[PPT] - The Higgs Particle and the Lattice KMI 2013 Julius Kuti University PowerPoint Presentation

SLIDE 1

KMI 2013

Julius Kuti University of California, San Diego KMI International Symposium 2013 Nagoya, December 11-13, 2013

The Higgs Particle and the Lattice

1

SLIDE 2

Outline

Lattice BSM after the Higgs discovery Light Higgs near conformality

light scalar (dilaton-like?) close to conformal window EW precision and S-parameter scale setting and spectroscopy

Running coupling

running (walking?) coupling from gradient flow

Chiral condensate

new stochastic method for spectral density large anomalous dimension

Early universe

EW phase transition dark matter

Summary and Outlook

near-conformal sextet theory

SLIDE 3

Large Hadron Collider - CERN

A Higgs-like particle is found

Is it the Standard Model Higgs? or

Near-conformal strong dynamics?
Composite PNGB-like Higgs?
SUSY?
5 Dim?

...

Primary focus of BSM lattice effort and this talk

primary mission:

Search for Higgs particle
Origin of Electroweak symmetry breaking

3

SLIDE 4

LATTICE GAUGE THEORIES AT THE ENERGY FRONTIER

Thomas Appelquist, Richard Brower, Simon Catterall, George Fleming, Joel Giedt, Anna Hasenfratz, Julius Kuti, Ethan Neil, and David Schaich (USQCD Collaboration)

(Dated: March 10, 2013)

4

USQCD BSM White Paper - community based effort input into US Snowmass 2013 planning:

USQCD and the composite Higgs at the Energy Frontier

The recent discovery of the Higgs-like particle at 126 GeV is the beginning of the experimental search for a deeper dynamical explanation of electroweak symmetry breaking beyond the Standard Model (BSM). The USQCD collaboration has developed an important BSM research direction with the primary focus on the composite Higgs mechanism as outlined in our recent USQCD BSM white paper [1] and in this short report. Deploying advanced lattice field theory technology, we are investigating new strong gauge dynamics to explore consistency with a composite Higgs particle at 126 GeV which will require new non-perturbative insight into this fundamental problem. The

rganizing principle of our program is to explore the dynamical implications of approximate scale

invariance and chiral symmetries with dynamical symmetry breaking patterns that may lead to the composite Higgs mechanism with protection of the light scalar mass, well separated from predicted new resonances, which maybe on the 1-2 TeV scale. Based on an underlying strongly-coupled theory, lattice calculations provide the masses and decay constants of these new particles, enabling concrete predictions for future experimental results at colliders and in dark matter searches. On the other hand, if the higher resonances are too heavy to be directly probed at the LHC, indirect evidence for Higgs compositeness may appear for example as altered rates for electroweak gauge boson scattering, changes to the Higgs coupling constants, or the presence of additional light Higgs-like resonances. Here lattice calculations are used to derive the low energy constants in an Effective Field Theory description to predict departures of a composite Higgs dynamics from the standard model predictions. Of course as new experimental evidence from the LHC is forthcoming, BSM lattice simulations will be focused on an increasingly narrower class of candidate theories, consistent with experimental constraints, increasing its power as a theoretical tool in the search for BSM physics. Two major components of our BSM lattice program are carefully planned and coordinated, as summarized below.

0.005 0.01 0.015 0.1 0.2 0.3 0.4 0.5 0.6

fermion mass m

triplet and singlet masses

0++ triplet state (connected) 0++ singlet state (disconnected)

Mt/s = at/s + bt/s m (fitting functions) =3.2 323× 64 F = 0.0279 (4) setting the EWSB scale MH/F ~ 1−3 range

Triplet and singlet masses from 0

++ correlators

FIG. 1.

This plot is unpublished and for illustration only. Some of the flavor singlet scalar data points are expected to remain in flux before final analysis and publication [3]. The ongoing work indicates the emergence of a light flavor singlet scalar state (red) with 0++ quantum numbers in the sextet rep of a fermion doublet with the minimal realization of the composite Higgs mechanism. Annihilation diagrams driven by strong gauge dynamics downshift the mass of the flavor singlet state close to the EWSB scale. Turning on a third massive EW singlet in the model might bring the β-function even closer to zero with minimal tuning. The fermion mass dependence of the isotriplet meson (blue) is also shown, not effected by disconnected annihilation diagram. In the chiral limit it is a heavy resonance above 1 TeV. The model predicts several resonances in the 1-2 TeV range.

FIG. 2. From [11], lattice simulation results for the S-parameter per electroweak doublet, comparing SU(3) gauge

theories with Nf = 2 (red triangles) and Nf = 6 (blue circles) degenerate strongly-coupled fermions in the fundamental representation. The horizontal axis is proportional to the pseudoscalar Goldstone boson mass squared, or equivalently the input fermion mass m. The Nf = 2 value of S is in conflict with electroweak precision measure- ments, but the reduction at Nf = 6 indicates that the value of S in many-fermion theories can be acceptably small, in contrast to more na¨ ıve scaling estimates [13].

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USQCD lattice BSM project sites (a few years ago map was empty)

UCSD UoP LLNL U Colorado FNAL Argonne Syracuse RPI Columbia Yale BU

It is a world-wide effort !

5

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It is a world-wide effort (latKMI is playing important role!)

6

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It is a world-wide effort (latKMI is playing important role!)

6

Leading effort on spectrum of 0++ vacuum (Higgs) channel:

latKMI and LHC group

Lattice Higgs Collaboration:

with Zoltan Fodor, Kieran Holland, Santanu Mondal, Daniel Nogradi, (Chris Schroeder), Chik Him Wong

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Congratulations latKMI for the excellent lattice BSM work !

SLIDE 9

After the Higgs is found why bother with BSM?

Nothing else was seen and perhaps no new physics below the Planck scale?

But Standard Model Higgs potential is

parametrization rather than dynamical explanation ? λϕ4 not a fundamental gauge force - consequences?

Built in cutoff from triviality with quadratic

divergences leading to fine tuning and the hierarchy problem; vacuum instability

Standard Model is low energy effective theory with

built in cut-off ?

Can new physics from compositeness hide within

the LHC run2 reach ?

Isn’t compositeness dead anyway and we

should not expect it in LHC run2 ?

8

Rational for BSM:

SLIDE 10

9

v

i

c e s : a l i g h t H i g g s

l

i k e s c a l a r w a s f

u

n d , c

n

s i s t e n t w i t h S M w i t h i n e r r

r

s , a n d c

m

p

s

i t e s t a t e s h a v e n

t

b e e n s e e n b e l

w

1 T e V . S t r

n

g l y c

u

p l e d B S M g a u g e t h e

r

i e s a r e H i g g s

l

e s s w i t h r e s

n

a n c e s b e l

w

1 T e V f a c t s : C

m

p

s

i t e n e s s a n d a l i g h t H i g g s s c a l a r a r e n

t

i n c

m

p a t i b l e ; s e a r c h f

r

c

m

p

s

i t e s t a t e s w a s n

t

b a s e d

n

s

l

i d p r e d i c t i

n

s b u t

n

n a i v e l y s c a l e d u p Q C D a n d u n a c c e p t a b l e

l

d t e c h n i c

l
r

g u e s s i n g g a m e s . R e s

n

a n c e s ,

u

t

f

L H C r u n 1 r e a c h , a r e i n t h e 2

3

T e V r a n g e i n t h e t h e

r

y I w i l l d i s c u s s l a t t i c e B S M p l a n s : L H C r u n 2 w i l l s e a r c h f

r

n e w p h y s i c s f r

m

c

m

p

s

i t e n e s s a n d S U S Y , a n d t h e l a t t i c e B S M c

m

m u n i t y i s p r e p a r i n g q u a n t i t a t i v e l a t t i c e b a s e d p r e d i c t i

n

s t

b

e r u l e d i n

r

r u l e d

u

t . W e b e t t e r g e t t h i s r i g h t !

Rational for BSM:

SLIDE 11

t h r e e U S Q C D B S M d i r e c t i

n

s b a s e d

n

g a u g e f

r

c e :

s

t r

n

g l y c

u

p l e d n e a r

c
n

f

r

m a l g a u g e t h e

r

i e s

l

i g h t s c a l a r i s e x p e c t e d f r

m

a p p r

x

i m a t e s c a l e i n v a r i a n c e ( d i l a t

n

,

r

j u s t l i g h t s c a l a r ? )

Q

C D i s N O T a p p r

x

i m a t e l y s c a l e i n v a r i a n t m a k i n g

l

d t e c h n i c

l
r

g u e s s i n g g a m e s i r r e l e v a n t

l

i g h t p s e u d

G
l

d s t

n

e b

s
n

( l i k e l i t t l e H i g g s )

s

t a r t s f r

m

a s c a l a r m a s s l e s s G

l

d s t

n

e b

s
n
e

x p e c t s t

m

a k e q u a n t i t a t i v e p r e d i c t i

n

s a b

u

t c

m

p

s

i t e s p e c t r u m a b

v

e 1 T e V

S

U S Y

f
r

b e t t e r u n d e r s t a n d i n g

f

d y n a m i c a l s y m m e t r y b r e a k i n g a n d t

e

x p l

r

e s u s y t h e

r

y s c e n a r i

s
We are making testable quantitative predictions

for LHC run2 (e.g. sextet)

10

Rational for BSM:

SLIDE 12

t h r e e U S Q C D B S M d i r e c t i

n

s b a s e d

n

g a u g e f

r

c e :

s

t r

n

g l y c

u

p l e d n e a r

c
n

f

r

m a l g a u g e t h e

r

i e s

l

i g h t s c a l a r i s e x p e c t e d f r

m

a p p r

x

i m a t e s c a l e i n v a r i a n c e ( d i l a t

n

,

r

j u s t l i g h t s c a l a r ? )

Q

C D i s N O T a p p r

x

i m a t e l y s c a l e i n v a r i a n t m a k i n g

l

d t e c h n i c

l
r

g u e s s i n g g a m e s i r r e l e v a n t

l

i g h t p s e u d

G
l

d s t

n

e b

s
n

( l i k e l i t t l e H i g g s )

s

t a r t s f r

m

a s c a l a r m a s s l e s s G

l

d s t

n

e b

s
n
e

x p e c t s t

m

a k e q u a n t i t a t i v e p r e d i c t i

n

s a b

u

t c

m

p

s

i t e s p e c t r u m a b

v

e 1 T e V

S

U S Y

f
r

b e t t e r u n d e r s t a n d i n g

f

d y n a m i c a l s y m m e t r y b r e a k i n g a n d t

e

x p l

r

e s u s y t h e

r

y s c e n a r i

s
We are making testable quantitative predictions

for LHC run2 (e.g. sextet)

10

c

m

p

s

i t e n e s s Rational for BSM:

SLIDE 13

t h r e e U S Q C D B S M d i r e c t i

n

s b a s e d

n

g a u g e f

r

c e :

s

t r

n

g l y c

u

p l e d n e a r

c
n

f

r

m a l g a u g e t h e

r

i e s

l

i g h t s c a l a r i s e x p e c t e d f r

m

a p p r

x

i m a t e s c a l e i n v a r i a n c e ( d i l a t

n

,

r

j u s t l i g h t s c a l a r ? )

Q

C D i s N O T a p p r

x

i m a t e l y s c a l e i n v a r i a n t m a k i n g

l

d t e c h n i c

l
r

g u e s s i n g g a m e s i r r e l e v a n t

l

i g h t p s e u d

G
l

d s t

n

e b

s
n

( l i k e l i t t l e H i g g s )

s

t a r t s f r

m

a s c a l a r m a s s l e s s G

l

d s t

n

e b

s
n
e

x p e c t s t

m

a k e q u a n t i t a t i v e p r e d i c t i

n

s a b

u

t c

m

p

s

i t e s p e c t r u m a b

v

e 1 T e V

S

U S Y

f
r

b e t t e r u n d e r s t a n d i n g

f

d y n a m i c a l s y m m e t r y b r e a k i n g a n d t

e

x p l

r

e s u s y t h e

r

y s c e n a r i

s
We are making testable quantitative predictions

for LHC run2 (e.g. sextet)

10

c

m

p

s

i t e n e s s Rational for BSM:

TeV

A1 ~ 2.4 TeV Rho~1.7 TeV scalar composite at 500 GeV?

bserved Higgs-like

EW self-energy

from approximate scale invariance

t W Z

then δM2

H ⌅ 12κ2r2 t m2 t ⌅

κ2r2

t (600 GeV)2.

SLIDE 14

t h r e e U S Q C D B S M d i r e c t i

n

s b a s e d

n

g a u g e f

r

c e :

s

t r

n

g l y c

u

p l e d n e a r

c
n

f

r

m a l g a u g e t h e

r

i e s

l

i g h t s c a l a r i s e x p e c t e d f r

m

a p p r

x

i m a t e s c a l e i n v a r i a n c e ( d i l a t

n

,

r

j u s t l i g h t s c a l a r ? )

Q

C D i s N O T a p p r

x

i m a t e l y s c a l e i n v a r i a n t m a k i n g

l

d t e c h n i c

l
r

g u e s s i n g g a m e s i r r e l e v a n t

l

i g h t p s e u d

G
l

d s t

n

e b

s
n

( l i k e l i t t l e H i g g s )

s

t a r t s f r

m

a s c a l a r m a s s l e s s G

l

d s t

n

e b

s
n
e

x p e c t s t

m

a k e q u a n t i t a t i v e p r e d i c t i

n

s a b

u

t c

m

p

s

i t e s p e c t r u m a b

v

e 1 T e V

S

U S Y

f
r

b e t t e r u n d e r s t a n d i n g

f

d y n a m i c a l s y m m e t r y b r e a k i n g a n d t

e

x p l

r

e s u s y t h e

r

y s c e n a r i

s
We are making testable quantitative predictions

for LHC run2 (e.g. sextet)

10

c

m

p

s

i t e n e s s Rational for BSM:

SLIDE 15

t h r e e U S Q C D B S M d i r e c t i

n

s b a s e d

n

g a u g e f

r

c e :

s

t r

n

g l y c

u

p l e d n e a r

c
n

f

r

m a l g a u g e t h e

r

i e s

l

i g h t s c a l a r i s e x p e c t e d f r

m

a p p r

x

i m a t e s c a l e i n v a r i a n c e ( d i l a t

n

,

r

j u s t l i g h t s c a l a r ? )

Q

C D i s N O T a p p r

x

i m a t e l y s c a l e i n v a r i a n t m a k i n g

l

d t e c h n i c

l
r

g u e s s i n g g a m e s i r r e l e v a n t

l

i g h t p s e u d

G
l

d s t

n

e b

s
n

( l i k e l i t t l e H i g g s )

s

t a r t s f r

m

a s c a l a r m a s s l e s s G

l

d s t

n

e b

s
n
e

x p e c t s t

m

a k e q u a n t i t a t i v e p r e d i c t i

n

s a b

u

t c

m

p

s

i t e s p e c t r u m a b

v

e 1 T e V

S

U S Y

f
r

b e t t e r u n d e r s t a n d i n g

f

d y n a m i c a l s y m m e t r y b r e a k i n g a n d t

e

x p l

r

e s u s y t h e

r

y s c e n a r i

s
We are making testable quantitative predictions

for LHC run2 (e.g. sextet)

10

c

m

p

s

i t e n e s s Rational for BSM:

TeV

resonances in 1-2 TeV range

bserved Higgs-like at 125 GeV

EW self-energy

PNGB (little Higgs) scenario

massless scalar pseudo-Goldstone

SLIDE 16

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 needle in the haystack?

spontaneous symmetry breaking Higgs mechanism

What is the composite Higgs mechanism?

SLIDE 17

light Higgs near conformality (dilaton-like?) sextet

QCD far from scale invariance

SLIDE 18

light Higgs near conformality (dilaton-like?) sextet

SLIDE 19

light Higgs near conformality (dilaton-like?) sextet

to illustrate: sextet SU(3) color rep

ne massless fermion doublet

three Goldstone pions become longitudinal components of weak bosons composite Higgs mechanism scale of Higgs condensate ~ F=250 GeV conflicts with EW constraints?

u d ⎡ ⎣ ⎢ ⎤ ⎦ ⎥

χSB on Λ~TeV scale

near-conformal (scale invariant)

SLIDE 20

light Higgs near conformality (dilaton-like?) sextet

auction for naming rights?

to illustrate: sextet SU(3) color rep

ne massless fermion doublet

three Goldstone pions become longitudinal components of weak bosons composite Higgs mechanism scale of Higgs condensate ~ F=250 GeV conflicts with EW constraints?

u d ⎡ ⎣ ⎢ ⎤ ⎦ ⎥

χSB on Λ~TeV scale

near-conformal (scale invariant)

SLIDE 21

walking coupling separates two scales? target of lattice BSM?

when chiral symmetry breaking turns conformal FP into walking

running coupling QCD-like far from conformal window

χSB

walking gauge coupling? fermion mass generation (effective EW int) composite Higgs mechanism ? broken scale invariance (dilaton) ?

r light non-SM composite Higgs

particle? Early work using sextet rep: Marciano (QCD paradigm, 1980) Kogut,Shigemitsu,Sinclair (quenched, 1984) recent work: Sannino and collaborators DeGrand,Shamir,Svetitsky IRFP or walking gauge coupling Lattice Higgs Collaboration Kogut,Sinclair finite temperature

χSB on Λ~TeV scale χSB

light Higgs near conformality (dilaton-like?) sextet

to illustrate: sextet SU(3) color rep

ne massless fermion doublet

three Goldstone pions become longitudinal components of weak bosons composite Higgs mechanism scale of Higgs condensate ~ F=250 GeV conflicts with EW constraints?

u d ⎡ ⎣ ⎢ ⎤ ⎦ ⎥

χSB on Λ~TeV scale

SLIDE 22

two expectations:

(1) χSB and confinement (2) light scalar close to CW (with walking) ?

walking coupling separates two scales? target of lattice BSM?

when chiral symmetry breaking turns conformal FP into walking

running coupling QCD-like far from conformal window

χSB

walking gauge coupling? fermion mass generation (effective EW int) composite Higgs mechanism ? broken scale invariance (dilaton) ?

r light non-SM composite Higgs

particle? Early work using sextet rep: Marciano (QCD paradigm, 1980) Kogut,Shigemitsu,Sinclair (quenched, 1984) recent work: Sannino and collaborators DeGrand,Shamir,Svetitsky IRFP or walking gauge coupling Lattice Higgs Collaboration Kogut,Sinclair finite temperature

χSB on Λ~TeV scale χSB

light Higgs near conformality (dilaton-like?) sextet

to illustrate: sextet SU(3) color rep

ne massless fermion doublet

three Goldstone pions become longitudinal components of weak bosons composite Higgs mechanism scale of Higgs condensate ~ F=250 GeV conflicts with EW constraints?

u d ⎡ ⎣ ⎢ ⎤ ⎦ ⎥

χSB on Λ~TeV scale

SLIDE 23

14

light Higgs near conformality (dilaton-like?)

mσ fσ → ?

m2

σ ⌅ 4

f 2

σ

⇧0| ⌃ Θµ

µ(0)

⌥

NP|0⌃ .

Partially Conserved Dilatation Current (PCDC) Will gradient flow based technology make the argument less slippery?

sextet

−

∂µDµ = Θµ

µ = β(α)

4α Ga

µνGaµν .

Dilatation current

−

⌅0|Θµν(x)|σ(p)⇧ = fσ

3 (pµpν gµνp2)eipx

−

⌅0|∂µDµ(x)|σ(p)⇧ = fσm2

σeipx .

−

Θµ

µ

⇥

NP = β(α)

4α

Ga

µνGaµν⇥ NP ,

removing the perturbative part of

Bardeen, Ellis, Yamawaki, Appelquist, ...

SLIDE 24

but how light is light ? then δM2

H ⌅ 12κ2r2 t m2 t ⌅

few hundred GeV Higgs impostor? Foadi, Fransden, Sannino

pen for spirited theory discussions

t W Z

κ2r2

t (600 GeV)2.

14

light Higgs near conformality (dilaton-like?)

mσ fσ → ?

m2

σ ⌅ 4

f 2

σ

⇧0| ⌃ Θµ

µ(0)

⌥

NP|0⌃ .

Partially Conserved Dilatation Current (PCDC) Will gradient flow based technology make the argument less slippery?

sextet

−

∂µDµ = Θµ

µ = β(α)

4α Ga

µνGaµν .

Dilatation current

−

⌅0|Θµν(x)|σ(p)⇧ = fσ

3 (pµpν gµνp2)eipx

−

⌅0|∂µDµ(x)|σ(p)⇧ = fσm2

σeipx .

−

Θµ

µ

⇥

NP = β(α)

4α

Ga

µνGaµν⇥ NP ,

removing the perturbative part of

Bardeen, Ellis, Yamawaki, Appelquist, ...

SLIDE 25

but how light is light ? then δM2

H ⌅ 12κ2r2 t m2 t ⌅

few hundred GeV Higgs impostor? Foadi, Fransden, Sannino

pen for spirited theory discussions

t W Z

κ2r2

t (600 GeV)2.

14

light Higgs near conformality (dilaton-like?)

mσ fσ → ?

m2

σ ⌅ 4

f 2

σ

⇧0| ⌃ Θµ

µ(0)

⌥

NP|0⌃ .

Partially Conserved Dilatation Current (PCDC) Will gradient flow based technology make the argument less slippery?

sextet

−

∂µDµ = Θµ

µ = β(α)

4α Ga

µνGaµν .

Dilatation current

−

⌅0|Θµν(x)|σ(p)⇧ = fσ

3 (pµpν gµνp2)eipx

−

⌅0|∂µDµ(x)|σ(p)⇧ = fσm2

σeipx .

−

Θµ

µ

⇥

NP = β(α)

4α

Ga

µνGaµν⇥ NP ,

removing the perturbative part of

0.005 0.01 0.015 0.1 0.2 0.3 0.4 0.5 0.6

fermion mass m

triplet and singlet masses

0++ triplet state (connected) 0++ singlet state (disconnected)

Mt/s = at/s + bt/s m (fitting functions) =3.2 323× 64 F = 0.0279 (4) setting the EWSB scale MH/F ~ 1−3 range

Triplet and singlet masses from 0

++ correlators

LHC

Nf=2 sextet scalar not fermiophobic?

283x56, 323x64, 483x96 m fit range 0.003 - 0.008

Bardeen, Ellis, Yamawaki, Appelquist, ...

SLIDE 26

but how light is light ? then δM2

H ⌅ 12κ2r2 t m2 t ⌅

few hundred GeV Higgs impostor? Foadi, Fransden, Sannino

pen for spirited theory discussions

t W Z

κ2r2

t (600 GeV)2.

14

light Higgs near conformality (dilaton-like?)

mσ fσ → ?

m2

σ ⌅ 4

f 2

σ

⇧0| ⌃ Θµ

µ(0)

⌥

NP|0⌃ .

Partially Conserved Dilatation Current (PCDC) Will gradient flow based technology make the argument less slippery?

sextet

−

∂µDµ = Θµ

µ = β(α)

4α Ga

µνGaµν .

Dilatation current

−

⌅0|Θµν(x)|σ(p)⇧ = fσ

3 (pµpν gµνp2)eipx

−

⌅0|∂µDµ(x)|σ(p)⇧ = fσm2

σeipx .

−

Θµ

µ

⇥

NP = β(α)

4α

Ga

µνGaµν⇥ NP ,

removing the perturbative part of

0.005 0.01 0.015 0.1 0.2 0.3 0.4 0.5 0.6

fermion mass m

triplet and singlet masses

0++ triplet state (connected) 0++ singlet state (disconnected)

Mt/s = at/s + bt/s m (fitting functions) =3.2 323× 64 F = 0.0279 (4) setting the EWSB scale MH/F ~ 1−3 range

Triplet and singlet masses from 0

++ correlators

LHC

Nf=2 sextet scalar not fermiophobic?

283x56, 323x64, 483x96 m fit range 0.003 - 0.008

dilaton-like scalar states in SCGT, or “just a light Higgs” ?

Bardeen, Ellis, Yamawaki, Appelquist, ...

SLIDE 27

Decay Mode ATLAS CMS Tevatron H → bb 0.2 + 0.7

− 0.6

1.15 ± 0.62 1.59 + 0.69

− 0.72

H → ττ 0.7 + 0.7

− 0.6

1.10 ± 0.41 1.68 + 2.28

− 1.68

H → γγ 1.55 + 0.33

− 0.28

0.77 ± 0.27 5.97 + 3.39

− 3.12

H → WW∗ 0.99 + 0.31

− 0.28

0.68 ± 0.20 0.94 + 0.85

− 0.83

H → ZZ∗ 1.43 + 0.40

− 0.35

0.92 ± 0.28 Combined 1.23 ± 0.18 0.80 ± 0.14 1.44 + 0.59

− 0.56

L = v2 4 h uµuµ i 1 + 2ω v S 1 ! + FA 2 p 2 h Aµν f µν

i

+ FV 2 p 2 h Vµν f µν

+ i + iGV

2 p 2 h Vµν[uµ, uν] i + p 2λS A

1 ∂µS 1h Aµνuν i ,

(1)

V V V V A A A A S S S S S S S S A A A V V V V A

light composite Higgs and EW constraints

NLO S-param global fits NLO T-param From Higgs potential and Top coupling: MH > 130 GeV absolute stable vacuum below MPl

bserved Higgs -> Metastable vacuum

nal state, in units of the µ ≡ σ · Br/(σSM · BrSM).

µ = 0.96 ± 0.11

effective theory of strongly coupled composite Higgs scenario u: Goldstone S: scalar (Higgs) f: gauge field A: axial resonances V: vector resonance

ω 1

global fit to electroweak pre- alues S = 0.03 ± 0.10 and es tree-level contributions

cision data determines T = 0.05 ± 0.12 from vector and axial-v

SLIDE 28

MV Ω

0.4 0.2 0.0 0.2 0.4 0.4 0.2 0.0 0.2 0.4

S T

light composite Higgs and EW constraints

FIG. 2. NLO determinations of S and T , imposing the two
WSRs. The approximately vertical curves correspond to con-

stant values of MV , from 1.5 to 6.0 TeV at intervals of 0.5 TeV. The approximately horizontal curves have constant values of ω: 0.00, 0.25, 0.50, 0.75, 1.00. The arrows indicate the directions of growing MV and ω. The ellipses give the experimen- tally allowed regions at 68% (orange), 95% (green) and 99% (blue) CL.

Pich, Rosell, Sanz-Cillero

S =

π

g

θW

Z 1

t

ρS t ρS t

,

t W B

S LO = 4π B B B B @ F2

V

M2

V

F2

A

M2

A

1 C C C C A , T = 4π g02 cos2 θW Z 1 dt t2 [ ρT(t) ρT(t)SM ] ,

From two Weinberg sum rules and from NLO loop expansion: MV, MA ~ 2 TeV or higher is compatible with S,T constraints (it is tight and arguably ambiguous) more work needed related body of work by Sannino and collaborators

SLIDE 29

β=3.2 A1/F ~ 9.5 MA1~ 2.37 TeV LHC14?

Nf=2 SU(3) sextet Ma0, Mρ, and MA1
three lowest states above light scalar “Higgs state”

17

0.002 0.004 0.006 0.008 0.01 0.012 0.1 0.2 0.3 0.4 0.5 0.6

m M and MA1

m fit range: 0.003 − 0.010

input from volumes 243× 48, 323× 64, 483× 96

MA1 = M0 + c1 m =3.2 M0= 0.264 ± 0.01 c1= 30.6 ± 2 2/dof= 1.1 sextet model A1 and Rho mesons split linear chiral fit

A1 A1 fit Rho Rho fit

250 GeV scale

0.002 0.004 0.006 0.008 0.01 0.012 0.01 0.02 0.03 0.04 0.05 0.06 0.07

m M2

m fit range: 0.003 − 0.006

inputs from volumes 323× 64 and 483× 96 quadratic fit =3.2 M2

= c1 m + c2 m2

c1 = 6.35 ± 0.21 c2 = −30.9 ± 45.3 2/dof = 2.05

sextet model Goldstone pion in PCAC channel

fitted not fitted linear part only quadratic fit

χSB

Goldstone mode of composite Higgs

0.002 0.004 0.006 0.008 0.01 0.012 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

m F

m fit range: 0.003 − 0.006 inputs from volumes 323× 64 and 483× 96 linear fit =3.2 F = c0 + c1 m c0 = 0.0279 ± 0.0004 c1 = 3.1 ± 0.1 2/dof = 0.923

sextet model F from PCAC channel

fitted not fitted linear fit

setting the EW scale F = c0 fitted 250 GeV scale

Spectroscopy and scale setting sextet Nf=2

SLIDE 30

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

test of technology:

LHC

Spectroscopy and scale setting (scalar) Nf=12

SLIDE 31

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:

LHC

Spectroscopy and scale setting (scalar) Nf=12

SLIDE 32

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 M 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 LHC used it for crosscheck good agreement Nf=8/12 KMI talks

Spectroscopy and scale setting (scalar) Nf=12

LHC group was holding back on Nf=8 (USBSM incite) It has always been a low-hanging fruit New development: LHC is doing Nf=8 now second generation rerun of earlier published work

SLIDE 33

Spectroscopy (scalar) sextet Nf=2

SLIDE 34

0.005 0.01 0.015 0.1 0.2 0.3 0.4 0.5 0.6

fermion mass m

triplet and singlet masses

0++ triplet state (connected) 0++ singlet state (disconnected)

Mt/s = at/s + bt/s m (fitting functions) =3.2 323× 64 F = 0.0279 (4) setting the EWSB scale MH/F ~ 1−3 range

Triplet and singlet masses from 0

++ correlators

LHC

Nf=2 sextet scalar not fermiophobic?

283x56, 323x64, 483x96 m fit range 0.003 - 0.008

Spectroscopy (scalar) sextet Nf=2

SLIDE 35

TeV

A1 ~ 2.4 TeV Rho ~ 1.7 TeV

scalar impostor few hundred GeV?

bserved Higgs-like?

EW self-energy

not ruled out from LHC run1 within reach of LHC run2 LHC is working on second generation precision now

t W Z

then δM2

H ⌅ 12κ2r2 t m2 t ⌅

κ2r2

t (600 GeV)2.

A0 ~ 1.5 TeV

Spectroscopy for LHC run2 sextet Nf=2

SLIDE 36

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 −3 −2 −1 1 2 3 4

MD time

Q topological charge =3.2 m=0.008 t=10, dt=0.05 32x64 sample size: 924 cfgs time history of Q topological charge

500 1000 1500 2000 2500 3000 3500 4000 4500 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5

MD time

Q topological charge =3.2 m=0.006 t=10, dt=0.05 32x64 sample size: 820 cfgs time history of Q topological charge

500 1000 1500 2000 2500 3000 3500 4000 4500 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2.5

MD time

Q topological charge =3.2 m=0.004 t=10, dt=0.05 32x64 sample size: 786 cfgs time history of Q topological charge

slowly changing topology complicates the analysis:

it is challenging to deal with it
effect on scalar spectrum is hardly detectable
slow topology can be synthesized by stochastic algorithms

but its practical utilization is unclear

slowly changing topology perhaps can be accelerated in
pen segments of very long lattices in time direction

3200 800 1600 2400 3200

TrajectoryNumbers

0.05 0.1 0.15 0.2 0.25

amf0 L

3xT=32 3x64,

β=3.20, m=0.006

SLIDE 37

0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.2 0.4 0.6 0.8 1 1.2

g2(L) ( g2(sL) − g2(L) )/log(s2)

step function from Wilson flow 1 loop 2 loop

gradient flow on gauge field Nf=4 fundamental rep (LHC) Fritzsch talk at lattice 2013

Nf=2 L ~ 0.4 fm SU(3)

gradient flow coupling with SF boundary conditions

−

−

αc(L) = 4π 3 ⇤t2E(t)⌅ 1 + δ(c)

−

−

while holding c = (8t)1/2/L fixed:

−

−

δ(c) = ϑ4

3(e−1/c2) 1 c4π2

3 Running coupling definition from gauge field gradient flow

⇤E(t)⌅ = 3 4πt2α(q)

1 + k1α(q) + O(α2)

⇥ , q = 1 ⇧ 8t, k1 = 1.0978 + 0.0075 ⇥ Nf.

−

−

massless fermions; antiperiodic all directions s=1.5 step Nf=4 staggered fermions; 4-stout; L=12-36 we have results for Nf=8,12 and Nf=2 sextet Nf=4 c=0.3 L=12-36 beta-function has non- universal but calculable correction beta-function has conventional loop expansion

running coupling and beta-function from gradient flow

SLIDE 38

The chiral (Higgs) condensate

New stochastic method
Direct determination of full spectral density and mode number

distribution on gauge configurations

To remove UV divergences at finite fermion mass
To investigate internal (in)consistencies with GMOR relation
To determine anomalous dimension of the chiral condensate

SLIDE 39

0.002 0.004 0.006 0.008 0.01 0.01 0.02 0.03 0.04 0.05 0.06 0.07

m ¯ ψψ ¯ ψψ = c0 + c1 · m

c0= 0.01037 ± 0.00030 c1= 7.278 ± 0.048 2/dof= 1.47

= 3.20

m range in fit: 0.003 − 0.008

¯ ψψ − χcon = d 0 + d 2 · m 2 chiral condensate and its subtracted form

0.002 0.004 0.006 0.008 0.01 0.005 0.01 0.015 0.02 0.025 c0= 0.01037 ± 0.00030 c1= 7.278 ± 0.048 2/dof= 1.47

m ¯ ψψ − m · χcon ¯ ψψ = c0 + c1 · m = 3.20

d0= 0.00982 ± 0.00010 d2= 209.95 ± 5.95

2/dof= 3.63

1 − m v

d dmv

¯

ψψ pq

mv=m = d 0 + d2 · m 2

subtracted chiral condensate

ρ(λ, m) = 1 V

∞

k=1

δ(λ − λk) lim

λ→0 lim m→0 lim V →∞ ρ(λ, m) = Σ

π

ν(M, m) = V Λ

−Λ

dλ ρ(λ, m), Λ =

M 2 − m2,

νR(MR, mR) = ν(M, mq)

control on UV divergences: mode number density of chiral condensate spectral density mode number density renormalized and RG invariant

(Giusti and Luscher)

The chiral condensate in the sextet theory

SLIDE 40

0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 3 3.5

eigenvalue scale

() spectral density () spectral density of full spectrum =3.20 m=0.003

63,700,9992 eigenvalues in D+D

483× 96

Passed all tests so far
example is from 483x96 lattices
allows the scale-dependent

determination of the anomalous dimension of the chiral condensate new stochastic method sextet Nf=2 direct determination of full spectral density and mode number distribution on gauge configurations

The chiral condensate in the sextet theory

SLIDE 41

3 3.5 4 4.5 5 5.5 x 10

−3

50 100 150 200 250 300

eigenvalue scale M

Mode number (m,M) Vol=483× 96 =3.20 m=0.003

6 configuration (sextet)

300 eigenvalues (m,M) = c0 + c1 M fit Σeff =

π c1 2Vol (1 − m2/M2) 1/2

Nf = 2 eff(M=0.0045/a) =0.0140 ± 0.0001

Mode number distribution (m,M) and condensate eff

new stochastic method sextet Nf=2
comparison with direct calculation
f mode number distribution from

eigenvalue spectrum

stringent test
details in forthcoming publication

The chiral condensate in the sextet theory

SLIDE 42

3 3.5 4 4.5 5 5.5 x 10

−3

50 100 150 200 250 300

eigenvalue scale M

Mode number (m,M) Vol=483× 96 =3.20 m=0.003

6 configuration (sextet)

300 eigenvalues (m,M) = c0 + c1 M fit Σeff =

π c1 2Vol (1 − m2/M2) 1/2

Nf = 2 eff(M=0.0045/a) =0.0140 ± 0.0001

Mode number distribution (m,M) and condensate eff

3 3.5 4 4.5 5 5.5 x 10

−3

50 100 150 200 250 300

eigenvalue scale M

Mode number (m,M)

Mode number distribution (m,M) and condensate eff

Vol=483× 96 =3.20 m=0.003

6 configuration (sextet)

300 eigenvalues (m,M) = c0 + c1 M fit Σeff =

π c1 2Vol (1 − m2/M2) 1/2

Nf = 2 eff(M=0.0045/a) =0.0140 ± 0.0001

new stochastic method sextet Nf=2
comparison with direct calculation
f mode number distribution from

eigenvalue spectrum

stringent test
details in forthcoming publication

The chiral condensate in the sextet theory

SLIDE 43

−0.5 0.5 1 1.5 2 2.5 3 3.5 x 10

−3

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Vol=483× 96 =3.20 m=0.003 Neig=300

= 2(m,)

= 0.0100 ± 0.0004 2 (m,) = c0 + c1 + c22 2/dof = 0.89 Nf = 2 condensate

condensate subtracted

new stochastic method sextet Nf=2 comparison with direct determination of spectral density from eigenvalue spectrum

new stochastic method sextet Nf=2
comparison with direct determination of

spectral density from eigenvalue spectrum

stringent test

The chiral condensate in the sextet theory

SLIDE 44

−0.5 0.5 1 1.5 2 2.5 3 3.5 x 10

−3

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Vol=483× 96 =3.20 m=0.003 Neig=300

= 2(m,)

= 0.0100 ± 0.0004 2 (m,) = c0 + c1 + c22 2/dof = 0.89 Nf = 2 condensate

condensate subtracted

−0.5 0.5 1 1.5 2 2.5 3 3.5 x 10

−3

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Vol=483× 96 =3.20 m=0.003 Neig=300

= 2(m,)

= 0.0100 ± 0.0004 2 (m,) = c0 + c1 + c22 2/dof = 0.89 Nf = 2 condensate

condensate subtracted

new stochastic method sextet Nf=2 comparison with direct determination of spectral density from eigenvalue spectrum

new stochastic method sextet Nf=2
comparison with direct determination of

spectral density from eigenvalue spectrum

stringent test

The chiral condensate in the sextet theory

SLIDE 45

Kogut-Sinclair work consistent with χSB phase transition Relevance in early cosmology (order of the phase transition?)

finite temperature EW phase transition?

Kogut-Sinclair

29

Early universe

SLIDE 46

30

10−2 10−1 100 101 102 mDM [TeV] 10−15 10−13 10−11 10−9 10−7 10−5 10−3 10−1 101 103 105 Rate, event / (kg·day)

Nf = 2 dis Nf = 2 ord Nf = 6 dis Nf = 6 ord XENON100 [1207.5988], expect ≈ 1 event XENON100 [1207.5988], ≥ 1 event with 95%

Dark matter

lattice BSM phenomenology of dark matter

pioneering LSD work

dark matter candidate sextet Nf=2

electroweak active in the application

there is room for third heavy fermion

flavor as electroweak singlet

rather subtle sextet baryon

construction (symmetric in color)

Dark matter

self-interacting? O(barn) cross section would be challenging The Total Energy of the Universe: Vacuum Energy (Dark Energy) ~ 67 % Dark Matter ~ 29 % Visible Baryonic Matter ~ 4 %

T. Appelquist, R. C. Brower, M. I. Buchoff, M. Cheng, S. D. Cohen

, G. T. Fleming, J. Kiskis, M. F. Lin, E. T. Neil, J. C. Osborn, C. Rebbi, D. Schaich, C. Schroeder , S. Syritsyn, G. Voronov, P.

Vranas, and J. Wasem

(Lattice Strong Dynamics (LSD) Collaboration)

Buchoff talk

Nf=2 Qu=2/3 Qd = -1/3

udd neutral dark matter candidate

Early universe

SLIDE 47

Summary and Outlook

Simplest composite Higgs is light near conformality

light scalar (dilaton-like) emerging close to conformal window running (walking) coupling in progress really challenging to do chiral condensate new method spectroscopy emerging resonance spectrum ~ 2 TeV dark matter implications are intriguing strong self-interactions?