Search

Abstract We elaborate how to apply the Hilbert series method to enumerating group covariants, which transform under any given representation, including but going beyond group invariants. Mathematically, group covariants form a module over the ring of the invariants. The number of independent covariants is given by the rank of the module, which can be computed by taking a ratio of two Hilbert series. In many cases, the rank equals the dimension of the group covariant representation. When this happens, we say that there is a rank saturation. We apply this technology to revisit the hypothesis of Minimal Flavor Violation in constructing Effective Field Theories beyond the Standard Model. We find that rank saturation is guaranteed in this case, leading to the important consequence that the MFV symmetry principle does not impose any restriction on the EFT, i.e. MFV SMEFT = SMEFT, in the absence of additional assumptions.

Abstract Recently, the Belle II collaboration announced the first measurement of the branching ratio B B + → K + ν ν ¯ $$ \mathcal{B}\left({B}^{+}\to {K}^{+}\nu \overline{\nu}\right) $$ , which is found to be about 2.7σ higher than the Standard Model (SM) prediction. We decipher the data with two new physics scenarios: the underlying quark-level b → sν ν ¯ $$ b\to s\nu \overline{\nu} $$ transition is, besides the SM contribution, further affected by heavy new mediators that are much heavier than the electroweak scale, or amended by an additional decay channel with undetected light final states like dark matter or axion-like particles. These two scenarios can be most conveniently analyzed in the SM effective field theory (SMEFT) and the dark SMEFT (DSMEFT) framework, respectively. We consider the flavour structures of the resulting effective operators to be either generic or satisfy the minimal flavour violation (MFV) hypothesis, both for the quark and lepton sectors. In the first scenario, once the MFV assumption is made, only one SM-like low-energy effective operator induced by the SMEFT dimension-six operators can account for the Belle II excess, whose parameter space is, however, excluded by the Belle upper bound of the branching ratio B B 0 → K ∗ 0 ν ν ¯ $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}\nu \overline{\nu}\right) $$ . In the second scenario, it is found that the Belle II excess can be accommodated by 22 of the DSMEFT operators involving one or two scalar, fermionic, or vector dark matters as well as axion-like particles. These operators also receive dominant constraints from the B 0 → K *0 + inv and B s → inv decays. Once the MFV hypothesis is assumed, the number of viable operators is reduced to 14, and the B + → π + + inv and K + → π + + inv decays start to put further constraints on them. Within the parameter space allowed by all the current experimental data, the q 2 distributions of the B → K (*) + inv decays are then studied for each viable operator. We find that the resulting prediction of the operator Q qχ = q ¯ p γ μ q r χ ¯ γ μ χ $$ {\mathcal{Q}}_{q\chi}=\left({\overline{q}}_p{\gamma}_{\mu }{q}_r\right)\left(\overline{\chi}{\gamma}^{\mu}\chi \right) $$ with a fermionic dark matter mass m χ ≈ 700 MeV can closely match the Belle II event distribution in the bins 2 ≤ q 2 ≤ 7 GeV2. In addition, we, for the first time, calculate systematically the longitudinal polarization fraction F L of K * in the B → K * + inv decays within the DLEFT. By combining the decay spectra and F L , almost all the DSMEFT operators are found to be distinguishable from each other. Finally, the future prospects at Belle II, CEPC and FCC-ee are also discussed for some of these FCNC processes.

Recently, the Belle II collaboration announced the first measurement of the branching ratio B B + → K + ν ν ¯ , which is found to be about 2.7σ higher than the Standard Model (SM) prediction. We decipher the data with two new physics scenarios: the underlying quark-level b → sν ν ¯ transition is, besides the SM contribution, further affected by heavy new mediators that are much heavier than the electroweak scale, or amended by an additional decay channel with undetected light final states like dark matter or axion-like particles. These two scenarios can be most conveniently analyzed in the SM effective field theory (SMEFT) and the dark SMEFT (DSMEFT) framework, respectively. We consider the flavour structures of the resulting effective operators to be either generic or satisfy the minimal flavour violation (MFV) hypothesis, both for the quark and lepton sectors. In the first scenario, once the MFV assumption is made, only one SM-like low-energy effective operator induced by the SMEFT dimension-six operators can account for the Belle II excess, whose parameter space is, however, excluded by the Belle upper bound of the branching ratio B B 0 → K ∗ 0 ν ν ¯ . In the second scenario, it is found that the Belle II excess can be accommodated by 22 of the DSMEFT operators involving one or two scalar, fermionic, or vector dark matters as well as axion-like particles. These operators also receive dominant constraints from the B0 → K*0 + inv and Bs → inv decays. Once the MFV hypothesis is assumed, the number of viable operators is reduced to 14, and the B+ → π+ + inv and K+ → π+ + inv decays start to put further constraints on them. Within the parameter space allowed by all the current experimental data, the q2 distributions of the B → K(*) + inv decays are then studied for each viable operator. We find that the resulting prediction of the operator Q qχ = q ¯ p γ μ q r χ ¯ γ μ χ with a fermionic dark matter mass mχ ≈ 700 MeV can closely match the Belle II event distribution in the bins 2 ≤ q2 ≤ 7 GeV2. In addition, we, for the first time, calculate systematically the longitudinal polarization fraction FL of K* in the B → K* + inv decays within the DLEFT. By combining the decay spectra and FL, almost all the DSMEFT operators are found to be distinguishable from each other. Finally, the future prospects at Belle II, CEPC and FCC-ee are also discussed for some of these FCNC processes. [ABSTRACT FROM AUTHOR]

We elaborate how to apply the Hilbert series method to enumerating group covariants, which transform under any given representation, including but going beyond group invariants. Mathematically, group covariants form a module over the ring of the invariants. The number of independent covariants is given by the rank of the module, which can be computed by taking a ratio of two Hilbert series. In many cases, the rank equals the dimension of the group covariant representation. When this happens, we say that there is a rank saturation. We apply this technology to revisit the hypothesis of Minimal Flavor Violation in constructing Effective Field Theories beyond the Standard Model. We find that rank saturation is guaranteed in this case, leading to the important consequence that the MFV symmetry principle does not impose any restriction on the EFT, i.e. MFV SMEFT = SMEFT, in the absence of additional assumptions. [ABSTRACT FROM AUTHOR]

Abstract We present comprehensive global fits of the SMEFT under the minimal minimal flavour violation (MFV) hypothesis, i.e. assuming that only the flavour-symmetric and CP-invariant operators are relevant at the high scale. The considered operator set is determined by this flavour assumption rather than the used datasets. We establish global limits on these Wilson coefficients using leading order and next-to-leading order SMEFT predictions for electroweak precision observables, Higgs, top, flavour and dijet data as well as measurements from parity violation experiments and lepton scattering. Our investigations reveal an intriguing crosstalk among different observables, underscoring the importance of combining diverse observables from various energy scales in global SMEFT analyses.

Abstract We present a comprehensive analysis of electroweak, flavor, and collider bounds on the complete set of dimension-six SMEFT operators in the U(2)5-symmetric limit. This operator basis provides a consistent framework to describe a wide class of new physics models and, in particular, the motivated class of models where the new degrees of freedom couple mostly to the third generation. By analyzing observables from all three sectors, and consistently including renormalization group evolution, we provide bounds on the effective scale of all 124 U(2)5-invariant operators. The relation between flavor-conserving and flavor-violating observables is analyzed taking into account the leading U(2)5 breaking in the Yukawa sector, which is responsible for heavy-light quark mixing. We show that under simple, motivated, and non-tuned hypotheses for the parametric size of the Wilson coefficients at the high scale, all present bounds are consistent with an effective scale as low as 1.5 TeV. We also show that a future circular e + e − collider program such as FCC-ee would push most of these bounds by an order of magnitude. This would rule out or provide clear evidence for a wide class of compelling new physics models that are fully compatible with present data.

We present comprehensive global fits of the SMEFT under the minimal minimal flavour violation (MFV) hypothesis, i.e. assuming that only the flavour-symmetric and CP-invariant operators are relevant at the high scale. The considered operator set is determined by this flavour assumption rather than the used datasets. We establish global limits on these Wilson coefficients using leading order and next-to-leading order SMEFT predictions for electroweak precision observables, Higgs, top, flavour and dijet data as well as measurements from parity violation experiments and lepton scattering. Our investigations reveal an intriguing crosstalk among different observables, underscoring the importance of combining diverse observables from various energy scales in global SMEFT analyses. [ABSTRACT FROM AUTHOR]

We present a comprehensive analysis of electroweak, flavor, and collider bounds on the complete set of dimension-six SMEFT operators in the U(2)5-symmetric limit. This operator basis provides a consistent framework to describe a wide class of new physics models and, in particular, the motivated class of models where the new degrees of freedom couple mostly to the third generation. By analyzing observables from all three sectors, and consistently including renormalization group evolution, we provide bounds on the effective scale of all 124 U(2)5-invariant operators. The relation between flavor-conserving and flavor-violating observables is analyzed taking into account the leading U(2)5 breaking in the Yukawa sector, which is responsible for heavy-light quark mixing. We show that under simple, motivated, and non-tuned hypotheses for the parametric size of the Wilson coefficients at the high scale, all present bounds are consistent with an effective scale as low as 1.5 TeV. We also show that a future circular e+e− collider program such as FCC-ee would push most of these bounds by an order of magnitude. This would rule out or provide clear evidence for a wide class of compelling new physics models that are fully compatible with present data. [ABSTRACT FROM AUTHOR]

Abstract We benefit from the lattice QCD determination by the HPQCD of the Standard Model (SM) form factors for the B ¯ s → D s $$ {\overline{B}}_s\to {D}_s $$ [Phys. Rev. D 101 (2020) 074513] and the SM and tensor ones for the B ¯ s → D s ∗ $$ {\overline{B}}_s\to {D}_s^{\ast } $$ ( arXiv:2304.03137 [hep-lat]) semileptonic decays, and the heavy quark effective theory (HQET) relations for the analogous B → D (*) decays obtained by F.U. Bernlochner et al. in Phys. Rev. D 95 (2017) 115008, to extract the leading and sub-leading Isgur-Wise functions for the B ¯ s → D s ∗ $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)} $$ decays. Further use of the HQET relations allows us to evaluate the corresponding scalar, pseudoscalar and tensor form factors needed for a phenomenological study of new physics (NP) effects on the B ¯ s → D s ∗ $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)} $$ semileptonic decay. At present, the experimental values for the ratios R D ∗ = Γ B ¯ → D ∗ τ − ν ¯ τ / Γ B ¯ → D ∗ e − μ − ν ¯ e μ $$ {\mathcal{R}}_{D^{\left(\ast \right)}}=\Gamma \left[\overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau}\left]/\Gamma \right[\overline{B}\to {D}^{\left(\ast \right)}{e}^{-}\left({\mu}^{-}\right){\overline{\nu}}_{e\left(\mu \right)}\right] $$ are the best signal in favor of lepton flavor universality violation (LFUV) seen in charged current (CC) b → c decays. In this work we conduct a study of NP effects on the B ¯ s → D s ∗ τ − ν ¯ τ $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } $$ semileptonic decays by comparing tau spin, angular and spin-angular asymmetry distributions obtained within the SM and three different NP scenarios. As expected from SU(3) light-flavor symmetry, we get results close to the ones found in a similar analysis of the B ¯ → D ∗ $$ \overline{B}\to {D}^{\left(\ast \right)} $$ case. The measurement of the B ¯ s → D s ∗ ℓ ν ¯ ℓ $$ {\overline{B}}_s\to {D}_s^{\left(\ast \right)}\ell {\overline{\nu}}_{\ell } $$ semileptonic decays, which is within reach of present experiments, could then be of relevance in helping to establish or rule out LFUV in CC b → c transitions.

Abstract We perform a model-independent analysis of top-philic New Physics scenarios, under the assumption that only effective operators involving top quarks are generated at tree level. Within the SMEFT framework, we derive indirect constraints on Wilson Coefficients by combining a large set of low-energy observables: B-meson and kaon decays, meson mixing observables, precision electroweak and Higgs measurements, anomalous magnetic moments, lepton flavour violating processes, lepton flavour universality tests, and measurements of the Cabibbo angle. We consider the renormalization group evolution of the operators and use the one-loop matching of the SMEFT onto the LEFT. The global analysis is then used to perform one-parameter, two-parameter, and global fits, as well as applications to explicit ultraviolet models. We find that the inclusion of measurements from different physics sectors reveals a strong interplay and complementarity among the observables. The resulting constraints are also compared to direct bounds provided by top quark productions at the LHC.

Abstract 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 C lq 3 $$ {C}_{lq}^{(3)} $$ , probing scales as high as 18 TeV, followed by the gluon dipole operator C uG 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 ≤ B B 0 → K ∗ 0 ν ν ¯ ≤ 11.13 ⋅ 10 − 6 $$ 4.25\cdot {10}^{-6}\le \mathcal{B}\left({B}^0\to {K}^{\ast 0}\nu \overline{\nu}\right)\le 11.13\cdot {10}^{-6} $$ and 2.26 ⋅ 10 − 6 ≤ B B + → K + ν ν ¯ ≤ 5.78 ⋅ 10 − 6 $$ 2.26\cdot {10}^{-6}\le \mathcal{B}\left({B}^{+}\to {K}^{+}\nu \overline{\nu}\right)\le 5.78\cdot {10}^{-6} $$ , 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.

Abstract Short-distance new physics at (or slightly) above the TeV scale should not excessively violate the approximate flavor symmetries of the SM in order to comply with stringent constraints from flavor-changing neutral currents. In this respect, flavor symmetries provide an effective organizing principle for the vast parameter space of the SMEFT. In this work, we classify all possible irreducible representations under U(3)5 flavor symmetry of new heavy spin-0, 1/2, and 1 fields which integrate out to dimension-6 operators at the tree level. For a general perturbative UV model, the resulting flavor-symmetric interactions are very restrictive and, in most cases, predict a single Hermitian operator with a definite sign. These leading directions in the SMEFT space deserve particular attention. We derive an extensive set of present experimental constraints by utilizing the existing global SMEFT fits, which incorporate data from top quark, Higgs boson, and electroweak measurements, along with constraints on dilepton and 4-lepton contact interactions. The derived set of bounds comprehensively summarises the present knowledge from indirect searches of flavor-blind new physics mediators.

We perform a model-independent analysis of top-philic New Physics scenarios, under the assumption that only effective operators involving top quarks are generated at tree level. Within the SMEFT framework, we derive indirect constraints on Wilson Coefficients by combining a large set of low-energy observables: B-meson and kaon decays, meson mixing observables, precision electroweak and Higgs measurements, anomalous magnetic moments, lepton flavour violating processes, lepton flavour universality tests, and measurements of the Cabibbo angle. We consider the renormalization group evolution of the operators and use the one-loop matching of the SMEFT onto the LEFT. The global analysis is then used to perform one-parameter, two-parameter, and global fits, as well as applications to explicit ultraviolet models. We find that the inclusion of measurements from different physics sectors reveals a strong interplay and complementarity among the observables. The resulting constraints are also compared to direct bounds provided by top quark productions at the LHC. [ABSTRACT FROM AUTHOR]

Abstract In the electroweak sector of the Standard Model, CP violation arises through a very particular interplay between the three quark generations, as described by the Cabibbo-Kobayashi-Maskawa (CKM) mechanism and the single Jarlskog invariant J 4. Once generalized to the Standard Model Effective Field Theory (SMEFT), this peculiar pattern gets modified by higher-dimensional operators, whose associated Wilson coefficients are usually split into CP-even and odd parts. However, CP violation at dimension four, i.e., at the lowest order in the EFT expansion, blurs this distinction: any Wilson coefficient can interfere with J 4 and mediate CP violation. In this paper, we study such interferences at first order in the SMEFT expansion, 𝒪(1/Λ2), and we capture their associated parameter space via a set of 1551 linear CP-odd flavor invariants. This construction describes both new, genuinely CP-violating quantities as well as the interference between J 4 and CP-conserving ones. We call this latter possibility opportunistic CP violation. Relying on an appropriate extension of the matrix rank to Taylor expansions, which we dub Taylor rank, we define a procedure to organize the invariants in terms of their magnitude, so as to retain only the relevant ones at a given precision. We explore how this characterization changes when different assumptions are made on the flavor structure of the SMEFT coefficients. Interestingly, some of the CP-odd invariants turn out to be less suppressed than J 4, even when they capture opportunistic CPV, demonstrating that CP-violation in the SM, at dimension 4, is accidentally small.

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 C lq 3 , 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 ≤ 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. [ABSTRACT FROM AUTHOR]

Short-distance new physics at (or slightly) above the TeV scale should not excessively violate the approximate flavor symmetries of the SM in order to comply with stringent constraints from flavor-changing neutral currents. In this respect, flavor symmetries provide an effective organizing principle for the vast parameter space of the SMEFT. In this work, we classify all possible irreducible representations under U(3)5 flavor symmetry of new heavy spin-0, 1/2, and 1 fields which integrate out to dimension-6 operators at the tree level. For a general perturbative UV model, the resulting flavor-symmetric interactions are very restrictive and, in most cases, predict a single Hermitian operator with a definite sign. These leading directions in the SMEFT space deserve particular attention. We derive an extensive set of present experimental constraints by utilizing the existing global SMEFT fits, which incorporate data from top quark, Higgs boson, and electroweak measurements, along with constraints on dilepton and 4-lepton contact interactions. The derived set of bounds comprehensively summarises the present knowledge from indirect searches of flavor-blind new physics mediators. [ABSTRACT FROM AUTHOR]

Abstract A powerful aspect of effective field theories is connecting scales through renormalisation group (RG) flow. The anomalous dimension matrix of the Standard Model Effective Field Theory (SMEFT) encodes clues to where to find relics of heavy new physics in data, but its unwieldy 2499 × 2499 size (at operator dimension 6) makes it difficult to draw general conclusions. In this paper, we study the flavour structure of the SMEFT one loop anomalous dimension matrix of dimension 6 current-current operators, a 1460 × 1460 submatrix. We take an on-shell approach, laying bare simple patterns by factorising the entries of the matrix into their gauge, kinematic and flavour parts. We explore the properties of different diagram topologies, and make explicit the connection between the IR-finiteness of certain diagrams and their gauge and flavour structure. Through a completely general flavour decomposition of the Wilson coefficient matrices, we uncover new flavour selection rules, from which small subsystems emerge which mix almost exclusively amongst themselves. We show that, for example, if we neglect all Yukawa couplings except for that of the top quark, the selection rules produce block diagonalisation within the current-current operators in which the largest block is a 61 × 61 matrix. We provide all the ingredients of the calculations in comprehensive appendices, including SM and SMEFT helicity amplitudes, and explicit results for phase space integrals and gauge contractions. This deconstruction of the matrix, and its resulting block-diagonalisation, provides a first step to understanding the IR-relevant directions in the SMEFT parameter space, hence closing in on natural places for heavy new physics to make itself known.

Abstract We constrain the flavor structure of Wilson coefficients in the Standard Model Effective Field Theory (SMEFT) from data. In the SMEFT, new physics effects in couplings of up-type and down-type quarks are related through the Cabibbo-Kobayashi-Maskawa mixing matrix. We exploit this relation to pin down potential new sources of flavor symmetry breaking in a global analysis of high- and low-energy data from the LHC, LEP, and b factory experiments. We demonstrate the power of such an analysis by performing a combined fit of effective four-quark and two-quark couplings contributing to a large set of flavor, top-quark, electroweak, and dijet observables. All four sectors are needed to fully resolve the flavor structure of left-chiral four-quark couplings without leaving blind directions in the parameter space. Although we work in the framework of minimal flavor violation, our strategy applies as well to other flavor patterns, like U(2) flavor symmetry or leptoquark scenarios.

In the electroweak sector of the Standard Model, CP violation arises through a very particular interplay between the three quark generations, as described by the Cabibbo-Kobayashi-Maskawa (CKM) mechanism and the single Jarlskog invariant J4. Once generalized to the Standard Model Effective Field Theory (SMEFT), this peculiar pattern gets modified by higher-dimensional operators, whose associated Wilson coefficients are usually split into CP-even and odd parts. However, CP violation at dimension four, i.e., at the lowest order in the EFT expansion, blurs this distinction: any Wilson coefficient can interfere with J4 and mediate CP violation. In this paper, we study such interferences at first order in the SMEFT expansion, 풪(1/Λ2), and we capture their associated parameter space via a set of 1551 linear CP-odd flavor invariants. This construction describes both new, genuinely CP-violating quantities as well as the interference between J4 and CP-conserving ones. We call this latter possibility opportunistic CP violation. Relying on an appropriate extension of the matrix rank to Taylor expansions, which we dub Taylor rank, we define a procedure to organize the invariants in terms of their magnitude, so as to retain only the relevant ones at a given precision. We explore how this characterization changes when different assumptions are made on the flavor structure of the SMEFT coefficients. Interestingly, some of the CP-odd invariants turn out to be less suppressed than J4, even when they capture opportunistic CPV, demonstrating that CP-violation in the SM, at dimension 4, is accidentally small. [ABSTRACT FROM AUTHOR]

Abstract We study the flavor structure of the lepton and baryon number-conserving dimension-6 operators in the Standard Model effective field theory (SMEFT). Building on the work of [1], we define several well-motivated flavor symmetries and symmetry-breaking patterns that serve as competing hypotheses about the ultraviolet (UV) dynamics beyond the SM, not far above the TeV scale. In particular, we consider four different structures in the quark sector and seven in the charged lepton sector. The set of flavor-breaking spurions is (almost) always taken to be the minimal one needed to reproduce the observed charged fermion masses and mixings. For each case, we explicitly construct and count the operators to the first few orders in the spurion expansion, providing ready-for-use setups for phenomenological studies and global fits. We provide a Mathematica package SMEFTflavor ( https://github.com/aethomsen/SMEFTflavor ) to facilitate similar analyses for flavor symmetries not covered in this work.

A powerful aspect of effective field theories is connecting scales through renormalisation group (RG) flow. The anomalous dimension matrix of the Standard Model Effective Field Theory (SMEFT) encodes clues to where to find relics of heavy new physics in data, but its unwieldy 2499 × 2499 size (at operator dimension 6) makes it difficult to draw general conclusions. In this paper, we study the flavour structure of the SMEFT one loop anomalous dimension matrix of dimension 6 current-current operators, a 1460 × 1460 submatrix. We take an on-shell approach, laying bare simple patterns by factorising the entries of the matrix into their gauge, kinematic and flavour parts. We explore the properties of different diagram topologies, and make explicit the connection between the IR-finiteness of certain diagrams and their gauge and flavour structure. Through a completely general flavour decomposition of the Wilson coefficient matrices, we uncover new flavour selection rules, from which small subsystems emerge which mix almost exclusively amongst themselves. We show that, for example, if we neglect all Yukawa couplings except for that of the top quark, the selection rules produce block diagonalisation within the current-current operators in which the largest block is a 61 × 61 matrix. We provide all the ingredients of the calculations in comprehensive appendices, including SM and SMEFT helicity amplitudes, and explicit results for phase space integrals and gauge contractions. This deconstruction of the matrix, and its resulting block-diagonalisation, provides a first step to understanding the IR-relevant directions in the SMEFT parameter space, hence closing in on natural places for heavy new physics to make itself known. [ABSTRACT FROM AUTHOR]

Abstract As SMEFT is a framework of growing importance to analyze high-energy data, understanding its parameter space is crucial. The latter is commonly split into CP-even and CP-odd parts, but this classification is obscured by the fact that CP violation is actually a collective effect that is best captured by considering flavor-invariant combinations of Lagrangian parameters. First we show that fermion rephasing invariance imposes that several coefficients associated to dimension-six operators can never interfere with operators of dimension ≤ 4 and thus cannot appear in any physical observable at O $$ \mathcal{O} $$ 1/Λ2. For those that can, instead, we establish a one-to-one correspondence with CP-odd flavor invariants, all linear with respect to SMEFT coefficients. We explicitly present complete lists of such linear CP-odd invariants, and carefully examine their relationship to CP breaking throughout the parameter space of coefficients of dimension ≤ 4. Requiring that these invariants all vanish, together with the Jarlskog invariant, the strong-CP phase, and the 6 CP-violating dimension-6 bosonic operators, provides 699(+1 + 1 + 6) conditions for CP conservation to hold in any observable at leading order, O $$ \mathcal{O} $$ (1/Λ2).

Abstract The LHCb experiment measured the time-dependent CP asymmetries C KK and S KK in B s → K + K − decay. Combining with the corresponding CP asymmetries C ππ and S ππ in B → π + π − decay, we find that the size of U-spin breaking in this system is of order 20%. Moreover, the data suggest that these effects are dominated by factorizable contributions. We further study the constraints on new physics contributions to b → u u ¯ q $$ u\overline{u}q $$ (q = s, d). New physics that is minimally flavor violating (MFV) cannot be distinguished from the Standard Model (SM) in these decays. However, new physics that is not MFV can mimic large U-spin breaking. Requiring that the U-spin breaking parameters remain below the size implied by the data leads to a lower bound of 5 − 10 TeV on the scale of generic new physics. If the new physics is subject to the selection rules that follow from the Froggatt-Nielsen (FN) mechanism or from General Minimal Flavor Violation (GMFV), the bound is relaxed to 2 TeV.

We constrain the flavor structure of Wilson coefficients in the Standard Model Effective Field Theory (SMEFT) from data. In the SMEFT, new physics effects in couplings of up-type and down-type quarks are related through the Cabibbo-Kobayashi-Maskawa mixing matrix. We exploit this relation to pin down potential new sources of flavor symmetry breaking in a global analysis of high- and low-energy data from the LHC, LEP, and b factory experiments. We demonstrate the power of such an analysis by performing a combined fit of effective four-quark and two-quark couplings contributing to a large set of flavor, top-quark, electroweak, and dijet observables. All four sectors are needed to fully resolve the flavor structure of left-chiral four-quark couplings without leaving blind directions in the parameter space. Although we work in the framework of minimal flavor violation, our strategy applies as well to other flavor patterns, like U(2) flavor symmetry or leptoquark scenarios. [ABSTRACT FROM AUTHOR]

We study the flavor structure of the lepton and baryon number-conserving dimension-6 operators in the Standard Model effective field theory (SMEFT). Building on the work of [1], we define several well-motivated flavor symmetries and symmetry-breaking patterns that serve as competing hypotheses about the ultraviolet (UV) dynamics beyond the SM, not far above the TeV scale. In particular, we consider four different structures in the quark sector and seven in the charged lepton sector. The set of flavor-breaking spurions is (almost) always taken to be the minimal one needed to reproduce the observed charged fermion masses and mixings. For each case, we explicitly construct and count the operators to the first few orders in the spurion expansion, providing ready-for-use setups for phenomenological studies and global fits. We provide a Mathematica package SMEFTflavor () to facilitate similar analyses for flavor symmetries not covered in this work. [ABSTRACT FROM AUTHOR]

The LHCb experiment measured the time-dependent CP asymmetries CKK and SKK in Bs→ K+K− decay. Combining with the corresponding CP asymmetries Cππ and Sππ in B → π+π− decay, we find that the size of U-spin breaking in this system is of order 20%. Moreover, the data suggest that these effects are dominated by factorizable contributions. We further study the constraints on new physics contributions to b → u u ¯ q (q = s, d). New physics that is minimally flavor violating (MFV) cannot be distinguished from the Standard Model (SM) in these decays. However, new physics that is not MFV can mimic large U-spin breaking. Requiring that the U-spin breaking parameters remain below the size implied by the data leads to a lower bound of 5 − 10 TeV on the scale of generic new physics. If the new physics is subject to the selection rules that follow from the Froggatt-Nielsen (FN) mechanism or from General Minimal Flavor Violation (GMFV), the bound is relaxed to 2 TeV. [ABSTRACT FROM AUTHOR]