Large scale separation and hadronic resonances from a new strongly interacting sector

Transcription

1 Large scale separation and hadronic resonances from a new strongly interacting sector Oliver Witzel Higgs Centre for Theoretical Physics Boston, MA, April 20, / 20

2 based on R. Brower, A. Hasenfratz, C. Rebbi, E. Weinberg, O.W. PRD 93 (2016) A. Hasenfratz, C. Rebbi, O.W. arxiv: / 20

3 Motivation Mass of the Higgs boson is 125 GeV Other states must be much heavier, likely > 1.5 TeV Standard Model not UV complete What is the origin of the electro-weak sector? Seek a model exhibiting a large separation of scales Near-conformal gauge theories / composite Higgs model 3 / 20

4 Near-conformal gauge theories Gauge-fermion system with N c 2 colors and N f flavors in some representation Using perturbative 2-loop results as guidance β g 0 g FP > > > > < < N g f IR freedom conformal phase chirally broken phase N c β g 0 g ren > > > > g 4 / 20

5 Composite Higgs models New, strongly interacting gauge fermion system Effective theory describing part of the dynamics Coupled to the Standard Model L UV L SD + L SM0 + L int L SM / 20

6 Composite Higgs models New, strongly interacting gauge fermion system Effective theory describing part of the dynamics Coupled to the Standard Model Higgs-less, massless SM full SM L UV L SD + L SM0 + L int L SM / 20

7 Composite Higgs models New, strongly interacting gauge fermion system Effective theory describing part of the dynamics Coupled to the Standard Model Add new strong dynamics coupled to SM L UV L SD + L SM0 + L int L SM +... This construction gives mass to: the SM gauge fields Full SM + states from L SD the SM fermions fields: 4-fermion interaction or partial compositeness 5 / 20

8 Composite Higgs models New, strongly interacting gauge fermion system Effective theory describing part of the dynamics Coupled to the Standard Model L UV L SD + L SM0 + L int L SM +... This construction gives mass to: the SM gauge fields Full SM + states from L SD the SM fermions fields: 4-fermion interaction or partial compositeness Does not explain mass of L SD fermions and 4-fermion interactions: L UV 5 / 20

9 Candidates for L SD Promising candidates are chirally broken in the IR but conformal in the UV [Luty and Okui JHEP 09(2006)070], [Dietrich and Sannino PRD75(2007)085018], [Vecchi arxiv: ], [Ferretti and Karateev JHEP 1403 (2014) 077],... conformal chirally broken UV IR fermion masses Higgs dynamics Λ UV Λ IR 6 / 20

10 Candidates for L SD Promising candidates are chirally broken in the IR but conformal in the UV [Luty and Okui JHEP 09(2006)070], [Dietrich and Sannino PRD75(2007)085018], [Vecchi arxiv: ], [Ferretti and Karateev JHEP 1403 (2014) 077],... conformal chirally broken UV IR fermion masses Higgs dynamics Λ UV Λ IR Many possibilities: SU(4) with 2 diff. representations SU(3) gauge with 8 flavors SU(3) gauge with 4 flavors SU(3) gauge with 2 sextet SU(2) gauge with 2 flavors 6 / 20

11 Candidates for L SD Promising candidates are chirally broken in the IR but conformal in the UV [Luty and Okui JHEP 09(2006)070], [Dietrich and Sannino PRD75(2007)085018], [Vecchi arxiv: ], [Ferretti and Karateev JHEP 1403 (2014) 077],... conformal chirally broken UV IR fermion masses Higgs dynamics Λ UV Λ IR Add fermions to push system into the conformal window If fermions are massive, they decouple at Λ IR Dynamics beyond Λ UV gives mass to add. fermions Many possibilities: SU(4) with 2 diff. representations SU(3) gauge with 8 flavors SU(3) gauge with 4 flavors SU(3) gauge with 2 sextet SU(2) gauge with 2 flavors 6 / 20

12 Candidates for L SD : the 4+8 model SU(3) gauge theory with 4 light (massless) and 8 heavy fundamental flavors conformal chirally broken UV IR fermion masses Higgs dynamics Λ UV Λ IR Add 8 heavy fundamental flavors N f = = 12: conformal dynamics SU(3) gauge theory with 4 light, fundamental flavors Chirally broken in the IR 4, 8, 12 are preferred for simulations with unrooted staggered fermions Walking gauge coupling, tunable by changing m h Anomalous dimensions correspond to the conformal IRFP Model features both pngb or dilaton-higgs scenarios 6 / 20

13 Two possibilities for a composite Higgs (IR sector) Spontaneous breaking of scale symmetry: Higgs is a dilaton Possibly light 0 ++ scalar F π = SM vev 246 GeV ideal 2 massless flavors in the IR closer to old technicolor ideas Spontaneous breaking of flavor symmetry: Higgs is a pngb Mass emerges from its interactions Non-trivial vacuum alignment F π = (SM vev)/ sin(χ) > 246 GeV ideal 4 massless flavors in the IR Vecchi: UV-complete models requiring at least two types of fermions in two different gauge group representations [arxiv: ] Ferretti: Classification of models with custodial symmetry and partial compositeness [JHEP 1403 (2014) 077] [JHEP 1606 (2016) 107] Ma and Cacciapaglia: Fundamental composite 2HDM with 4 flavors in SU(3) gauge [JHEP 03 (2016) 211] 7 / 20

14 Fundamental composite 2HDM with 4 flavors Global symmetry at low energies: SU(4) SU(4) broken to SU(4) diag 15 pngb transform under custodial symmetry [Ma and Cacciapaglia JHEP 03 (2016) 211] SU(2) L SU(2) R 15 SU(4)diag = (2, 2) + (2, 2) + (3, 1) + (1, 3) + (1, 1) One doublet plays the role of the Higgs doublet field Other doublet and triplets are stable; could play role of dark matter Vecchi: choose the right couplings to RH top [Edinburgh talk] (2, 2) + (2, 2) + (3, 1) + (1, 3) + (1, 1) effectively SU(4)/Sp(4) 8 / 20

15 Implementation on the lattice Choose N f flavors above the conformal window Split the masses: N f = N l + N h N h flavors are massive, we will vary m h decouple in the IR N l flavors are massless, extrapolate m l 0 chirally broken We have 3 parameters: g irrelevant coupling m l 0 (chiral limit) m h : sets the scale allows to tune walking 9 / 20

16 Conformal systems: Wilson RG predicts hyperscaling Scale change: µ µ = µ/b, with b > 1 Transforms the bare masses m = am: m(µ) m(µ ) = b ym m(µ) (increase) The bare coupling approaches its fixed point: g g Any 2-point correlator: C H (t; g, m, µ) b 2y H C H (t/b; g i, b ym m, µ) Now C H (t) exp( M H t) am H ( m) 1/ym (hyperscaling) Likewise amplitudes (F π ) show hyperscaling M H /F π are constant 10 / 20

17 Hyperscaling in mass-split systems Light flavors of mass m l and heavy flavors of mass m h : C H (t; g, m h, m l, µ) b 2y H C H (t/b; g, b ym m h, b ym m l, µ) b 2y H C H (t/b; g, b ym m h, m l / m h, µ) Since C H (t) exp( M H t) am H ( m) 1/ym f H (m l /m h ) with f H (m l /m h ) a universal function M H can be build up of only light, light and heavy, or only heavy flavors Does not follow a system with only N l (large m h ) or N f degenerate (conformal) flavors 11 / 20

18 Hyperscaling in mass-split systems Masses / amplitudes scale as am H ( m) 1/ym f H (m l /m h ) Ratios are universal functions of m l /m h M H1 /M H2 = Φ H (m l /m h ) M H /F π = Φ H (m l /m h ) Chiral limit (m l = 0): dimensionless ratios are independent of m h Known F π : rest of the spectrum is predicted no free parameters There are however corrections to scaling Very different form QCD! 12 / 20

19 Light-light spectrum: ratios of M H /F π 14 am h = am h = am h = am h = MH/Fπ Ma1 /Fπ Mn/Fπ Ma1 /Fπ Mn/Fπ Ma1 /Fπ Mn/Fπ Ma1 /Fπ Ma0 /Fπ M /Fπ Ma0 /Fπ M /Fπ Ma0 /Fπ M /Fπ Ma0 /Fπ Mn/Fπ M /Fπ Mπ/Fπ M0 ++/Fπ Mπ/Fπ M0 ++/Fπ Mπ/Fπ M0 ++/Fπ Mπ/Fπ M0 ++/Fπ m l /m h m l /m h m l /m h m l /m h Pion, rho, a 0, a 1, nucleon, and 0 ++ scalar 0 ++ is light (M 0 ++ < M ρ ), it tracks the pion. Chiral limit? M π /F π bends down indicates system is chirally broken 13 / 20

20 Light-light spectrum: ratios of M H /F π 14 am h = am h = am h = am h = MH/Fπ Ma1 /Fπ Mn/Fπ 2 Ma0 /Fπ M /Fπ Mπ/Fπ M0 ++/Fπ 0 QCD m l m l /m h 0.8 Ma1 /Fπ Ma0 /Fπ Mπ/Fπ Mn/Fπ M /Fπ M0 ++/Fπ m l /m h Ma1 /Fπ Ma0 /Fπ Mπ/Fπ Mn/Fπ M /Fπ M0 ++/Fπ m l /m h Ma1 /Fπ Ma0 /Fπ Mπ/Fπ Mn/Fπ M /Fπ M0 ++/Fπ m l /m h 12f avg For growing m h and m l 0 we approach QCD [PDG values] For decreasing m h and m l m h we approach degenerate 12 flavors [LatHC PLB 703(2011) 348] [LatKMI PRD86 (2012) ][LatKMI PRL 111 (2013) ] [Cheng et al. PRD 90 (2014) ] 13 / 20

21 Light-light spectrum: ratios of M H /F π 14 am h = am h = am h = am h = MH/Fπ Ma1 /Fπ Mn/Fπ 2 Ma0 /Fπ M /Fπ Mπ/Fπ M0 ++/Fπ 0 QCD m l m l /m h 0.8 Ma1 /Fπ Ma0 /Fπ Mπ/Fπ Mn/Fπ M /Fπ M0 ++/Fπ m l /m h Ma1 /Fπ Ma0 /Fπ Mπ/Fπ Mn/Fπ M /Fπ M0 ++/Fπ m l /m h Ma1 /Fπ Ma0 /Fπ Mπ/Fπ Mn/Fπ M /Fπ M0 ++/Fπ m l /m h 12f avg Ratios appear largely independent of m h! M ϱ /F π and M n /F π also show very little dependence on m l 13 / 20

22 Hyperscaling at work MH/Fπ am h = am h = am h = M a1 /F π M /F π am h = M π/f π m l /m h am h = am h = am h = am h = M n/f π M a0 /F π M 0 ++/F π m l /m h M n /F π 11 M ϱ /F π 8 M 0 ++/F π 4 5 (taking the chiral limit is difficult but 0 ++ well separated from the ϱ) 14 / 20

23 The system is chirally broken a ml and a Fπ amh = amh = Fπ amh = a ml amh = m l /m h M /Mπ amh = amh = amh = amh = flavors m l /m h a F π is finite 4-flavors (QCD-like): ratio diverges 12-flavors: almost constant ratio [Cheng at al. 2014] 15 / 20

24 Light-light and heavy-heavy spectrum ηc pseudoscalar amh = amh = amh = amh = M hh π /Fπ Mπ/Fπ J/ψ vector amh = amh = amh = amh = M hh /Fπ M /Fπ χc1 axial amh = amh = amh = amh = M hh a1 /Fπ Ma1 /Fπ Mps/Fπ ηs π 0 PDG m l / m l /m h 12f avg Mvt/Fπ φ 0 PDG m l / m l /m h 12f avg Max/Fπ f1 a1 0 PDG m l / m l /m h 12f avg 4+8 heavy-heavy spectrum is not QCD-like; QCD is not hyperscaling M hh /F π increases but F π is finite in the chiral limit M hh ϱ 3M ϱ could be accessible 16 / 20

25 Ratios over M ϱ and M hh ϱ M hh H /M am h = am h = am M hh h = a1 /M am M hh h = π m l /m h M hh H /Mhh am h = am h = am h = am h = M hh a1 /Mhh M hh π /M hh m l /m h Heavy-heavy states increase mostly due to light-light quantity in denominator Hyperscaling also expected for heavy-light states (directly coupled to SM) 17 / 20

26 Irrelevance of coupling g Data with am h = 0.100, 0.080, 0.060, simulated at β = 4.0 Additional simulations at β = 4.4 and am h = [arxiv: ] Mπ/Fπ pseudoscalar vector axial amh = amh = amh = amh = amh = preliminary M hh π /Fπ Mπ/Fπ m l /m h M /Fπ amh = amh = amh = amh = amh = preliminary M hh /Fπ M /Fπ m l /m h Ma1 /Fπ amh = amh = amh = amh = amh = preliminary M hh a1 /Fπ Ma1 /Fπ m l /m h 18 / 20

27 Concluding remarks Mass-split models are great to explore near conformal dynamics Allow to investigate pngb and dilaton-like Higgs scenarios Limiting cases of 4 and 12 flavors help to understand what is happening 4+8 is chosen for convenience of unrooted staggered fermions N f = 12 is above the conformal window its anomalous dimension is however small γ m 0.25 Walking gauge coupling (controlled by m h ) Hyperscaling predictive Heavy-heavy (and heavy-light) spectrum accessible but not QCD-like Future: decay constants, π π scattering, etc. 19 / 20

28 Resources and Acknowledgments USQCD: Ds, Bc, and pi0 cluster (Fermilab) BU: engaging (MGHPCC) XSEDE: Stampede (TACC) and SuperMic (LSU) 20 / 20

29 appendix 21 / 20

30 On the lattice Setup Goals References SU(3) gauge group Fundamental adjoint gauge action with β a = β/4 [Cheng et al. arxiv: ][cheng et al. PRD 90 (2014) ] nhyp smeared staggered Fermions [Hasenfratz et al. JHEP 05 (2007) 029] Most simulations/measurements performed with FUEL [J. Osborn] Explore near conformal or conformal dynamics Compute the iso-singlet 0 ++ [JETP 120 (2015) 3, 423] [PoS Lattice ] [CCP proceedings 2014] [PRD 93 (2016) ] [arxiv: ] (a longer, detailed paper is in preparation) 22 / 20

31 Performed simulations (β = 4.0) a m h Nf= "4+8" m l = m h "8+4" a m l Symbols indicate volumes and colors finite volume effects red: squeezed yellow: marginal green: OK : or : : Up to 40k MDTU 23 / 20

32 running coupling 24 / 20

33 Running coupling form gradient flow Gradient flow defines the renormalized coupling [Narayanan and Neuberger JHEP 03 (2006) 064], [Lüscher JHEP 08 (2010) 071] ggf 2 (µ = 1/ 8t) = t 2 E(t) /N t: flow time; E(t) energy density is used for scale setting g 2 GF g 2 GF (t = t 0) = 0.3/N ( t 0 -scale ) Can determine renormalized running coupling on large enough volumes and large enough flow times in the continuum limit 25 / 20

34 Running coupling form gradient flow: 4+8 flavors g 2 (µ;mh) m h = m h = m h = m h = N f = 4 Extrapolated to m l = 0 N f = 4 shows fast running Shoulder increases for smaller m h walking 5 τ 0 = c 0 µ/µ 0 Walking range is tuned as function of m h Data with error bars! 26 / 20

35 The / 20

36 Computationally challenging Same quantum numbers as the vacuum (large background) Fermionic states can mix with glueballs Computing the glueball spectrum is a challenge on its own Connected and disconnected (only gluon-lines) contributions For large t: disconnected part dominates Stochastic determination of disconnected parts Mass-split systems: light-light, heavy-light and heavy-heavy 0 ++ can mix More expensive but noisier than connected meson spectrum Easier to compute in some BSM theories if 0 ++ is light am 0 ++ < 2aM π i.e. not as difficult as in QCD 28 / 20

37 Calculating the disconnected spectrum (0 ++ scalar) Numerical measurement on the lattice 6 U(1) sources with dilution on each time slice, color and even/odd spatially Variance reduced ψψ Analysis strategy Correlated fit to both parity states (staggered) Vacuum subtraction introduces very large uncertainties Advantageous to fit additional constant C(t) = c 0 ++ cosh ( M 0 ++ ( NT 2 t )) + c πsc ( 1) t cosh ( M πsc ( NT 2 t )) + ν Equivalent to fitting the finite difference: C(t + 1) C(t) 29 / 20

38 Comparison of D ll and D ll C ll am preliminary 24 3 fitted mass D ll (t) C ll (t) 32 3 fitted mass D ll (t) C ll (t) 24 3 fitted mass D ll (t) 32 3 fitted mass D ll (t) m h = m l = t min For t : D ll and D ll C ll should agree (up to mixing effects) Compare fits with different t min and t max = N T /2 Compare results for two volumes Consistent results! 30 / 20

39 model amh = amh = amh = amh = M /Fπ M 0 ++/Fπ Mπ/Fπ 8flavor 12 flavor (LatKMI) 2f sextet (LatHC) MH/Fπ QCD m l m l /m h Ma1 /Fπ Mπ/Fπ M /Fπ Mn/Fπ M0 ++/Fπ a m q M0 ++/Fπ Mπ/Fπ M /Fπ am q [PDG] [LSD PRD 93 (2016) ] [J. Kuti, Argonne 2016] [PRD 93 (2016) ] [arxiv: ] [LatKMI PRD86 (2012) ] [LatKMI PRL 111 (2013) ] 31 / 20

40 Magic model amh = amh = amh = amh = M /Fπ M 0 ++/Fπ Mπ/Fπ 8flavor 12 flavor (LatKMI) 2f sextet (LatHC) MH/Fπ QCD m l m l /m h Ma1 /Fπ Mπ/Fπ M /Fπ Mn/Fπ M0 ++/Fπ a m q M0 ++/Fπ Mπ/Fπ M /Fπ am q [PDG] [LSD PRD 93 (2016) ] [J. Kuti, Argonne 2016] [PRD 93 (2016) ] [arxiv: ] [LatKMI PRD86 (2012) ] [LatKMI PRL 111 (2013) ] 31 / 20