For the final parallel session of the conference, I've decided to stay on the top floor for what is another flavour session.

Muon magnetic moment has been considered in 2HDM before. Usually done in particular contexts,

Aligned 2HDM is defined by a particular relationship between the two Yukawa matrices: both can be diagonalised simultaneously, and are proportional in this basis.

Need large coupling of second doublet to leptons (large couplings to quarks ruled out by perturbativity and flavour contraints). Advantage of Type III over Type X is that large top loop effects are allowed. (Other Z2-preserving 2HSM models ruled out as explanations.)

Performed a numerical scan including a whole lot of constraints, especially flavour. Three regions survive: light pseudoscalar (2-loop), very light scalar (below 20 GeV, 1-loop) and light CP even (30 to 50 GeV, 2-loop).

Higgs properties require small mixing, primarily from τ coupling constraints. Enhanced coupling to τs plus non-zero coupling to tops mean LHC signal in τ-rich final states. Indeed, already constraints from searches of this type.

Sign of loop contributions? Fixed at 1-loop, not at 2-loop.

Charged Higgs loop? Never dominant.

Main problem of SO(10) GUT: doublet-triplet splitting of fermions. All Yukawas come from single coupling. Extend matter sector with three additional

SO(10) in tension with high-scale SUSY, because high-scale SUSY wants small tan β for Higgs mass. Normally SO(10) wants large tan β. Extra matter alleviates this.

With everything heavy, main signal is

MFV framework, effective operators. Assume three heavy, degenerate right-handed neutrinos. Attempt to explain b → sγ anomalies, and see what that implies for LFV.

Turns out that have vanishing contributions to up-type quark and b → u/c transistions. (No explanation for Bd anomalies.) However, you do get effects in charm leptonic decays.

Most interesting prediction is that B → Keμ is only one-quarter of current limit, might then be found soon.

Bounds from flavour conserving processes? Extra free parameter that only shows up in these processes.

The problem addressed here is R

Problem with BGL model is global U(1) in scalar potential, leading to Goldstone mode. Solution adopted here is to gauge that U(1). Anomaly cancellation demands that leptons be charged under the flavour symmetry. Two-parameter class of solutions.

Need scalar singlet to give Z' mass. Will mediate additional FCNC processes. Proportional to CKM matrix in down sector (all sectors?). Prefer Z' mass of 10s of TeV, but this is enough to explain R

Another type-III 2HDM. Use Cheng-Sher ansatz for couplings, where ij-element proportional to m

Explanation of B → D

Tau polarisation? No effects.

Problem: lepton and quark mixing matrices have different structures.

Treat PMNS matrix as TBM form with small perturbations. This is role of the S

Alternative choice for flavon VEV, still 2-parameter solution, allows non-zero lightest neutrino mass (but still inverted hierachy).

CPV phases predicted? Yes, but only in terms of other phases.

**4:00 pm:***Explaining (g−2)*, Joshua Sayre_{μ}in the A2HDMMuon magnetic moment has been considered in 2HDM before. Usually done in particular contexts,

*e.g.*Type-II or Type-X. Aim here is to work in morer general framework of Type-III. In such models, the Higgs basis where only one doublet gains a VEV is a natural one to take. Focus here on CP-conserving case.Aligned 2HDM is defined by a particular relationship between the two Yukawa matrices: both can be diagonalised simultaneously, and are proportional in this basis.

Need large coupling of second doublet to leptons (large couplings to quarks ruled out by perturbativity and flavour contraints). Advantage of Type III over Type X is that large top loop effects are allowed. (Other Z2-preserving 2HSM models ruled out as explanations.)

Performed a numerical scan including a whole lot of constraints, especially flavour. Three regions survive: light pseudoscalar (2-loop), very light scalar (below 20 GeV, 1-loop) and light CP even (30 to 50 GeV, 2-loop).

Higgs properties require small mixing, primarily from τ coupling constraints. Enhanced coupling to τs plus non-zero coupling to tops mean LHC signal in τ-rich final states. Indeed, already constraints from searches of this type.

__Question__Sign of loop contributions? Fixed at 1-loop, not at 2-loop.

Charged Higgs loop? Never dominant.

**4:20 pm:***Flavour violating Z' from SO(10) SUSY GUT in High-Scale SUSY*, Yu MuramatsuMain problem of SO(10) GUT: doublet-triplet splitting of fermions. All Yukawas come from single coupling. Extend matter sector with three additional

**10**of SO(10). Mixing between**5**of**10**and**5**of**16**will lead to different Yukawas. In particular, different choices for**10**and**5**of**16**.*Z'*is within GUT group. Assume it survives to low energies. Ordinarily, it would couple universally to different generations. However, the new**5**from the**10**have different U(1) charges to those from the**16**.SO(10) in tension with high-scale SUSY, because high-scale SUSY wants small tan β for Higgs mass. Normally SO(10) wants large tan β. Extra matter alleviates this.

With everything heavy, main signal is

*Z'*-mediated flavour violation. Current bounds OK, but signals expected especially in lepton sector.**4:40 pm:***Lepton Flavour Violation Implications of Anomalies in Rare B-Meson Decays*, Jusak TandeanMFV framework, effective operators. Assume three heavy, degenerate right-handed neutrinos. Attempt to explain b → sγ anomalies, and see what that implies for LFV.

Turns out that have vanishing contributions to up-type quark and b → u/c transistions. (No explanation for Bd anomalies.) However, you do get effects in charm leptonic decays.

Most interesting prediction is that B → Keμ is only one-quarter of current limit, might then be found soon.

__Question__Bounds from flavour conserving processes? Extra free parameter that only shows up in these processes.

**5:00 pm:***Violation of Lepton Universality in B-Meson Decays: A Z' Opportunity*, Hugo SerodioThe problem addressed here is R

_{K}; large deviations in lepton universality in B → Kll decays. Lots and lots of models attempting to address this. Model here is extention of the Branco-Grimus-Lavoura (BGL) model, a 2HDM with an abelian flavour symmetry. In particular, flavour symmetry enforces that Yukawas of the two Higgs are complementary: where one is non-zero, the other vanishes. Suppresses FCNC completely (up sector) or by quark masses (down sector).Problem with BGL model is global U(1) in scalar potential, leading to Goldstone mode. Solution adopted here is to gauge that U(1). Anomaly cancellation demands that leptons be charged under the flavour symmetry. Two-parameter class of solutions.

Need scalar singlet to give Z' mass. Will mediate additional FCNC processes. Proportional to CKM matrix in down sector (all sectors?). Prefer Z' mass of 10s of TeV, but this is enough to explain R

_{K}.**5:20 pm:***B → D*, Xing-Bo Yuan^{(*)}τν and top quark FCNC processes within general two-Higgs doublet modelAnother type-III 2HDM. Use Cheng-Sher ansatz for couplings, where ij-element proportional to m

_{i}m_{j}.Explanation of B → D

^{(*)}τν comes from s-channel charged Higgs. Require Higgs to around 500 GeV, with large couplings to taus and ct. Alignment limit for SM gauge couplings means no contributions to top decay to charm-Higgs. However, do have large contributions to the production process cc to tt. Also must worry about t to cg. However, this is below current and 14 TeV bounds.__Question__Tau polarisation? No effects.

**5:40 pm:***Dirac and Majorana phases in S*, Yusuke Shimizu_{4}model of neutrinosProblem: lepton and quark mixing matrices have different structures.

Treat PMNS matrix as TBM form with small perturbations. This is role of the S

_{4}group, the group of permutations of four objects/symmetry group of octahedron. 5 irreducible representations; two singlets, a doublet and two triplets. For leptons, SU(2) doubles form a 3; the first two generations of right-handed fermions a 2; and the third generation a 1. Additional flavon fields. Neutrino matrix defined by two complex parameters. Exact prediction that third neutrino is massless (inverted hierarchy). Symmetry constrains the phases in the lepton sector quite tightly. Predictions for neutrinoless double beta decay somewhat small for planned experiments; some hope at SNO+ and CUORE.Alternative choice for flavon VEV, still 2-parameter solution, allows non-zero lightest neutrino mass (but still inverted hierachy).

__Question__CPV phases predicted? Yes, but only in terms of other phases.

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