Recent B Physics Anomalies a First Hint for Compositeness?

Transcription

1 p r i s m a & m i t p eth zurich Recent B Physics Anomalies a First Hint for Compositeness? Adrian Carmona Bermudez PRISMA Cluster of Excellence & Mainz Institute for Theoretical Physics April 10, 2018 Slide 1/34

2 Outline 1 Recent B-physics anomalies 2 Violation of Lepton Flavor Universality in Composite Higgs Models AC, Goertz: PRL 116 (2016) no.25, ; arxiv: ; AC, Goertz: arxiv: Conclusions

3 Flavor Anomalies Charged currents A combined 4 σ anomaly on charged current semileptonic B D ( ) decays R ( ) D = Γ( B D ( ) τ ν) Γ( B D ( ) l ν) ; R D/R SM D = 1.37 ± 0.17 R D /R SM D = 1.28 ± 0.08 R(D*) BaBar, PRL109,101802(2012) Belle, PRD92,072014(2015) LHCb, PRL115,111803(2015) Belle, PRD94,072007(2016) Belle, arxiv: Average 2 χ = 1.0 contours SM Predictions R(D)=0.300(8) HPQCD (2015) R(D)=0.299(11) FNAL/MILC (2015) R(D*)=0.252(3) S. Fajfer et al. (2012) HFAG Summer 2016 P(χ 2 ) = 70% R(D)! Requires very light NP, since it has to compete with the SM tree-level prediction

4 Flavor Anomalies Neutral currents There are several prominent deviations in b sll transitions Observable Experiment SM prediction pull P 5 [4,6] 0.30 ± ± P 5 [6,8] 0.51 ± ± R [1,6] K ± ± R [0.045,1.1] K ± ± R [1.1,6] K ± ± where R [q2 0,q2 1 ] K B(B+ K + µ + µ ) B(B + K + e + e ), R [q2 0,q2 1 ] [q 2 0,q 2 1 ] K B(B0 K µ + µ ) B(B 0 K e + e ) and P 5 is some complicated angular observable in B K µµ. [q 2 0,q 2 1 ]

5 The case for RK ( ) From the NP point of view, R K and R K stand out for several reasons 1 They are very clean observables! For R K Perturbative and non-perturbative QCD contributions cancel log(m l ) enhanced QED corrections are at the O(1%) level [Bordone, Isidori, Pattori, 16] For R K, QCD contributions cancel within the SM 2 It is a loop level effect in the SM 3 They probe a somehow fundamental feature of the SM: lepton flavor universality!

6 EFT approach In order to compute the NP effects in b sll we use the following effective Hamiltonian H eff = 4G F 2 (V tsv tb ) i Ĉ l i O l i (µ), with the relevant operators being O 7 = e 16π 2 m b ( sσ αβ P R b) F αβ, O 7 = e 16π 2 m b ( sσ αβ P L b) F αβ, O l 9 = α 4π ( sγ αp L b) ( lγ α l ), O l 9 = α 4π ( sγ αp R b) ( lγ α l ), O l 10 = α 4π ( sγ αp L b) ( lγ α γ 5 l ), O l 10 = α 4π ( sγ αp R b) ( lγ α γ 5 l ), and Ĉi = C SM i and C l SM 7,9,10 = 0. + C NP i. We have C l SM 9 = 4.07, C l SM 10 = 4.31, C SM 7 = 0.29.

7 EFT approach There are also (pseudo)scalar operators O ( ) S = α 4π ( sp R,Lb)( ll), O ( ) P = α 4π ( sp R,Lb)( lγ 5 l), as well as tensor ones O T(5) = α 4π ( sσµν b)( lσ µν (γ 5 )l). However, only O S O P and O S + O P are non zero when one goes from the dim-6 SM EFT to H eff [Alonso, Grinstein, Martin-Camalich '14] B(B 0 s l + l ) very sensitive to (pseudo)scalar operators NP contributions there have to be small NP in b sll transitions can be very well parametrized by O ( ) 9,10,7

8 EFT approach We can also use for convenience the chiral basis, H eff = 4G F (V tsv tb ) α O 7 + O 7 + C bsx l 2 4π Y O bsx l Y + h.c., with X,Y=L,R l=e,µ,τ O bsx l Y = ( sγ µ P X b)( lγ µ P Y l), since often NP models treat a certain chirality in a special way and one can take advantage of the hierarchy of SM contributions Cbs SM L l L = 8.38 Cbs SM L l R = In this basis R K = C bs L µ L +C bsr µ L 2 + C bsl µ R +C bsr µ R 2 C bsl e L +C bsr e L 2 + C bsl e R +C bsr e R 2

9 EFT approach We can also use for convenience the chiral basis, H eff = 4G F (V tsv tb ) α O 7 + O 7 + C bsx l 2 4π Y O bsx l Y + h.c., with X,Y=L,R l=e,µ,τ O bsx l Y = ( sγ µ P X b)( lγ µ P Y l), since often NP models treat a certain chirality in a special way and one can take advantage of the hierarchy of SM contributions In this basis Cbs SM L l L = 8.38 Cbs SM L l R = R K Re[CSM bs L l L (C NP bs L µ L +Cbs NP R µ L Cbs NP L e L Cbs NP R e L )] Cbs SM L l L 2 + CNP bs L µ R + C NP bs R µ R 2 C NP bs L e R + C NP bs R e R 2 C SM bs L l L 2

10 EFT approach Analogously, R K R K 4p Re[CSM bs L l L (C NP bs R µ L Cbs NP R e L )] Cbs SM L l L 2 4p Re[CNP bs L µ R Cbs NP R µ R C NP bs L e R Cbs NP R e R] Cbs SM where p 0.86 L l L NP C bsr (μ-e) L NP C bsx μ R NP C bsl (μ-e) L 1.2 NP C bsr (μ-e) L NP C bsx μ R NP C bsl (μ-e) L R K * 1.0 NP C bs(l=r) μ R R K * 1.0 NP C bs(l=r) μ R 0.8 NP C bs(l=r) e R NP C bsx e R 0.8 NP C bs(l=r) e R NP C bsx e R RK RK

11 Model building Three main possibilities: s l s l s l b l b l b l Z resonance spin 0/1 leptoquark loop stuff Most of the models are ad-hoc solutions to the flavor anomalies The connection with naturalness was largely unexplored Can it be the first hint of a bigger picture?

12 Violation of LFU in CHMs

13 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 They can naturally lead to a light Higgs m 2 π = m 2 h g2 el µ2 /16π 2

14 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] φ A a µ, Aāµ +πâ πâ πâ πâ They can naturally lead to a light Higgs m 2 π = m 2 h g2 el µ2 /16π 2

15 Higgs Potential The gauge contribution is aligned in the direction that preserves the gauge symmetry [Witten '83] However, the linear mixings L mix = λ q L q LO q L + λt R t R OR t + h.c. needed to generate the fermion masses λ q L h λ t R t L t R Y Q 1 T 1 break the NGB symmetry and will be also responsible for EWSB t R t R λ t R λ t R λ t R + T 1 T 1 Q 1 λ t R λ q L t L λ q L +...

16 Higgs Potential One can promote the linear mixings to spurions of G and expand in powers of λ/g [ ( ) 2 ( ) 4 V m 4 N c λ λ 16π 2 V 2 (h/f) + V 4 (h/f) +...] m = g f g g The large value of the top yukawa y top Y λ q f M Q λ t f M T 1 makes the top contribution (typically) responsible for triggering EWSB [Contino, da Rold, Pomarol, '06] and since m 2 H λ 4 /g 4 We expect to have anomalously light top partners M Ψ m

17 Light Top Partners at the LHC We can see e.g. the MCHM 5, [AC, Goertz, JHEP 1505 (2015) 002] min m 2/ 3 [TeV ] P m Y * q =0.7 Y * q =1.4 Y * q = m H [GeV] m min 2/ 3 [TeV ] f = 0.8 TeV, g 4.4. Y q = 0.7 is the maximum allowed Yukawa

18 Leptons can play a role Leptons are typically disregarded since one could naively expect λ l /g 1. However, They are not just a scaled version of the quark sector The mixing angles in the lepton sector are highly non-hierarchical Neutrinos could have Majorana masses! H N R H H Φ H H Σ R H l L l L l L l L l L l L type I type II type III

19 Leptons can play a role 1 A normal lepton sector will look like L λ l Λ γ l l L O l + λ e Λ γe ē R O e + λ Σ Λ γσ ΣR O Σ 1 2 M ΣTr ( Σc R Σ R ) + h.c.

20 Leptons can play a role 1 A normal lepton sector will look like L λ l l Λ γ L O l + λ e l Λ ē R O e + λ Σ ΣR O Σ 1 γe Λ γσ 2 M ΣTr ( Σc ) R Σ R + h.c. 2 Since M Σ Λ M Pl, avoiding too small neutrino masses (M ν ) light v 2 ϵ 2 lϵ 2 Σ (M Σ ) 1, ϵ l,σ λ l,σ ( µ Λ ) γl,σ requires 0 ϵ Σ

21 Leptons can play a role 1 A normal lepton sector will look like L λ l l Λ γ L O l + λ e l Λ ē R O e + λ Σ ΣR O Σ 1 γe Λ γσ 2 M ΣTr ( Σc ) R Σ R + h.c. 2 Since M Σ Λ M Pl, avoiding too small neutrino masses (M ν ) light v 2 ϵ 2 lϵ 2 Σ (M Σ ) 1, ϵ l,σ λ l,σ ( µ Λ ) γl,σ requires 0 ϵ Σ 3 The 14 = (1, 1) (2, 2) (3, 3) of SO(5) makes possible to unify all the RH leptons in only one multiplet! L λl L l Λ γ L O l + λ R Ψ l Λ γ R O R 1 R 2 M ΣTr ( Σc ) R Σ R + h.c. with Ψ R e R, Σ R, O l 5 and O R 14

22 Lifting the top partners This is really interesting since Since the contribution to the Higgs quartic from the 14 arises at O(λ 2 R /g2 ), moderate values of λ R can have an impact The three charged lepton RH fields will contribute to the potential min m 2/ 3 [TeV ] 3 2 P m m H [GeV] m min 2/ 3 [TeV ]

23 Violation of LFU Vector resonances are ubiquitous in CHMs. In the particular case of SO(5) U(1) X /[SO(4) U(1) X ] one gets 10 = (3, 1) (1, 3) (2, 2), 1 = (1, 1) l R l R l R l R g 2 /g g (ϵ l R )2 RH leptons are custodially symmetric and transform as (1, 1) so they only couple (beforew EWSB) to the hypercharge (1, 1)

24 Violation of LFU Since M e vϵ l and (M ν ) light v 2 ϵ 2 lϵ 2 RM 1 Σ, having hierarchical charged lepton masses and anarchical neutrino masses leads to 0 ϵ τ R ϵ µ R ϵe R and to a violation of LFU b L e R, µ R s L e R, µ R g 2 /m 2 (ϵ sl ϵ bl ϵ 2 R )

25 Violation of LFU 0.4 Cbs L μ R - Cbs L e R Cbs L μ R + Cbs L e R C bsl e R - C bsr e R C bsl e R + C bsr e R

26 Violation of LFU R K* R K

27 Constraints There are four irreducible constraints 1 B s ll 2 B s B s mixing b l b b s l s s 3 pp ll q l 4 EWPD e e q l ē ē

28 1. B s ll B(B s l + l ) B(B s l + l ) SM = 1 + CNP bs L l R C NP bs L l L C NP bs R l R +C NP C SM bs L l R C SM bs L l L bs R l L 2 B(Bs μ + μ - )/B(Bs μ + μ - )SM

29 2. B s B s mixing M Bs M SM 1 + ( Re C LR V Re[C LL V + C RR V ] ) TeV 2 B s OV XY = ( sγ µ P X b)( sγ µ P Y b) RK* R K

30 2. Bs B s mixing and P 5[4.3,8.68] 0.0 P5 ' RK

31 3. Dilepton searches (Δ L μμ ) min % CL limits on MFV Z' from p p μ + μ - ATLAS 13 TeV, 36.1 fb -1 R(K (*) 2σ Δ L qq g * M Z ' [TeV ] [Altmannshofer, Straub, '14] M Z' [GeV] For M Z 3 TeV, couplings to first generation quarks have to be small [Greljo, Marzocca, '17] MFV-like couplings to quarks is already excluded! We have 4 TeV Z s with very small couplings to light quarks

32 3. Dilepton searches Moreover, by naturalness, one expects the channel Z Ll to be open and dominate the branching ratio L l R vs l R l R g ϵ l R g (ϵ l R )2 Chala, Spannowsky '18 ml [TeV] BR(V LL) > m V [TeV] BR(V Ll) 0

33 3. Dilepton searches Moreover, by naturalness, one expects the channel Z Ll to be open and dominate the branching ratio L l R vs l R l R g ϵ l R g (ϵ l R )2 Chala, Spannowsky '18 ml [TeV] BR(V LL) > m V [TeV] BR(V Ll) 0

34 3. Dilepton searches Moreover, by naturalness, one expects the channel Z Ll to be open and dominate the branching ratio L l R vs l R l R g ϵ l R g (ϵ l R )2 Chala, Spannowsky '18 ml [TeV] BR(V LL) > m V [TeV] BR(V Ll) 0

35 4. EWPD One of the biggest tensions arises from EWPD on four-fermion interactions (e R γ µ e R )(e R γ µ e R ) g2 m 2 (ϵ er ) cee [4 GF/ 2 ] fπ [TeV]

36 What about LFV? In principle, one expects to generate dangerous FCNCs leading to extremely constrained lepton flavor violating processes µ eγ, µ 3e, µ e conv, τ µγ,... Some of them are an issue even for elementary leptons! [Beneke, Moch, Rohrwild, '15]

37 A flavor protection We would like to have a global flavor symmetry in the Composite Sector gauge symmetry in the bulk and the IR brane 5DMFV :[Fitzpatrick,Perez,Randall, 07], [Perez,Randall, 08], [Csaki,Perez,Surujon,Weiler, 09 UV brane IR brane

38 A flavor protection We would like to have a global flavor symmetry in the Composite Sector gauge symmetry in the bulk and the IR brane 5DMFV :[Fitzpatrick,Perez,Randall, 07], [Perez,Randall, 08], [Csaki,Perez,Surujon,Weiler, 09 UV brane IR brane Since we only have two 5D multiplets: ζ ll 5 and ζ lr 14, we make them triplets of G F = SU(3) L SU(3) R ζ L (3, 1) ζ R (1, 3)

39 A flavor protection We can then assume that all the breaking of G F comes from one spurion such that Y (3, 3) and c L M L R 1 + YY m S Y c R M R R 1 + Y Y m B Y

40 A flavor protection We can then assume that all the breaking of G F comes from one spurion such that Y (3, 3) and c L M L R 1 + YY m S Y c R M R R 1 + Y Y m B Y By unifying all RH fields we sit in the alignment limit of 5DMFV

41 A flavor protection We can then assume that all the breaking of G F comes from one spurion such that Y (3, 3) and c L M L R 1 + YY m S Y c R M R R 1 + Y Y m B Y By unifying all RH fields we sit in the alignment limit of 5DMFV Then, all the flavor mixing comes via the Majorana masses!

42 Conclusions R K and R K provide very clean probes of higher energies Both R K and R K anomalies can be succesfuly addresed with NP in the RH electron sector This can happen naturally in CHMs with a minimal type-iii seesaw In this setup, the absence of top partners can be translated into LFU! Observed values in other observables like B s µ + µ, M Bs or P 5 can be reproduced Therefore, R K < 1 and R K < 1 could be the first probe of the dynamics of EWSB

43 Thanks!

44 Back-up Slides

45 B Kl + l The individual branching fractions are given by db(b Kl + l ) dq 2 = G2 F α2 V tb V ts 2 (4π) 5 m 3 ([m 2 B K ]2 2m 2 B+K q2 +q 4 ) 3 2 ( FV 2 + F A 2 ) B where F V (q 2 ) =(C bsr l R +C bsl l L +C bsr l L +C bsl l R )/2 f + (q 2 ) + 2m b m B + m K (C 7 + C 7)f T (q 2 ) + h K (q 2 ) F A (q 2 ) =(C bsr l R C bsl l L C bsr l L +C bsl l R )/2 f + (q 2 ) m 2 A±B m2 A ± m2 B, and we neglected lepton masses, CP violation, and higher order corrections

46 B 0 K l + l db(b 0 K l + l ) dq 2 τ B 0 G 2 F α2 V tb V ts 2 3 (4π) 5 m 3 ([m 2 B K ]2 2m 2 B+K q2 +q 4 ) 1 2 q 2 B ( A ll 2 + A L 2 + A L L R) A ll,r A ll,r = + 2m B (1 q 2 /m 2 B) [ C bsl l L,R + C bsr l L,R ] ξ = 2m B (1 q 2 /m 2 B) [ C bsl l L,R C bsr l L,R ] ξ A ll,r 0 = m3 B (1 q2 /m 2 B )2 2 q m K Defining the integrated form factors [ CbsL l L,R C bs R l L,R ] ξ q 2 g [q2 min,q2 max ] max,,0 = dq 2 ([m 2 q 2 B K ]2 2m 2 B+K q2 +q 4 ) 1 2 2(q3 m 2 B q)2 m 2 B min { ξ 2, ξ 2, (m2 B q2 ) 2 ξ 8q 2 m 2 2 g 0 + g }, p K g 0 + g + g

47 B s B s mixing 1.4 Ms/( Ms)SM R K q 2 [1,6]GeV 2

48 Talking to Fermions A priori, we have two different ways of introducing the mixing with the elementary fermions: 1 Quadratically, à la Technicolor λ Λ γ q Lt R O(x), [O(x)] = 1 + γ = m q f 4π N ( µ Λ) γ, γ > 0 2 Linearly, via partial compositeness [Kaplan '91] λ L Λ γ L q L O L (x), λ R Λ γ R m q v t R O R (x), [O L,R (x)] = 5/2+γ L,R, γ L,R > 1 N 4π ( µ Λ ) γl +γ R or m q v 4π N γl γ R Very well mimicked by Randal-Sundrum models!

49 AdS/CFT correspondence Models with warped extra dimensions are weakly duals to strongly coupled 4D theories [Maldacena '98] They provide a calculable framework for composite Higgs models UV brane IR brane The 5D realizations of models where the Higgs is a pngb are models of gauge-higgs unification (GHU), πâ(x) Aâ5 (x)

50 AdS/CFT correspondence We can explain the huge hierarchy existing between the different fermion masses (m u,d ) ij v 2 Y f q i fu,d j We also obtain naturally the hierarchical mixing observed in the quark sector U u,d f q i /fq j U u,d f u,d i /f u,d j i j ij ij L R

51 Composite RH neutrinos When the operator λ R Λ γ R Ψ R O R is relevant, i.e., γ R < 0, a very large kinetic term is induced λ 2 R Λ 2γ d 4 p d 4 q Ψ R ( p) O R (p)ōr( q) Ψ R (q) R ( µ λ 2 2γR R d Λ) 4 x Ψ R (x)i Ψ R (x) Canonically normalizing Ψ R requires Ψ R 1 ( µ ) γr ΨR λ R Λ and leads to M Σ M Σ λ 2 R (µ/λ) 2γ R and M D vλ l ( µ Λ ) γl

52 EWPD For elementary fermions and a composite Higgs, ˆT [ˆα 2 ˆβ + ˆγ], Ŝ [ ˆβ + ˆγ], W = Y ˆγ where ˆα and L, 1/ L, ˆβ L g /g el. Thus, ˆγ ˆT L, Ŝ 1, W = Y 1/L ˆT Ŝ W, Y We can make ˆT and δz l R l R small enough thanks to our custodial setup [Agashe,Delgado,May,Sundrum, '03] [Agashe,Contino,Da Rold,Pomarol, '06]