Potential Implications of the Higgs Boson

Potential Implicationsof the Higgs Boson

Christopher T. HillFermilab

Colloquium, Oct. 23, 2013

Electromagnetic force U(1)

Quark color force SU(3)

Massless Gauge Fields

All Gauge theories are basedupon charge conservation.

The continuous symmetry that leads, by Noether’s Theorem, to charge

conservationis called Local Gauge Invariance


The continuous symmetry that leads, by Noether’s Theorem, to charge

conservationis called Local Gauge Invariance

Local Gauge Invariancedefines the full structure of

electrodynamics


Local Gauge Symmetry U(1):

electron = electron + collinear gauge field

phase of electron’swave function is

strictly unobservable

Local U(1) Gauge Invariance Wallet Card

Standard Electroweak Model

u

d

e

nuW

SU(2)L x U(1)

Weak Force

(left-handed fields):

Weak Force

(left-handed fields):

u

d

e

nuW What gives rise to the masses of

W and Z boson?

SU(2)L x U(1)

Massive Gauge Fields

Standard Electroweak Model

Can a gauge field have a mass and still have gauge symmetry?

massless scalar field

Can a gauge field have a mass and still have gauge symmetry?

Spontaneous Continuous Symmetry Breaking

Where can we find a massless scalar?

Higgs Boson: small radial oscillations massive mode

Nambu-Goldstone Boson: angular motion with no cost

in energy massless mode

Goldstone TheoremU(1) symmetry

v = “VEV” = 175 GeV

Radius of hat:

Curvature in brim:mHiggs

Physicists Find Elusive Particle Seen as Key to Universe

July 4th, 2012

v = “VEV” = 175 GeV

Radius of hat:

Curvature in brim:mHiggs = 126 GeV

The Higgs Boson is required to explain fermion mass

(as well as gauge boson mass)

The Higgs Boson is required to explain fermion mass

(as well as gauge boson mass)

This traces back to parity violation,i.e., the difference between left and right.

Fermion Mass and Chirality

+z axis

time

light cone

A massless right-handed fermionsz = +1/2

+z axis

time

spin

momentum

+z axis

time

spin

momentum

A massless left-handed fermionsz = +1/2

Couple electron to the photon

+z axis

time

right-handed

right-handed

Chirality is conserved!

Couple electron to the photon

+z axis

time

left-handed

left-handed

Chirality is conserved

How do we make a massive electron?

+z axis

time

light cone

The left-handed and right-handedelectrons have the same electric charge

QED is “vectorlike”ergo, no parity violation

A massive fermion oscillates inchirality through spacetime:

right-handed

right-handed

right-handed

left-handed

left-handed

Chirality is not conserved by mass!

electric charge isconserved

spin isconserved

m

m

m

m

But, only left-handed fermions haveelectroweak charge and form doublets

under SU(2)

Right handed’s are “sterile” under SU(2)

Parity is violated

Helicity of decay products in pion decay:

?

?

Mirror Images

Parity is violated in pion decay:(Lederman)

Couple LH fermions to the W-boson

+z axis

time

left-handed

left-handed

How do we make a massive fermionbut conserve weak charge?

right-handed

right-handed

left-handed

left-handed

left-handed

Mass Violates Electroweak Gauge Symmetry!!!

mass violatesweak charge!!!

Couple to a “Higgs boson”

+z axis

time

left-handed

right-handed

Weak charge is conserved !

Higgs boson

Higgs Boson Condenses in vacuum

+z axis

time

Weak charge is hidden in vacuum

Higgs bosonvacuum expectation

value = 175 GeV

Fermion Masses in Electroweak Theory

right-handed

right-handed

left-handed

left-handed

left-handed

Fermion Mass requires Higgs to maintainElectroweak Gauge Symmetry!!!

The Higgs Boson Explains the Masses of Elementary Particles

July 4th, 2012

The Higgs Boson Explains the Masses of Elementary Particles

Or Does it?

July 4th, 2012

It was hoped that a fundamental Higgs Mechanismwould explain the origin of electroweak mass

We now know that a fundamental Higgs Bosonexists and explains the masses of quarks, leptons, W and Z


But, the Higgs Boson does NOT explain the origin of the electroweak mass-scale:

Vweak = 175 GeV



i.e., what is the originof the Higgs Boson mass itself?




Vweak = 175 GeV

i.e., what is the originof the Higgs Boson mass itself?




Vweak = 175 GeV

This is either very sobering, or itpresents theoretical opportunities

The world of masslessnessfeatures a symmetry:


Scale Invariance


Scale Invariance

Scale Invariance is (almost) always broken by quantum effects


Scale Invariance

Scale Invariance is (almost) always broken by quantum effects

Feynman Loops h -

Scale Symmetry in QCDis broken by quantum loops

and this gives rise to:

The Origin of the Nucleon Mass(most of the visible mass in

the Universe)

Gell-Mann and Low:

Khriplovitch (1969); t’ Hooft (1972)Gross, Politzer and Wilczek (1973):

Gell-Mann and Low:

QCD:

Khriplovitch (1969); t’ Hooft (1972)Gross, Politzer and Wilczek (1973):

“running coupling constant” | |

Gell-Mann and Low:

QCD:

QCD running coupling constant

| |

A Puzzle: Murray Gell-Mann lecture ca 1975

Noether current of Scale symmetry



Current divergence



Current divergence

Yang-Mills Stress Tensor



Current divergence


Compute:



Current divergence


Compute:

QCD is scale invariant!!!???

Resolution: The Scale Anomaly

gluon

gluon

gluons and quarks

See Murraypalooza talk:Conjecture on the physical implications of the scale anomaly.

Christopher T. Hill (Fermilab) . hep-th/0510177

Resolution: The Scale Anomaly

Origin of Mass in QCD = Quantum Mechanics

http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Hill,%20ChristopherT.%22

http://www.slac.stanford.edu/spires/find/inst/www?icncp=Fermilab

Murraypalooza Santa Fe July 2005

‘t Hooft Naturalness:

Small ratios of physical parameters are controlled by symmetries. In the limit that a

ratio goes to zero, there is enhanced symmetry (“custodial symmetry”).


0






0 h - 0

0



ratio goes to zero, there is enhanced symmetry (custodial symmetry).

Classical Scale Invariance is the “Custodial Symmetry” of QCD

0 h - 0

0



ratio goes to zero, there is enhanced symmetry (custodial symmetry).

0 h - 0

0

Large hierarchies are natural!

Many theories were proposed to imitate QCDfor the electroweak scale.


All of these featured “strong dynamics” and classical scale invariance as the custodial symmetry of vWeak <<

MGut, Planck


(1)Technicolor(2)Supersymmetric Technicolor(3)Extended Technicolor(4)Multiscale Technicolor(5)Walking Extended Technicolor(6)Topcolor Assisted Technicolor(7)Top Seesaw(8)Supersymmetric Walking Extended Technicolor(9)Strong dynamics from extra-dimensions(10)….


MGut, Planck


(1)Technicolor(2)Supersymmetric Technicolor(3)Extended Technicolor(4)Multiscale Technicolor(5)Walking Extended Technicolor(6)Topcolor Assisted Technicolor(7)Top Seesaw(8)Supersymmetric Walking Extended Technicolor(9)Strong dynamics from extra-dimensions(10)….


MGut, Planck

Mass extinction of theories on July 4th 2012

Susy is still alive?

Susy is still alive?

But, where is it?

F e me

2

_

e mede = 2

(me/MeV)

( /GeV)2= 0.2 x 10-16 (e-cm) x _______

Current limit: de < 10-27 e-cm

> 1.4 x 105 GeV

Why EDM’s are so powerful:

Are EDM’s telling us something about SUSY?:

Fe me

_

Mselectron > 6.8 x 103 GeV ( sin)1/2

e e

selectron

wino wino

= sinsin2 1/Mselectron

Future limit: de < 10-29 e-cm -- 10-32 e-cm ?

It is possible that we need only the strongest coupled SUSY

partners to the Higgs Boson to be nearby in mass

e.g., “The More minimal supersymmetric standard model”A, G. Cohen , D.B. Kaplan, A.E. Nelson Phys.Lett. B388 (1996) 588-598

e.g., “Natural SUSY” : A Light Stop

Weak Scale SUSY was seriously challengedbefore the LHC turned on (e.g. EDM’s)

MSSM now copes with severe direct limits;Some nMSSM models survive

If SUSY is the custodial symmetrywe should see it in LHC RUN-II

Bardeen: Classical Scale Invariancecould be the custodial symmetry of a fundamental, perturbatively

light Higgs Boson.

On naturalness in the standard model.William A. Bardeen

FERMILAB-CONF-95-391-T, Aug 1995. 5pp.

The only manifestations of Classical Scale Invariance breaking by

quantum loops are d = 4 scale anomalies

http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Bardeen,%20William%20A.%22

Can a perturbative Higgs Boson masscome from quantum mechanics?

v = “VEV” = 175 GeV

Radius of hat:

Curvature in brim:mHiggs = 126 GeV

i.e., can quantum mechanics makea Mexican hat?

4

2_

v

Start with the Classically Scale Invariant Higgs Potential

Scale Invariance -> Quartic Potential -> No VEV

v

2

__

Quantum loops generate a logarithmic “running” of the quartic coupling, ala Gell-Mann & Low

(v) log (v/M)

~

running couplings have many possible trajectories, each parameterized by some

M

v

Quantum loops generate a logarithmic “running” of the quartic coupling

Nature chooses a particular trajectorydetermined by dimensionless cc’s.

v

2

__(v) log (v/M)

~

v

this is the relevant behavior passing from 0 to 0 requires 0~

2

__(v) log (v/M)

~

Quantum loops generate a logarithmic “running” of the quartic coupling

~ ~

Result: “Coleman-Weinberg Potential”

2

__(v)

v

v

4

Potential Minimum arises from running ofi.e. Quantum Mechanics

~

Classical potential

V =

Quantum running of

Expand around a hypothetical VEV, v

runs according to RG equation:

A bit more mathematically:

The resulting potential:

Demand that v is an extremum:

Demand v is a minimum, boson mass:

|H|4

2_

<H> = v

Start with the Classically Scale Invariant Higgs Potential

Apply this to the Higgs Boson

Scale Invariance -> Quartic Higgs Potential -> No VEV

v

Extremum, and curvature of potential (mass):

Higgs mass

Higgs VEV, v

What do we need to make a Mexican Hatfrom quantum mechanics?

Renormalization Group Equation of Gell-Mann and Low

topH

top

g = top Yukawa cc

What does theory predict for ?

(I am ignoring small EW contributionsfor simplicity of discussion)

R is negative in Standard Model

No solution !

approximate SM physical values:

Top Yukawa cc:Higgs quartic cc:

We require positive to have aminimum, stable (mh

2 0) potential

v

Requires New Bosonic physics beyond the standard model

Bardeen, Eichten, CTH, G G Ross …

Simplest hypothesis:

The missing bosonic matter may bea second Higgs doublet

that has no VEV:

“Dormant” or “Inert” Higgs Boson

Requires New Bosonic physics beyond the standard model

Bardeen, Eichten, CTH, G G Ross …

Item Type: Thesis (Dissertation (Ph.D.))

Degree Grantor: California Institute of Technology

Division: Physics, Mathematics and Astronomy

Major Option: Physics

Thesis Availability: Public (worldwide access)

Research Advisor(s): •Gell-Mann, Murray

Thesis Committee: •Gell-Mann, Murray (chair)•Tollestrup, Alvin V.•Barish, Barry C.•Ross, Graham•Feynman, Richard Phillips

http://thesis.library.caltech.edu/4505/

CTH, C N Leung, S RaoNPB262 (1985) 517

Masslesstwo doublet

potential

Two doubletRG

equations

H2

H

H

H

H

Positive can come from the second Higgs Doublet

This modifies the RG equation:

Note: I include the full one-loop RG eqns.with EW cc’s etc in the analysis, but omitit in the discussion for simplicity.

Can now solve for :

g = gtop 1

Extremum, and curvature of potential (mass):

M2 is determined heavy “dormant” Higgs doublet

Production, mass, and decay details are model dependent

No VeV but coupled to SU(2) xU(1):

“Dormant” Higgs Doublet (vs. “Inert”)

The New Doublet has a positive M2

If Dormant Higgs couples to SU(2) x U(1) but not fermions

Parity H2 H2 implies stabity:H2 H2

0 + (eif MM0

Then H20

is stable dark matter WIMP

CalcHEP estimatesvery preliminary!!!

pp -> H0 H0

pp -> H+ H-

pp -> H+ H0

fb

The Dormant Doublet is pair producedabove threshold near 2MH 800 GeV

pp X *, W*, h*) X H H*

H0

-> bb = 45 GeV Assume gb‘ = 1

H+ -> tb = 14 GeV fb

fb More work needed

The trilinear and quartic Higgs couplings will be significantly different than in SM case

R Demisek,T H Jung, H D Kim[hep-ph] 1308.0891

Trilinear term = (5/3) x SM

Quartic term = (11/3) x SMThis may be doable at LHC !

The trilinear and quartic Higgs couplings will be significantly different than in SM case

GeV) = 4.79 (black) GeV) = -0.1 (red) GeV) = 0.1 (green)gtop= 1 (blue)= = 0

Landau Pole = 9.5 TeV

UV instabilityimplying strong scale?

Landau Pole -> Composite H2

New Strong Dynamics

Log(vweak)

Log(vweak)

Hambye-Strumia model has nice features[hep-ph]1306.2329

H2 develops a Coleman-Weinberg potential and VEV v2

3 is negative and gives the Higgs boson its -m2 |H2 |2

The model does not require large quartic cc’s, hassensible UV behavior

H2 and associatedgauge fields becomeviable dark matter

I think this is a very important scientific question:

Is the Higgs potential Coleman-Weinberg?

• Examined a “maximally visible” scheme• Requires new bosonic contribution(s) to RG

• Dormant Higgs Boson from std 2-doublet scheme M 400 GeV

• May be observable, LHC run III?• Higgs trilinear and quartic couplngs non-standard

• UV problem -> new strong scale 10 TeV• New bosons may be dark matter

Perhaps we live in a world where allMass comes from quantum effects

No classical mass input parameters.

QCD and Higgs may be telling ussomething very profound:

All mass in nature may be a quantum phenomenon !

“All mass is a quantum phenomenon”

Max Planck

“All mass is a quantum phenomenon”is almost as jolting as being told that

“light comes in quanta!”

Max Planck

(a heretic)

What if all mass comes from Quantum Physics?

It’s a very heretical conjecture:

We live in D=4!

Cosmological constant is zero in classical limit

QCD scale is generated in this way; Hierarchyis naturally generated

Testable in the Weak Interactions!

“Predictions” of the Conjecture:

We live in D=4!




String Theory RULED OUT (classical string scale)


Conjecture on the physical implications of the scale anomaly.Christopher T. Hill (Fermilab) . hep-th/0510177

We live in D=4!




Weyl Gravity in D=4 is QCD-like:



Weyl Gravity?Weyl Gravity is Renormalizeable!

The Planck Mass Comes From Quantum Mechanics!

See:(and refs.therein)

Predicts D=4!

http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Hill,%20ChristopherT.%22

http://www.slac.stanford.edu/spires/find/inst/www?icncp=Fermilab

The String-o-Centric Universe

-infinity

Planck Scaleat the center

Hubble Scale

QCD Scale

Weak Scale

Log()

A more Copernican idea:The “Scaloplex”

Log() infinity-infinity

The classical “Scaloplex” isinfinite, uniform, and isotropic

infinity-infinity

Planck ScaleHubble Scale

Log()

Physics is determined by local values ofdimensionless coupling constants at any log

infinity-infinity

Planck ScaleHubble Scale

g0 = g

Log()

infinity-infinity

Planck Scale’Hubble Scale’

an equivalent universe 101000 x

Log()

Physics is determined by local values ofdimensionless coupling constants

g0 = g(101000)

g0 = g’

infinity-infinity

Planck Scale’’Hubble Scale’’

an equivalent universe 10-1000 x

Log()

Physics is determined by local values ofdimensionless coupling constants

g0 = g(10-1000)

g0 = g’’

Conjecture: Can a local translational symmetryin the scaloplex enforce ‘t Hooft naturalness

of all small mass ratios?

m

M__ m’

M__

Additive relationships between large and small are then forbidden:

m

m+M

_____ m’ +M

M______ m

M

M

Dilaton?

We live in D=4!




Weyl Gravity in D=4 is QCD-like:



Weyl Gravity:Weyl Gravity is Renormalizeable!

The Planck Mass Comes From Quantum Mechanics!

Predicts D=4!

We Live in a Scaloplex !!!

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Potential Implications of the Higgs Boson

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