Possible implications ofb anomalies

Possible implications ofb anomalies Jim Cline, NBI & McGill University NBIA Current Themes Workshop, 21 Aug. 2017 J.Cline, McGill U. p. 1

Anomaly: B K ( ) µ + µ versusee R X = B( B Xµ + µ ) B( B Xe + e ), a hadronically clean observable Experimental and predicted values for R K and R K : - R(K) R(K ) (low 2 ) R(K ) (high 2 ) SM 1 0.92 1 HCb 0.745±0.09±0.036 0.660 0.070 +0.110 ±0.024 0.685+0.113 0.069 ±0.047 Correlated anomalies also seen in dirty observables, and B(B K µ + µ ), angular distribution P 5 B(B s φµ + µ ) J.Cline, McGill U. p. 2

HCb onr K, B s φµµ, B s µµ BR(B s µµ) HCb BR(B s µµ) SM = (3.0±0.6) 10 9 (3.65±0.23) 10 9 = 0.82±0.20 J.Cline, McGill U. p. 3

Model-independent fit The single effective operator (D Amico et al.,1704.05438) O b µ = 1 Λ 2( s γ α b )( µ γ α µ ) gives a good fit to the data, with Λ = 36TeV. Should be = 0.15 (SM contribution). 4σ significance O b µ looks like Z exchange, but Fierz rearrangement O b µ 1 Λ 2( s γ α µ )( µ γ α s ) looks like vector leptouark exchange. Of course, SM contribution comes at one loop b µ W W µ s Can improve fit somewhat by also including Ob e J.Cline, McGill U. p. 4

Popular models: Z or leptouark s µ µ + s b Ζ µ + b Q µ or via new physics in loop s µ b µ + In this talk I present examples of each kind. All three models happen to predict new physics at the TeV scale (not my goal), accessible to HC! J.Cline, McGill U. p. 5

Guiding principle A theory of B decay anomalies should explain more than just B decay anomalies Z model: spontaneously broken flavor symmetry is origin of the Z ; we explain origin of fermion masses. JC & J. Martin Camalich, 1706.08510 oop model: one of the particles in the loop is dark matter. eptouark model: the Q is a composite meson from strong dynamics at the TeV scale. Dark matter is a composite baryon. JC & J.Cornell, 1709.xxxxx J.Cline, McGill U. p. 6

Z model: bottom-up construction Want to connect the anomalies to the origin of flavor. Spontaneously broken gauged horizontal (flavor) symmetry could give SM Yukawa couplings, and Z s. Chiral couplings ( s γ α b )( µ γ α µ ) motivate the chiral flavor symmetry SU(3) SU(3) R with SU(3) acting on left-handed fermions, and SU(3) R acting on right-handed fermions It contains 16 Z s! We need only one to explain R K ( ) Expect SU(3) SU(3) R SU(3) at scale of right-handed neutrino masses ( 10 10 GeV?) Flavor constraints imply SU(3) U(1) Z at 10 4 TeV. J.Cline, McGill U. p. 7

SU(3) SU(3) R theory of flavor SU(3) SU(3) R symmetry forbids the usual Yukawa couplings Qi Hu R,i, Qi Hd R,i, i Hν R,i, i He R,i We introduce new heavy fermions, U,R, N,R, N,R, E,R, and scalars M, Φ u, Φ d, Φ ν, Φ l to induce them, _ M (3,3) giving u R (1,3) U R U (3,1) (1,3) Φ u (1,8) H (1,1) Q (3,1) yuk = 1 Λ u Q H Φu u R + 1 Λ d Q H Φ d d R + 1 Λ l H Φ l l R + 1 Λ ν H Φν ν R J.Cline, McGill U. p. 8

WhichZ? Only one of the 8 possible Z s is phenomenologically acceptable, Z 8, coupling to SU(3) generator T 8 : T 8 = 1 2 3 1 0 0 0 1 0 0 0 2 Other choices have too large K- K mixing. I.e., T 3 = 1 2 diag(1, 1,0) contributes to K- K with only Cabibbo angle suppression, if fermion masses are minimally flavor violating... J.Cline, McGill U. p. 9

Quark Currents Diagonalizing mass matrices as usual, via f V f f, f R V R f f R the left-handed Z currents become g f (V f T8 V f )γµ f Assume Vu = 1, then Vd = V CKM V. The up-type uark current remains diagonal, T 8, while the down-type gets CKM-induced mixing (example of minimal flavor violation, MFV): 3 2 g ( V tb V ts( s γ µ b )+ V tb V td ( d γ µ b )+V ts V td ( d γ µ s ) We want the first term for R K ( ), while the other two come without a choice, all with SM-like CKM structure The last term affects K- K mixing, just within limits. Any other generator (e.g., T 3 ) would make it too large! J.Cline, McGill U. p. 10 )

epton Currents Without Vl rotation, T 8 has the wrong structure: predicts R K ( ) = 1, with B Kτ + τ having the anomaly. Instead we need V l T8 V l = 1 2 3 1 0 0 0 2 0 0 0 1 i.e., Vl must be close to a permutation. If Vl R = Vl, it means that lepton masses were in the wrong order in original basis: m µ 0 0 m l = 0 m τ 0 0 0 m e This may seem weird, but nothing forbids it! J.Cline, McGill U. p. 11

Fitting R K ( ) (plusb s µ + µ ) Uniuely: we predict not only deficit in B K ( ) µ + µ, but a (2 smaller) excess in B K ( ) e + e. Unavoidable, due to tracelessness of SU(3) generators. Defining H eff = V tb Vts α em 4πv 2 C bl ( s γ µ b )( l γ µ l ) l=e,µ we get best fit (with C be = 1 2 C bµ) at Implies C bµ = 0.93, C be = +0.46, m Z g = 5.3 +0.8 0.6 TeV B s µ + µ agrees well in our fit J.Cline, McGill U. p. 12

Constraints / Predictions The model predicts several signals, some close to experimental limits: 11% excesses in B K ( ) e + e, K ( ) τ + τ but no deviation in B K ( ) ν ν (interference vanishes) Similar excesses/deficits for B π 0 l + l, ρ 0 l + l Resonant production of Z decaying to l + l at HC, and vectorlike uarks at a few TeV New contributions to K- K and B- B mixing Deviations in Z ll, CKM unitarity Possible lepton flavor violation, µ 3e, τ 3l J.Cline, McGill U. p. 13

Resonant dileptons Z ll is constrained by ATAS search (ATAS-CONF-2017-027) Our Z has unsuppressed couplings to light uarks = large production cross section. 10 0 σb (pb) 10-1 10-2 10-3 10-4 we adjust limit to compensate for smaller branching ratio into ee in our model 10-5 0 1000 2000 3000 4000 5000 M Z (GeV) Reuires m Z > 4.3TeV, hence g > 0.7 J.Cline, McGill U. p. 14

Meson-antimeson mixing We predict new physics contribution to K- K, B d - B d, B s - B s mixing, C NP K ( s γ µ d ) 2 Ζ New contributions still compatible with current limits d s d s prediction experiment ε K C εk = Im K0 H w K 0 Im K 0 H SM w K 0 B d B s C B = B H w B B Hw SM B 0.9 0.95 1 1.05 1.1 1.15 C M J.Cline, McGill U. p. 15

HC observables We already expect m Z few TeV, in reach of HC? What about heavy fermions? yuk λ uūmu R +λ D d MD R +λ l Since M gives mass to Z, Ē ME R +λ ν N MN R m Z g heavy fermion masses are = M = 5.3TeV (1) M f = λ f M = λ f 5.3TeV also in reach of HC. These are heavy vector-like uarks and leptons F, decaying to SM fermion f plus Higgs, F F or g FH, F fh J.Cline, McGill U. p. 16

Part 2: B anomalies and dark matter A simple way to get B anomaly from a loop diagram: introduce new fermions ψ, S and scalar doublet φ Q φ S ψ φ* Q = λ f Q f,a φ a Ψ+λ f Sφ a a f f = flavor index, a = SU(2) index Couples only to H SM fermions; induces desired operator = λ 2 λ 3 λ 2 2 96π 2 M 2( s γ µ b )( µ γ µ µ ) f 1 (m S /M) where M m φ m Ψ m S. S can be neutral under SM: dark matter candidate J.Cline, McGill U. p. 17

Challenge: flavor constraints New contributions to meson mixing and flavor violating decays, Q Q φ ψ ψ φ* Q Q φ* S S φ K K, B B, B s B s µ 3e, τ l i l j l k γ φ µ e S φ b ψ µ eγ b sγ γ s In particular, b sµ + µ and B s - B s mixing both depend on λ 2,3 : λ 2 λ 3 λ 2 2 M 2 = = λ 2 > 1.3 ( ) 1 2 λ 2 λ3, 1.0 TeV M 1 1.7 TeV ( ) M 1/2 need largish coupling, M TeV TeV J.Cline, McGill U. p. 18

A (barely) working model With M = 2TeV and couplings to d i and µ, λ 1 = 0.06, λ2 = 0.7, λ3 = 2.0, λ 2 = 2.0 we saturate constraints on B and D meson mixing; couplings to u i are λ i = V CKM,ij λ j : λ 1,2,3 = 0.09, 0.65, 2.0 epton flavor violation: µ 3e implies λ 1 < 0.3, and µ eγ = λ 1 < 0.008 (Analogous b sγ amplitude is 4 times smaller than upper limit) Flavor constraints sueeze us into small (but not absurd) region of parameter space J.Cline, McGill U. p. 19

Dark matter constraints S S φ µ + µ,ν µ,ν µ Dark matter relic density can be realized through S S µ + µ +ν µ ν µ annihilation in early universe. σv rel = λ 2 4 m 2 S 8π(m 2 φ +m2 S )2 Gives correct relic density if m S = 360GeV Dark matter gets a magnetic moment µ S = 3 λ 2 2 em S 32π 2 m 2 φ γ φ from S µ S Constrained by direct detection J.Cline, McGill U. p. 20

Direct detection Constraint from magnetic moment interaction with protons: log 10 g M -1.5-2 -2.5-3 XENON100 (Banks et al.) UX (2016) PandaX-II (2016) UX (2017) -3.5 predicted imiting mass m S > 360 GeV -4 1.4 1.6 1.8 2 2.2 2.4 2.6 log 10 (m DM / GeV) imit is marginally satisfied for chosen parameters: must make λ 2, λ 3 and m φ even bigger to relax the tension. J.Cline, McGill U. p. 21

HC constraints Production of new φ, Ψ particles necessarily gives dark matter (missing energy) _ γ, Z,W φ φ* looks like sleptons! g g ψ ψ _ φ _ S_ S _ S _ S _ g _ g φ* ψ ψ ψ _ φ φ _ S _ S_ S _ S _ ATAS slepton search is insensitive in our region m φ = 2.4TeV, m S = 360GeV J.Cline, McGill U. p. 22

HC constraints Ψ bµ + S resembles stop decay t bw bµ + ν µ, _ g S _ S γ, Z,W φ _ φ* S _ φ S φ* _ ψ g _ ψ b S ψ b S _ S _ ψ _ φ µ ψ _ φ S _ µ g _ g b µ b µ looks like stop pairs ATAS search must be reinterpreted to get limits... J.Cline, McGill U. p. 23

A model with strong dynamics A simple but profound elaboration: et φ, S and Ψ be charged under a confining SU(N) HC hypercolor interaction with scale Λ HC : λ f Qf,a φ a A ΨA +λ f SA φ A a a f Integrate out φ and Fierz transform: λ f λ g m 2 ( Q f Ψ)( S g ) = φ +Λ2 HC λ f λ g 2(m 2 φ +Λ2 HC )( Q f γ µ g )( S A γ µ Ψ A ) ( Sγ µ Ψ) is interpolating field for a composite vector leptouark! Now we get new physics from tree-level exchange of composite particles, avoiding loop suppression factor. J.Cline, McGill U. p. 24

Global constraints Direct detection dominates over ATAS and indirect detection J.Cline, McGill U. p. 25

Tree-level anomalous decays The box diagrams of previous model become tree-level exchange of different kinds vector meson bound states Q S ψ The effective interaction is, e.g., Q S Q ψ Q S Q ψ Q g S Φ ψ µ Q f λ f λ g m Φ f Φ m 2 φ +Λ2 HC f Φ Λ HC is the vector leptouark decay constant ( Q f γ µ g )Φ µ Tree diagram has same structure as box diagram, with replacement 1 96π 2 f 2 X m2 φ 4(m 2 φ +Λ2 HC )2 1 16 if m φ Λ HC Couplings can be smaller by factor 3. J.Cline, McGill U. p. 26

A robust working model We fit B decay anomaly with m φ Λ HC 1TeV and λ 1 = 0.011, λ 2 = 0.14, λ 3 = 0.39, λ 2 = 0.55 Meson mixing amplitudes are factor of 2 below experimental limits. epton flavor constraints give µ eγ = λ 1 < 0.008, τ 3µ = λ 3 < 0.22 Couplings smaller, upper limits no longer saturated There are also composite vectorlike heavy fermions F = Ψφ = uark partner, F l = Sφ = lepton partner that mix with SM Q and doublets J.Cline, McGill U. p. 27

Composite dark matter Dark matter is the baryonic bound state Σ = S N HC, previously studied JC, Huang, Moore 1607.07865; Mitridate et al., 1707.05830 Before confinement phase transition, S S GG (G =hypergluon), depleting relic density Thermal relic density too small by factor 100: need dark matter asymmetry S magnetic moment µ S from loop as before. If N HC odd, µ Σ N HC µ S, while m Σ N HC Λ HC (uark model). Direct detection constraint weakened: m S < 500GeV if N HC = 3, m φ = m Σ = TeV J.Cline, McGill U. p. 28

HC constraints Dominant signal is resonant production of bound state vector and pseudoscalar mesons or uark partner _ γ, Z,W φ γ, Z,W φ* _ g φ* ψ g _ g ψ ψ _ g Constrained by HC searches for dijets, diphotons E.g., V = Ψ Ψ bound state is like uarkonium, _ g g ψ ψ _ g (γ) g (γ) σ( V) = 132π2 αs ψ(0) 2 2 9m 3 V with ψ(0) 2 m V Λ 2 HC, and δ(s m 2 B) σ(pp V) = 132π2 α 2 sλ 2 HC 9sm 2 V parton = 9fb ATAS limit J.Cline, McGill U. p. 29

Dijet and diphoton limits Dijet limit allows m V 3TeV for vector meson Pseudoscalar P production cross section is σ(pp P) = π2 Γ(P gg) 8sm P parton = 0.02pb for mp = 1TeV and B(P γγ) = 0.006, so σb = 0.1 fb, < diphoton limit J.Cline, McGill U. p. 30

Conclusions B decay anomalies seem the best current hope of new physics If true, we may hope that the underlying theory explains more than just the R ( ) K observations Our examples hint that new heavy states may be soon discovered at HC: resonant Z in dileptons vectorlike uark or lepton partners composite resonances in dijets...? J.Cline, McGill U. p. 31