Possible implications ofb anomalies

Transcription

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

2 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 HCb 0.745±0.09± ± ±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

3 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

4 Model-independent fit The single effective operator (D Amico et al., ) 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

5 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

6 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, 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

7 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 ( GeV?) Flavor constraints imply SU(3) U(1) Z at 10 4 TeV. J.Cline, McGill U. p. 7

8 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

9 WhichZ? Only one of the 8 possible Z s is phenomenologically acceptable, Z 8, coupling to SU(3) generator T 8 : T 8 = 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

10 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 )

11 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 = 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 m e This may seem weird, but nothing forbids it! J.Cline, McGill U. p. 11

12 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 = TeV B s µ + µ agrees well in our fit J.Cline, McGill U. p. 12

13 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

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

15 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 C M J.Cline, McGill U. p. 15

16 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

17 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 π 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

18 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 TeV ( ) M 1/2 need largish coupling, M TeV TeV J.Cline, McGill U. p. 18

19 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 < (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

20 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

21 Direct detection Constraint from magnetic moment interaction with protons: log 10 g M XENON100 (Banks et al.) UX (2016) PandaX-II (2016) UX (2017) -3.5 predicted imiting mass m S > 360 GeV 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

22 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

23 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

24 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

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

26 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 ) if m φ Λ HC Couplings can be smaller by factor 3. J.Cline, McGill U. p. 26

27 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

28 Composite dark matter Dark matter is the baryonic bound state Σ = S N HC, previously studied JC, Huang, Moore ; Mitridate et al., 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

29 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

30 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

31 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