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Flavor symmetries: finding tests & alternatives
Heinrich Päs
Miami 2010
Heinrich PäsFlavor symmetries: Tests & alternatives
‣ The Higgs as a harbinger of flavor symmetry
‣ Knotted strings & leptonic flavor structure
G. Bhattacharyya, P. Leser, H. Päs, arXiv:1006.5597
T.W. Kephart, P. Leser, H. Päs, work in progress
Heinrich PäsNeutrinos & the Terascale
Neutrino status review
‣ Solar neutrino oscillations → large mixing
‣ Atmospheric neutrino oscillations → maximal mixing
‣ No short-baseline νe disappearance → small mixing
⇒Neutrinos have masses ⇒Mass eigenstates ≠Flavor eigenstates
!! =!
i
U!i!i
Heinrich PäsNeutrinos & the Terascale
Absolute mass bounds
m +qL
ei
ei
i2 L2i
P
dW
u
e
U
U
!=! q !mP
ud We
Heinrich PäsNeutrinos & the Terascale
Flavor Symmetries
Fact: ‣ Large/Maximal lepton vs. small quark mixing
‣ Mild lepton vs. strong quark hierarchies
S3, A4, S4, D4, Q4, D5, D6, Q6, D7,…
‣ Discrete Flavor symmetry?
‣ Anarchy? Masses and Mixings random numbers?
[e.g. Ma, Altarelli, Feruglio, King, Ross, Varzielas, Frampton, Kephart...]
[Hall, Murayama, Weiner, Haber, de Gouvea, ’99, ’00, ’03]
Heinrich PäsNeutrinos & the Terascale
A landscape of Flavor symmetry
‣ 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
[Albright, Chen, Rodejohann; ’06,’08] [Parattu, Wingerter, SUSY’10]
1048 groups 41086 models for A4×C3
86 models
Heinrich PäsNeutrinos & the Terascale
Probing flavor models at the LHC
A prototypical flavor model based on S3:[Chen, Frigerio, Ma, ’04]
1 2
3
‣ 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 irreducible representations: 1, 1′,2‣ Basic multiplication rules: 1′×1′=1 and 2×2=1+1′+2
‣ Assign matter fields to irreps as follows:
(L1, L2) ! 2 L3, !c3, !c1 ! 1 !c2 ! 1!
(Q1, Q2) ! 2 Q3,"c3,"c1, d
c3, d
c1 ! 1 "c2, d
c2 ! 1!
(#1,#2) ! 2 #3 ! 1
Heinrich PäsNeutrinos & the Terascale
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
M! =
!"#ƒ4"3 ƒ5"3 00 ƒ1" !ƒ2"0 ƒ1" ƒ2"
$%&
→Such models exhibit an extraordinary Higgs phenomenology!
Heinrich PäsNeutrinos & the Terascale
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 off-diagonal Yukawas
‣ FCNCs are suppressed
Heinrich PäsNeutrinos & the Terascale
Probing flavor models at the LHC
0.6
0.7
0.8
0.9
1
110 130 150 170 190
!b-
>aa /
!to
t
mb [GeV]
k50 = 29.4k75 = 29.4
k50 = 5.2k75 = 6.1
(a)
ma = 50 GeVma = 75 GeV
1e-06
1e-05
0.0001
0.001
0.01
0.1
1
50 100 150 200 250 300
Bran
chin
g ra
tios
for h
a
ma [GeV]
(b)
µ!c
sbc
ctc
0.01
0.1
1
20 60 100 140Br
anch
ing
ratio
for t
! h
a cma [GeV]
(c)
‣ 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 (sbc, ma < mt )or ctc (ma > mt )
k:3-scalar- / hbWW-coupling
Spectacular signals at the LHC!
‣ ha , hb might already be buried in existing LEP or Tevatron data!
Heinrich PäsNeutrinos & the Terascale
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?
Heinrich PäsNeutrinos & the Terascale
Alternative: Knotted strings & flavor
31 knot
321 link
(3 crossings, 1 component)
(3 crossings, 2 components)
[Buniy, Kephart ’03] [Dale Rolfson: Knots and Links]
Heinrich PäsNeutrinos & the Terascale
Alternative: Knotted strings & flavor
‣ Lengths of the smallest knots and links
‣ Several numbers lying closeby!
‣ Numerology?
[Ashton, Cantarella, Piatek, Rawdon, arXiv:1002.1723]
Heinrich PäsNeutrinos & the Terascale
Alternative: Knotted strings & flavor
[Buniy, Kephart ’03,’05; Buniy, Holmes, Kephart ’09]
knot energies
Glue
ball
cand
idat
es
‣ What’s relating knot lengths and particle physics?
‣ Assume knot length knot energy (flux tube model) ∝
‣ Excellent fit to the spectrum of glueball candidates!
(non
qq-
J++ s
tate
s)
Heinrich PäsNeutrinos & the Terascale
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! =
!0 mdiag
D
mdiagD MR
"
➘MR =
!
"link1 knot1 knot2knot1 link2 knot3knot2 knot3 link3
#
$
Mixing purely from right-handed sector!
Heinrich PäsNeutrinos & the Terascale
Alternative: Knotted strings & flavor
Preliminary results:
‣ Excellent fit: χ2 ≈0.04
‣ Comparison with random numbers favorable
‣ Normal hierarchy preferred (bad news for 0νββ decay search)
Preli
minary
Heinrich PäsNeutrinos & the Terascale
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?)