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Violation of Lepton Flavor Universality as a probe of Composite Sectors

Adri´ an Carmona

Institute for Theoretical Physics, ETH Zurich arXiv:1410.8555, JHEP 1505 (2015) 002 and work in progress

6th Higgs Hunting

July 30, 2015 Slide 1/10

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Composite Higgs

• One interesting solution to the hierarchy problem is making the

Higgs composite, the remnant of some new strong dynamics

[Kaplan, Georgi ’84]

• It is particularly compelling when the Higgs is the pNGB of some

new strong interaction. Something like pions in QCD

[Agashe, Contino, Pomarol ’04]

CFT

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The Higgs Effective Potential

• The coupling to the elementary sector breaks the global symmetry,

generating a Higgs potential at the loop level

• The gauge contribution is aligned in the direction that preserves the

EW symmetry [Witten ’83]

• However, the linear mixings needed to generate the fermion masses

λq

L∆1

h λt

RΓ1

Q1 T1 tL tR can be also responsible for a viable EWSB tR Q1 λt

R

λt

R

T1 T1 + λt

R

λt

R

λq

L

λq

L

tL tR + . . .

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Light Top Partners at the LHC

In general mH ∼ 125 GeV and mtop ∼ 170 GeV ⇒ light top partners 1 TeV which leads to some tension with current top partner searches performed by ATLAS and CMS

600 650 700 750 800 600 650 700 750 800 BR(bW) BR(tZ) BR(tH)

1 1 0.2 0.4 0.6 0.8 1

CMS Preliminary = 8 TeV s ,

• 1

19.6 fb Multileptons

Observed T Quark Mass Limit [GeV]

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Lepton Sector

It is not necessarily true that the lepton sector has to be fully elementary

• The lepton mixing matrix is non-hierarchical (flavor-symmetries?)
• Neutrinos can be Majorana and exhibit a seesaw mechanism

Let us consider e.g. a type-III seesaw ΣR lL lL H H ΣR ∼ 30 In a PLR symmetric case, for each lepton generation ℓ, we have ℓR ∼ (1, 1), lℓ

L ∼ (2, 2),

Σℓ

R ∼ (3, 3)

which could in principle fill a complete 14 = (1, 1) ⊕ (2, 2) ⊕ (3, 3)

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A Minimal Lepton Sector

Different chiralities will talk to different conformal operators but we can still have just one operator for both RH fields, Σℓ

R and ℓR,

L ⊃ λℓ

L

Λγℓ

L

¯ lℓ

LOℓ L + λℓ R

Λγℓ

R

¯ Ψℓ

ROℓ R + h.c.,

Oℓ

L ∼ 5,

Oℓ

R ∼ 14

Since the Majorana mass is generated at the UV MM ∼ MPlanck, we need sizable ǫℓ

R ∼ λℓ R(µ/Λ)γℓ

R to obtain not too small neutrino masses

Mν ∼ v 2ǫ2

Lǫ2 RM−1 M

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A Minimal Lepton Sector

Different chiralities will talk to different conformal operators but we can still have just one operator for both RH fields, Σℓ

R and ℓR,

L ⊃ λℓ

L

Λγℓ

L

¯ lℓ

LOℓ L + λℓ R

Λγℓ

R

¯ Ψℓ

ROℓ R + h.c.,

Oℓ

L ∼ 5,

Oℓ

R ∼ 14

Since the Majorana mass is generated at the UV MM ∼ MPlanck, we need sizable ǫℓ

R ∼ λℓ R(µ/Λ)γℓ

R to obtain not too small neutrino masses

Mν ∼ v 2ǫ2

Lǫ2 RM−1 M

Just the overall size of the neutrino masses ask for partially composite ℓR, for all three generations!

Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 6/10

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A Minimal Lepton Sector

This has a number of interesting consequences:

1 Since the RH fields mix with a 14, the ℓR contribution to the Higgs

quartic is O(ǫ2

R), which can be sizeable even for not so big ǫR

• In particular, this can partially cancel a bigger top contribution and

make thus the top partners heavier

• Moreover, the lepton contribution can even trigger the EWSB,

allowing for minimal quark setups that were not allowed before

2 Embeding this setup in a MFV scenario allows for only one flavon

(connecting the LH and RH sectors) and thus no FCNC or LFV

3 Finally, the different values of ǫℓ R can reproduce the observed

violation of lepton flavor universality, [LHCb arXiv:1406.6482] RK = B(B+ → K +µ+µ−) B(B+ → K +e+e−) = 0.745+0.090

−0.074 ± 0.036

Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 7/10

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Lifting Top Partners

Quarks: 5 − 1 − 5 − 1 Leptons: 5 − 14

50 100 150 200 250 1 2 3 4 5 mH [GeV] m2/3

min [TeV]

1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 m2/ 3

min [TeV ]

Pm

Y l

∗ = 0.7,

Y q

∗ = 0.7,

fπ = 0.8 TeV, gψ ∼ 4.4

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Violation of Lepton Flavor Universality

Mν ∼ v 2(ǫℓ

Lǫℓ R)2M−1 M ,

Mℓ ∼ vǫℓ

L

⇒ ǫτ

R ≤ ǫµ R ≤ ǫe R

bL ¯ sL bL ¯ sL O1 ∼

g 2

ρ

m2

ρ (ǫb

L)2(ǫs L)2 ≤ 1/Λ2 max

bL ¯ sL ℓ+

R

ℓ−

R

Oℓ

LR ∼ g 2

ρ

m2

ρ ǫb

Lǫs L(ǫℓ R)2

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Violation of Lepton Flavor Universality

Mν ∼ v 2(ǫℓ

Lǫℓ R)2M−1 M ,

Mℓ ∼ vǫℓ

L

⇒ ǫτ

R ≤ ǫµ R ≤ ǫe R

0.5 0.6 0.7 0.8 0.9 1.0 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 RK 1/Λ2 [1/TeV2] Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 9/10

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Conclusions

• The inclusion of a lepton sector in CHMs can in some cases

significantly change the picture

• Minimality can link disparate features like the size of neutrino

masses and the masses of top partners

• This is welcome in the framework of MFV
• Violation of LFU could be the first probe of these scenarios!

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Back-up Slides

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Partial Compositeness

The fermionic Lagrangian reads L = Lel + Lmix + Lcomp with Lel = ¯ lℓ

Li

Dlℓ

L + ¯

ℓRi DℓR + ¯ Σℓ

Ri

DΣℓ

R − 1

2

• Mℓℓ′

M Tr

• ¯

Σℓc

R Σℓ′ R

• + h.c.
• and

Lmix = λℓ

L

Λγℓ

L

¯ lℓ

LOℓ L + λℓ R

Λγℓ

R

¯ Ψℓ

ROℓ R + h.c.

For γℓ

R < 0, we get a large correction to the RH kinetic terms

λℓ2

R

Λ2γℓ

R

• d4pd4p ¯

Ψℓ

R(−p)Oℓ R(p) ¯

Oℓ′

R (−q)Ψℓ′ R (q)

∼ δℓℓ′λℓ2

R

µ Λ 2γℓ

R

d4x ¯ ΨR(x)i✁ ∂ΨR(x)

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RK

In order to compute RK we use the following effective Hamiltonian Heff = −4GF √ 2 (V ∗

tsVtb)

• i

ˆ C ℓ

i Oℓ i (µ),

with the relevant operators being O7 = e 16π2 mb (¯ sσαβPRb) F αβ, O′

7 =

e 16π2 mb (¯ sσαβPLb) F αβ, Oℓ

9

= αem 4π (¯ sγαPLb) ¯ ℓγαℓ

• ,

Oℓ′

9 = αem

4π (¯ sγαPRb) ¯ ℓγαℓ

• ,

Oℓ

10

= αem 4π (¯ sγαPLb) ¯ ℓγαγ5ℓ

• ,

Oℓ′

10 = αem

4π (¯ sγαPRb) ¯ ℓγαγ5ℓ

• ,

and ˆ Ci = C SM

i

+ C NP

i

. Using C SM

9

= 4.228 and C SM

10 = −4.410, we get

RK ≈ |C SM

10 + C µ 10 + C ′µ 10|2 + |C SM 9

+ C µ

9 + C ′µ 9 |2

|C SM

10 + C e 10 + C ′e 10|2 + |C SM 9

+ C e

9 + C ′e 9 |2

Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 3/4

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RK

In order to compute RK we use the following effective Hamiltonian Heff = −4GF √ 2 (V ∗

tsVtb)

• i

ˆ C ℓ

i Oℓ i (µ),

with the relevant operators being O7 = e 16π2 mb (¯ sσαβPRb) F αβ, O′

7 =

e 16π2 mb (¯ sσαβPLb) F αβ, Oℓ

9

= αem 4π (¯ sγαPLb) ¯ ℓγαℓ

• ,

Oℓ′

9 = αem

4π (¯ sγαPRb) ¯ ℓγαℓ

• ,

Oℓ

10

= αem 4π (¯ sγαPLb) ¯ ℓγαγ5ℓ

• ,

Oℓ′

10 = αem

4π (¯ sγαPRb) ¯ ℓγαγ5ℓ

• ,

and ˆ Ci = C SM

i

+ C NP

i

. Using C SM

9

= 4.228 and C SM

10 = −4.410, we get

RK ≈ |C SM

10 + C µ LR|2 + |C SM 9

+ C µ

LR|2

|C SM

10 + C e LR|2 + |C SM 9

+ C e

LR|2

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