Heinrich Päs - University of Miami · Neutrinos & the Terascale Heinrich Päs Neutrino status...

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


Absolute mass bounds

m +qL

ei

ei

i2 L2i

P

dW

u

e

U

U

!=! q !mP

ud We


Neutrinos & physics beyond the SM

what is it?


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]


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


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



‣ 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!



‣ 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



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!


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?



31 knot

321 link

(3 crossings, 1 component)

(3 crossings, 2 components)

[Buniy, Kephart ’03] [Dale Rolfson: Knots and Links]



‣ Lengths of the smallest knots and links

‣ Several numbers lying closeby!

‣ Numerology?

[Ashton, Cantarella, Piatek, Rawdon, arXiv:1002.1723]



[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)



‣ 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!



Preliminary results:

‣ Excellent fit: χ2 ≈0.04

‣ Comparison with random numbers favorable

‣ Normal hierarchy preferred (bad news for 0νββ decay search)

Preli

minary


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?)

Heinrich Päs - University of Miami · Neutrinos & the Terascale Heinrich Päs Neutrino status...

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