Technidilaton in light of LHC-Run II
Shinya Matsuzaki(Institute for Advanced Research &Department of Physics, Nagoya U.)@ Nagoya Univ. 03/05/2014

Current status on 125 GeV Higgs discovered at LHC
CMS-PAS-HIG-13-005

ATLAS: PLB726 (2013)* measured coupling properties consistent w/ the SM Higgs so far* BUT, is it really the SM Higgs?
--- origin of mass put in by hand?
--- unnatural elementary Higgs?

It could be a composite scalar, Techni-dilaton (TD)* TD : composite scalar:

Yamawaki et al (1986); Bando et al (1986)-- predicted in walking technicolor
giving dynamical origin of mass by technifermion condensate-- arises as a pNGB for SSB of (approximate) scale symmetry
technifermion condensate-- lightness protected by the scale symmetry(naturalness), and hence can be, say, ~ 125 GeV.
S.M. and K. Yamawaki (2012)• 125 GeV TD signatures at LHC are consistent withcurrent data
Today: comparison is updated

Contents of this talk:
1. Introduction
2. Walking TC and Technidilaton
3. 125 GeV TD signal vs. current LHC data
4. Toward LHC-Run II
5. Summary

2. Walking technicolor and TDYamawaki et al (1986); Bando et al (1986)

Walking TC and techni-dilaton
QCD-like“walking”~ O(4 π Fπ)= O(1TeV)~1000TeV:Pseudo IRFP

β“walking”* Techni-dilaton (TD) emerges as (p)NGB for approx. scale symmetry
SSB of (approximate) scale sym.
α starts “running”(walking) up to mF
Nonpert. scale anomaly
induced by mF itself

TD gets massiveLight techni-dilaton
S.M and K.Yamawaki , PRD86 (2012)* One suggestion from holographic formula for TD mass--- TD mass (lowest pole of dilatation current correlator)“conformal limit”

125 GeV TD is realized by a large gluonic effect : G 〜 10for one-family model w/ Fπ = 123 GeV (c.f. QCD case, G ~ 0.25 )125 GeVTD Lagrangian below mF
walking regime

S.M. and K. Yamawaki, PRD86 (2012)* effective theory below mF
after TF decoupled/integrated out& confinement :governed by TD and other light TC hadrons~O(TeV)~10^3TeV* Nonlinear realization of scale andchiral symmetries
Nonlinear base χ for scale sym. w/ TD field ΦTD decay constant FΦNonlinear base U for chiral sym. w/ TC pion field πeff. TD Lagrangiani) The scale anomaly-free part:ii) The anomalous part (made invariant by including spurion field “S”):
reflecting ETC-induced
TF 4-fermi w/ (3-γm)iii) The scale anomaly part:which correctly reproduces the PCDC relation:

βF: TF-loop contribution
t0 beta function

TD couplings to the SM particles* TD couplings to W/Z boson (from L_inv)* TD couplings to γγ and gg (from L_S)

βF: TF-loop contribution
t0 beta function

TD couplings to the SM particles* TD couplings to W/Z boson (from L_inv)* TD couplings to γγ and gg (from L_S)

βF: TF-loop contribution
t0 beta function

The same form as
SM Higgs couplings
except FΦ and betas

* TD couplings to SM fermions*in WTC to get realitic masses w/o FCNC concerning 1st and 2nd generations

2*Miransky et al (1989); Matsumoto (1989); Appelquist et al (1989)

in Strong ETC to accommodate masses of the 3rd generations (t, b, tau)1

Thus , the TD couplings to SM particles
essentially take the same form as those of
the SM Higgs! :Just a simple scaling from the SM Higgs:

But, note φ-gg, φ-γγ depending on particle
contents of WTC models.
βF: TF-loop contribution
t0 beta function

To be concerete, we consider one-family model (1FM)

evaluate betas at one-loop level:3. 125 GeV TD Signal vs. LHC-Run I Data* relevant production processes at LHC
similar to SM Higgs:
ggF , VBF, VH, ttH* relevant decay channels(for NTC=4)
BR---------------------------------------Φ  gg
: ~ 75%Φ  bb: ~ 19 %
Φ  WW: ~ 3.5%Φ  ττ
: ~ 1.1 %Φ  ZZ: ~ 0.4%
Φ  γγ: ~ 0.1%

enhanced by extra
coloredtechni-quark
contribution

Updated from S.M. and Yamawaki
The signal strength fit toPLB719(2013)
the LHC-Run I full data---------------------------------------------------------------[vEW/FΦ ]bestχ^2 min /d.o.f.
One-parameter fit (Fφ) NTC---------------------------------------------------------------30.28
37/17 = 2.2--------------------------------------------------------------40.24
19/17 = 1.1---------------------------------------------------------------50.17
33/17 = 1.9---------------------------------------------------------------NTC=3NTC=5

NTC=4*SM HiggsCompared w/ SM Higgs
χ^2/d.o.f = 17/18 = 1.0Current LHC has favored TD
at almost the same level as
SM Higgs!

The TD signal strengths (μ = σ x BR/SM Higgs)
vs. the current data (i)(i) ggF+ttH category
TD signal strength

ATLAS* one-family model w/ NTC=4, vEW/Fφ = 0.24
* Consistent at 1 sigma level (except CMS-diphoton)

CMS

The TD signal strengths (μ = σ x BR/SM Higgs)
vs the current data (ii)(ii) VBF +VH category
TD signal strength

ATLAS

CMS

* Consistent within 2 sigma error* VBF: contamination from ggF by about 30% taken into account, except bb channel (b-tag)* Smaller VBF+VH signal (particularly, bb-channel), compared to the SM Higgs

 Conclusive answer needs high statistic LHC-Run II !

4. Toward LHC Run-IIDetermining TD decay constant FΦ
Precise estimate is needed for LHC-Run II* Theoretical predictions so far
ladder approximation:

S.M. and Yamawaki (2012)

holographic estimate:More rigorous estimate should be made directlyby lattice simulations!
--- needs a way of measuring FΦ on lattice
It is actually provided by scale-invariant ChPT!

Scale-invariant ChPT (sChPT) -- Determining TD decay
constant FΦ and mass MΦ on lattice
S.M. and K. Yamawaki, 1311.3784 (2013)* sChPT is formulated so as to reproduce chiral/scale WT identity:

hard-breaking term

soft- breaking termand PCDC (and PCAC) at the leading O(p^2):

Soft-breaking mass

Note the dilaton mass formula
as direct consequence of WT (and PCDC):

hard-breaking mass (chiral-limit mass)

Soft-breaking mass proportional to mf:

* Building-blocks and order-counting rule

* The leading-order O(p^2) chiral and scale-invariant Lagrangian

Note: soft-breaking term is uniquely fixed by stabilizationof dilaton potential in the presence of current mass mf

* Dilaton mass formula at O(p^2) is reproduced:* Prefactor*

fairly insensitive to exact value of γmin walking theory
is Independent of Nf

Holography (large Ntc limit )(S.M. and K.Yamawaki, 2012)

Just a sample value in between
Fitting to LHC phenomenology(S.M. and K.Yamawaki, 2012 and this talk)* Chiral log (pion mass) corrections to dilaton mass at O(p^4)

Counterterms:

* Plot of MΦ vs. Mπ at O(p^4)
w/ assuming counterterms =0 @ μ=Λχ

Chiral log corrections get significant as mπ  0--- crucial for chiral-limit TD mass and decay constant!

5. Summary

* TD is the characteristic light scalar in WTC:
the mass can be 125 GeV: the lightness isprotected by approximate scale invariance.
* The 125 GeV TD in 1FM gives the LHC signal consistentw/ current LHC data.
* More precise measurements in VBF+VH categories
will tell us whether TD is the LHC Higgs, or not.
* Toward LHC-Run II:--- needs rigorous estimate of TD decay constant--- it is doable on lattices via dilaton mass formula.
* Smoking gun of WTC:
discovering walking TPs & Techni-rhos(Terashi & Kurachi’s talks)

Backup Slides

K. Haba , S.M. and K. Yamawaki , PRD82 (2010);
S.M. and K.Yamawaki, 1209.2017

More on holographic
estiamtes
HolographicTD

S.M. and K.Yamawaki, 1209.2017* Ladder approximation : gluonic dynamics is neglected* Deformation of successful AdS/QCD model (Bottom-up approach)
Da Rold and Pomarol (2005); Erlich, Katz, Son and Stephanov (2005)

incorporates nonperturbative gluonic effects
05d SU(NTF)L x SU(NTF)RzUVIRQCDWTC

AdS/CFT dictionary:* UV boundary values = sources* IR boundary values:chiral condensate
gluon condensate

* AdS/CFT recipe:
generating functionalclassical solutions
sources = UV boundary values
for bulk scalar, vector, axial-vector fields

Current collerators
are calculated as a function of three IR –boundary values anddual: IR value of bulk scalar: IR value of bulk scalar: IR-brane position:

The model parameters:Φ IRvalueΦx IRvalue

IR braneposition

5dcoupling

matching tocurrent correlators

Φ UVvalueΦx UVvaluecoeff.
of M

set explicit breaking
sources = 0ΠV

ΠS
Leading log term

Leading log term

Fixcoeff.
of Φx

3 phenomenological input values
Fπ = 246 GeV/√ND = 123 GeV (1FM)MΦ = 125 GeV
S = 0.1

ΠVG^2 term

S.M. and K.Yamawaki, 1209.2017

Other holographic predictions (1FM w/ S=0.1)
NTC = 3Techni-ρ , a1 masses
Techni-glueball (TG) mass
TG decay constantdynamical TF mass mF::::

Mρ = Ma1 = 3.5 TeV
MG = 19 TeV
FG = 135 TeV
mF = 1.0 TeV::::

Mρ = Ma1 = 3.6 TeV
MG = 18 TeV
FG = 156 TeV
mF = 0.95 TeV::::

Mρ = Ma1 = 3.9 TeV
MG = 18 TeV
FG = 174 TeV
mF = 0.85 TeV

NTC = 4
Techni-ρ , a1 masses
Techni-glueball (TG) mass
TG decay constantdynamical TF mass mF
NTC = 5Techni-ρ , a1 masses
Techni-glueball (TG) mass
TG decay constantdynamical TF mass mF

Direct consequences ofWard-Takahashi identities S.M. and K. Yamawaki, PRD86 (2012)* Coupling to techni-fermions

TCDilaton poledominance
w/ TD decay constant Fphi

Yukawa vertex func.

* Couplings to SM fermions
No direct coupling

TCtransform

Techni-fermion loop induces

ETC induced4-fermi

f-fermion mass:

Yukawa coupling to SM-fermion

* Couplings to SM gauge bosons
WT identity  scale anomaly term + anomaly-free term

TCTF

TFTCpTD pole
The loop integrals are actually saturated by IR contributions (γm = 2)
βF: TF-loop contribution
t0 beta function

βF: TF-loop contribution
t0 beta function* For SU(2)W gauge bosons: W –”broken” currents

Coupling to W
ND = TF -EW-doublets* For unbroken currents coupled to photon, gluon:

Coupling to γγ & gluonsLadder estimate of TD mass
A composite Higgs mass

* LSD + BS in large Nf QCD
Harada et al (1989); Kurachi et al (2006)～500 GeV
for one-family model (1FM)still larger than ~ 125 GeV* LSD via gauged NJL
Shuto et al (1990); Bardeen et al (1992);
Carena et al (1992) ; Hashimoto (1998)* This is reflected in PCDC (partially conserved dilatation current)
Miransky et al (1989):
Hashimoto et al (2011):

wherefiniteonlyNo massless NGB limit:

Estimate of: #1 – Ladder approximation* PCDC (partially conserved dilatation current)* criticality condition

Appelequist et al (1996)* Pagels-Stokar formula# of EW doublets* Recent ladder SD analysis(large Nf QCD)
Hashimoto et al (2011)

* Inclusion of theoretical uncertainties
Ladder approximation is subject to about 30% uncertainty
for estimate of critical coupling and QCD hadron spectrum
critical coupling : T. Appelquist et al (1988);
Hadron spectrum : K. -I. Aoki et al (1991); M. Harada et al (2004).

±0.3
30%

Estimate
w/ uncertainty included30%

* Calculation of beta functions

The loop is dominated at IR (γm = 2)
(well approximated byconstant mass )IRTF

Ladder approx.
Yukawa vertex

The resultant betas coincide
just one-loop perturbative expressions:IRconstant

TD mass stability below mF S.M. and K. Yamawaki, PRD86 (2012)
walking regime = scale symm well protected(natural enough)Can TD mass be as small as 125GeV below mF?

 YES!!!
~1TeV~10^3TeV

Work on the eff. TD Lagrangian:
Dominant corrections come from top-loop (quadratic div.)
cutoff by mF ~ 4 π Fπ ~ 1TeV (~ FΦ) :w/

naturally light thanks to large FΦ (i.e. weak coupling)