SEARCHING FOR BSM PHYSICS INHIGGS COUPLINGS TO FERMIONS ANDFLAVOUR SYMMETRIES
Based on:• J. Alonso-Gonzales, L. Merlo and SP, JHEP 06(2021) 166• J.Alonso-Gonzales, A. di Giorgi, L.Merlo and SP, to appear

SM:yh ¯p2=mv

MOTIVATION(GENERAL)FLAVOUR IS ESSENTIALLY A BEYOND THE SM CONCEPTAND THE NEW PHYSICS SCALE BEHIND THE FLAVOUR
PARADIGM MAY BE DIFFERENT FROM THE ELECTROWEAKSCALE, USUALLY LINKED TO THE HIERARCHY PROBLEM
MOTIVATION (SPECIFIC)ELECTROWEAK BARYOGENESIS NEEDS NEW SOURCES OFCP VIOLATION (BEYOND THE CKM MATRIX)

THE MOST NATURAL SCENARIO (IF NOT THE ONLY ONE?) IS THAT YUKAWACOUPLINGS HAVE A CP VIOLATING COMPONENT.
CP VIOLATING INTERACTIONS ACROSS THE EXPANDING WALLS OF THEBUBBLES OF THE VEVs OF THE HIGGS FIELD WOULD CREATE A CHIRAL ASYMMETRY,THEN CONVERTED TO A BARYON ASYMMETRY BY THE WEAK SPHALERON PROCESS.
(VERY RICH LITERATURE ON THIS SUBJECT:
most recent E. FUCHS, M.Losada, Y. Nir and Y. VIERNIK)MOTIVATION contSEVERAL SOURCES OF INFORMATION ON THE BSM PHYSICS IN YUKAWAS:• HIGGS BOSON PRODUCTION AND DECAYS, DIRECTLY DEPENDENT ON THEYUKAWA COUPLINGS (COLLIDERS)• VERY HIGH PRECISION LOW ENERGY FLAVOUR OBSERVABLES, INCLUDINGMAGNETIC AND ELECTRIC DIPOLE MOMENTS AND A VARIETY OF FCNCPROCESSES, DEPENDENT ON THE YUKAWA COUPLINGS VIA HIGGSEXCHANGE CONTRIBUTIONS TO THEIR AMPLITUDESCOMPLEMENTARITY OF DIFFERENT EXPERIMENTS INTHEIR SENSITIVITY TO THE BSM PHYSICS IN YUKAWA COUPLINGS?
ITS DEPENDENCE ON THE FLAVOUR STRUCTURE OF THE BSM PHYSICS?

HAS THE BSM PHYSICS IN THE HIGGS COUPLINGS ANYFLAVOUR STRUCTURE ?
WHAT CAN WE EXPECT FOR IT ?

IN THE SMEFT FRAMEWORK, INCLUDING DIM 6 OPERATORS, THEREIS ONLY ONE OPERATOR CONTRIBUTING TO YUKAWA COUPLINGS:L=Q̄JL H̄Yu0JK uKR(Q̄JL H̄Cu0JK uKRY, C 0Q̄JL HYd0JK dKRQ̄JL HCd0JK dKRL̄JL HYe0JK eKR†HHJ0JK KL̄L HCe eR ) 2 + h.c⇤

ARE 3x3 COMPLEX MATRICES IN THE FLAVOUR SPACETWO INTERESTING HYPOTHESIS FOR FLAVOUR PARADIGM IN THE BSM PHYSICS:MINIMAL FLAVOUR VIOLATION OR IT RESPECTS A FLAVOUR SYMMETRY OFTENINVOKED TO EXPLAIN FERMION MASSES AND MIXINGS.

IN BOTH CASES THE YUKAWA MATRICES AND THE WILSONCOEFFICIENT MATRICES ARE RELATED TO EACH OTHER.
STRONG IMPLICATIONS FOR THE EMERGING PICTURE OF POTENTIALDEVIATIONS FROM THE SM PREDICTIONS,MUCH DIFFERENT FROM WHAT COULD BE IF THE WILSON COEFFICIENTS HAVENO FLAVOUR STRUCTURE.

TWO EXAMPLES:IMPLICATIONS FOR ELECTROWEAK BARYOGENESISLOWER BOUNDS ON THE SCALE OF NEW PHYSICS FROMFLAVOUR DATA WITH AND WITHOUT FLAVOUR SYMMETRIESIN THE PRESENCE OF DIM 6 OPERATORS THE FERMION MASSESAND THE FERMION COUPLINGS TO THE HIGGS,IN THE MASS EIGENSTATE, READvvv¯
L = ūL Yu uR pdL Yd dR pēL Ye eR p
22222v2vv
h¯[ūL (Yu + 2 Cu )uR + dL (Yd + 2 Cd )dR + ēL (Ye + 2 Ce )eR ] p + h.c⇤⇤⇤2Yu =p2/v(mu , mc , mt )Yd =p2/v(md , ms , mb )Ye =CF = VF† C 0 UFVF , UF

ARE THE MATRICES WHICH DIAGONALIZE THE MASS TERMS

p2/v(me , mµ , m⌧ )

DEFINING, FOR DIAGONAL YUKAWASLef f =mf(f f¯f + i̃f f¯ 5 f )hv

THE MATCHING WITH THE EFFECTIVE YUKAWAS

f , ̃f

GIVES, E.G

Ku = diag(u , c , t )v2
Y K = Y + 2 diag(ReC),⇤v2
Y K̃ = 2 diag(ImC)⇤AND THE NON_DIAGONAL COUPLINGS (IF PRESENT) ARE GIVEN BY THE
NON-DIAGONAL ENTRIES IN THE MATRICES CELECTROWEAK BARYOGENESIS: TO EXPLAIN THE BARYONASYMMETRY OF THE UNIVERSE WITH A SINGLE COMPLEX YUKAWACOUPLING ONE NEEDS (FUCHS ET AL)|̃t | ⇡ 0.06|̃b | ⇡ 3

HOWEVER, THERE ARE EXPERIMENTAL BOUNDS ON|̃⌧ | ⇡ 0.12|̃|THEY COME FROM THE ELECTRON EDM, WHICH IS GIVEN BY THE TWO-LOOP
BARR-ZEE DIAGRAM

“ÂECe≠ADe≠“Be≠

BARR-ZEE DIAGRAM CONTRIBUTION TO THE ELECTRON EDM:de⇠ [e ̃f f1 (x) + ̃e f f2 (x)]em2fx= 2mh|de | < 1.1 ⇥ 10 29 e cmASSUMING ONLY ONE THIRD GENERATION FERMION RUNNING IN THE LOOPONE GETS THE BOUNDS|̃t |  0.0012|̃b |  0.27

̃e  0.0017|̃⌧ |  0.3

ONLY THE IMAGINARY PART OF THE TAU YUKAWA COUPLING CAN SAVE BAU BUT….

2v ImC11̃e = 2⇤ye
WITH THE BOUNDv 2 ImC33
̃⌧ = 2⇤y⌧̃e  0.0017

me ImC33
˜⌧ < 0.0017
m⌧ ImC11ONE GETSMINIMAL FLAVOUR VIOLATION00C =cY
HENCE WE GET0WHERE C’ is a flavour blind complex number̃⌧ < 0.0017

FROGGATT-NIELSEN MODELS- FLAVOUR U(1) SYMMETRY- AS A GENERIC EXAMPLE̃⌧ < O(1)0.0017

IN SUCH TYPICAL FLAVOUR SCENARIOS, THE ELECTRON EDM BOUNDSEXCLUDE SUCCESSFUL ELECTROWEAK BARYOGENESSISSEARCHING FOR CP VIOLATION INh ! ⌧⌧IS CRUCIAL FOR TESTING THE VIABILITY OF THE
ELECTROWEAK BARYOGENESISISANOTHER EXAMPLE, THIS TIME FOR THE EMERGING PICTURE FOR THE BOUNDSON THE NP SCALES (= SENSITIVITY OF DIFFERENT OBSERVABLES TO NP)CONSIDER BOUNDS ON NP COMING FROMADDING TO THE SM A GENERIC4-FERMION OPERATOR✏K

15(s¯d)(s¯d)!
⇤>O(10)T eVR LL R2⇤ADDING 4-FERMION OPERATOR GENERATED BY THREE LEVEL HIGGSEXCHANGE WITH GENERIC NONDIAGONAL COUPLINGS OBTAINED FROM THE DIM 6OPERATOR2v ¯fi fj h ! ⇤ > O(300)T eV2⇤ADDING 4-FERMION OPERATOR GENERATED BY TREE LEVEL HIGGSEXCHANGE WITH NONDIAGONAL WILSON COEFFICIENTS OF THE DIM 6OPERATOR CONTROLLED BY FROGGATT-NIELSEN MODELSv2 ¯Cij 2 fi fj h ! ⇤ > O(2)T eV⇤Cij ⇡ O(1)✏nQi , ndjnQi +ndj i✓ij-FERMION CHARGES GIVINGGOOD DESCRIPTION OF FERMIONMASSES AND MIXINGe✏ = 0.23 (Cabibbo angle)

HIGH BOUNDS ON NP FROM SELECTED OBSERVABLES = SENSITIVITY TOHIGH SCALES OF NP IN THOSE OBERVABLES BUT VERY LIMITED ACCESSIBILITY
OTHERWISELOW MAXIMAL BOUNDS- INTERESTING PROSPECTS FOR FUTURE EXPERIMENTS⇤ > O(2)TeV--à DEVIATIONS UP TO O(1-2)% IN THE HIIGSCOUPLINGS STILL POSSIBLE(GOOD NEWS FOR THE FUTURE PRECISIONHIGGS MEASUREMENTS IN COLLIDERS)

SUMMARYTHE SCALE OF BEYOND THE SM PHYSICS CONTRIBUTING TO THE HIGGS FERMIONCOUPLINGS MAY BE DIFFERENT FROM E.G. ELECTROWEAK BSM PHYSICSIF IN THE EFT APPROACH THE WILSON COEFFICIENTS OF THE RELEVANTOPERATORS RESPECT SOME FLAVOUR STRUCTURE, LIKE MINIMAL FLAVOURVIOLATION OR A FLAVOUR SYMMETRY RESPONSIBLE FOR THE FERMIONMASSES AND MIXING, THERE ARE BAD AND GOOD NEWS:BAD NEWS: ELECTROWEAK BARYOGENESIS LOOKS UNLIKELYGOOD NEWS FOR COLLIDERS: A COUPLE OF PER CENT DEVIATIONS FROM THE SMPREDICTIONS IN THE HIGGS COUPLINGS TO FERMIONS ARE STILL POSSIBLE,CONSISTENTLY WITH VERY HIGH PRECISION FCNC DATA.