Profound Implications of the Higgs Boson Christopher T. Hill Fermilab ATLAS Collaboration meeting Argonne Nat’l. Lab July 15, 2013

A fundamental Higgs Mechanism was supposed to explain the origin of electroweak mass

A fundamental Higgs Mechanism was supposed to explain the origin of electroweak mass We now know that a fundamental Higgs Boson exists and explains the masses of quarks, leptons, W and Z

A fundamental Higgs Mechanism was supposed to explain the origin of electroweak mass But, the Higgs Boson does NOT explain the origin of the electroweak mass-scale We now know that a fundamental Higgs Boson exists and explains the masses of quarks, leptons, W and Z

A fundamental Higgs Mechanism was supposed to explain the origin of electroweak mass The Higgs Boson does NOT explain the origin of the electroweak mass-scale i.e., what is the origin of the Higgs Boson mass itself? We now know that a fundamental Higgs Boson exists and explains the masses of quarks, leptons, W and Z

A fundamental Higgs Mechanism was supposed to explain the origin of electroweak mass The Higgs Boson does NOT explain the origin of the electroweak mass-scale i.e., what is the origin of the Higgs Boson mass itself? This is either very sobering, or it presents theoretical opportunities We now know that a fundamental Higgs Boson exists and explains the masses of quarks, leptons, W and Z

Nature may be telling us something very profound:

Point-like spin-0 bosons are natural afterall ! Nature may be telling us something very profound:

Nature may be telling us something very profound: Point-like spin-0 bosons are natural afterall ! All mass in nature may be a quantum phenomenon !

“All mass is a quantum phenomenon” is almost as jolting as being told that “light comes in quanta!” Max Planck

The world of masslessness features a symmetry:

Scale Invariance

The world of masslessness features a symmetry: Scale Invariance Scale Invariance is (almost) always broken by quantum effects

The world of masslessness features a symmetry: Scale Invariance Scale Invariance is (almost) always broken by quantum effects Feynman Loops  h -

Scale Symmetry in QCD is broken by quantum loops and gives rise to the

Scale Symmetry in QCD is broken by quantum loops and gives rise to the Origin of the Nucleon Mass

Scale Symmetry in QCD is broken by quantum loops and gives rise to the Origin of the Nucleon Mass (aka, the visible mass in the universe)

Gell-Mann and Low:

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

Khriplovitch (1969); t’ Hooft (1972) Gross, Politzer and Wilczek (1973): Gell-Mann and Low: “running coupling constant” |

QCD running coupling constant |

Murraypalooza Santa Fe July 2005

A Puzzle: Murray Gell-Mann lecture ca 1975 Noether current of Scale symmetry

A Puzzle: Murray Gell-Mann lecture ca 1975 Noether current of Scale symmetry Current divergence

A Puzzle: Murray Gell-Mann lecture ca 1975 Noether current of Scale symmetry Current divergence Yang-Mills Stress Tensor

A Puzzle: Murray Gell-Mann lecture ca 1975 Noether current of Scale symmetry Current divergence Yang-Mills Stress Tensor Compute:

A Puzzle: Murray Gell-Mann lecture ca 1975 QCD is scale invariant!!!??? Noether current of Scale symmetry Current divergence Yang-Mills Stress Tensor Compute:

Resolution: The Scale Anomaly

See Murraypalooza talk: Conjecture on the physical implications of the scale anomaly. Christopher T. Hill (Fermilab). hep-th/ Christopher T. HillFermilab Resolution: The Scale Anomaly

Origin of Mass in QCD = Quantum Mechanics Resolution: The Scale Anomaly

‘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”).

‘t Hooft Naturalness:  0  Small ratios of physical parameters are controlled by symmetries. In the limit that a ratio goes to zero, there is enhanced symmetry (“custodial symmetry”).

‘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 h - 0  0 

‘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). Classical Scale Invariance is the “Custodial Symmetry” of  QCD 0 h - 0  0 

Many theories were proposed to imitate QCD for the electroweak scale.

Many theories were proposed to imitate QCD for the electroweak scale. All of these featured “strong dynamics” and classical scale invariance as the custodial symmetry of v Weak << M Gut, Planck

Many theories were proposed to imitate QCD for the electroweak scale. (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)…. All of these featured “strong dynamics” and classical scale invariance as the custodial symmetry of v Weak << M Gut, Planck

Many theories were proposed to imitate QCD for the electroweak scale. (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)…. All of these featured “strong dynamics” and classical scale invariance as the custodial symmetry of v Weak << M Gut, Planck

Many theories were proposed to imitate QCD for the electroweak scale. (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)…. All of these featured “strong dynamics” and classical scale invariance as the custodial symmetry of v Weak << M Gut, Planck Mass extinction of theories on July 4 th 2012

Susy is different

Supersymmetry is the custodial symmetry of v Weak  M Gut, Planck in SUSY models

Susy is different Supersymmetry is the custodial symmetry of v Weak  M Gut, Planck in SUSY models This generally requires that SUSY partners should be close together in mass with ordinary particles

Susy is still alive?

In my opinion the MSSM is dead

Susy is still alive? But, SUSY may be relevant at higher energy scales In my opinion the MSSM is dead

     F   e m e 22 _ d e = 22 (m e / MeV ) (  / GeV ) 2 = 0.2 x (e-cm) x _______ Current limit: d e < e-cm  > 1.4 x 10 5 GeV EDM’s are a powerful constraint:

    F   e m e  _ M selectron > 10 TeV ( sin  ) 1/2 e e selectron wino   =  sin  sin 2  1/M selectron   Future limit: d e < e-cm e-cm ? This is why I love Project-X ! EDM’s are a powerful constraint:

It is possible that we need only the strongest coupled SUSY partners to the Higgs Boson to be nearby in mass

It is possible that we need only the strongest coupled SUSY partners to the Higgs Boson to be nearby in mass The More minimal supersymmetric standard model A, G. Cohen, D.B. Kaplan, A.E. Nelson Phys.Lett. B388 (1996) “Natural SUSY” : A Light Stop

But what has then become of scale symmetry, which is already established as custodial symmetry of QCD?

Bardeen: Classical Scale Invariance could be the custodial symmetry of a fundamental, perturbatively light Higgs Boson. On naturalness in the standard model. William A. Bardeen FERMILAB-CONF T, Aug pp.

Bardeen: The only manifestations of Classical Scale Invariance breaking by quantum loops are d = 4 scale anomalies On naturalness in the standard model. William A. Bardeen FERMILAB-CONF T, Aug pp.

Bardeen: Classical Scale Invariance implies there are no additive quadratic (or quartic) divergences. A small Higgs mass (and  c  is technically natural ! On naturalness in the standard model. William A. Bardeen FERMILAB-CONF T, Aug pp. Classical scale invariance can play a similar role as SUSY

Bardeen: Perturbatively light Higgs Boson mass could come from quantum mechanics. Aspects of the Dynamical Breaking Of Scale Symmetries William A. Bardeen Myron Bander Symposium, June 8, 2013

Higgs Potential  M      2 _

Scale Invariant Higgs Potential   2 _

|H||H| 2 _   v Start with a Classically Scale Invariant Higgs Potential How can mass come perturbatively from Quantum Mechanics? Scale Invariance -> Quartic Higgs Potential -> No VEV v

2 __ Quantum loops generate a logarithmic “running” of the quartic coupling constant (v)  R log (v) ~ running coupling constant v

2 __ Quantum loops can generate a logarithmic “running” of the quartic coupling constant (v)  v  R log (v) this is the relevant behavior  passing from  0 to  0 requires R  0 ~ running coupling constant ~

Result: “Coleman-Weinberg Potential” 2 __ (v)  v v4v4 Potential Minimum arises from running of  i.e. Quantum Mechanics ~

Result: “Coleman-Weinberg Potential 2 __ (v) Higgs Mass is determined by curvature at minimum  R Require R  0 for a minimum, positive curvature v4v4 ~  v min

How do we compute R ?

Renormalization Group Equation of Gell-Mann and Low applied to in Standard Model  top H g = top Yukawa cc How do we compute R ?

R is negative in standard model No solution ! approximate physical values : Top Yukawa cc : Higgs quartic cc : We require positive R to have a minimum, stable (m h 2  0) potential

R is negative in standard model No solution ! Requires New Bosonic physics beyond the standard model approximate values : Top Yukawa cc : Higgs quartic cc :

One compelling and simple theory : H2H2 H H H H Positive R can come from a second Higgs Doublet This modifies the RG equation:

( ) Compute Higgs potential and calibrate R from Higgs Mass … 

( ) Compute Higgs potential and calibrate R from Higgs Mass  … Both R and  v  are determined

The two doublet model implies: Top Yukawa cc: Can now solve for  :   

… M 2 is determined heavy Dormant Higgs doublet

No VeV: “Dormant” Higgs Doublet The New Doublet has a positive M 2 Production, mass, and decay details are model dependent

Assume Dormant Higgs couples to SU(2) x U(1) but not to fermions Parity H 2  H 2 implies stabity: H 2   H (e   if M   M 0 Then H 2 0  is stable dark matter WIMP

Assume Dormant Higgs couples to SU(2) x U(1) Can break the parity with new interactions: H 2   h, 2h + h * Then H 2 0  is no longer stable WIMP Becomes visible !

The Dormant Doublet is pair produced above threshold near 2M H  800 GeV pp  X  Z *, W * )  X  H H *  X  6h (if allowed) Hard to see since weakly produed; If dark matter, most of final state is missing ET; Variations on the model can lead to different final states. Bardeen, Hill, Eichten, work in progress

Some Relevant References: S. Iso arXiv: [hep-ph] and refs therein. Higgs properties in the Stealth Doublet Model G. Wouda. Jun 28, 2013, arXiv: [hep-ph] | Dynamical generation of the weak and Dark Matter scale T. Hambye, A. Strumia. Jun 10, pp. arXiv: [hep-ph] | W. Bardeen, C. T. Hill, E. Eichten (work in progress)

What if all mass comes from Quantum Physics?

(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; Hierarchy is naturally generated Testable in the Weak Interactions! “Predictions” of the Conjecture:

We live in D=4! Cosmological constant is zero in classical limit QCD scale is generated in this way; Hierarchy is naturally generated Testable in the Weak Interactions! String Theory RULED OUT (classical string scale) “Predictions” of the Conjecture:

Conjecture on the physical implications of the scale anomaly. Christopher T. Hill (Fermilab). hep-th/ Christopher T. HillFermilab We live in D=4! Cosmological constant is zero in classical limit QCD scale is generated in this way; Hierarchy is naturally generated Testable in the Weak Interactions! Weyl Gravity in D=4 is QCD-like: String Theory RULED OUT (classical string scale) “Predictions” of the Conjecture: Weyl Gravity: Weyl Gravity is Renormalizeable! The Planck Mass Comes From Quantum Mechanics! See: (and refs.therein) Predicts D=4!

Coming to a bookstore near you In Fall 2013