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Training School on High Energy Physics Data-Driven Flavour Model

This training school covers topics on the Flavour Puzzle, BSM Flavour Problem, and objectives of Data-Driven Flavour Models in High Energy Physics. It explores anomalies, model building, symmetry breaking patterns, phenomenology, and more.

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Training School on High Energy Physics Data-Driven Flavour Model

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  1. TAE 2019 - COST Training School on High Energy Physics Data DrIvenFlavourModel Author: Carlos Bouthelier Madre Director: Dr. Luca Merlo May 7, 2019

  2. Index • TheFlavourPuzzle, BSM FlavourProblem and objectives. • MinimalFlavourViolation. • U(2) models. • Data DrivenFlavourModel. • B anomalies. • Comparison, conclusionand foresights.

  3. FlavourPuzzle, BSMFP and objectives. TheFlavourPuzzle BSM FP Objectives • Experimental problems: Prediction vs measurements • Theoreticalproblems: Naturalnessprinciple • Masshierarchiesforfermionsand not-order-oneYukawas. • Mixings in quark and lepton sector.

  4. FlavourPuzzle, BSMFP and objectives. TheFlavourPuzzleBSM FP Objectives TheFlavourPuzzle BSM FP Objectives TheFlavourPuzzleObjectives • Masshierarchyforfermions. Expectedto be order 1 Yukawa Parameters or

  5. FlavourPuzzle, BSMFP and objectives. TheFlavourPuzzle BSM FP Objectives TheFlavourPuzzle BSM FP Objectives TheFlavourPuzzleObjectives • Masshierarchyforfermions. Yukawa Parameters are expectedto be order 1 or

  6. FlavourPuzzle, BSMFP and objectives. TheFlavourPuzzle BSM FP Objectives TheFlavourPuzzle BSM FP Objectives TheFlavourPuzzleObjectives • Hierarchical vs democraticmixings.

  7. FlavourPuzzle, BSMFP and objectives. TheFlavourPuzzleBSM FPObjectives BSM FlavourProblem. Objectives • Modelbuilding & Beyond Standard ModelFlavourProblem. • B-Anomalies. Statisticaldeviations of SM predictionfrommeasurementson B mesonsemileptonicdecays. New FlavourPhysics (NR) Experimental evidence New model (Eff. Th.) yields Must be compatible Scale of NP Suppresses Validuntil Withoutpushingtoohigh

  8. FlavourPuzzle, BSMFP and objectives. TheFlavourPuzzle BSM FPObjectives • Global, continuous, non-abbelianflavoursymmetryspontaneouslybrokenbyspurions, followingtheMinimumFlavourViolationprinciple. • Review top-downmodels: and . • Propose a new bottom-up model, studyitsphenomenology (BSM FP) and compare withpreviousmodels. • Describingthe B anomaliesundersuchflavoursymmetrywiththreeleptoquarkcandidates as mediators.

  9. MinimalFlavourViolation SymmetrybreakingpatternPhenomenology • Minimal FlavourViolationPrinciple.

  10. MinimalFlavourViolation Symmetrybreakingpattern. Phenomenology SymmetrybreakingpatternPhenomenology • Minimal FlavourViolationPrinciple. • Biggestsymmetryallowedbykineticterms:

  11. MinimalFlavourViolation Symmetrybreakingpattern. Phenomenology SymmetrybreakingpatternPhenomenology • Minimal FlavourViolationPrinciple. • Biggestsymmetry: • Quark sector: Spurionsand theirBVs SSB

  12. MinimalFlavourViolation Symmetrybreakingpattern. Phenomenology SymmetrybreakingpatternPhenomenology • Minimal FlavourViolationPrinciple. • Biggestsymmetry: • Quark sector: • Whyis Yukawa top higher? 2HDM or fine tuning! Spurionsand theirBVs SSB

  13. MinimalFlavourViolation Symmetrybreakingpattern. Phenomenology SymmetrybreakingpatternPhenomenology • Lepton sector. • Minimal Field Content Extended Field Content

  14. MinimalFlavourViolation Symmetrybreakingpattern. Phenomenology SymmetrybreakingpatternPhenomenology • Lepton sector • Minimal Field Content Extended Field Content

  15. MinimalFlavourViolation Symmetrybreakingpattern. Phenomenology SymmetrybreakingpatternPhenomenology • Lepton sector • Minimal Field Content Extended Field Content Violates MFV principle Expandingparameter Predictivity

  16. MinimalFlavourViolation SymmetrybreakingpatternPhenomenology • Quark sector. Dimensionsixoperatorsbuilt of bilinears:

  17. MinimalFlavourViolation SymmetrybreakingpatternPhenomenology • Quark sector. Dimensionsixoperatorsbuilt of bilinears:

  18. MinimalFlavourViolation SymmetrybreakingpatternPhenomenology • Quark sector. d=6 operatorsbuilt of FlavourInvariantbilinears: • Flavour Factor

  19. U(2) Symmetrybreakingpattern. Phenomenology • Considers MFV symmetryisalreadybrokenbythirdgeneration. • Quark sector

  20. U(2) Symmetrybreakingpattern. Phenomenology • Considers MFV symmetryisalreadybrokenbythirdgeneration. • Quark sector

  21. U(2) Symmetrybreakingpattern. Phenomenology • Considers MFV symmetryisalreadybrokenbythirdgeneration. • Quark sector • Needs 2HDM

  22. U(2) Symmetrybreakingpattern. Phenomenology • Lepton sector.

  23. U(2) Symmetrybreakingpattern. Phenomenology • Lepton sector. . Complex SB without top-downjustification.

  24. U(2) Symmetrybreakingpattern. Phenomenology • Lepton sector. . Complex SB without top-downjustification. • Notminimalscenario,

  25. U(2) Symmetrybreakingpattern. Phenomenology • Lepton sector. . Complex SB without top-downjustification. • Notminimalscenario: a lot of spurions. • Pseudodegenerate neutrino massspectrum.

  26. U(2) Symmetrybreakingpattern. Phenomenology • Phenomenology of B and K mesons similar to MFV with 2HDM. • Unableto cope withallflavour data with SM content. • SUSY istheonlywaytoachievecompatibility! • However, SUSY’s 2HDM doesnotallow

  27. Data DrivenFlavourModel Symmetrybreakingpattern. Phenomenology • Bottom-up approachlookingfor a minimalscenario. • Order 1 for top yukawacoupling. • Hierarchicalmassstructureforallfermionsbutfor neutrinos. • sds • Hierarchicalmixing in quark sector, democratic in lepton sector.

  28. Data DrivenFlavourModel Symmetrybreakingpattern. Phenomenology

  29. Data DrivenFlavourModel Symmetrybreakingpattern. Phenomenology Quark sector • Yukawa termforthe top quark isflavourinvariant w/o spurions. • 3 spurionsfortherest of the quark sector masses and mixing. • Up-massbasis:

  30. Data DrivenFlavourModel Symmetrybreakingpattern. Phenomenology Lepton sector • 2 spurionsforthechargedlepton sector masses. • Diagonal form in massbasis: • Neutrino sector isexactly as in MFV. • Otherchoice of basiswould lead topredictivityissues (not MFV).

  31. Data DrivenFlavourModel SymmetrybreakingpatternPhenomenology • FCNC for LH down quarks withoutspurions, lesssuppressed, yieldsthesamephenomenology as MFV, and therefore • Verysuppressedflavourchangingphenomenology (duetospurioninsertions) for RH down quarks and LH or RH up quarks. Thisis a prediction of themodelthatcould be usefulforitsdistinction in dedicatedexperiments. • Leptonphenomenologyis as in MFV.

  32. B anomalies. Theanomalies. LQ interactions Global fit

  33. B anomalies. Theanomalies. LQ interactions Global fit • Threecandidates • Flavourinvariantinteractions, suppressedbyspurions.

  34. B anomalies. Theanomalies. LQ interactions Global fit • rules outthelasttwo LQ candidates.

  35. B anomalies. Theanomalies. LQ interactions Global fit • SM and LQ contributions. • SM and LQ contributions

  36. B anomalies. Theanomalies. LQ interactionsGlobal fit • Some of thestrongestconstraintsarisefrom box diagrams: MLQ>200MeV

  37. B anomalies. Theanomalies. LQ interactionsGlobal fit • Strongdependenceon neutrino masses, ordering and scale of LNV. • RD cannot be describedcoherentlywithotherphenomena, itneedsverysmall LQ masses(MLQ<2 GeV). • RK isproperlydescribedwithin a widephasespace 6GeV<MLQ<250 GeV • , and can be describedcoherentlywith RK within a relativelywidephasespace. • Succesfully copes withotherflavourconstraints and LHC constraintsonthemass of LQ duetothelowscale of thespurions.

  38. Conclusion • The Data DrivenFlavourModelsuccessfully describes theFlavourPuzzle and copes withthe BSM FlavourProblemwiththesamescale of New Physics as MinimalFlavourViolation. • Itpresentsuniquephenomenologicalfeatures, such as verysuppressed FCNC for up quarks and RH down quarks thatwouldallowto test it in futurededicatedexperiments. • Itsbuillt in a minimalway, withonlyoneHiggs and withoutthe non-minimalsymmetrybreakingpattern of adding a U(1). • Togetherwith a vector singletLeptoquark can describe neutral B anomalies, with a massforsuchleptoquarks of a fewGeVs. Italso copes withtheanomaly (g-2) of the muon and decays of chargedleptonsintothreechargedleptonswithin a widephasespace.

  39. Foresights • Themodel, despitebeing a promisingdescriptionof theFlavourPuzzle, lacksanultravioletcompletionto be regarded as anexplanation. Howeveritisnotcompletelyad hoc: SU(5) GUT inspired. • Itisnotexplainedwherethebackgroundvalues of thespurionsarisefrom, theconstruction of a potentialabletogivesuchminimaisnecessary. • A lot of variations of themodelcould be considered, such as gaugingthesymmetrygroup, consideringtheadition of abeliansymmetriestothepicture, promotingthespurionstodynamicalfields (and theirBackgroundvaluestoVEVs), etc.

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