Flavor symmetries: finding tests & alternatives Miami 2010 The Higgs as a harbinger of flavor symmetry G. Bhattacharyya, P. Leser, H. Päs, arxiv:1006.5597 Knotted strings & leptonic flavor structure T.W. Kephart, P. Leser, H. Päs, work in progress Flavor symmetries: Tests & alternatives
Neutrino status review Solar neutrino oscillations large mixing Atmospheric neutrino oscillations maximal mixing No short-baseline νe disappearance small mixing ν α = i U αi ν i Neutrinos have masses Mass eigenstates Flavor eigenstates
Absolute mass bounds d d u W e Uei m i +q ν=ν PL q 2 m P U ei e W u 2 L i
Neutrinos & physics beyond the SM what is it?
Flavor Symmetries Fact: Large/Maximal lepton vs. small quark mixing Mild lepton vs. strong quark hierarchies Discrete Flavor symmetry? S3, A4, S4, D4, Q4, D5, D6, Q6, D7, [e.g. Ma, Altarelli, Feruglio, King, Ross, Varzielas, Frampton, Kephart...] Anarchy? Masses and Mixings random numbers? [Hall, Murayama, Weiner, Haber, de Gouvea, 99, 00, 03]
A landscape of Flavor symmetry 86 models 1048 groups 41086 models for A4 C3 [Albright, Chen, Rodejohann; 06, 08] [Parattu, Wingerter, SUSY 10] Huge variety of models Predictions spanning a large part of the parameter space Search for new tests of Flavor symmetry Search for alternatives of Flavor symmetry
Probing flavor models at the LHC A prototypical flavor model based on S3: [Chen, Frigerio, Ma, 04] Symmetry group of the permutation of 3 objects. (equivalent to symmetry group of equilateral triangle) Contains 6 elements: (123), (312), (231), (132), (321), (213) 3 3 irreducible representations: 1, 1,2 Basic multiplication rules: 1 1 =1 and 2 2=1+1 +2 Assign matter fields to irreps as follows: 1 2 (L 1,L 2 ) 2 L 3, l c 3, lc 1 1 lc 2 1 (Q 1,Q 2 ) 2 Q 3, c 3, c 1,dc 3,dc 1 1 c 2,dc 2 1 (ϕ 1, ϕ 2 ) 2 ϕ 3 1
Probing flavor models at the LHC the same Higgses breaking EWSB also break Flavor! 3 Higgs SU(2) doublets necessary Vaccum alignment v1=v2 v for maximal mixing (extremum ) Large Flavor violating terms cancel between up and down-type quarks Neutrino masses generated by additional Higgs SU(2) triplet Large Flavor violation translates as mismatch between charged leptons and neutrinos directly into PMNS matrix ƒ 4 3 ƒ 5 3 0 M l = 0 ƒ 1 ƒ 2 0 ƒ 1 ƒ 2 Such models exhibit an extraordinary Higgs phenomenology!
Probing flavor models at the LHC Minimization of the general S3 invariant scalar potential Rotation into the mass basis Physical CP-even neutral scalars: mb light (< 200 GeV), mc heavier (200 GeV < mc < 450 GeV), ma < 350 GeV SM-Higgs-like scalars hb and hc, except each can decay dominantly into pairs of ha ha without 3-point vertex gauge interactions and only offdiagonal Yukawas FCNCs are suppressed
Probing flavor models at the LHC Dominant decay for a light ha: hb/c -> ha ha Production of ha possible through t -> ha c with subsequent decay ha-> μτ ha decays dominantly off-diagonally into jets (sb c, ma < mt )or ct c (ma > mt ) k:3-scalar- / hbww-coupling! b->aa /! tot 1 0.9 0.8 (a) k 50 = 5.2 k 75 = 6.1 k 50 = 29.4 k 75 = 29.4 0.7 m a = 50 GeV m a = 75 GeV 0.6 110 130 150 170 190 m b [GeV] Spectacular signals at the LHC! ha, hb might already be buried in existing LEP or Tevatron data! Branching ratios for h a 1 0.1 0.01 0.001 0.0001 1e-05 1e-06 (b) Branching ratio for t! h a c 0.1 µ! c sb c ct c 0.01 50 100 150 200 250 300 m a [GeV] 1 (c) 20 60 100 140 m a [GeV]
Alternative: Knotted strings & flavor Major achievement of Flavor models: motivate degenerate mass matrix entries to fit TBM: [e.g. Altarelli, Feruglio] Alternative: Anarchy... Anything else? Other phenomena in Nature with close numbers?
Alternative: Knotted strings & flavor 31 knot (3 crossings, 1 component) 3 2 1 link (3 crossings, 2 components) [Buniy, Kephart 03] [Dale Rolfson: Knots and Links]
Alternative: Knotted strings & flavor Lengths of the smallest knots and links Several numbers lying closeby! Numerology? [Ashton, Cantarella, Piatek, Rawdon, arxiv:1002.1723]
Alternative: Knotted strings & flavor What s relating knot lengths and particle physics? Assume knot length knot energy (flux tube model) Glueball candidates (non qq-j ++ states) knot energies [Buniy, Kephart 03, 05; Buniy, Holmes, Kephart 09] Excellent fit to the spectrum of glueball candidates!
Alternative: Knotted strings & flavor String theory (+ AdS/QCD duality): glueballs, gravitons and modulinos are open strings [Arkani-Hamed, Dvali, Dimopoulos, March-Russell + some 400 cites]: Right-handed neutrinos can be closed string modulinos Obtain Leptonic flavor structures by assuming right-handed neutrino masses are dominated by knot and link energies? 6 6 seesaw matrix: m ν = ( 0 m diag D m diag D M R ) MR = Mixing purely from right-handed sector! link 1 knot 1 knot 2 knot 1 link 2 knot 3 knot 2 knot 3 link 3
Alternative: Knotted strings & flavor Preliminary results: Excellent fit: χ 2 0.04 Comparison with random numbers favorable Normal hierarchy preferred (bad news for 0νββ decay search) Preliminary
Conclusions Huge variety of flavor models Neither generic predictions nor discriminators in the ν sector For models where the same Higgses break EW and Flavor characteristic Higgs sectors Spectacular signals at the LHC But also: Symmetry and Anarchy are not the only explanation for the leptonic Flavor structure Example: seesaw models with right-handed ν s as knotted strings (realistic string model?)