we miss you another Minimal Composite Higgs (through LHC bumps) - - PowerPoint PPT Presentation

dedicated to the memory of Peter Hasenfratz

we miss you

Argonne BSM workshop

another

Minimal Composite Higgs

(through LHC bumps)

2

with the Lattice Higgs Collaboration (LatHC) Zoltan Fodor, Kieran Holland, JK, Santanu Mondal, Daniel Nogradi, Chik Him Wong

Julius Kuti University of California, San Diego

Argonne'BSM'workshop:'Composite'Dynamics'in'2016'

April 21, 2016 Argonne National Laboratory

3.2 β 2 4 6 8 10 12 14 16 18 20 22 M / F 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 M / TeV MN Ma1 Mρ

0++ scalar Higgs?

a0 scalar isovector?

We want to understand:

light scalar separated from 2-3 TeV resonance spectrum More complex scalar spectrum close to CW?

what is the eta’? diphoton bump?

entangled scalar-goldstone dynamics sigma model or dilaton? tuning to CW and away from CW? bridge between UV and IR scale? scale-dependent gauge coupling - high precision what list of predictions independent of mass generation? related phenomenology consistent EW embedding ➞ dark matter lattice: actually have to solve the theory BSM needs new lattice tools RMT and delta-regime

scaled up QCD cannot do this

diphoton res?

The light 0++ scalar BSM lattice challenges

LHiggs → −1 4FµνFµν + i ¯ QγµDµQ + . . .

⇤

R

e-writing the Higgs doublet field H = 1 ⌦ 2 ⇤ ⇤2 + i ⇤1 ⌅ i ⇤3 ⌅

1 ⌦ 2 ⌅ + i⌦ ⇧ · ⌦ ⇤⇥ ⇧ M .

DµM = µM i g WµM + i g⌥M Bµ , with Wµ = Wa

µ

⇧a 2 , Bµ = Bµ ⇧3 2

The Higgs Lagrangian is L = 1 2Tr ⇧ DµM†DµM ⌃

• m2

M

2 Tr ⇧ M†M ⌃ 4 Tr ⇧ M†M ⌃2

strongly coupled gauge theory fermions (Q) in gauge group reps: light scalar separated from has to be unlike QCD 2-3 TeV resonance spectrum spontaneous symmetry breaking Higgs mechanism

What is our composite Higgs paradigm?

elementary scalar?

composite Higgs mechanism (textbook TC paradigm)

We want something different from scaled up QCD (near-conformal theory):

• m=0 fermion doublet SU(2) flavor QCD

▸ light scalar is the excitation of the chiral

condensate

▸ Goldstone particle important in

composite Higgs mechanism …

▸ fπ sets the EW scale ~ 250 GeV and

gauge coupling g

▸ Higgs mechanism does not depend

• n hypercharge of fermion multiplet!

▸ 29 MeV ➛ 90 GeV scaled-up QCD ?

three lattice BSM models with light scalars and SU(3) color:

SCGT Theory Space Nf=2 sextet rep massless fermions SU(2) doublet 3 Goldstones > weak bosons minimal realization of Higgs mechanism adding lepton doublets is a choice adding EW singlet massive flavor is also a choice QCD intuition for near-conformal compositeness is plain wrong Technicolor thought to be scaled up QCD motivation of the project: composite Higgs-like scalar close to the conformal window with 2-3 TeV new physics

u(+e/2 d(-e/2) ⎡ ⎣ ⎢ ⎤ ⎦ ⎥

minimal EW embedding QCD far from scale invariance sextet rep near-conformal?

sextet from haystack: Marciano in qcd Sannino and Tuominen BSM early lattice work: DeGrand/Shamir/Svetitsky LatHC Kogut-Sinclair recent Boulder work and CP3 nf = 8 and nf=12 are popular: LatKMI and LSD PNGB is the opposite approach what do we do with unwanted nf=8 goldstones which pull away from CW when made massive? Hence the tag minimal for the sextet model its gauge group is SU(3) and predicts new Electroweak physics (gauge anomaly) what happens to the flavor singlet Goldstone? aka eta’ (axial anomaly)

u(+2/3e d(-1/3e) ⎡ ⎣ ⎢ ⎤ ⎦ ⎥

0.5 1 1.5 2 2.5 1 2 3 4 5 6 7 ( g2(sL) - g2(L) ) / log(s2) g2(L) fund Nf = 4 c = 3/10 s = 3/2 fund Nf = 8 c = 3/10 s = 3/2 sextet Nf = 2 c = 7/20 s = 3/2 fund Nf = 12 c = 1/5 s = 2

LatHC and Boulder Nf = 2 sextet LatHC Nf = 4 fundamental LatHC and Boulder Nf = 8 fundamental sextet beta function! Boulder Nf = 12 fundamental

scale-dependent coupling of the 3 lattice BSM models

without the gradient flow based method this accuracy would not have been possible New analysis ? IRFP?

6.6 6.8 7 7.2 7.4 7.6 7.8 8 2 4 6 8 10 12 14 16

renormalized gauge coupling g2 t0 scale of g2 in chiral limit

6/g2

0=3.25

6/g2

0=3.20

cubic spline interpolation

renormalized gauge coupling in chiral limit

running coupling at fixed β

leading dependence of g2(t,m) on Mπ

2 is linear

based on gradient flow chiPT B!! ar and Golterman works better than expected chiral logs are not detectable decoupling of the scalar has to be better understood

scale change at fixed renormalized g2 a → 0 needed

nstructed at flow time 0 depend on t

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 1 2 3 4 5 6 7 8 9 10

M2

π

t0 scale of g2 in chiral limit

6/g0

2 = 3.25

m=0.003−0.006,0.008 fitted Chiral PT fits excellent χ2 fits

t0 scale of selected g2 series in m=0 chiral limit

the two scale dependent couplings to be matched to leave no room for further speculations on conformal fixed points topic: how to do this right in ChiPT with low lying scalar coupled to Goldstone dynamics?

scale-dependent coupling of the 3 lattice BSM models

bridge between UV scale and IR scale

−1000 1000 2000 3000 4000 5000 6000 0.1 0.2 0.3 0.4 0.5 0.6

−log(m2/µ2) α(m2/µ2)

• ne massless flavor

two flavors with mass m α(m2/µ2) runs with scale µ sextet running coupling from mass dependent β function

−log(m2/µ2) α(m2/µ2) sextet running coupling from mass dependent β function

scale-dependent coupling mass dependent tuning?

walking very close to weak coupling Nf=3 IRFP two massive flavors freeze out

in 1+2 freeze-out scenario anything to learn about strong coupling dynamics of single massless flavor? Similarly, in 2+1 freeze-out scenario anything to learn about strong coupling dynamics of doublet massless flavor? Not clear that light scalar mass can be tuned effectively LSD 4+8 model topic: reverse pulling from IRFP with 4-fermion operator?

0.5 1 1.5 2 2.5 1 2 3 4 5 6 7 ( g2(sL) - g2(L) ) / log(s2) g2(L) fund Nf = 4 c = 3/10 s = 3/2 fund Nf = 8 c = 3/10 s = 3/2 sextet Nf = 2 c = 7/20 s = 3/2 fund Nf = 12 c = 1/5 s = 2

LatHC and Boulder Nf = 2 sextet LatHC Nf = 4 fundamental LatHC and Boulder Nf = 8 fundamental sextet beta function! Boulder Nf = 12 fundamental

scale-dependent coupling of the 3 lattice BSM models

without the gradient flow based method this accuracy would not have been possible New analysis ? IRFP?

√sσ = 441+16

−8 − i 272+9 −12.5 MeV

nt for all sources of uncertainty and a

sources of uncertainty and are an order of m ate √sσ = (400 - 1200) - i (250 - 500) MeV q e dispersive representation of the S-matrix ele

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

GeV

50 100 150 200

δ

Roy solutions with 78.3

• < δ

0(sA) < 92.3

• Bugg 2006

Achasov & Kiselev 2007 Kaminski, Pelaez & Yndurain 2008 Albaladejo & Oller 2008

the failure of old Higgs-less technicolor: 0++ scalar in QCD (bad Higgs impostor)

estimate in Particle Data Book

π-π phase shift in 0++ “Higgs” channel

Leutwyler: dispersion theory combined with ChiPT broad Mσ ~ 1.5 TeV in old technicolor, based

• n scaled up QCD, hence the tag “Higgs-less”

This is expected to be different in near- conformal strongly coupled gauge theories Low scalar mass renormalizes F! Will require new low energy effective action

The light 0++ scalar nf= 2 4 higgs-less

Bernard et al. first lattice result QCD 2+1 flavor f0 mass (σ particle) 750(150) MeV heavy pion

lattice BSM 0++ scalar has to be very different The light 0++ scalar nf=2-4 QCD higgs-less

0.5 1 1.5 2 2.5 1 2 3 4 5 6 7 ( g2(sL) - g2(L) ) / log(s2) g2(L) fund Nf = 4 c = 3/10 s = 3/2 fund Nf = 8 c = 3/10 s = 3/2 sextet Nf = 2 c = 7/20 s = 3/2 fund Nf = 12 c = 1/5 s = 2

LatHC and Boulder Nf = 2 sextet LatHC Nf = 4 fundamental LatHC and Boulder Nf = 8 fundamental sextet beta function! Boulder Nf = 12 fundamental

scale-dependent coupling of the 3 lattice BSM models

without the gradient flow based method this accuracy would not have been possible New analysis ? IRFP?

5 10 15 20 25 −1 1 2 3 4 5 6 7 8 9 x 10

−5

t

Csinglet(t) ~ exp(-M0++·t) fitting function: Nf=12

Nf=12

Lowest 0++ scalar state from singlet correlator aM0++=0.304(18) 243x48 lattice simulation 200 gauge configs β=2.2 am=0.025

+

6 8 10 12 14 16 18 20 22 24 26 −0.5 0.5 1 1.5 2 2.5 3 x 10

−7

t

Cnon-singlet(t): Nf=12 Lowest non-singlet scalar from connected correlator aMnon-singlet = 0.420(2) !=2.2 am=0.025

−

−

−

−

C(t) = ⇤

n

• Ane−mn(ΓS⊗ΓT)t + (−1)tBne−mn(γ4γ5ΓS⊗γ4γ5ΓT)t⇥

staggered correlator

similar analysis in sextet model with Nf=2 test of technology:

LatKMI and LatHC early 2013 game begins

light 0++ scalar nf=12 LatKMI and LatHC

4 8 12 16

t

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

a0 σ Only D(t) mπ

Effective mass mf=0.06

Non-singlet scalar a0: −C+(t) Singlet scalar σ: 3D+(t) − C+(t) σ: D(t) i.e. mσ < ma0 Consistent mσ with smaller error mσ < mπ at mf = 0.06

also Jin and Mawhinney

0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.1 0.2 0.3 0.4 0.5

pion mass Mπ 0++ singlet masses

KMI (blue) LHC (red)

323×64 363×48 303×40 243×48 363×48 243×48

Nf=12 fundamental rep from singlet 0++ correlator

LatKMI first result LatHC used it for crosscheck good agreement Nf=8 latKMI Lattice 2013

LatKMI and LatHC early 2013

LatHC group started focusing on sextet model two different technologies

light 0++ scalar nf=12 (and nf=8) LatKMI LatHC

light 0++ scalar and spectrum nf=8 LSD new

mass spectrum decay constants

M0++ ~ 1 TeV?

light 0++ scalar and spectrum nf=8 LSD new

M0++ ~ 1 TeV? discussion topic: what do we do with pletora of goldstones?

0.5 1 1.5 2 2.5 1 2 3 4 5 6 7 ( g2(sL) - g2(L) ) / log(s2) g2(L) fund Nf = 4 c = 3/10 s = 3/2 fund Nf = 8 c = 3/10 s = 3/2 sextet Nf = 2 c = 7/20 s = 3/2 fund Nf = 12 c = 1/5 s = 2

LatHC and Boulder Nf = 2 sextet LatHC Nf = 4 fundamental LatHC and Boulder Nf = 8 fundamental sextet beta function! Boulder Nf = 12 fundamental

scale-dependent coupling of the 3 lattice BSM models

without the gradient flow based method this accuracy would not have been possible New analysis ? IRFP?

3.2 β 2 4 6 8 10 12 14 16 18 20 22 M / F 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 M / TeV MN Ma1 Mρ

0++ scalar Higgs?

a0 scalar isovector?

light 0++ scalar and spectrum sextet model LatHC

does not fit hyperscaling

0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M / Fπ a0 π f0 β=3.25 0.01 0.02 0.03 0.04 0.05 Mπ

2

2 4 6 8 10 12 14 M/Fπ 0.5 1 1.5 2 2.5 3 M / TeV N a1 ρ β=3.20 Decreasing Mπ Decreasing Mπ

also CP3

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5

m M2

π/2m

rooted staggered chiral perturbation theory

Nf = 2 sextet rep β = 3.20 323× 64 to 563× 96 volumes (extrapolated) B = 1.06 ± 0.29 F = 0.017 ± 0.0024 Λ3 = 0.4085 ± 0.0096 Λ4 = 0.578 ± 0.043 CM = 2.597 ± 0.97 CF = −0.644 ± 0.044 ∆ = 0.005 input

χ2/dof = 0.86 Q = 0.53

m fit range: 0.001 − 0.005

1 2 3 4 5 6 7 x 10

−3

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

m M2

π

Nf = 2 sextet rep β = 3.20 323× 64 to 563× 96 volumes (extrapolated) B = 1.06 ± 0.29 F = 0.0165 ± 0.0024 Λ3 = 0.4085 ± 0.0096 Λ4 = 0.578 ± 0.043 CM = 2.597 ± 0.97 CF = −0.644 ± 0.044 ∆ = 0.005 input χ2/dof = 0.86 Q = 0.53 m fit range: 0.001 − 0.005

rooted staggered chiral perturbation theory

1 2 3 4 5 6 7 x 10

−3

0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

m Fπ

B = 1.06 ± 0.29 F = 0.017 ± 0.002 Λ3 = 0.4085 ± 0.0096 Λ4 = 0.578 ± 0.04 CM = 2.597 ± 0.97 CF = −0.644 ± 0.044 ∆ = 0.005 input χ2/dof = 0.855 Q = 0.53 Nf = 2 sextet rep β = 3.20 323× 64 − 563× 96 volumes (extrapolated) m fit range: 0.001 − 0.005

rooted staggered chiral perturbation theory

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5

m M2

π/2m

rooted staggered chiral perturbation theory

Nf = 2 sextet rep β = 3.20 323× 64 to 563× 96 volumes B = 1.78 ± 0.73 F = 0.021 ± 0.0043 Λ3 = 0.4318 ± 0.015 Λ4 = 0.656 ± 0.071 CM = 1.203 ± 0.87 CF = −0.632 ± 0.019 ∆ = 0.005 input

χ2/dof = 1.2 Q = 0.3

m fit range: 0.0015 − 0.005

rsChiPT analysis of Mpi and Fpi

fitting results

two outstanding spectroscopy problems:

• 1. effective low energy theory for Goldstone

dynamics coupled to the low mass scalar topic: nonlinear sigma model or dilaton?

• 2. effect of slow topology on the analysis

topic: ChiPT at fixed topology?

Goldstone dynamics coupled to low mass scalar

π

σ

fπ

Mπ, Fπ, Mσ are calculated now to 1-loop: extended chiral SU(2) flavor dynamics We are analyzing the small pion mass region in the Mπ = 0.07- 0.013 range

• f the p-regime, and lower in the RMT regime

To reach the nonlinear sigma model range requires very small pion masses how to differentiate from effective dilaton action? work in progress

0.5 1 1.5 2 1 2 3 4 5 <q-

v qv> / !

MvvL Nf = 2, mu=10 MeV, L=2 fm new formula ("=0) p-expansion (#=0) $-expansion ("=0) 0.5 1 1.5 2 5 10 15 20 25 30 %&"(')/ ! '!V Nf = 2, L=2 fm, mu=10 MeV new formula ("=0) p-expansion (#=0) $-expansion ("=0)

epsilon regime, p regime to epsilon regime crossover

2 4 6 8 10 12 14 16 18 20 1 2 x 10

−4

eigenvalue scale z

microscopic spectral density ρ(z,m)

Vol=643× 96 β=3.25 m=0.001 40 configurations with Q=0 flow time t=3 z=λ⋅Σ V

microscopic spectral density ρ(z,m)

2 4 6 8 10 12 14 16 18 20 1 2 3 4 5 6

scale z

mode number

Vol=643× 96 β=3.25 m=0.001 40 configurations with Q=0 flow time t=3 z=λ⋅Σ V

Mode number distribution of eigenvalues

0.005 0.01 0.015 0.02 0.025 0.03 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

valence mass m Fπ

m fit range: 0.006 − 0.014 643× 96 NLO linear fit β=3.25 m = 0.001 original ensemble Fπ = F + pF⋅ m F = 0.0125 ± 0.00024 pF = 0.424 ± 0.021 χ2/dof = 0.534

sextet mixed action at flow time t=3 Fπ (rwall pion channel)

fitted linear fit

0.2 0.4 0.6 0.8 1 1.2 x 10

−3

0.5 1 1.5 2 2.5 3 3.5 4 x 10

−3

eigenvalue scale λ

spectral density 2πρ(λ,m)

Vol=643× 96 β=3.25 m=0.001 40 configurations with Q=0 direct eigenvalue spectrum: blue Chebyshev expansion 8K and 20 noise vectors: magenta spectral density

taste symmetry restored

mixed action RMT regime

0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

λ scale of spectrum

γ(λ,m)

643× 96 (magenta) β=3.25 m=0.001 LatHC anomalous mass dimension from full Dirac spectrum (sextet rep)

anomalous mass dimension

new, preliminary

The chiral condensate mass anomalous dimension

Del Debbio and collaborators and Boulder group pioneered fitting procedures

ν R(M R,mR) = ν(M,m) ≈ const ⋅ M

4 1+γ m (M ),

• r equivalently, ν(M,m) ≈ const ⋅λ

4 1+γ m (λ) , with γ m(λ) fitted

new results for nf=12

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 2 3 4 5 6 7 x 10

7

λ eigenvalue scale

Mode Number

full spectrum counted correctly 10 gauge configurations Chebyshev order: T

1(t) − T8,000(t)

20 noise vectors 643× 96 β=3.25 m=0.001

Mode number distribution flow time t=0

UV scale IR scale

lim

|x|→∞

ρ(x)ρ(0)

• Q = 1

Ω Q 2 Ω − χt −

c4 2χtΩ

• + O
• Ω−3

,

• e c4 = −(Q 4−3Q 22)/Ω. T

an average in a given topolog

C(t1 − t2) ≡

• Q (t1)Q (t2)
• =
• x1,

x2

ρ(x1)ρ(x2)

• ,

0.000138

• 0.000

0.0001

matlab_s

• 0.000114

5 10 15 20 25 30 35 −1 −0.5 0.5 1 1.5 2 2.5 3 x 10

−11

sub-volume idea to explore technology for visualizing topological density

eta’ ? diphoton bump?

eta’ ? diphoton bump?

Kogut-Sinclair EW phase transition Relevance in early cosmology (order of the phase transition?) LatHC is doing a new analysis using different methods

28

Early universe

• Nf=2 Qu=2/3 Qd = -1/3 fundamental rep

udd neutral dark matter candidate

• dark matter candidate sextet Nf=2

electroweak active in the application

• 1/2 unit of electric charge (anomalies)
• rather subtle sextet baryon

construction (symmetric in color)

• charged relics not expected?

Three SU(3) sextet fermions can give rise to a color singlet. The tensor product 6⌦6⌦6 can be decomposed into irreducible representations of SU(3) as, 6⌦6⌦6 = 12⇥810103⇥27282⇥35 where irreps are denoted by their dimensions and 10 is the complex conjugate of 10. Fermions in the 6-representation carry 2 indices, ψab, and transform as ψaa0 ! Uab Ua0b0 ψbb0 and the singlet can be constructed explicitly as εabc εa0b0c0 ψaa0 ψbb0 ψcc0.

topic: challenges of baryon spectroscopy and dark matter implications?

3.2 β 2 4 6 8 10 12 14 16 18 20 22 M / F 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 M / TeV MN Ma1 Mρ

0++ scalar Higgs?

a0 scalar isovector?

We want to understand:

light scalar separated from 2-3 TeV resonance spectrum More complex scalar spectrum close to CW? what is the eta’? diphoton bump? entangled scalar-goldstone dynamics sigma model or dilaton? tuning to CW and away from CW? bridge between UV and IR scale? scale-dependent gauge coupling - high precision what list of predictions independent of mass generation? related phenomenology consistent EW embedding ➞ dark matter lattice: actually have to solve the theory BSM needs new lattice tools RMT and delta-regime scaled up QCD cannot do this

diphoton res?

summary: topics for further discussions