ( 35) allow to obtain the Drell-Yan cross sections σ(pp → ℓℓ) and σ(pp → ℓν) from the partonic cross section σ as The sum includes all quark combinations appropriate for CC or NC currents except for the top.
The parton-parton luminosities for the different NC quark combinations are shown in Fig. 1, and for the CC combinations in Fig. 2 as a function of the partonic center-of-mass energy √ ŝ.We use the PDF set NN23LO [41] and show 1σ ranges (shaded bands) and central values (dark solid or dashed lines).To illustrate the impact of the various flavor combinations on the global MFV fit, the CC parton-parton luminosities are weighted by a factor |V ij | for u i dj or ūi d j fusion.This CKM factor arises from the MFV parameterization in Eq. ( 22), resulting in a suppression of CC transitions, similar to the SM.For the FCNC combinations, the interference term between the SM and the SMEFT amplitude is absent, so that no contribution linear in C arises.Thus, we weight the corresponding FCNC parton-parton luminosities by |V ti V tj | 2 , the modulus-squared of the term proportional to a 2 , see (20).For the CC and FCNC combinations that include an up or a down quark, the parton-parton luminosities of the charge-conjugated combination are visualized with dashed lines.If no up or down quark is present, the luminosities of the charge-conjugated processes are identical, since the PDFs of sea-quarks are equal to those of their antiquarks.For the up and down quark, however, which constitute the valence quarks of the proton, the PDF of the quark is significantly larger than the PDF of the related anti-quark, resulting in a difference between the charge conjugated parton-parton-luminosities.Our L q i qj are consistent with Ref. [21].
In contrast to the top-quark observables, the Drell-Yan measurements included in our analysis are not unfolded, so that hadronization and detector effects have to be taken into account.As the number of events is directly proportional to the cross section, a parameterization of the total event number analogous to Eq. ( 33) can be employed.We simulate the SMEFT contribution to the cross section separated into the different initial-state quark flavor compositions.We generate 400 000 events for every operator and every initial-state flavor combination in order to ensure a sufficiently high number of events in the high-p T tails.Here, the statistics of the samples are typically diminished, resulting from the PDF-suppression at high momentum fractions.We employ Pythia 8.3 [60] to simulate the parton shower and hadronization.Detector effects are included by performing a parametric detector simulation with Delphes3 [61].The signal extraction is carried out with ROOT [62], following the analysis strategy and the cuts outlined in the corresponding experimental analysis.
We assume that the background events are predominantly accounted for by the SM, so that any potential NP contributions to the background are neglected.This simplification seems acceptable considering that in most analyses, the Drell-Yan production cross section is assumed to dominate over the sum of all background contributions.Only in the τ τ -channel, a significant fraction of the events are attributed to jets faking hadronic τ -leptons, which might potentially be altered by NP contributions in multijet production.These effects have, however, already been investigated and are tightly constrained [63].
The NC Drell-Yan process is sensitive to all semileptonic four-fermion operators as well as to the two-fermion penguin-operators.For operators comprising two left-handed quark doublets, the lq .This adds another linearly independent direction in the parameter space of the Drell-Yan fit, which further improves the bounds.
With regard to the large partonic center-of-mass energy that can be accessed with the tails of Drell-Yan measurements, a sufficiently high value for Λ has to be assumed in order to ensure the validity of the EFT approach.We therefore set the NP scale to Λ = 10 TeV in all fits For the computation of the asymmetry observables and the ratios we employ flavio [64], whereas the SMEFT contributions to the hadronic cross section are simulated using Mad-Graph5_aMC@NLO with the SMEFTsim 3.0 UFO model [25,43].For the fit we take into account the combined LEP-measurement, including correlations [65]

D. B-physics observables
We follow Ref. [13] and consider various B-physics observables involving b → sγ and b → sℓ + ℓ − transitions along with B s -meson mixing.These include (differential) branching ratios and angular observables, as well as the B s − Bs -mass difference ∆m s .The WET contributions to these observables are computed using flavio [64] together with the Python package wilson [29] as described in Ref. [13].Details on the B → K form factors are provided in App.VII D. For the B → K * form factors, we employ a combined fit [66] to Light-Cone Sum Rules [66] and lattice QCD [67] results.
The observables and measurements are compiled in Tab.III.
In contrast to Ref. [13], the measurements of the B s → ϕµ + µ − observables as well as the branching ratio B s → µ + µ − have been updated.The latter has recently been measured by CMS [68] and the experimental value is now closer to SM prediction [69], compared to the previous result by LHCb [70].We employ only the more precise CMS result, as no combined world average is available, and correlations matter [38].An overview of the Wilson coefficients probed in the B-observables is given in Tab.IV. [74] [75] φq

E. B meson decays into neutrinos
While the b → sℓ + ℓ − FCNCs predominantly probe C+ lq , the corresponding dineutrino processes b → sν ν probes C− lq .A combination of both processes is thus crucial to disentangle the singlet and triplet Wilson coefficients and to resolve this otherwise flat direction in a fit of b → s flavor observables.Searches for b → sν ν transitions have not yielded an observation.Present 90 % CL upper limits on the B 0 → K * 0 ν ν and B + → K + ν ν branching ratios read [81,82] The SM and SMEFT predictions can be computed with the effective Lagrangian given in Eq. ( 2).
Within the MFV approach, only the left handed operator Q L in Eq.
For charged B-mesons a background from tau-leptons via tree-level decays B + → τ + (→ K + ν)ν exists that constitutes an additional contribution of O(10%) [86], and needs to be considered in the experimental extraction of the FCNC branching ratio.
New results and the first observation of these branching ratios are expected from the Belle II experiment in the near future, with a predicted precision of roughly 30% [87].These results will provide important input for global fits and give further insights into possible NP contributions in b → s FCNCs.
To investigate the impact of these future measurements, we perform fits for three different benchmark scenarios.In the SM scenario, we assume SM-like branching ratios for B(B 0 → K * 0 ν ν) and B(B + → K + ν ν) with an experimental uncertainty of 26% and 30%, respectively, as presumed in Ref. [87].This corresponds to a hypothetical benchmark "BM SM" measurement of Moreover, we employ two benchmark scenarios with a simultaneous deviation of 2σ in both branching ratios to investigate the implications of a possible anomalous measurement.We consider the prospective of enhanced branching ratios by a 2σ amplification in both modes "BM + 2σ" as well as with decreased branching ratios by reducing the signals by 2σ "BM − 2σ" The EFT contributions to the branching ratios in WET are computed with the flavio [64] package.

V. FITS TO DATA
We use a fit procedure analogous to Refs.[4,13,38] for which we employ a Bayesian approach as implemented in EFTf itter [88], based on BAT.jl [89].All uncertainties are assumed to be Gaussian distributed and correlations are included as far as they are provided.We include systematic and statistical uncertainties of the experimental measurements as well as theory uncertainties arising in the computation of the SM prediction, whereas the theory uncertainties of the BSM corrections are neglected.The EFT contributions are implemented using the parameterization given in Eq. (33).
We further employ the MFV-parameterization as described in Sec.III and allow all Wilson coefficients contributing to a given set of observables to be present simultaneously.We assume a flat prior distribution for the SMEFT Wilson coefficients as well as for the MFV ratios γ a and γ b in the global fit.
For the fits to the individual sectors, we chose a fixed value for γ a and γ b in order to reduce the degrees of freedom and to ensure convergence of the fit.We recall that while γ a = 0 would decouple the b → s sector, γ a = −1 would lead to the decoupling of the top-quark sector so that both of these values are unsuitable as representative benchmarks.Instead, we set γ a,b = 1 in all fits of individual sectors, as this value provides a natural scale for the b → s transitions that are directly proportional to γ a .Moreover, when neglecting the flavor-diagonal terms, this is the benchmark that directly corresponds to the top-philic approach employed in [13], allowing for a better comparison of the results.Note that γ a,b = 1 gives an additional prefactor for some of the Wilson coefficients depending on the flavor, which is important when comparing our results to the literature.For instance, the left-handed down-type couplings for the quark combination dL i d L i receive a factor ) compared to a flavor-universal approach, as stated in Eq. ( 20).This results in a factor Similarly, the top-quark Wilson coefficients are scaled by a factor of 2 in this setting, following from the factor (γ a,b + 1) in Eqs. ( 28) and (30).The light up-type and all right-handed down-type Wilson coefficients are unaffected by the MFV ratios γ a and γ b .
In Sec.V A, we compare the results derived from the updated top-quark measurements to those obtained from the data analyzed in Ref. [13] utilizing fits of the top sector only.Moreover, we conduct a dedicated analysis of the Drell-Yan production processes in Sec.V B including both, flavor-specific fits of the Drell-Yan measurements as well as an analysis within the MFV framework.
The results of the global MFV fit are presented in Sec.V C. In Section V D we analyze the impact of hypothetical measurements of the dineutrino branching ratios on the global fit.Conversely, we use global fit results to predict the b → s dineutrino branching ratios in MFV in Sec.V E.

A. Updated Fit of the top-quark sector
Compared to the data used in Ref. [13], we employ updated measurements for all observables in the top-quark sector.In addition, we extend the set of observables to encompass the cross sections for the associated production of a top-quark pair with a Higgs boson, t tH, as well as the associated production of a W boson and a top-quark pair, t tW .A further improvement arises from the differential t t, t tZ and t tγ cross sections, which add a large number of measurements through the multitude of bins.The results of this updated fit compared to the previous one from Ref. [13] are presented in Fig. 3.We give the 90% credible intervals in Tab.V.
Especially the bounds on CuG are significantly improved in the updated fit due to the inclusion of various differential observables that add a multitude of measurements sensitive to this operator.
Moreover, one observes improved bounds on CuB and CuW due to the differential t tγ and t tZ cross section.The latter also slightly improves the bounds on the penguin operators Cφu , C(1) φq and -1.0 -0.5 0 0.5 1.0

C(3)
φq .The triplet coupling C(3) φq as well as CuW are moreover probed by the top-quark width Γ t , for which the experimental uncertainties have decreased.Similarly, the experimental precision of the measurement of the helicity fractions f 0 and f L has also been improved, which further tightens the limits on CuW .

B. Fit of Drell-Yan observables
In order to assess the impact of the Drell-Yan measurements on the global fit, we conduct an analysis including only the Drell-Yan observables using the MFV framework described in Sec.III.We consider all SMEFT operators except for the dipoles, whose contributions to Drell-Yan production vanish due to neglecting the light Yukawa couplings in our setup (19).The fit is performed assuming   Tab.II and fit all 11 coefficients simultaneously while setting γ a,b = 1.In addition, we perform separated fits including only the NC or the CC measurements.In the CC fit, only the triplet Wilson coefficients C(3) φq and C(3) lq are considered as degree of freedom, since all other operators are insensitive to this process.The results are presented in Fig. 4, showing the 90% credible intervals as well as the total width of these intervals.The 90% credible intervals are furthermore listed in Tab.VI. 0 0.2 0.4 0.6 0.8 (1) q CC CC + NC NC -0.002 0 0.002 -0.02 0 0.02 10 4  10 3 10 2 10 1 10 0 total width of 90% intervals Our study shows that the four-fermion operators can be potently constrained by the Drell-Yan measurements, with bounds of the order 10 −3 within the MFV framework.The limits on the penguin operators, in contrast, are approximately two orders of magnitude inferior with widths of the order 10 −1 to 10 0 .This difference between the two types of operators is consistent with the different scaling with energy.The triplet operators C(3) φq and C(3) lq are especially well constrained since they contribute to the CC Drell-Yan process exclusively.
In addition to the Drell-Yan fit within the MFV framework, we furthermore conduct flavorspecific fits with regard to the lepton as well as to the quark flavor in order to investigate the impact of the different flavor compositions.Again, we impose the benchmark γ a = 1 and allow all Wilson coefficients of a given quark flavor combination to be present simultaneously.Following from the MFV parameterization outlined in Sec.III C, we assume no lepton-flavor violating contributions.This is particularly relevant for the CC process, as it involves neutrinos whose flavor cannot be   We also perform fits of the FCNC quark combinations ds, db and sb, for which the bounds are, however, several orders of magnitude larger due to the CKM suppression arising in the MFV framework.Therefore, we do not show the limits of the FCNC processes in the plots, but give the ranges in the appendix in Tab.XII.The strongest individual constraint arises from the CC pp → µν process for the Wilson coefficient lq with a 90% credible interval of [-0.0001, 0.0003] for the ud quark flavor combination.In general, the constraints on the Wilson coefficients arising from the measurements including muons are slightly better than the ones obtained from electron or tau lepton measurements, due to the differences in the detection and reconstruction efficiency.Regarding the quark flavor, the best limits are found for up and down quark as expected from the parton-parton luminosities shown in Fig. 1.
In contrast, flavor combinations involving b quarks are the least well constrained.We find that our bounds are consistent with the limits derived in Ref. [22].
The MFV fit improves the bounds on the Wilson coefficients in comparison to the flavor-specific fits, since it combines all flavor-specific limits.Specifically, each lepton flavor couples universally and all quark combinations contribute simultaneously to a given Wilson coefficient, resulting in an enhancement of the bounds on the Wilson coefficients.These findings demonstrate that the Drell-Yan observables are a powerful tool to constrain the Wilson coefficients within the MFV scenario.This is especially pronounced for the four-fermion operators, which further profit from the energy enhancement present in the high−p T tails of the distributions.

C. Global analysis
We perform a global fit of all sectors, beauty, Z, top and Drell-Yan, in order to investigate and exploit the synergies arising in the combination of the different types of observables.The resulting bounds on the Wilson coefficients are presented in Fig. 7 and the 90% credible limits are listed in Tab.VII.We compare the results of this global fit to analyses of the individual sectors in which we set γ a,b =1 and include only the Wilson coefficients contributing to the respective sector as degrees of freedom.The b → s measurements are fitted together with the Z observables in order to ensure the convergence of the fit, which is otherwise difficult to achieve due to the high number of contributing Wilson coefficients in the matching at the one-loop level.In the b → s and Z fit, there is no sensitivity to C(1) lq and C(3) lq , but only on their linear combination C+ lq .Therefore, we constrain C+ lq instead of the individual Wilson coefficients in this fit.
-0.01 -0.005 0 0.005 0.01 10 4 10 3 10 2 10 1 10 0 Total width of 90% intervals Our findings demonstrate that the combination of the various sectors leads to synergies that improve the bounds on the Wilson coefficients.This is especially pronounced for CuG , C the other fits.This leads to a widening of the 90% credible interval in the combined fit.
Furthermore, the limits on the four-fermion operators are strongly dominated by the Drell-Yan measurements as expected from their energy enhancement and the results presented in Sec.V B.
The penguin operators, on the other hand, are predominantly constrained by the Z observables while the dipole operators receive the strongest bounds from the top-quark sector.The Wilson coefficient that is best constrained is C(3) lq with a 90% credible interval of [ -1.8•10 −4 , 0.8•10 −4 ], resulting from the strong bounds due to the NC as well as especially the CC Drell-Yan process.
The global fit also probes the MFV parameters γ a and γ b defined in Eqs.(29), (31).The onedimensional marginalized posterior probability distributions of these two parameters are presented in Fig. 8.
Our results indicate that the fit is not very sensitive to γ b .This parameter is probed by the significantly smaller than the bounds on Cuū , so that there is only a minor sensitivity on γ b .The parameter γ a , in contrast, shows a distinct double-peak behaviour with a large peak at roughly γ a = −1.2 and a smaller peak at γ a = 1.9.The posterior probability distribution further features a minimum around γ a = 0.
These findings indicate that the second order of the MFV expansion for left-handed quarks is favored to have a slightly larger absolute value compared to the leading, flavor diagonal term of the MFV expansion.Higher order terms at order one have also been noted in [12,90].In case of the maximum near γ a = −1.2,both terms conspire to cancel each other in part in the top quark coupling given in Eq. (20), which is proportional to 1 + γ a .
The minimum at γ a = 0 is caused by the anomalies in the b → sµµ observables, such as the B 0 → K * 0 µ + µ − decay distributions measured by LHCb which exhibit a tension with the SM predictions at approximately 3σ [76].These b → s observables are directly proportional to is favored in the scenario with B-data at SM values (green), supporting the hypothesis that the anomalies present in the b → s FCNCs are responsible for the minimum at γ a = 0 in the global fit (dark blue).For comparison, we also show p(γ a ) using Drell-Yan data only (light blue).We learn that the latter are consistent with a wide range of γ a , with a maximum at zero, as expected since the Drell-Yan data are in agreement with the SM predictions.
To further investigate the impact of the different sectors on the MFV parameters, we repeat the global fit and separately exclude the Z (red), or the top (orange) measurements from the fit, shown in the right panel of Fig. 9.We learn that neither the Z nor the top data alone are central to deciphering the flavor structure.However, excluding the t t-observables significantly loosens bounds on the dipole operators, whereas removing the Z-pole data decreases the sensitivity to the penguins.

D. Impact of dineutrino measurements on the global fit
We perform the global fit including the hypothetical benchmark measurements of the B 0 → K * 0 ν ν and B + → K + ν ν branching ratios detailed in Sec.IV E. The resulting 90% credible intervals of the Wilson coefficients are shown in Fig. 10 and the marginalized one-dimensional posterior probability distributions of γ a in Fig. 11.
-0.005 -0.0025 0 0.0025 0.005 We learn that the hypothetical dineutrino benchmarks have a significant impact on the Wilson coefficients, particularly on the penguin operators as well as the four-fermion operators with lefthanded quarks, see Fig. 10.A measurement with the expected sensitivity of Belle II can signal NP in the SMEFT coefficients Cφd , Cqe or C(1) lq .Notably, even a SM-like measurement would imply a deviation in Cqe and Cφd , which can be accounted for by the anomalies in the b → sℓ l observables as well as the persistent tension of the Z → b b observables from the SM prediction [91].
A hypothetical measurement with a 2σ decrease of the branching ratios would further increase this tension, whereas a measurement with a 2σ excess would result in 90% credible intervals for Cqe and Cφd compatible with Ci = 0.In the latter case we would, however, observe a non-zero value for C(1) lq , which is in agreement with the SM in the other two benchmark scenarios.These findings highlight that a measurement of the dineutrino branching ratio would provide a useful input to the global fit to disentangle BSM physics.
Our analysis further indicates that a measurement of the dineutrino branching ratios can have a significant impact on the MFV parameter γ a , especially if a deviation from the SM would be observed, see Fig. 11.Enhanced dineutrino branching ratios would be in line with the fit to current data and yield a similar shape of the posterior probability distribution of γ a , as shown in the left panel.On the other hand, the benchmarks featuring reduced branching ratios (right panel) show an increase of the height of the second peak favoring positive values of γ a while the presently favored one at γ a ∼ −1.2 is reduced in comparison.

E. Predictions of dineutrino branching ratios from the global fit
In addition to studying the impact of future measurements of the dineutrino branching ratios on the global fit in Sec.V D, here, we infer predictions on the dineutrino branching ratios from the global fit.We employ the posterior probability distributions obtained in Sec.V C and insert them into the parameterization of the branching ratios derived in Sec.IV E to compute the allowed ranges of B → K ( * ) ν ν branching ratios within our MFV setup.The resulting probability distributions are presented in Fig. 12 together with the current experimental upper limits (red) at 90% confidence level [81,82] and the SM prediction (41) (grey) including its 1σ uncertainty.
We obtain the following 68% credible intervals from the MFV-based fit with corresponding 90% upper limits 13.13 • 10 −6 and 6.82 • 10 −6 , respectively, which are below the current experimental limits (40).The dineutrino modes are maximally positive correlated in our setup, since both are affected by a single Wilson coefficient only, C L in WET.The corresponding right-handed Wilson coefficient vanishes as we neglect all down-type Yukawas (19).The ratio of branching fractions hence depends only on form factors and meson masses, whereas the CKM elements and the Wilson coefficient cancel.We obtain which equals the value in the SM [64].This prediction can be verified experimentally in order to test the leading order MFV hypothesis.We note that the dineutrino branching ratios (45) from our global MFV fit are not significantly altered with respect to their SM values (41).This can be accounted for by the fact that the Wilson coefficients are all compatible with Ci = 0, corresponding to SM-like measurements.We also note that in simplified NP models with C lq only, or dominating over C lq , the dineutrino modes are enhanced relative to the SM as a result of the suppression of the b → sµµ ones [92].This can be understood from the matching in App.VII A and the fact that leading effects are from SM-NP interference and that the leading SM contributions have opposite sign, C SM at a muon collider [97,98].Further future directions for flavorful SMEFT fits include the study of up-quark sector FCNCs, induced by finite down-type Yukawa couplings that switch on other higher order terms of MFV, or an analysis that covers b → d data, which are presently consistent with MFV [99], although within large experimental uncertainties.
The results of the global fit also allows to predict the branching ratios of FCNC dineutrino decays B → K ( * ) ν ν decays, for which presently only upper limits, about a factor few higher than the SM predictions, exist.Our predictions (45) include the SM and are in reach of Belle II [87].We also find that a future measurement of the dineutrino branching ratios provides useful information on the global fit to disentangle BSM physics.
Note added: While this paper was under review, Belle II published their first measurement of the B + → K + ν ν branching ratio at 2.4 ± 0.7 • 10 −5 [100], which is enhanced relative to the SM prediction (41) and challenges MFV, see Fig. 12.

Acknowledgments
We are happy to thank Rigo Bause and Hector Gisbert for useful discussions.

VII. AUXILIARY INFORMATION A. Analytical Matching
We match the SMEFT onto the WET within the MFV framework introduced in Sec.III.The tree-level matching equations read: The one-loop matching equations read [31,101,102]: Note that the one-loop matching of φq and Cqe onto C 9 as well as C 10 have been corrected with regard to Ref. [13].We further only consider the leading contributions to C mix

V,LL
with regard to CKM suppression.
The one loop functions for the matching of the dipole operators read [101]: The loop functions for the matching of the vertex correcting penguin operators read [31]: Note that we correct the overall and relative signs in comparison to [13].We agree with the matching in [103] and extend it by higher orders in the MFV expansion.The loop functions for the matching of the four-fermion operators onto C 9 , C 10 read [101], [31] : The numerical matching conditions at the scale µ = m W read: C. Fit results of Drell-Yan measurements The individual limits for initial state quark-flavor compositions are given in Tab.VIII for the e + e − channel, in Tab.IX for the µ + µ − channel, in Tab.X for the τ + τ − channel and in Tab.XI for the CC processes.We furthermore give the bounds on the FCNC quark-flavor combinations in Tab.XII.parameterization [104] f i (q 2 ) = 1 with the pole factors the pole masses M B i = M B * s = for f +,T and M B i = M B 0 s for f 0 , and the conformal mapping where t + = (M B + + M K + ) 2 .We chose t 0 = (M B + + M K + )( √ M B + − √ M K + ) 2 , which maps the physically allowed values of q 2 onto the region with |z| < 0.15.As numerical inputs, we use M B * s = 5.4154 GeV [105] and M B 0 s = 5.711 GeV [106].We use K = 3, resulting in three parameters a i n per form factor. Eq. ( 85) implies f i (0) = a i 0 , hence the consistency relation f + (0) = f 0 (0) can be implemented in a straightforward way by using a common parameter a +/0 0 = a + 0 = a 0 0 .We fit the latest lattice LQCD results from the HPQCD collaboration [107] together with results from LCSRs [66].As LQCD is most precise for high values of q 2 , we include synthetic data generated at q 2 ∈ (18, 20, 22) GeV 2 .LCSRs are, in contrast, only valid for low q 2 , so that we include LCSR data for q 2 ∈ (−15, −10, −5) GeV 2 .The resulting parameters a i n together with the uncertainties and the correlation matrix are given in Tab.XIII.We furthermore illustrate the results in Fig. 13 as a function of q 2 and compare it to other recent fit results [66,108].We find that our results are consistent with the literature and that the uncertainties are significantly reduced due to the recent HPQCD results.67) -0.966(64) 0.12(11) 0.214(57) -0.12(13) 0.3177(95) -0.999(86) 0.17 ( 85) with K = 3 and consider data from LCSRs [66] as well as the latest LQCD results from the HPQCD collaboration [107].the data employed for the fit [66,107].We compare our results to the z-expansion fit with LCSR data and the previous HPQCD results [66,109], as well as to the results using LQCD results only [108].
i are operators of mass dimension d ≥ 5 composed out of SM fields, C (d) i are the corresponding Wilson coefficients and Λ denotes the scale of NP, which is assumed to be sufficiently above the electroweak scale governed by the vacuum expectation value of the Higgs, v = 246 GeV.

7 and Q 8
correspond to FCNC b → sγ and b → sg vertices, respectively.Semileptonic decays to charged leptons, b → sℓ + ℓ − involve the operators Q 9 and Q 10 ; the corresponding FCNC transitions to neutrinos, b → sνν, are described by Q L .Further operators exist that are, however, suppressed in MFV by light quark Yukawas, see Sec.III A, such as the ones obtained from the above (3) by flipping the chiralities of the quark fields.We do not consider NP contributions to those flipped operators, as well as to four-quark operators.Contributions from the latter, however, are taken into account in the SM predictions.
respect G F due to the non-trivial transformation of the spurions which cancel the transformations of the fermions.MFV requires the terms in the SMEFT Lagrangian to be singlets under G F .This implies constraints on the flavor structure of the Wilson coefficients, because they have to cancel the flavor transformations of the fermions in the operators.Denoting Wilson coefficients for the moment generically by C ij , with flavor indices i, j = 1, 2, 3, one obtains for the different quark bilinears where the ellipsis indicate higher order terms.The MFV coefficients a k , b k , c k , d k , e k parameterize the flavor structure of the quark bilinears.It is sensible to use identical MFV coefficients for all operators containing a given bilinear up to an overall, operator-dependent Wilson coefficient 1 .
Again, all higher powers of the top-Yukawa with terms b 2n (Y † u Y u ) n can be absorbed into γ b as they lead to the same flavor structure as the leading correction b 2 Y † u Y u .A similar argument holds for the dipole operators of the type qL u R , which comprise the operators O uB , O uG and O uW .In MFV, these couplings are proportional to Y u .Hence, these operators only induce a coupling to top quarks that is proportional to the rescaled coefficient Cqū = v 2 Λ 2 y t (c 1 + c 2 y 2 t + c 4 y 4 t ...).The right-handed down-quark bilinear dR d R is relevant for the operators O φd , O ed and O ld .Since we neglect the down-type Yukawas, only the rescaled universal and flavor-diagonal coefficient at leading order MFV Cd d = v 2

i
between the SMEFT and the SM, and the pure SMEFT contribution σ BSM ij .The latter includes the contribution of the individual operators squared as well as the interference between different SMEFT operators.The interference terms between dimension-eight operators and the SM, which are formally of the same order 1/Λ4 φq are present.Hence, several Wilson coefficients can be constrained individually without having issues with large cancellations, i.e., flat directions in the parameter space.

FIG. 1 :FIG. 2 :
FIG. 1: Parton-parton luminosities of the quark combinations contributing to the flavor-diagonal NC (left panel) and FCNC (right panel) Drell-Yan process.The FCNC combinations are scaled by |V ti V tj | 2 to illustrate the impact on the MFV fit.Shaded bands correspond to 1σ ranges and dark solid or dashed lines to central values.
4 .C. Z-pole observables We incorporate the Z → b b observables A b FB and R b , denoting the forward-backward asymmetry and the ratio of Z → b b to Z → hadrons, respectively, as well as the corresponding Z → cc observables A c FB and R c into the fit.The cc-couplings probed by the latter are given by the diagonal terms of the left-and right-handed up-type quark couplings in the MFV parameterization Eqs.(20) and (21).These couplings are absent in the top-philic scenario, marking a significant difference between the two flavor patterns.The Z-pole observables provide important constraints on the penguin operators, in particular for O φu and O φd with coupling to right-handed quarks, which are otherwise only weakly constrained by Drell-Yan and b → s observables.

( 3 )
contributes to the b → sν ν process while right-handed currents are absent.The branching ratios are thus proportional to the Wilson coefficient |C L | 2 , the CKM factor |V tb V * ts | 2 and to the integral over the form factors multiplied by a known q 2 -dependent function.We compute the SM predictions for the branching ratios following [83], using |V tb V * ts | = (41.3± 0.8) × 10 −3 [84] and C SM L = −6.32 ± 0.07 [85] as numerical inputs.For the B → K * form factors, we employ the results of Ref. [66], while the B → K form factors are discussed in more detail in App.VII D. For the SM-predictions, we obtain

FIG. 3 :
FIG. 3: Constraints on the SMEFT Wilson coefficients Ci from the top-quark measurements included in Ref. [13] (Before 2021) and from the updated data set listed in Tab.I (This work) assuming Λ =10 TeV and γ a,b = 1.Shown are the 90% credible intervals (left) and the total width of these intervals (right).

[ 13 ](
Before 2021) and from the updated data set listed in Tab.I (This work).We use Λ = 10 TeV and γ a,b = 1.

FIG. 4 :
FIG. 4: Constraints on the SMEFT Wilson coefficients Ci from the Drell-Yan measurements presented in Tab.II assuming Λ =10 TeV and γ a = 1.Shown are the 90% credible intervals (left) and the total width of these intervals (right).

FIG. 7 :
FIG. 7: Constraints on the SMEFT Wilson coefficients Ci assuming Λ =10 TeV and a flat prior in the range [-1, 1] for Ci .Shown are the 90% credible intervals (left) and the total width of these intervals (right).We compare the result of the global fit including top, B-physics, Z-decay and Drell-Yan measurements to the fit results of the individual sectors.For the global fit, we simultaneously fit γ a,b with a flat prior in the range −10 ≤ γ a,b ≤ 10, whereas this parameter is set to γ a,b =1 for the individual fits.In the B + Z fit, we can only constrain C + lq .See text for details.

φq , Cφd and C( 1 )
lq .For other Wilson coefficients, in particular C(1) φq and Cqe , the limits of the combined fit are slightly inferior to the bounds derived from the individual sectors.This results from the increased number of degrees of freedom in the global fit in comparison to the analyses of the individual sectors, for example the Z-fit which comprises only four free parameters.Moreover, the 90% credible interval of C(1) φq in the top-quark fit is slightly shifted with regard to the results from 90% credible intervals multiplied by 10 3 of the global MFV Fit as well as the fits of the individual sectors.The fits are performed assuming Λ = 10 TeV and a flat prior in the range [-1, 1] for all Wilson coefficients Ci .In the global fit, γ a,b are included as degrees of freedom whereas we set them to γ a,b = 1 in the fits to individual sectors.In the B + Z fit, we can only constrain C + lq .See text for details.

FIG. 8 :
FIG. 8: Marginalized posterior probability distributions of the MFV parameters γ a and γ b defined in Eqs.(29), (31) for Λ = 10 TeV obtained from the global fit including top, B-physics, Z-decay and Drell-Yan measurements.We choose a uniform distribution in the interval −10 ≤ γ a,b ≤ 10 as the prior probability distribution.

γFIG. 9 :
FIG.9: Impact of the b → s anomalies and other sectors on the marginalized posterior distribution of γ a .In the left panel we compare the global MFV fit (dark blue) to a scenario in which all b → s measurements are set to their SM prediction while keeping uncertainties unchanged (green).We also show the distribution from a pure Drell-Yan fit (light blue).In the right panel we show the global fit (dark blue) and fits excluding all top-quark observables (orange) and one excluding the Z observables (red).All fits are performed assuming Λ = 10 TeV.

FIG. 10 :
FIG. 10: Impact of hypothetical benchmark measurements of the branching ratios B 0 → K * 0 ν ν and B + → K + ν ν on the 90% credible intervals of the SMEFT Wilson coefficients in the global MFV fit.We compare the results from the global fit without b → sν ν observables to the fits including a hypothetical SM-like measurement (BM SM) (42), a benchmark with a 2σ excess (BM +2σ) (43) and a benchmark with a 2σ decrease (BM −2σ) (44) in the branching ratios.All fits are performed assuming Λ = 10 TeV and a flat prior in the range −10 ≤ γ a,b ≤ 10.

FIG. 11 :
FIG.11: Impact of hypothetical benchmark measurements of the dineutrino branching ratios B 0 → K * 0 ν ν and B + → K + ν ν on the one-dimensional marginalized posterior probability distribution of γ a .We compare the results from the global fit without b → sν ν observables to the fits including a hypothetical SM-like measurement (BM SM)(42) and benchmarks with enhanced branching ratios (left) as well as to decreased branching ratios (right).All fits are performed assuming Λ = 10 TeV and a flat prior for γ a .
LN is supported by the doctoral scholarship program of the Studienstiftung des Deutschen Volkes.GH gratefully acknowledges an IPPP DIVA fellowship.This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG) through the PUNCH4NFDI consortium supported by the DFG fund NFDI 39/1.
90% credible limits of the FCNC flavor combinations of the DY fit considering only one quarkflavor combination in each fit.Shown are the results of the pp → e + e − fit (upper left), the pp → µ + µ − fit (upper right) and the pp → τ + τ − fit (lower center).The fits are performed assuming Λ = 10 TeV.

2 )FIG. 13 :
FIG. 13: Results of our form factor expansion multiplied by the corresponding pole factors together with , b k , c k , d k , e k of arbitrary size are allowed.Hence, MFV can be viewed as a parameterization of the BSM flavor structure rather than a restriction.The relative magnitude of the expansion parameters becomes then of interest, as it provides insights into the flavor structure of BSM physics.Specifically, textures |a k≥2 | ≲ |a 1 |, that is, with a dominant first order term, Process Observable SMEFT operators Experiment Ref. SM Ref.

TABLE II :
References to the measurements of the NC (left) and CC (right) DY process together with the corresponding integrated luminosity.All measurements are carried out at √ s = 13 TeV.

TABLE IV :
Sensitivities of B-physics processes to WET and SMEFT Wilson coefficients.The contributions marked as { Ci } are induced by the RGE running in SMEFT and WET at O(α s ) only.
TeV to ensure the validity of the EFT framework.We employ all measurements listed in

TABLE V :
90% credible intervals of the top-quark fits employing the measurements included in Ref.
[31,102]e loop functions I lq3 (x t ) I φq3 1 (x t ) and I φq3 2 (x t ) are corrected w.r.t.[13].The loop functions for matching onto C mix V,LL read[31,102]:The loop functions for the matching of the dineutrino Wilson coefficient C L read:

TABLE XIII :
Fit results and correlation matrix of the z-expansion coefficients.We employ the BSZ parameterization in Eq. (