Z Explanations of Neutral Current B Anomalies by Ben Allanach - PowerPoint PPT Presentation

Z ′ Explanations of Neutral Current B Anomalies by Ben Allanach (University of Cambridge) • Can we directly discover particles from explanations? • Third Family Hypercharge Model • General SM × U (1) model BCA, Gripaios, You, arXiv:1710.06363 ; BCA, Davighi, arXiv:1809.01158 ; BCA, Corbett, Dolan, You, arXiv:1810.02166 Ben Allanach (University of Cambridge) 1

Ben Allanach (University of Cambridge) 2

Ben Allanach (University of Cambridge) 3

Ben Allanach (University of Cambridge) 4

LHC Upgrades High Luminosity (HL) LHC: go to 3000 fb − 1 (3 ab − 1 ). High Energy (HE) LHC: Put FCC magnets (16 Tesla rather than 8.33 Tesla) into LHC ring: roughly twice collision energy: 27 TeV. 5

R K ( ∗ ) Measurements LHCb results from 7 and 8 TeV: q 2 = m 2 ll . q 2 /GeV 2 LHCb 3 fb − 1 SM σ 0 . 745 +0 . 090 R K [1 , 6] 1 . 00 ± 0 . 01 2.6 − 0 . 074 0 . 66 +0 . 11 R K ∗ [0 . 045 , 1 . 1] 0 . 91 ± 0 . 03 2.2 − 0 . 07 0 . 69 +0 . 11 R K ∗ [1 . 1 , 6] 1 . 00 ± 0 . 01 2.5 − 0 . 07 2 . 0 R K ∗ 0 R K ∗ 0 1 . 0 1 . 5 0 . 8 0 . 6 1 . 0 LHCb BIP 0 . 4 CDHMV 0 . 5 LHCb EOS 0 . 2 BaBar flav.io LHCb LHCb JC Belle 0 . 0 0 . 0 0 1 2 3 4 5 6 0 5 10 15 20 q 2 [GeV 2 /c 4 ] q 2 [GeV 2 /c 4 ] Ben Allanach (University of Cambridge) 6

c l Wilson Coefficients ¯ ij In SM, can form an EFT since m B ≪ M W : sγ µ P i b )(¯ O l ij = (¯ lγ µ P j l ) . c l ij � � � O l L eff ⊃ ij , Λ 2 l,ij l = e,µ,τ i = L,R j = L,R α � V tb V ∗ c l LL O l c l LR O l � = ¯ LL + ¯ ts LR 4 πv 2 l = e,µ,τ c l RL O l c l RR O l � +¯ RL + ¯ RR c l ij = (36 TeV / Λ) 2 c l ⇒ ¯ ij . c l ij ∼ ±O (1) all predicted by weak interactions in SM. Ben Allanach (University of Cambridge) 7

Which Ones Work? Options for a single BSM operator : c e • ¯ ij operators fine for R K ( ∗ ) but are disfavoured by global fits including other observables. c µ • ¯ LR disfavoured: predicts enhancement in both R K and R K ∗ c µ c µ RL disfavoured: they pull R K and R K ∗ in opposite • ¯ RR , ¯ directions . c µ LL = − 1 . 33 ± 0 . 34 fits well globally 1 . • ¯ 1 D’Amico et al, 1704.05438 . 8

Statistics 2 c µ � χ 2 SM − χ 2 ¯ LL best clean − 1 . 33 ± 0 . 34 4.1 dirty − 1 . 33 ± 0 . 32 4.6 all − 1 . 33 ± 0 . 23 6.2 C µ c µ c µ � χ 2 SM − χ 2 9 = (¯ LL + ¯ LR ) / 2 best clean − 1 . 51 ± 0 . 46 3.9 dirty − 1 . 15 ± 0 . 17 5.5 all − 1 . 19 ± 0 . 15 6.7 Table 1: A fit to flavour anomalies for ‘clean’ ( R K , R K ∗ , B s → µµ ) and ‘dirty’ (100 others) observables 2 D’Amico, Nardecchia, Panci, Sannino, Strumia, Torre, Urbano 1704.05438 Ben Allanach (University of Cambridge) 9

Ben Allanach (University of Cambridge) 10

Simplified Models for c µ LL At tree-level, we have: At loop-level, there are many more possibilities but the particles are 4 π lighter: they are much easier to detect. Principle of Maximal Pessimism Ben Allanach (University of Cambridge) 11

B s − ¯ B s Mixing s s ¯ Z ′ ¯ b b M Z ′ < g sb ¯ ∼ 148 TeV . L Ben Allanach (University of Cambridge) 12

R D ( ∗ ) = BR ( B − → D ( ∗ ) τν ) /BR ( B − → D ( ∗ ) µν ) Ben Allanach (University of Cambridge) 13

R D ( ∗ ) : BSM Explanation . . . has to compete with L eff = − 2 c L γ µ b L ) (¯ Λ 2 (¯ τ L γ µ ν τL ) + H.c. Λ = 3 . 4 TeV A factor 10 lower than required for R K ( ∗ ) ⇒ different explanation? PAMP ⇒ we ignore R D ( ∗ ) . Ben Allanach (University of Cambridge) 14

Z ′ µµ ATLAS 13 TeV 36 fb − 1 ATLAS analysis: look for two track-based isolated µ , p T > 30 GeV. One reconstructed primary vertex. Keep only highest scalar sum p T pair 3 . µ 1 µ 2 = ( p µ 1 + p µ m 2 � � 2 ) p 1 µ + p 2 µ CMS also have released 4 a similar 36 fb − 1 analysis. 3 1707.02424 4 1803.06292 Ben Allanach (University of Cambridge) 15

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High m µµ = 2 . 4 TeV Event 17

ATLAS µµ limits Ben Allanach (University of Cambridge) 18 1607.03669

Simplified Z ′ Models 5 ıve model: only include couplings to ¯ s and µ + µ − Na¨ bs / b ¯ ( less model dependent ). + g µµ L min. g sb L Z ′ sγ ρ P L b + h.c. L Z ′ µγ ρ P L µ , � � ⊃ ρ ¯ ρ ¯ Z ′ which contributes to the O µ LL coefficient with L g µµ 4 πv 2 g sb c µ L ¯ LL = − , α EM V tb V ∗ M 2 ts Z ′ � 2 � 36 TeV L g µµ ⇒ g sb = − 1 . 33 ± 0 . 34 (clean) . L M Z ′ 5 BCA, Queiroz, Strumia, Sun arXiv:1511.07447 Ben Allanach (University of Cambridge) 19

Simplified Z ′ Models 6 � � L i λ ( Q ) L i λ ( L ) ij γ ρ Q ′ ij γ ρ L ′ Z ′ Q ′ L j + L ′ L Z ′ f = ρ , L j L V d L and PMNS U = V † After CKM mixing of V = V u † ν L V e L , � u L V Λ ( Q ) V † γ ρ u L + d L Λ ( Q ) γ ρ d L + L = � n L U Λ ( L ) U † γ ρ n L + e L Λ ( L ) γ ρ e L Z ′ ρ , where Λ ( Q ) ≡ V † Λ ( L ) ≡ V † d L λ ( Q ) V d L , e L λ ( L ) V e L . 6 BCA, Corbett, Dolan, You, arXiv:1810.02166 Ben Allanach (University of Cambridge) 20

Limiting Cases Mixed Up Model: all quark mixing is in left-handed ups     0 0 0 0 0 0 Λ ( Q ) = g bs Λ ( L ) = g µµ 0 0 1  , 0 1 0  ,       0 1 0 0 0 0 Mixed Down Model: all quark mixing is in left-handed downs     0 0 0 0 0 0 Λ ( Q ) = g tt V † · Λ ( L ) = g µµ 0 0 0  · V, 0 1 0  ,       0 0 1 0 0 0 Ben Allanach (University of Cambridge) 21

⇒ g bs = V ∗ ts V tb g tt = 0 . 04 g tt : the quark couplings are weaker than the leptonic ones Ben Allanach (University of Cambridge) 22

Widths: pick g bs to fit anomalies at each point. Ben Allanach (University of Cambridge) 23

Ben Allanach (University of Cambridge) 24

Ben Allanach (University of Cambridge) 25

Ben Allanach (University of Cambridge) 26

During the 1990s We wanted to be the Grand Architects, searching for the string model to rule them all 27

During the 2010s We are happy with any beyond the Standard Model roof 28

Third Family Hypercharge Model Add complex SM singlet scalar θ and gauged U (1) F : SU (3) × SU (2) L × U (1) Y × U (1) F � θ � ∼ Several TeV SU (3) × SU (2) L × U (1) Y � H � ∼ 246 GeV SU (3) × U (1) em • SM fermion content • anomaly cancellation • 0 F charges for first two generations 29

Unique Solution F Q ′ i = 0 F u R ′ i = 0 F d R ′ i = 0 F L ′ i = 0 F e R ′ i = 0 F H = − 1 / 2 F Q ′ 3 = 1 / 6 F u ′ R 3 = 2 / 3 F d ′ R 3 = − 1 / 3 F L ′ 3 = − 1 / 2 F e ′ R 3 = − 1 F θ � = 0 ′ L Ht ′ 3 L H c b ′ L H c τ ′ ′ R + Y b Q ′ L = Y t Q 3 R + Y τ L 3 R + H.c., • First two families massless at renormalisable level • Their masses and fermion mixings generated by small non-renormalisable operators This explains the hierarchical heaviness of the third family and small CKM angles 30

Z − X mixing Because F H = − 1 / 2 , Z − X mix:   g ′ 2 − gg ′ g ′ g F − B µ N = v 2 M 2 − gg ′ g 2 − W 3 − gg F   µ 4   g ′ g F − gg F g 2 F (1 + 4 F 2 θ r 2 ) − X µ • v ≈ 246 GeV is SM Higgs VEV • g F = U (1) F gauge coupling • r ≡ v F /v ≫ 1 , where v F = � θ � • F θ is F charge of θ field 31

Z − X mixing angle � 2 � M Z g F sin α z ≈ ≪ 1 . g 2 + g ′ 2 M ′ � Z This gives small non-flavour universal couplings to the Z boson propotional to g F and: − sin θ w B µ + cos θ w W 3 � � Z µ = cos α z + sin α z X µ , µ 32

� 1 6 u L Λ ( u L ) γ ρ u L + 1 6 d L Λ ( d L ) γ ρ d L − L Xψ = g F 1 2 n L Λ ( n L ) γ ρ n L − 1 2 e L Λ ( e L ) γ ρ e L + 2 3 u R Λ ( u R ) γ ρ u R − � 1 3 d R Λ ( d R ) γ ρ d R − e R Λ ( e R ) γ ρ e R Z ′ ρ ,   0 0 0 V † Λ ( I ) ≡ I ξV I , ξ = 0 0 0     0 0 1 Z ′ couplings , I ∈ { u L , d L , e L , ν L , u R , d R , e R } 33

Example Case Take a simple limiting case: V u L = 1 ⇒ V d L = V , the CKM matrix. V u R = V d R = V e R = 1 for simplicity and the ease of passing bounds.     1 0 0 1 0 0 V d L = 0 cos θ sb − sin θ sb  , V e L = 0 U µ 2 U µ 3        0 sin θ sb cos θ sb 0 U τ 2 U τ 3 V e R = 1 ⇒ V ν L = V e L U † , where U is the PMNS matrix. 34

Important Z ′ Couplings      0 0 0 d L  1 sin 2 θ sb ′ 1  / g F 0 2 sin 2 θ sb Z s L  + 6 d L        cos 2 θ sb 1 0 2 sin 2 θ sb b L      0 0 0 e L − 1 ′ | U τ 2 | 2 U ∗  / 0 τ 2 U τ 3 Z µ L 2 e L          0 U τ 2 U ∗ | U τ 3 | 2 τ L τ 3 | U τ 2 | ≈ 0 . 6 , | U τ 3 | ≈ 0 . 7 . Put | sin θ sb | = | V ts | = 0 . 04 , so g µµ ≫ g bs , which helps us survive B s − B s constraint 35

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12 Allanach and Davighi, 2018 10 B s -B s bar 8 R K (*) LEP LFU g F 6 4 2 R K (*) 0 0 2 4 6 8 10 M Z' /T eV Ben Allanach (University of Cambridge) 37