Violation of Lepton Flavor Universality as a probe of Composite - PowerPoint PPT Presentation

i t p , e t h z u r i c h eth zurich 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 6 th Higgs Hunting July 30, 2015 Slide 1/10

e t h z u r i c h i t p , e t h z u r i c h 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 Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 2/10

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 λ q h λ t L ∆ 1 R Γ 1 t L t R Q 1 T 1 can be also responsible for a viable EWSB λ t t R R t R λ t λ t λ t . . . R R + R + λ q L T 1 T 1 t L λ q Q 1 L

e t h z u r i c h i t p , e t h z u r i c h Light Top Partners at the LHC In general m H ∼ 125 GeV and m top ∼ 170 GeV ⇒ light top partners � 1 TeV which leads to some tension with current top partner searches performed by ATLAS and CMS -1 CMS Preliminary 19.6 fb , s = 8 TeV Multileptons BR(bW) 1 Observed T Quark Mass Limit [GeV] 800 800 0.8 750 750 0.6 0 0 700 700 0.4 650 650 0.2 600 600 1 0 1 BR(tZ) BR(tH) Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 4/10

e t h z u r i c h i t p , e t h z u r i c h 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 Σ R H H Σ R ∼ 3 0 l L l L In a P LR symmetric case, for each lepton generation ℓ , we have l ℓ Σ ℓ ℓ R ∼ ( 1 , 1 ) , L ∼ ( 2 , 2 ) , R ∼ ( 3 , 3 ) which could in principle fill a complete 14 = ( 1 , 1 ) ⊕ ( 2 , 2 ) ⊕ ( 3 , 3 ) Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 5/10

e t h z u r i c h i t p , e t h z u r i c h A Minimal Lepton Sector Different chiralities will talk to different conformal operators but we can still have just one operator for both RH fields, Σ ℓ R and ℓ R , L ⊃ λ ℓ L + λ ℓ ¯ ¯ L l ℓ L O ℓ R Ψ ℓ R O ℓ O ℓ O ℓ R + h . c ., L ∼ 5 , R ∼ 14 Λ γ ℓ Λ γ ℓ L R Since the Majorana mass is generated at the UV �M M � ∼ M Planck , we R ( µ/ Λ) γ ℓ R to obtain not too small neutrino masses need sizable ǫ ℓ R ∼ λ ℓ M ν ∼ v 2 ǫ 2 L ǫ 2 R M − 1 M Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 6/10

e t h z u r i c h i t p , e t h z u r i c h A Minimal Lepton Sector Different chiralities will talk to different conformal operators but we can still have just one operator for both RH fields, Σ ℓ R and ℓ R , L ⊃ λ ℓ L + λ ℓ ¯ ¯ L l ℓ L O ℓ R Ψ ℓ R O ℓ O ℓ O ℓ R + h . c ., L ∼ 5 , R ∼ 14 Λ γ ℓ Λ γ ℓ L R Since the Majorana mass is generated at the UV �M M � ∼ M Planck , we R ( µ/ Λ) γ ℓ R to obtain not too small neutrino masses need sizable ǫ ℓ R ∼ λ ℓ M ν ∼ v 2 ǫ 2 L ǫ 2 R M − 1 M Just the overall size of the neutrino masses ask for partially composite ℓ R , for all three generations! Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 6/10

e t h z u r i c h i t p , e t h z u r i c h A Minimal Lepton Sector This has a number of interesting consequences: 1 Since the RH fields mix with a 14 , the ℓ R contribution to the Higgs quartic is O ( ǫ 2 R ), which can be sizeable even for not so big ǫ R • 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 ǫ ℓ R can reproduce the observed violation of lepton flavor universality, [LHCb arXiv:1406.6482] R K = 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

e t h z u r i c h i t p , e t h z u r i c h Lifting Top Partners Quarks: 5 − 1 − 5 − 1 Leptons: 5 − 14 5 1.0 4 0.8 3 0.6 min [ TeV ] P m m 2 / 3 0.4 2 0.2 1 0.0 0 0 1 2 3 4 50 100 150 200 250 min [ TeV ] m H [ GeV ] m 2 / 3 Y l Y q ∗ = 0 . 7 , ∗ = 0 . 7 , f π = 0 . 8 TeV , g ψ ∼ 4 . 4 Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 8/10

e t h z u r i c h i t p , e t h z u r i c h Violation of Lepton Flavor Universality R ≤ ǫ µ M ν ∼ v 2 ( ǫ ℓ L ǫ ℓ R ) 2 M − 1 M ℓ ∼ v ǫ ℓ ǫ τ R ≤ ǫ e M , ⇒ L R ℓ + b L b L b L R ℓ − s L ¯ ¯ s L s L ¯ R g 2 g 2 L ) 2 ≤ 1 / Λ 2 L ) 2 ( ǫ s R ) 2 ρ ( ǫ b O ℓ ρ ǫ b L ǫ s L ( ǫ ℓ O 1 ∼ ρ LR ∼ ρ max m 2 m 2 Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 9/10

e t h z u r i c h i t p , e t h z u r i c h Violation of Lepton Flavor Universality R ≤ ǫ µ M ν ∼ v 2 ( ǫ ℓ L ǫ ℓ R ) 2 M − 1 M ℓ ∼ v ǫ ℓ ǫ τ R ≤ ǫ e M , ⇒ L R 0.0012 0.0010 0.0008 1 / Λ 2 [ 1 / TeV 2 ] 0.0006 0.0004 0.0002 0.0000 0.5 0.6 0.7 0.8 0.9 1.0 R K Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 9/10

e t h z u r i c h i t p , e t h z u r i c h 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! Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 10/10

e t h z u r i c h i t p , e t h z u r i c h Back-up Slides Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 1/4

e t h z u r i c h i t p , e t h z u r i c h Partial Compositeness The fermionic Lagrangian reads L = L el + L mix + L comp with R − 1 � � � � L el = ¯ L + ¯ D ℓ R + ¯ M ℓℓ ′ ¯ R Σ ℓ ′ l ℓ L i � Dl ℓ ℓ R i � Σ ℓ R i � D Σ ℓ Σ ℓ c M Tr + h . c . R 2 and L mix = λ ℓ L + λ ℓ ¯ ¯ L l ℓ L O ℓ R Ψ ℓ R O ℓ R + h . c . Λ γ ℓ Λ γ ℓ L R For γ ℓ R < 0, we get a large correction to the RH kinetic terms λ ℓ 2 � d 4 p d 4 p ¯ R ( p ) ¯ O ℓ ′ R ( − q ) � Ψ ℓ ′ R Ψ ℓ R ( − p ) �O ℓ R ( q ) Λ 2 γ ℓ R � 2 γ ℓ � µ R � ∼ δ ℓℓ ′ λ ℓ 2 d 4 x ¯ Ψ R ( x ) i ✁ ∂ Ψ R ( x ) R Λ Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 2/4

e t h z u r i c h i t p , e t h z u r i c h R K In order to compute R K we use the following effective Hamiltonian H eff = − 4 G F � C ℓ ˆ i O ℓ ( V ∗ √ ts V tb ) i ( µ ) , 2 i with the relevant operators being e e s σ αβ P R b ) F αβ , s σ αβ P L b ) F αβ , O 7 = 16 π 2 m b (¯ O ′ 7 = 16 π 2 m b (¯ α em 9 = α em � ¯ � ¯ O ℓ ℓγ α ℓ O ℓ ′ ℓγ α ℓ � � = 4 π (¯ s γ α P L b ) , 4 π (¯ s γ α P R b ) , 9 α em 10 = α em � ¯ � ¯ O ℓ ℓγ α γ 5 ℓ O ℓ ′ ℓγ α γ 5 ℓ � � = 4 π (¯ s γ α P L b ) , 4 π (¯ s γ α P R b ) , 10 and ˆ C i = C SM + C NP . Using C SM = 4 . 228 and C SM 10 = − 4 . 410, we get i i 9 10 | 2 + | C SM 10 + C µ 10 + C ′ µ + C µ 9 + C ′ µ R K ≈ | C SM 9 | 2 9 10 | 2 + | C SM | C SM 10 + C e 10 + C ′ e + C e 9 + C ′ e 9 | 2 9 Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 3/4

e t h z u r i c h i t p , e t h z u r i c h R K In order to compute R K we use the following effective Hamiltonian H eff = − 4 G F � C ℓ ˆ i O ℓ ( V ∗ √ ts V tb ) i ( µ ) , 2 i with the relevant operators being e e s σ αβ P R b ) F αβ , s σ αβ P L b ) F αβ , O 7 = 16 π 2 m b (¯ O ′ 7 = 16 π 2 m b (¯ α em 9 = α em � ¯ � ¯ O ℓ ℓγ α ℓ O ℓ ′ ℓγ α ℓ � � = 4 π (¯ s γ α P L b ) , 4 π (¯ s γ α P R b ) , 9 α em 10 = α em � ¯ � ¯ O ℓ ℓγ α γ 5 ℓ O ℓ ′ ℓγ α γ 5 ℓ � � = 4 π (¯ s γ α P L b ) , 4 π (¯ s γ α P R b ) , 10 and ˆ C i = C SM + C NP . Using C SM = 4 . 228 and C SM 10 = − 4 . 410, we get i i 9 LR | 2 + | C SM 10 + C µ + C µ R K ≈ | C SM LR | 2 9 LR | 2 + | C SM | C SM 10 + C e + C e LR | 2 9 Adri´ an Carmona — Violation of LFU as a probe of Composite Sectors — Higgs Hunting 2015 Slide 3/4