Constraining top-quark couplings combining top-quark and $\boldsymbol{B}$ decay observables

We present a first, consistent combination of measurements from top-quark and $B$ physics to constrain top-quark properties within the Standard Model Effective Field Theory (SMEFT). We demonstrate the feasibility and benefits of this approach and detail the ingredients required for a proper combination of observables from different energy scales. Specifically, we employ measurements of the $t\bar t\gamma$ cross section together with measurements of the $\bar B\rightarrow X_s\gamma$ branching fraction to test the Standard Model and look for new physics contributions to the couplings of the top quark to the gauge bosons within SMEFT. We perform fits of three Wilson coefficients of dimension-six operators considering only the individual observables as well as their combination to demonstrate how the complementarity between top-quark and $B$ physics observables allows to resolve ambiguities and significantly improves the constraints on the Wilson coefficients. No significant deviation from the Standard Model is found with present data.


Introduction
The experiments at the Large Hadron Collider (LHC) conduct various searches for physics beyond the Standard Model (BSM). The searches for direct production of new particles have not yet resulted in any discovery of BSM physics. A complementary approach are indirect searches, where precise measurements of total rates and kinematic distributions are compared to their Standard Model (SM) predictions. If the new particles are heavier than the experimental energy scale, the Standard Model Effective Field Theory (SMEFT) can be a e-mail: stefan.bissmann@tu-dortmund.de b e-mail: johannes.erdmann@tu-dortmund.de c e-mail: cornelius.grunwald@tu-dortmund.de d e-mail: ghiller@physik.uni-dortmund.de e e-mail: kevin.kroeninger@tu-dortmund.de applied to parametrize potential deviations from the SM in a model-independent way [1][2][3]. For energies below the scale of BSM physics, Λ , effects of new particles and interactions can be described in a series of higher-dimensional operators constructed from SM fields.
Additional constraints on BSM contributions to top-quark physics come from B physics (see e.g. Refs. [19][20][21]). Especially flavor-changing neutral currents are excellent probes of BSM physics due to suppression by the Fermi constant, small CKM matrix elements and loop factors. The Weak Effective Field Theory (WET) Lagrangian describing b → s transitions is not invariant under the full SM gauge group due to EWSB at the scale v. Since the scale Λ has to be above v, BSM physics needs to be integrated out before EWSB. To constrain SMEFT coefficients using low-energy observables, the effective Lagrangian must be matched onto the WET Lagrangian by integrating out all particles heavier than the b quark [19][20][21][22][23].
Matching and renormalization group equation (RGE) evolution enable to combine measurements at different energy scales in one analysis that allows to investigate the impact of measurements from top-quark and B physics on the top-quark sector of SMEFT.
In this paper, we consider ttγ cross sections and thē B → X s γ branching fraction to perform a first consistent fit of SMEFT Wilson coefficients using a combination of top-quark and B physics observables that have a common set of relevant dimension-six operators. Similar analyses have been performed for top-Higgs couplings in Refs. [24,25]. We present the steps necessary for such a combined analysis of BSM contributions to top-quark interactions and highlight possible pitfalls in this procedure. We determine the dependence of the observables on the Wilson coefficients and compare our computations to results obtained with existing tools. We estimate the gain in the sensitivity for BSM contributions when considering top-quark and B physics observables in a combined fit.
The outline of this paper is as follows. In Sec. 2 we introduce the SMEFT and WET Lagrangians and introduce conventions used throughout this paper. In Sec. 3 we discuss the steps necessary to calculate low energy observables in dependence of SMEFT Wilson coefficients. The measurements used to constrain the SMEFT Wilson coefficients are presented in Sec. 4. In Sec. 5 we describe the corresponding computations of the SM and BSM contributions. In Sec. 6 we determine constraints on the SMEFT Wilson coefficients. We investigate the individual impact of top-quark and B observables and demonstrate how the combination of these observables improves the constraints. In Sec. 7 we conclude. Auxiliary information is given in several appendices.

Effective field theories at different scales
In this section we describe the effective field theory approach to ttγ production and b → sγ transitions, for which a set of common dimension-six operators exists. In Sec. 2.1 we give the SMEFT operators considered in our analysis. In Sec. 2.2 we introduce the effective theory for b → sγ transitions.

Effective Lagrangian for ttγ production
The effects of heavy BSM particles with mass scale Λ can be described at lower energies E Λ in a basis of effective operators with mass dimension d > 4 [1,2]. Such higherdimensional operators are constructed from SM fields and are required to be Lorentz invariant and in accord with SM gauge symmetries. The SMEFT Lagrangian L SMEFT is an expansion in powers of Λ −1 . Higher-dimensional operators O Operators of dimension d = 5 and d = 7 are not considered in this work since they violate lepton and baryon number conservation [26,27]. In the following, we only consider operators with mass dimension d = 6, which are the leading BSM contributions to LHC physics. A complete basis containing 59 independent operators for one generation (2499 for three generations [28]) of fermions is presented in Ref. [3] in the Warsaw basis, which is used in the following. Fortunately, for any class of observables only a small subset of operators has to be considered.
We study the dimension-six operators affecting ttγ production at the LHC. Examples for lowest order Feynman diagrams with both gluons and quarks as initial states are shown in Fig. 1. We consider only operators involving thirdgeneration quarks and bosonic fields, including the Higgs field. The corresponding operators can be written as with q L the SU(2) doublet, u R the up-type SU(2) singlet, the gauge field strength tensors B µν , W I µν and G A µν of U(1) Y , SU(2) L and SU(3) C and the generators T A and τ I of SU(3) C and SU(2) L , respectively. The Higgs-doublet is denoted by ϕ andφ = iτ 2 ϕ * . Contributions from dipole operators with right-handed b quarks, which contribute to top-quark decay and via one-loop diagrams to b → s transitions, are suppressed by a factor m b /m t relative to the ones with righthanded top quarks, and therefore neglected. Generally, the effective operators in Eq. (2) are non-hermitian which leads to complex-valued Wilson coefficients. In this analysis, we assume all Wilson coefficients to be real valued. Four-quark operators can in principle also affect ttγ production. As tt production at the LHC is dominated by the gg channel (∼ 75 % and ∼ 90 % at 8 TeV and 13 TeV, respectively [14]), we neglect contributions from four-quark operators. We allow for BSM effects in top-quark decay via O uW , see Fig. 1.

Effective Lagrangian forB → X s γ decays
Rare b → sγ processes can be described by the Weak Effective Field Theory (WET) Lagrangian [29] where V i j are elements of the CKM matrix, G F is the Fermi coupling constant, Q i are effective operators andC i are the corresponding Wilson coefficients including both SM and BSM contributions. The effective operators relevant for the processes considered here are the four-fermion operators as well as the dipole operators with chiral left (right) projectors L (R) and the field strength tensor of the photon F µν . We neglect contributions proportional to the small CKM matrix element V ub and to the strange-quark mass.

Matching at one-loop level
To describe BSM physics at energies below the electroweak scale µ W , the SMEFT Lagrangian in Eq. (1) has to be matched onto the WET Lagrangian as illustrated in Fig. 2. Top-quark measurements allow to constrain the values of Wilson coefficients at the scale µ t ∼ m t . At the scale µ b ∼ m b , B measurements can be used to constrain the values of the WET coefficients. To express B observables in terms of SMEFT Wilson coefficients at the scale µ t , the following steps have to be performed, extending the procedure described in Ref.
[22]: First, RGE evolution of the SMEFT Wilson coefficients from the scale µ t to µ W has to be performed. As a next step, L SMEFT has to be matched onto L WET . Finally, the RGE evolution of the WET Wilson coefficients from µ W to µ b has to be carried out. These three steps allow the computation of observables, such as BR(B → X s γ), at the scale µ b in dependence of the SMEFT Wilson coefficients C i (µ t ) at the scale µ t . In the following, we describe each of the three steps for the b → sγ process considered in this work.

RGE evolution in SMEFT
The computation of the RGEs in SMEFT is based on Refs. [28,30,31]. To describe the RGE evolution of the operators in Eq.
(2) at O(α s ), the following SMEFT operators have to be included due to mixing: withG A µν = 1 2 ε µναβ G Aαβ (ε 0123 = +1). To compute the anomalous dimension matrix at O(α s ), the effective operators have to be rescaled [32]: where g , g and g s are the coupling constants corresponding to U(1) Y , SU(2) L and SU(3) C , respectively, and y denotes a Yukawa coupling. The Wilson coefficients change with inverse powers of the couplings. In terms of the rescaled coefficients, the RGEs in SMEFT read and O uG contributes to the running of the four-quark operators where i, j are isospin indices and ε 12 = +1. These contributions are suppressed by small down-type Yukawa couplings and neglected in Eq. (8). Further more, we see from Eq. (8) that C ϕG and C ϕG do not change their values due to running at O(α s ). Since O ϕG and O ϕG have no sizable effect on ttγ production [14] and b → sγ transitions, we neglect O ϕG and O ϕG under the assumption that only operators including the top quark are generated at the scale Λ . The operator O uϕ does not directly affect the observables we study but is needed to absorb the UV divergence in the top-quark mass corrections from O uG in SMEFT NLO computations [33]. We compute the BSM contributions at LO QCD and neglect O uϕ .

Matching SMEFT onto WET
In Fig. 3 we give examples for one-loop diagrams including contributions from operators in Eq.
i denotes BSM contributions at order α 0 s to the coefficients in L WET . TheC i denote rescaled Wilson coefficients where v = 246 GeV is the Higgs vacuum expectation value. Explicit expressions for the x t -dependent functions E uW 7 , F uW 7 , E uW 8 and F uW 8 can be found in Ref.
[22] and are given in Appendix B.

RGE evolution in WET
At the scale µ W , both the SM and BSM contributions are matched onto L WET . The RGEs are then used to evolve the coefficientsC i from µ W to µ b . By doing so, large logarithms are resummed to all orders in perturbation theory. Instead of the original coefficientsC i it is convenient to use the effective coefficients [34,35] One finds y = (0, 0, −1/3, −4/9, −20/3, −80/9) and z = (0, 0, 1, −1/6, 20, −10/3) [29] in the MS scheme with fully anticommuting γ 5 . The RGEs for the effective coefficients read with the anomalous dimension matrix γ eff . The perturbative expansion of this matrix is given as The matrices γ (0)eff and γ (1)eff are given in Ref. [29]. The matrix γ (2)eff is specified in Ref. [36]. Analogously, the coefficients expanded in powers of α s read The SM values of the effective coefficients at the scale µ W are known at NNLO QCD [37][38][39].
Obviously, performing the matching ofC i to ∆C

Measurements
In this section, the measurements of the ttγ production cross section and of theB → X s γ branching fraction that we use for constraining the Wilson coefficients are described.

Measurements of the ttγ cross section
Cross sections of ttγ production have been measured at different center-of-mass energies by the ATLAS [40][41][42] and CMS [43] experiments. For our fits, we consider the cross sections determined in the 13 TeV analysis performed by the ATLAS collaboration using 2015 and 2016 LHC data corresponding to an integrated luminosity of 36.1 fb −1 [42]. In this analysis, the ttγ production cross section is reported as a fiducial cross section for final states containing one or two leptons (in the following referred to as single-lepton or dilepton channel, respectively), where the leptons can be either electrons or muons (or their corresponding antiparticles). The fiducial regions for both channels are defined in Sec. 7.1 of Ref. [42]. The measured values of the single-lepton and dilepton fiducial cross sections are reported as Within uncertainties, the measurements agree well with the SM predictions at NLO QCD [42,44]:

Measurements of BR(B → X s γ)
For the branching fraction ofB → X s γ multiple measurements, performed by the BaBar [45][46][47], Belle [48][49][50] and CLEO [51] experiments, are available. A combination of these measurements has been performed by the Heavy Flavor Averaging Group (HFLAV) [52], taking into account the different minimum photon energy requirements applied in the respective analyses. The differences are corrected for by performing an extrapolation according to the method described in Ref. [53]. For our fits we use the most recent result of the combination of BR(B → X s γ) measurements [54], with a minimum photon energy requirement of E γ > 1.6 GeV. This value agrees well with the NNLO SM prediction [55] BR SM (B → X s γ) = (336 ± 23) × 10 −6 .

Modeling observables
In the following we describe the computation of the SM and BSM contributions to the observables. In Sec. 5.1 we discuss how to model the fiducial ttγ cross section and in Sec. 5.2 we describe the computation of BR(B → X s γ).

Computation of σ (ttγ)
The ttγ production cross section can be computed at LO QCD for any given configuration of Wilson coefficients using Monte Carlo (MC) simulations. Since the MC simulations take too long to be directly interfaced to the fit of Wilson coefficients, we determine a parametrization of σ (ttγ) in terms of the Wilson coefficients. By squaring the matrix element of processes including dimension-six operators, the cross section in the presence of Wilson coefficientsC i can be expressed as where σ interf.
i are terms coming from the interference between SM and EFT diagrams and σ BSM i j are purely BSM contributions. Using cross sections computed with MC simulations for different configurations of Wilson coefficients as sampling points, an interpolation to Eq. (19) can be performed, yielding numerical values for the σ i terms and thus a parametrization of the cross section as a function of the Wilson coefficients that can be used in the fit.
To parametrize the impact of the dimension-six operators O uB , O uG and O uW on the ttγ production cross section, we perform simulations using MADGRAPH5 aMC@NLO [56] with the dim6top LO UFO model [16]. We generate MC samples similar to the signal sample described in Ref. [42] to make sure that the simulations are suitable for a fit to the fiducial measurements. The samples are generated using 2 → 7 processes for both, the single-lepton and the dilepton channel, allowing for BSM contributions from O uW in topquark decay. For the BSM contributions only one insertion of a dimension-six operator is allowed at a time and the BSM energy scale is set to Λ = 1 TeV. The dimension-six operators we consider in this paper are O uB , O uG and O uW , as given in Eq. (2). In the dim6top LO UFO model different degrees of freedom are chosen than in this analysis, so that it is not possible to directly specify the value of the coefficientC uB but only the value of the linear combinatioñ where θ W is the Weinberg angle (in the notation of Ref. [16] C tZ is used instead of C uZ ). Thus, we generate sampling points in the space of the Wilson coefficientsC uG ,C uW and C uZ and use the equivalent representation in terms ofC uB , C uG andC uW for determining constraints on the coefficients hereinafter. We choose 201 different sampling points, where up to two Wilson coefficients at a time can take non-zero values. For each of the sampling points, 50 000 events are generated. Comparing the SM value obtained with the cross section of the LO signal sample described in Ref. [42], we find good agreement with a relative deviation of less than 4 %.
We determine the parametrization of the ttγ cross sections as a function of the Wilson coefficientsC uG ,C uW andC uZ by performing an interpolation according to Eq. (19). For the interpolation we apply a least squares fit with the Levenberg-Marquardt algorithm provided by the LsqFit.jl package [63].
The sampling points and the result of the interpolation are shown in Fig. 4 as slices of the phase space where only one Wilson coefficient is varied at a time, while the others are set to zero. We find that the simulated cross sections are well described by the interpolation, as the relative differences between the simulated values and the interpolation, calculated at all sampling points, have a standard deviation of only 0.2 %. To obtain fiducial acceptances, we apply parton showering to the events using PYTHIA8 [57] and perform a particle-level event selection with MadAnalysis [58][59][60]. For the clustering of particle jets, the anti-k t algorithm [61] with a radius parameter R = 0.4 is applied using FastJet [62]. At each sampling point we determine the fiducial acceptances for the single-lepton and dilepton channels using an event selection that is similar to the definition of the fiducial regions described in Ref. [42]. Comparisons of the fiducial acceptances for the SM sampling point with the values given in Ref. [42] show that we obtain the same fiducial acceptance for the dilepton channel and only a small deviation of 3 % for the single-lepton channel.
It should be noted that performing a parton-level simulation and applying the fiducial cuts at this level, which might be considered as a first approximation, is not sufficient as the resulting LO fiducial cross sections deviate from the LO SM predictions in Ref. [42] by about 50 % for the single-lepton and 25 % for the dilepton channel.
The dependence of the fiducial acceptance A on the Wilson coefficientsC i can be parametrized as where the denominator is the parametrization of the cross section σ as given in Eq. (19). The acceptances A i account for changes in kinematics due to BSM contributions. With the parameters σ i already determined in the previous interpolation of the cross section, we perform a least squares fit of the fiducial acceptances to Eq. We obtain the dependence of the fiducial cross sections on the Wilson coefficients by multiplying the interpolation of the total cross section with the interpolations of the fiducial acceptances. As our simulations are performed at LO QCD and NLO calculations of the SM fiducial cross sections are available, we apply a SM k-factor by setting the SM contributions to the according values of the NLO predictions presented in Sec. 4.1.
In Fig. 6 the resulting parametrizations of the fiducial ttγ cross sections as functions of the Wilson coefficients C uB ,C uG andC uZ are shown for the single-lepton and dilepton channels. The dependence onC uB is determined using Eq. (20). Shown are slices of the phase space where only one Wilson coefficient is varied at a time, while the others are set to zero. In both channels, we observe a comparable behavior of the fiducial cross sections and similar sensitivities to the Wilson coefficients.

Computation of BR(B → X s γ)
The most recent estimate of theB → X s γ branching fraction at NNLO QCD has been presented in Ref. [55], following the algorithm described in Ref. [39]. We adapt this procedure in our computation of BR(B → X s γ) and extend it to LO BSM contributions. Applying the notation of Ref. [64], the branching fraction can be expressed as where α e is the fine structure constant, E 0 = 1.6 GeV is the photon energy cut and P(E 0 ) and N(E 0 ) denote perturbative and non-perturbative corrections, respectively. The factor C is given as with an experimental value C exp = 0.568 ± 0.007 ± 0.01 [65]. The quantity P(E 0 ) is given as where the matrix K(E 0 , µ b ) expanded in α s reads: The coefficients K (1) i j can be derived from the NLO results given in Ref. [66]. For the computation of P(E 0 ) at approximate NNLO we include the effects of charm and bottom masses in K   1(2)7 [39]. Contributions of three-body and fourbody final states to K (2) 88 [71,72] and K (2) 1(2)8 [72] are included in the Brodsky-Lepage-Mackenzie (BLM) approximation [73]. For the computation of non-perturbative corrections we include results from [74][75][76]. The scales are chosen to be µ W = m W and µ b = 2 GeV. For the SM central value we find BR SM (B → X s γ) = 336 × 10 −6 , matching the results in Ref. [55].
In Fig. 7 we give the dependence of BR(B → X s γ) on the SMEFT coefficients at the scale µ = m t . Only one coefficient is varied while the other two are set to zero. We also indicate the averaged measurements described in Sec. 4.2. The branching fraction BR(B → X s γ) shows the strongest dependence onC uB , whereas the dependence onC uG andC uW is weaker. Numerically, Eq. (12) reads for real-valued Wilson coefficients ∆C andC uG is of higher order in α s . As a cross check for our computation, we apply flavio [77] together with wilson [78] and Eq. (12) and Eq. (13) to compute the branching fraction. Since wilson provides only tree-level matching between SMEFT and WET, the matching conditions in Eq. (12) and Eq. (13) are not included. We therefore apply wilson

Constraining Wilson coefficients
With the parametrizations of the ttγ cross sections and of theB → X s γ branching fraction determined in Sec. 5, we perform fits to the measurements described in Sec. 4 to constrain the Wilson coefficientsC uB ,C uG andC uW . We use a new implementation of the EFTfitter tool [79] based on the Bayesian Analysis Toolkit -BAT.jl [80,81]. This allows to perform fits of Wilson coefficients in a Bayesian reasoning, yielding (marginalized) posterior probability distributions of the parameters. We include both the experimental uncertainties and the SM theory uncertainties given in Sec. 4 in the fit. Focusing on the combination of observables from different energy scales, we make the simplifying assumption that the uncertainties of the measurements included are gaussian distributed [79] and uncorrelated. This assumption seems reasonable for the correlations between top-quark and B physics measurements and also for the correlation between the statistical uncertainties of the two channels contributing to σ (ttγ). The systematic and theoretical uncertainties of both channels can in principle be correlated in a non-negligible manner. As no information about the correlations is available, we investigate their impact afterwards by performing several fits varying the corresponding correlation coefficients.
To illustrate the benefit of combining observables from top-quark and B physics, we first constrain the Wilson coefficients using only one set of measurements at a time (Secs. 6.1, 6.2) before performing the combined fit (Sec. 6.3).

B physics only
Considering only BR(B → X s γ), we perform a fit to the HFLAV average described in Sec. 4.2 using the description of the branching fraction given in Sec. 5.2. TreatingC uB , C uG andC uW as free parameters of the fit and providing no prior knowledge about their distributions, we assign uniform prior probability distributions in the range of [-1, 1] to them. Larger values of the rescaled Wilson coefficientsC would not be reasonable and would lead to a breakdown of the EFT expansion.
When performing the fit, we observe that onlyC uB can be constrained using this setup. No constraints on the other two coefficients can be obtained, as the resulting marginalized posterior probabilities ofC uG andC uW are uniformly distributed. As can be seen from Fig. 7,C uB is the Wilson coefficient with the largest impact on theB → X s γ branching fraction, thus receiving stronger constraints thanC uG andC uW in a fit with three free parameters and a single observable.
The marginalized posterior distribution ofC uB is shown in Fig. 8. Two regions forC uB are favored by the fit. Comparing with Fig. 7, the two regions with the highest probability at aboutC uB ≈ −0.5 andC uB ≈ 0.0 are reasonable since the quadratic shape of BR(B → X s γ) as a function ofC uB leads to an agreement with the measurement in these two regions. Apparently, without further information, neither of them can be rejected. Indeed, as is well-known, this ambiguity can be resolved by studies of semileptonic b → s + − decays [82], notably, angular distributions thereof, whose measurements support the close-to-the-SM branch [83]. Since the purpose of this work is to demonstrate complementarity and feasibility of a joint bottom and top SMEFT-analysis rather than performing a most global fit, we leave the study of further observables beyond BR(B → X s γ) and σ (ttγ) for future work.

Top physics only
We perform a fit of the Wilson coefficients using σ (ttγ) only. We apply the parametrizations of the single-lepton and dilepton channel fiducial cross sections obtained in Sec. 5.1 and fit to the corresponding measurements described in Sec For the combined fit, we apply the same uniform priors as in the individual fits and constrainC uB ,C uG andC uW using both BR(B → X s γ) and σ (ttγ). The resulting smallest areas containing 90 % of the posterior probability are shown in Fig. 10 for the 2D marginalized distributions. The plots also include the corresponding 90 % regions from the previously described fits including only one set of observables at a time. In Fig. 10 it is noticeable that the ambiguity inC uB , which is observed in the fit including only the BR(B → X s γ) measurement, is resolved in the combined fit. It is recognizable that even though the branching fraction measurement alone constrains onlyC uB , in the combination with the ttγ cross sections the constraints on all three Wilson coefficients improve as the sizes of the areas containing 90 % of the probability decrease in all plots. The 90 % area of the fit using only BR(B → X s γ) in the upper left plot of Fig. 10 has a size of 12 % of the total parameter spaceC uB ∈ [−1, 1] and C uG ∈ [−1, 1] specified by the priors. For the fit considering only σ (ttγ) the corresponding area is of a similar size, taking up about 11 % of the allowed space. Due to the orthogonality of the observables, combining top and bottom measurements gives, on the other hand, a 90 % posterior region reduced by more than an order of magnitude, yielding an area that corresponds to only about 1 % of the allowed parameter space. The same numbers apply also for the upper right plot ofC uB vs.C uW . Even in the bottom plot of Fig. 10, which does not directly depend onC uB and is thus not directly constrained by the branching fraction measurement, the 90 % area is reduced. In combination with the BR(B → X s γ) measurement, the 90 % area decreases by a factor of 1.9 compared to the fit considering only the σ (ttγ) measurements. This is a consequence of the reduction of allowed regions in the three-dimensional parameter space.
A different representation of the same fit results is given in the left plot of Fig. 11, where the smallest intervals containing 90 % probability of the 1D marginalized posterior distributions are shown for the combined fit as well as for the fits using only one of the measurements.
In the right plot of Fig. 11 the smallest intervals containing 90 % probability of the 1D marginalized posterior distribution are shown for individual fits in which only one of the Wilson coefficients is allowed to vary at a time, while the other two are fixed to zero. Overall, a similar behaviour of the results can be observed compared to the fits with three free parameters. As there are fewer degrees of freedom in the fits, stronger constraints on the Wilson coefficients can be obtained. It is noticeable that in the individual fits not only the ambiguity inC uB can be resolved by the ttγ measurement but that also an ambiguity in the top-measurements interval ofC uW can be resolved by BR(B → X s γ).
As mentioned above, we study the impact of correlations between the systematic and theoretical uncertainties of the single-lepton and dilepton channels of σ (ttγ). For this purpose, we perform the combined fit assuming different correlations between the two channels for these uncertainties. We vary the correlation coefficient of the systematic uncertainties between values of −0.9 and 0.9 as negative correlations are conceivable. The correlation coefficient of the theory uncertainties is varied up to a value of 0.9 since we do not expect negative correlations for these uncertainties. When comparing the sizes of the areas containing 90 % of the marginalized posterior probability to the results assuming uncorrelated uncertainties, we observe only minor changes for the two distributions ofC uB vs.C uG andC uB vs.C uW . We find relative changes in the size of the areas of about 4 % at maximum and no changes in the general shape or positions compared to the combination shown in the two upper plots of Fig. 10. As the distribution ofC uG vs.C uW is dominantly constrained by the σ (ttγ) measurements, we observe larger changes due to variations of the correlation coefficients. The size of the 90 % area can change by up to 30 % for this distribution. Again, the general shape and the positions are not affected but only the width of the ring in the bottom plot of Fig. 10 varies. Therefore, we conclude that even in the presence of correlations between the systematic or theoretical uncertainties of the single-lepton and dilepton channels our previously presented findings are valid.
It should be noted that our focus is to demonstrate how observables from B and top-quark physics can be combined in a single fit of the SMEFT Wilson coefficients. Using only two observables, we do not obtain the most stringent constraints on the coefficients considered. Including further observables would certainly improve the constraints. For example, the Wilson coefficientsC uG andC uW are strongly constrained by the tt production cross section and W -boson helicity-fraction measurements, respectively [14,17], whereas measurements of semileptonic b → s + − decays, especially B → K * µ + µ − angular distributions [83], exclude valuesC uB ≈ −0.5 which are allowed by BR(B → X s γ). Effective theories provide a systematic toolbox to exploit multi-observable systems and probe the SM in a modelindependent way. The SMEFT-framework allows to combine data from the precision flavor and the high energy frontiers. We exploited synergies between top-quark and B-physics measurements from the LHC and precision flavor factories.
Specifically, we performed an exploratory study combining data on theB → X s γ branching ratio and on fiducial ttγ production cross sections within SMEFT, after detailing the ingredients required to connect measurements from different energy scales. We pointed out that for the processes considered in this work it is necessary to perform a dedicated matching that goes beyond the tree-level matching that is currently available in tools. Using MC simulations and a particle-level event selection, we performed interpolations of the total ttγ production cross section and the fiducial acceptances to parametrize the dependence of the fiducial cross sections on the Wilson coefficients.
We demonstrated that due to the different sensitivities of the observables to the SMEFT operators, a combination of the fiducial ttγ cross section with theB → X s γ branching fraction improves the constraints on the Wilson coefficients (Sec. 6). The complementarity of the different observables used in the fit allows to resolve ambiguities and to reduce posterior regions in the marginalized parameter space by up to an order of magnitude.
Further, more global analyses of combined top-quark and flavor physics measurements should be pursued in the future with more precise data expected from LHCb [84] and Belle II [85] and the high-p T -experiments [86], to decipher physics at higher energies and pursue the quest for BSM physics.

Appendix B: Matching condition
The functions E uW 7 , F uW 7 , E uW 8 and F uW 8 are given by