Hiroshi Ohki RIKEN BNL Research Center, Brookhaven National - PowerPoint PPT Presentation

Many-flavor QCD dynamics on the lattice Hiroshi Ohki RIKEN BNL Research Center, Brookhaven National Laboratory Recent references: 
 Phys. Rev. D87, 094511 , arXiv:1302.6859 [hep-lat]. arXiv:1305.6006 [hep-lat] 
 Phys. Rev. D89 (2014) 111502 arXiv:1501.06660, Lattice for Beyond the Standard Model Physics 2016, Nf=8 full paper in preparation April 21, 2016 (LatKMI collaboration)

1. Introduction 2. Nf=8 QCD result • Flavor singlet scalar ( σ ) spectrum (composite Higgs) • Baryon Dark matter • Flavor singlet pseudo scalar ( η ’) mass 3. Summary

“Higgs boson” Higgs like particle (125 GeV) has been • found at LHC. Consistent with the Standard Model Higgs. • But true nature is so far unknown. • ATLAS & CMS 2012 Many candidates for beyond the SM. • one interesting possibility is Dynamical breaking of electroweak symmetry -> composite Higgs – (walking) technicolor • “Higgs” = dilaton (pNGB) due to breaking of the approximate scale invariance 750 GeV diphoton resonance may suggest strong dynamics? ( η -like particle?) •

Many-flavor QCD: benchmark test of walking dynamics : Number of flavor α ( µ ): running gauge coupling Asymptotic non-free Conformal window Walking technicolor QCD-like – typical QCD like theory: M Had >>F π (ex.: QCD: m ρ /f π ~8) • Naive TC: M Had > 1,000 GeV • 0 ++ is a special case: pseudo Nambu-Goldstone boson of scale inv. ➡ is it really so ?

Many-flavor QCD: benchmark test of walking dynamics : Number of flavor α ( µ ): running gauge coupling Asymptotic non-free Conformal window Walking technicolor QCD-like – typical QCD like theory: M Had >>F π (ex.: QCD: m ρ /f π ~8) • Naive TC: M Had > 1,000 GeV • 0 ++ is a special case: pseudo Nambu-Goldstone boson of scale inv. ➡ is it really so ? Lattice!!

Many-flavor QCD on the Lattice 
 
 [LatKMI collaboration] Yasumichi Aoki, Tatsumi Aoyama, Ed Bennett, Masafumi Kurachi, Toshihide Maskawa, Kei-ichi Nagai, Kohtaroh Miura, HO, Enrico Rinaldi, Akihiro Shibata, KoichiYamawaki, TakeshiYamazaki

LatKMI project : Many-flavor QCD Systematic study of flavor dependence in many flavor QCD (Nf =4, 8, 12) using common setup of the lattice simulation Status (lattice): Nf=16: likely conformal Nf=12: controversial, probably conformal? Nf=8: controversial, our study suggests walking behavior? Nf=4: chiral broken and enhancement of chiral condensate Nf=8 is good candidates of walking (near-conformal) technicolor model.

Simulation setup L 3 × T N cf [ N st ] m f SU(3), Nf=8 • 0.012 42 3 × 56 2300[2] 0.015 36 3 × 48 5400[2] • HISQ (staggered) fermion and tree level Symanzik gauge action 0.02 36 3 × 48 5000[1] Volume (= L^3 x T) 0.02 30 3 × 40 8000[1] L =24, T=32 • 0.03 30 3 × 40 16500[1] L =30, T=40 • L =36, T=48 • 0.03 24 3 × 32 36000[2] L =42, T=56 • Bare coupling constant ( ) 0.04 30 3 × 40 12900[3] beta=3.8 • 0.04 24 3 × 32 50000[2] bare quark mass 0.04 18 3 × 24 9000[1] mf= 0.012-0.06, • (5 masses) 0.06 24 3 × 32 18000[1] • high statistics (more than 2,000 configurations) 0.06 18 3 × 24 9000[1] • We use a noise reduction technique for disconnected correlator. (use of Ward-Takahashi identity[Kilcup-Sharpe, ’87, Venkataraman-Kilcup ’97] )

Flavor singlet scalar from fermion bilinear operator O S ( t ) ≡ ¯ D ( t ) = � O S ( t ) O S (0) � � � O S ( t ) �� O S (0) � ψ i ψ i ( t ) , Staggered fermion case • Scalar interpolating operator can couple to two states of ( 1 ⊗ 1 ) & ( γ 4 γ 5 ⊗ ξ 4 ξ 5 ) C (2 t ) + → a 0 (continuum limit) • 0+(non-singlet scalar) : • 0-(scPion) : C (2 t ) − → scPion (continuum limit) C ± (2 t ) ≡ 2 C (2 t ) ± C (2 t + 1) ± C (2 t − 1) • Flavor singlet scalar can be evaluated with disconnected diagram. C σ (2 t ) = − C + (2 t ) + 2 D + (2 t ) (8 flavor) = 2 × (one staggered fermion)

m σ for Nf=8, beta=3.8, L=36, mf=0.015 0.5 2D + (t) - C + (t) 2D(t) 0.4 - C - (t) m π 0.3 m σ 0.2 0.1 0 0 4 8 12 16 20 t 2 D + ( t ) − C + ( t ) → A σ e − m σ 2 t D + ( t ) = A σ e − m σ 2 t + A a 0 e − m a 0 2 t → A σ e − m σ 2 t , (if m σ < m a 0 ) (in the continuum limit)

Many-flavor QCD highlight: Nf=8 QCD mass spectra σ L=42 σ L=36 0.5 σ L=30 σ L=24 σ L=18 0.4 π ρ (PV) m 0.3 0.2 0.1 0 0 0.01 0.02 0.03 0.04 0.05 0.06 m f M ρ > M π ~ M σ (outer error : both statistical and systematic errors added.) Nf=8 QCD is in sharp contrast to the real-life QCD (right figure: Nf=2 lattice QCD result) (c.f. LatHC Collab. (’14), Hietanen et.al. (’14), Athenodorou et.al. (’15)).

Many-flavor QCD highlight: Nf=8 QCD mass spectra c.f. Nf=2 lattice QCD result [T. Kunihiro,et al., n f =2 QCD SCALAR Collaboration, 2003] SCALAR Collaboration σ L=42 σ L=36 0.5 2 σ L=30 σ ρ σ L=24 π σ L=18 0.4 π 1.5 ρ (PV) m m had 0.3 1 0.2 0.5 0.1 0 0 0.05 0.1 0.15 m q 0 0 0.01 0.02 0.03 0.04 0.05 0.06 m f M ρ > M π ~ M σ (outer error : both statistical and systematic errors added.) Nf=8 QCD is in sharp contrast to the real-life QCD (right figure: Nf=2 lattice QCD result) (c.f. LatHC Collab. (’14), Hietanen et.al. (’14), Athenodorou et.al. (’15)).

M σ for Nf=8, beta=3.8 though it is too far, so far 0.15 • 2 ways: σ L=42 σ L=36 σ L=30 • naive linear m σ =c 0 +c 1 m f σ L=24 2 0.1 • dilaton ChPT m σ 2 =d 0 +d 1 m π 2 m π differ only at higher order 2 m 0.05 • Fit result: 0 c 0 = 0.063(30)(+4/-142) -0.05 0 0.025 0.05 0.075 0.1 d 0 = − 0.0028(98)(+36/-313 ) 2 m π m σ 2 = 3 . 0( +3 . 0 − 8 . 6 ) In the chiral limit √ F π / • possibility to have ~125GeV Higgs (We need to simulate lighter fermion mass region for precision determination) σ (Flavor singlet scalar) ~ (Techni) dilaton [Composite Higgs]

Technibaryon Dark Matter

Technibaryon • The lightest baryon is stable due to the technibaryon number conservation • Good candidate of the Dark matter (DM) • Boson or fermion? (depend on the #TC) our case: DM is fermion (#TC=3). • Direct detection of the dark matter is possible.

DM effective theory Technibaryon(B) interacts with quark(q), gluon in standard model µ ν G aµ ν + Bi ∂ µ γ ν B O µ ν + · · · BBG a 1 L eff = c ¯ qq + c ¯ M ¯ BB ¯ One of the dominant contributions in spin-independent interactions comes from the microscopic Higgs (technidilaton σ ) mediated process (below diagram) B : DM B : DM Technibaryon-scalar effective y ¯ BB σ coupling σ nucleon-scalar effective coupling y ¯ nn σ Nucleon Nucleon How do we calculate the scalar-technibaryon coupling (y BB σ ) ?

(Techni)baryon Chiral perturbation theory leading order of BChPT L = ¯ B ( i γ µ ∂ µ − m B + g A 2 γ 5 γ µ u µ ) B u µ = i u † ( ∂ µ − i r µ ) u − u ( ∂ µ − i l µ ) u † � � U = u 2 = e 2 π i/F π

(Techni)baryon Chiral perturbation theory with dilaton leading order of BChPT L = ¯ B ( i γ µ ∂ µ − m B + g A 2 γ 5 γ µ u µ ) B u µ = i u † ( ∂ µ − i r µ ) u − u ( ∂ µ − i l µ ) u † � � U = u 2 = e 2 π i/F π L = ¯ B ( i γ µ ∂ µ − e σ /F σ m B + g A 2 γ 5 γ µ u µ ) B χ = e σ /F σ

(Techni)baryon Chiral perturbation theory with dilaton leading order of BChPT L = ¯ B ( i γ µ ∂ µ − m B + g A 2 γ 5 γ µ u µ ) B u µ = i u † ( ∂ µ − i r µ ) u − u ( ∂ µ − i l µ ) u † � � U = u 2 = e 2 π i/F π L = ¯ B ( i γ µ ∂ µ − e σ /F σ m B + g A 2 γ 5 γ µ u µ ) B χ = e σ /F σ c.f. Pion ChPT with dilaton Ref.[Matsuzaki-Yamawaki ‘13] L = F 2 2 ( ∂ µ χ ) 2 + F 2 4 χ 2 tr[ ∂ µ U † ∂ µ U ] + · · · σ π Invariant under the scale transformation δχ = (1 + x ν ∂ ν ) χ , δ U = x ν ∂ ν U, δ B = ( 3 2 + x ν ∂ ν ) B,

(Techni)baryon Chiral perturbation theory with dilaton leading order of BChPT L = ¯ B ( i γ µ ∂ µ − m B + g A 2 γ 5 γ µ u µ ) B u µ = i u † ( ∂ µ − i r µ ) u − u ( ∂ µ − i l µ ) u † � � U = u 2 = e 2 π i/F π L = ¯ B ( i γ µ ∂ µ − e σ /F σ m B + g A 2 γ 5 γ µ u µ ) B χ = e σ /F σ The dilaton-baryon effective coupling (leading order) is uniquely determined as y ¯ BB σ = m B /F σ ( F σ · · · Dilaton decay constant)

DM Direct detection B B Spin-independent cross section with nucleus σ SI ( χ , N ) = M 2 π ( Zf p + ( A − Z ) f n ) 2 R σ + 2 m B y ¯ f ( n,p ) 9 f ( n,p ) BB σ � f ( n,p ) = (3 − γ ∗ )( ) √ T q T G 2 m 2 F σ q = u,d,s σ Nucleon Nucleon = (3 − γ ∗ ) v EW g σ ff Note: Yukawa coupling is different from the SM : g h SM ff F σ | i f ( N ) ⌘ h N | m q ¯ qq | N i /m N Nucleon sigma term in QCD T q Nucleon matrix element non-perturbatively determined by lattice QCD calculation Lattice calculation for both nucleon and technibaryon interactions

How to calculate Dilaton decay constant?