B decay anomalies and dark matter from strong dynamics

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1 B decay anomalies and dark matter from stron dynamics Jim Cline, McGill University attice for BM Physics 2018, CU Boulder, 6 April, 2018 J.Cline, McGill U. p. 1

2 tron dynamics beyond the M U(3) c exists in nature; why not an additional U(N) hc (hypercolor) at a hiher scale? Need not be composite His (technicolor), could be unconnected to electroweak symmetry breakin Has proven useful for explainin past anomalies... p p χ χ χ G γ, γ, Z Z γ γ resonant 750 GeV diphotons at HC Crai, Draper, Kilic, Thomas many others annihilation of partially composite DM to photons (Fermi 130 GeV anomaly) JC, Frey, Moore J.Cline, McGill U. p. 2

3 tron dynamics beyond the M And dark matter model-buildin in a hidden sector: lueballs Forestell, Morrissey, iurdson, ; ony, Zhan, , , + Xiao ; Acharya, Fairbairn, Hardy ; Halverson, Nelson, Ruehle, mesons ewis, Pica, annino ; + Hietanen Hietanen, Pica, annino, onderaard , JC, iu, Moore, baryons attice tron Dynamics (D) Collaboration, , Antipin, Redi, trumia, Viiani, Huo, Matsumoto, Tsai, Yanaida, Fodor, Holland, Kuti, Mondal, Noradi, Won JC, Huan, Moore ; Mitridate, Redi, mirnov, trumia Partly motivated by cosmoloical hints of stron DM self-interactions, natural in composite models J.Cline, McGill U. p. 3

4 New anomaly: B K ( ) µ + µ vs.ee 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 ) (hih 2 ) M HCb 0.745±0.09± ± ±0.047 Correlated anomalies also seen in dirty observables, and B(B K µ + µ ), anular distribution P 5 B(B s φµ + µ ) J.Cline, McGill U. p. 4

5 HCb onr K, B s φµµ, B s µµ BR(B s µµ) HCb BR(B s µµ) M = (3.0±0.6) 10 9 (3.65±0.23) 10 9 = 0.82±0.20 J.Cline, McGill U. p. 5

6 Model-independent fit The sinle effective operator (D Amico et al., ) O b µ = 1 Λ 2( s γ α b )( µ γ α µ ) ives a ood fit to the data, with Λ = 36TeV. hould be = 0.15 (M contribution). 4σ sinificance O b µ looks like Z exchane, but Fierz rearranement O b µ 1 Λ 2( s γ α µ )( µ γ α s ) shows that vector leptouark exchane also works. M contribution comes at one loop; sensitive probe of new physics b µ W W µ s J.Cline, McGill U. p. 6

7 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 a model with composite leptouark and dark matter, and new stron dynamics at the TeV scale based on arxiv: [Phys. Rev. D 97, (2018)] J.Cline, McGill U. p. 7

8 A simple model with stron dynamics New particles: vectorlike uark partner Ψ, RH neutrino partner, inert His doublet φ, chared under U(N) HC and accidental Z 2 : U(3) U(2) U(1) y U(1) em U(N) HC Z 2 Ψ 3 1 2/3 2/3 N N 1 dark matter! φ 1 2 1/2 (0, 1) N 1 Couplins to M left-handed uarks and leptons: ( = λ f Qf,a φ a AΨ A +λ f A φ A α α f α = U(2), A = hypercolor ) Ψ bound state is composite leptouark, pseudoscalar Π or vector Φ µ, G φ Q 0 ( γ µ γ 5 Ψ) Π = f Π p µ Π, 0 ( γ µ Ψ) Φ λ = f Φ m Φ ǫ µ λ Pseudoscalar couplins to uarks and leptons are suppressed by m or m l, only vector can couple more stronly. J.Cline, McGill U. p. 8

9 Composite-induced anomalous decays Besides leptouark, we et other composite vectors mediatin flavor-chanin neutral currents Q The effective interaction is, e.., Q Q Q Q Q b Q a ρ µ = ( ) 1/2 NHC λa λ b (m +m Ψ )(0) 4m ρ (m 2 φ +m ( Q a γ µ b )ρ µ m Ψ ) }{{} ab ρ where m Ψ m and = wave function of bound state To fit B-decay anomaly, need ρ 22 ρ 32 m 2 ρ = TeV 2 J.Cline, McGill U. p. 9

10 eptouark couplin to andq Effective couplin ρ ab can be inferred from decay rate of bound state ρ µ b Qa (Kan, uty ) Γ(ρ µ b Qa ) = σv rel ( Ψ b Qa ) (0) 2 = ab ρ 2 24π m ρ To compute bound state mass m ρ and wave function at oriin Ψ(0), need model of confinement. We take nonrelativistic 1/r +r (Cornell) potential V c = α ( HC(µ ) N HC 1 ) +2(N HC 1)Λ 2 2r N HCr HC and hydroen-like ansatz e µ r/2. Minimize enery, find µ and bindin enery E b in terms of Λ HC and constituent mass M. Wave function at oriin = (0) = µ 3/2 / 8π. Bound state mass = m Φ = 2M +E b. Works well for J/Ψ and Υ (if luon vertex loop correction is included) J.Cline, McGill U. p. 10

11 Nonperturbative input All nonperturbative physics in effective couplin is in a dimensionless function of r M/Λ HC : (0) 2 /m 3 ρ ζ(r) (0) 2 / m R N=2 N=3 m 0 N=4 m m Ψ Maximized near M (2 3)Λ HC and m m Ψ r = M / Λ HC Then λ 2 2 λ 2 λ3 = 0.3 ( ) M 2 ( ) 3 TeV N HC to fit B decay anomalies J.Cline, McGill U. p. 11

12 A workin model We can fit B decay anomaly with and m = m φ = m = 2.5Λ HC = 1TeV λ 1 = 0.01, λ2 = 0.1, λ3 = 0.66, λ 2 = 2.1 There is no flavor protection mechanism, FCNCs are lare. Contributions to B 0 - B 0, B 0 s- B 0 s, D 0 - D 0 mixin amplitudes b d are close to experimental limits. d b b s s b c u u c J.Cline, McGill U. p. 12

13 Reducin the flavor tension We can adjust parameters somewhat: λ 2 2 λ 2 λ3 M 2 is fixed by B anomalies λ 2 i λ 2 j M 2 is constrained by FCNCs E.., lowerin M to 800GeV and all λ i by 0.8 with λ 2 fixed reduces meson mixin rates by factor = 0.4. Allowin λ 2 > 2.1 can further reduce FCNCs. J.Cline, McGill U. p. 13

14 epton flavor violation Nothin forces us to turn on couplins λ 1,3 to e,τ, e W x ν e but it looks strane to take λ 2 1 and λ 1,3 = 0. φ Radiative contributions from λ 2 are suppressed by neutrino masses, can be inored. If λ 1,3 0, products λ 1 λ 2, λ 3 λ 2 are constrained by rare decays µ 3e, τ 3l µ leadin to the limits e e e τ l l l λ 1 < 0.2, λ 3 < 0.9 J.Cline, McGill U. p. 14

15 FCNC Radiative decays Radiative transitions µ eγ, b sγ are induced by heavy composite fermions, F l = φ (lepton partner) & F = Ψφ (uark partner) They have mass-mixin with M uarks and leptons, λ f Qf,α φ α Ψ+λ f φ α α f (0) M ( λf Qf F +λ f Fl f ) And they have transition manetic moments with M uarks and leptons, (Guberina, Kühn, Peccei, Rückl 1980) F Q Q/ Q/2 + k, µ Q/2++k λ i Q k f i F Q Q k f Q/2 + Q/2+ Q/2+ k k, µ Mass diaonalization induces FCNC transition moments λ i i J.Cline, McGill U. p. 15

16 Transition manetic moments We find transition moments for the M fermions e f ( ) λ i ( ) λ j (0) 2 m j f 2M M 4 F ( f,iσ µν f R,j)F µν b sγ amplitude is factor of 30 below experimental limit µ eγ (τ µγ) limit implies λ 1 < (λ 3 < 0.6). More strinent than µ 3e Contribution to muon anomalous manetic moment a µ = ( 2) µ 2 = m2 µ λ 2 2 (0) 2 M M 4 F is too small to explain outstandin discrepancy J.Cline, McGill U. p. 16

17 Composite dark matter Vectorlike confinement enerically produces a stable relic the lihtest particle chared under U(N) HC In our model, dark matter is the baryonic bound state Σ = N HC Its stability is ensured by hyperbaryon conservation, analoous to baryons in M η -like meson can decay to µ µ,, γγ G φ G Ψ γ, γ, J.Cline, McGill U. p. 17

18 Dark matter mass The potential model for baryons is a little different; Coulomb attraction and strin tension between are smaller than for, V c V c N HC 1, σ σ (fit to QCD) 15 and must sum over all pairs. 6 5 Λ HC = 400 GeV N = 4 DM mass is m Σ (TeV) N = 3 N = 2 m Σ = N HC m +E b (1 6)TeV where E b = bindin enery m (TeV) J.Cline, McGill U. p. 18

19 Dark matter relic density Cosmoloy of baryonic bound states was studied in JC, Huan, Moore ; Mitridate et al., Before confinement phase transition, GG (G =hyperluon), depletin relic density Thermal relic density too small by factor 1000: need dark matter asymmetry We do not specify the mechanism for ettin an asymmetry (after all, oriin of baryon asymmetry is unknown) J.Cline, McGill U. p. 19

20 Direct detection ets a manetic moment µ at one loop: γ φ ( ) m f m φ µ = e λ 2 2 m 32π 2 m 2 φ µ If N HC odd, Σ has manetic moment and uark model predicts µ Σ = NHC µ. Σ scatters from protons. 0 lo 10 Σ -1-2 XENON100 limit (Banks et al.) composite Σ dark matter Direct detection constraint on yromanetic ratio (updated from Banks, Fortin, Thomas ) -3-4 PandaX-II lo 10 (m Σ / GeV) implies m 800GeV J.Cline, McGill U. p. 20

21 HC constraints Dominant sinal is resonant production of bound state vector and pseudoscalar mesons or uark partner γ, Z,W φ γ, Z,W φ* l l φ* Probed by HC searches for dijets, diphotons, dileptons E.., ρ Ψ = Ψ Ψ bound state is like uarkonium, (γ) (γ) σ( ρ Ψ ) = N HC 64π 3 α 2 s (0) 2 hence (recall ζ = (0) 2 /m 3 ρ Ψ ) 9m 3 ρ Ψ δ(s m 2 B) σ(pp ρ Ψ ) = N HC 64π 3 α 2 s 9s ζ parton J.Cline, McGill U. p. 21

22 Dijet, diphoton, dilepton limits σ A (pb) A = 50 % Λ HC = 0.42 m Ψ s = 13 TeV, N HC = 3 Π Ψ jj, ρ Ψ jj vector ρ Ψ pseudoscalar Π Ψ heavy uark F CM ATA m R (TeV) 100 Dijet limit allows m V 3TeV for 10 vector meson σ B γγ (fb) s = 13 TeV, N HC = 3 Λ HC = 0.4 m Ψ Π Ψ γγ ATA m ΠΨ (GeV) σb (pb) ρ φ µµ ATA dilepton m ρφ (GeV) Bound state masses must exceed 2.3 TeV (dijet) This implies limit m Ψ > 820GeV for N HC = 3, Λ HC /m Ψ = 0.4. J.Cline, McGill U. p. 22

23 Pair production at HC Besides resonant production, pair production could be relevant γ, Z φ φ* γ γ γ, Z φ φ* γ, Z φ φ* φ* φ W + γ γ W φ* φ γ γ φ* γ φ* φ* φ φ* γ Need not be suppressed by wave function at oriin since hadronization must occur followin production of hypercolored constituents J.Cline, McGill U. p. 23

24 Pair production at HC Pairs containin are lihter if m < m Ψ,m φ, easiest to produce: γ, Z φ φ* γ γ φ* γ The bound states are leptouarks ρ or heavy lepton partners F l ; production constrained by CM searches for ρ µj, F l µγ 0.1 N = 2 N = 3 N = 2 N = 3 N = 4 Λ HC = 100 GeV β = 1/4 10 N = 2 N = 4 σ β 2 (pb) 0.01 CM µµ CM ττ N = 4 σ B (fb) CM excited muon m ρ (GeV) m Fl (TeV) (β = branchin ratio of leptouark into chared µ or τ) J.Cline, McGill U. p. 24

25 Puttin it on the lattice N HC = 3 is promisin for phenomenoloy. Then our model is QCD with 4 flavors of heavy uarks (one lihter than the rest, to et dark matter) plus one heavy scalar uark. We want the uark masses (possibly exceptin m ) Λ HC ; no chiral limit needed. To compute: masses and decay constants of the mesons (can be bosonic or fermionic); mass and manetic moment of the lihtest baryon Importance of the scalar: We can write a much simpler and more explicit model (compared to most composite His models) by virtue of the scalar φ; it allows direct couplin of new fermions to left-handed M fermions The M uantum numbers carried by the scalar allow one of the fermions to be dark matter (If we tried to make the scalar be the dark matter, it would not work because of confinement, e.., ǫ ABC φ A φ B φ C = 0 and φφ bound state can decay to µ + µ by exchane) J.Cline, McGill U. p. 25

26 Conclusions B decay anomalies seem the best current hope of new physics If true, we may hope that the underlyin theory explains more than just the R K ( ) observations Our example suests that other flavor observables could be close to showin new anomalies It also contains new states with mass 3TeV that could be accessible at HC Nonperturbative studies of vectorlike confinement would be welcome for sharpenin predictions. attice collaborations, opportunity for new models to explore J.Cline, McGill U. p. 26