Strongly coupled gauge theories: What can lattice calculations teach us?

Transcription

1 Strongly coupled gauge theories: What can lattice calculations teach us? Anna Hasenfratz University of Colorado Boulder Rencontres de Moriond, March

2 Higgs era of particle physics The 212 discovery of the Higgs boson completed the SM, yet we needed 3 more years to get a glimpse of what might be beyond: Hint of a 2 TeV vector resonance 75 GeV scalar resonance

3 An attractive BSM possibility: New, strongly interacting gauge-fermion system coupled to the Standard Model The model spontaneously breaks chiral symmetry Goldstone pions induces electroweak symmetry breaking Physical scale is set by Fπ ~ SM vev (25GeV) The 125 GeV Higgs is a composite fermion bound state Many other resonances in the 1-4 TeV range

4 Composite Higgs models: Need a light Higgs : Spontaneously broken symmetry massless Goldstone bosons Higgs is a pseudo-goldstone Flavor symmetry: SSB leads to massless pions Scale symmetry: SSB leads to dilaton: near-conformal models Suppress FCNC Suppress the S parameter Fermion masses generation Scaled-up QCD does not work: Near-conformal model is needed

5 Theory Composite space: Higgs - strong dynamics SU(N color 2 ) gauge fields + N flavor fermions in some representation N flav or IR freedom Conformal phase Chirally broken phase N color

6 Theory Composite space: Higgs - strong dynamics SU(N color 2 ) gauge fields + N flavor fermions in some representation N flav or IR freedom Conformal phase Chirally broken phase N color

7 Composite Higgs Is there a system with Nc color, Nf flavor in given rep that is close enough to the conformal window?

8 Composite Higgs Is there a system with Nc color, Nf flavor in given rep that is close enough to the conformal window? Possible, but accidental

9 Composite Higgs Is there a system with Nc color, Nf flavor in given rep that is close enough to the conformal window? Possible, but accidental How can we ensure walking & chiral symmetry breaking? with a model that is - conformal in the UV (walking) - chirally broken in the IR Build it on a conformal fixed point! (ex. Luty, Okui, hep-ph/49274)

10 A lattice realization: Take Nf flavors above the conformal window (Nf=8-16) Split the masses: Nf = Nll + Nh Nh flavors are massive, mh varies decouple in the IR Nll (=2-4) flavors are massless, mll = chirally broken

11 A lattice realization: Take Nf flavors above the conformal window (Nf=8-16) Split the masses: Nf = Nll + Nh Nh flavors are massive, mh varies decouple in the IR Nll (=2-4) flavors are massless, mll = chirally broken IR N l flavors ˆ = a IRFP UV β 1/g 2 N l + Nh flavors

12 A lattice realization: Take Nf flavors above the conformal window (Nf=8-16) Split the masses: Nf = Nll + Nh Nh flavors are massive, mh varies decouple in the IR Nll (=2-4) flavors are massless, mll = chirally broken IR N l flavors ˆ = a How predictive is this model? g 2,,m l IRFP UV β 1/g 2 N l + Nh flavors

13 A lattice realization: Take Nf flavors above the conformal window (Nf=8-16) Split the masses: Nf = Nll + Nh Nh flavors are massive, mh varies decouple in the IR Nll (=2-4) flavors are massless, mll = chirally broken IR N l flavors ˆ = a How predictive is this model? g 2,,m l IRFP UV β 1/g 2 N l + Nh flavors irrelevant coupling

14 A lattice realization: Take Nf flavors above the conformal window (Nf=8-16) Split the masses: Nf = Nll + Nh Nh flavors are massive, mh varies decouple in the IR Nll (=2-4) flavors are massless, mll = chirally broken IR N l flavors ˆ = a How predictive is this model? g 2,,m l IRFP UV β 1/g 2 N l + Nh flavors irrelevant coupling m l =

15 A lattice realization: Take Nf flavors above the conformal window (Nf=8-16) Split the masses: Nf = Nll + Nh Nh flavors are massive, mh varies decouple in the IR Nll (=2-4) flavors are massless, mll = chirally broken IR N l flavors ˆ = a How predictive is this model? g 2,,m l IRFP UV β 1/g 2 N l + Nh flavors irrelevant coupling hyperscaling m l = Mass ratios are independent of

16 Pilot lattice study: 4+8 mass split system N l +Nh = 4 + 8=12 : conformal in the UV, N l =4 flavor in the IR in collaboration with R. Brower, C. Rebbi, E. Weinberg, O. Witzel arxiv: , This is an effective model: we do not ask how the masses are generated nor how it couples to the Standard Model Why 4+8? We use staggered fermions: 4 and 8 flavors do not require rooting

17 Running coupling : 4+8 flavors 25 2 m l = =.5 =.6 =.8 =. There are error bars on this plot! N f = 4 g 2 (µ; mh) 15 5 g 2 GF (µ) τ = c µ/µ Nf=4 : running fast develops a shoulder as mh : this is walking! Walking range can be tuned arbitrarily with mh

18 Running coupling : 4+8 flavors 25 2 m l = =.5 =.6 =.8 =. There are error bars on this plot! N f = 4 g 2 (µ; mh) 15 mh 5 g 2 GF (µ) τ = c µ/µ Nf=4 : running fast develops a shoulder as mh : this is walking! Walking range can be tuned arbitrarily with mh

19 Running coupling : 4+8 flavors 25 2 m l = =.5 =.6 =.8 =. There are error bars on this plot! N f = 4 g 2 (µ; mh) 15 Nf=12 5 g 2 GF (µ) τ = c µ/µ Nf=4 : running fast develops a shoulder as mh : this is walking! Walking range can be tuned arbitrarily with mh

20 Compare spectrum, 4+8 flavors Ratios M H / F π as function of mll at mh =.8 M /Fπ 14 =.8 preliminary M a1 /F π M n /F π 2 M a /F π M ϱ /F π M π /F π M ++/F π a m l pion, rho, a, a1, nucleon and ++ scalar The ratios are very similar to QCD or Nf=12 but not identical ++ is just above, closely following the pion

21 Compare spectrum, 4+8 flavors Ratios M H / F π as function of mll at mh =.8 MH/Fπ M /Fπ =.8 preliminary 8 6 pion, rho, a, a1, nucleon and ++ scalar The ratios are very similar to QCD or Nf=12 but not identical M a1 /F π M a /F π M n /F π M ϱ /F π ++ is just above, closely following the pion M π /F π M ++/F π QCD m l a m l 12f avg

22 Compare spectrum, 4+8 flavors Ratios M H / F π as function of mll at mh = =.8 preliminary 12 There is a 2 TeV vector resonance MH/Fπ M /Fπ M a1 /F π M n /F π 2 M a /F π M ϱ /F π M π /F π M ++/F π QCD m l a m l 12f avg But M ρ / F π 8 in - QCD - 4-flavor SU(3) fund. - 8 flavor SU(3) fund. - 2 flavor sextet - 12 flavor SU(3) fund. Appears to be a general feature of SU(3)

23 Test of hyperscaling: many heavy mh =.5,.6,.8,. preliminary rho, nucleon and ++ scalar MH/Fπ M /Fπ =.5 =.6 =.8 =. QCD m l a m l M n /F π M ϱ /F π M ++/F π 12f avg

24 Test of hyperscaling: many heavy mh =.5,.6,.8,. preliminary rho, nucleon and ++ scalar MH/Fπ M /Fπ The ratios are close to M N / F π 11 M N 2.8 TeV M ρ / F π 8 M ρ 2 TeV M ++ / F π 3.9 M ++!1 TeV =.5 =.6 =.8 =. QCD m l a m l M n /F π M ϱ /F π M ++/F π 12f avg

25 Test of hyperscaling: many heavy mh =.5,.6,.8,. preliminary rho, nucleon and ++ scalar MH/Fπ M /Fπ The ratios are close to M N / F π 11 M N 2.8 TeV M ρ / F π 8 M ρ 2 TeV M ++ / F π 3.9 M ++!1 TeV =.5 =.6 =.8 =. QCD m l a m l M n /F π M ϱ /F π M ++/F π 12f avg ++ : chiral limit is difficult but well separated from the rho Light scalar! (loop corrections will push it further down)

26 Mass split models The 4+8 system is not ideal: Nf =12 is far above the conformal window with small anomalous dimension γm.25 we might want only 2 light flavors ( but maybe not) Yet it shows: hyperscaling : predictive! walking gauge coupling similar general properties as Nf=12, even QCD, but still distinguishable Light ++, well separated froeavier excitations

27 Summary Many interesting possibilities in strongly coupled near conformal systems all require non-perturbative lattice investigations Lattice models are effective models There are some very general features between different models: light ++ state walking gauge coupling several resonances in the 1-3 TeV range, M ρ / F π 8 LHC could verify / falsify many of the BSM soon