The Higgs Boson & Beyond Tao Han PITT PACC, Univ. of Pittsburgh TsingHua U. / CFHEP, Beijing Joint Colloquium National Taiwan University, Dec. 8, 2015
François Englert and Peter W. Higgs "for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN's Large Hadron Collider"
The discovery: � July 4 th , 2012: A neutral boson decay to two photons At λ ≈ 10 -9 nm. The combined signal significance: ATLAS: 5.9 σ CMS: 5.0 σ Phys. Lett. B716, 1 (2012) Phys. Lett. B716, 30 (2012)
Summer 2015 update: 5 σ for both fermion coupling h à ττ & bosonic coupling WW à h F V κ m v 1.6 ATLAS and CMS t ATLAS and CMS V 1 � LHC Run 1 Z LHC Run 1 Preliminary or Preliminary 1.4 W F Observed m 1 v � 10 1.2 SM Higgs boson F � 1 2 � 10 � 0.8 b 3 � µ 10 0.6 ATLAS SM 68% CL CMS 0.4 4 � Best fit 95% CL ATLAS+CMS 10 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1 2 � 10 10 1 10 κ Particle mass [GeV] V - it’s neutral, a boson - it’s spin-0, parity-even - it couples to mass, non-universally All indications point to the SM Higgs !
A milestone discovery: It is a brand new class! 50 years theoretical work … 25 years experimental work … Congratulations to our CMS colleagues in Taiwan !
The Nature of Forces: long range ~( G N m 1 m 2 )/ r 2 long range ~( α e 1 e 2 )/ r 2 short range ~ e -mr /r 2
E&M: Most Successful in Theory & Practice! L = − 1 4 F µ ν F µ ν + ¯ ψ ( i γ µ D µ − m e ) ψ F µ ν = ∂ µ A ν − ∂ ν A µ , D µ = ∂ µ + ieA µ • At low energies à Maxwell’s theory; vector-like coupling by a U em (1) gauge symmetry • At high energies à Quantum-mechanical, renormalizable, most accurate (in science!): a part of trillion a theo = 0 . 001159652181643(763) e a exp = 0 . 00115965218073(28) e • QED becomes strongly interacting asymptotically (screening effects) α ( Q 2 0 ) α ( Q 2 ) = 1 − α ( Q 2 0 ) ln( Q 2 /Q 2 0 ) 3 π At ultra-violet (UV) à theory is invalid.
The strong force: SU c (3) Quantum Chromo-Dynamics Successful Theory, Challenging in Practice! n f L = − 1 µ ν F aµ ν + X 4 F a q f ( i γ µ ∂ µ − g s γ µ A µ − m f ) q f ¯ f F µ ν = ∂ µA ν − ∂ µA ν + ig s [ A µ , A ν ] 8 X A µ ( x ) = A ( x ) µ a T a , [ T a , T b ] = if abc T c . • At short distances/high energies à 1 asymptotically free (anti-screening effects) Sept. 2013 12 π α s (Q) τ decays (N 3 LO) α s ( Q 2 ) = Lattice QCD (NNLO) DIS jets (NLO) (33 − 2 n f ) ln( Q 2 / Λ 2 ) Heavy Quarkonia (NLO) 0.3 e + e � jets & shapes (res. NNLO) Z pole fit (N 3 LO) ( � Highly predictable at high energies: ) pp � > jets (NLO) 0.2 Crucial for HEP, early Universe … 0.1 QCD α s (M z ) = 0.1185 ± 0.0006 • At long distances/low energies > 10 -13 cm 1 10 100 1000 Q [GeV] à Strongly interacting: quarks condensate ( π 0 , π ± …) & (colorless) hadrons (p + , n) formed. Short range force by a dynamical mass: e -m π r /r 2
The Weak force: Quark & Lepton Flavor Transitions Beta decay n à p + e - ν ➔ Charged current interaction: W ± Inspired by EM current-current interactions, Fermi proposed (1934) L weak = − G F 2 J µ ( p + n ) J µ ( e − ν ) √ p G F ∼ M − 1 W ∼ 10 − 18 m force range ∼ Weak interaction based on SU(2) x U(1): (Glashow, ‘63) g Ψ i γ µ (1 − γ 5 )( T + W + µ + T − W − � µ ) Ψ i √ − B µ ν = @ µ B ν − @ ν B µ 2 2 i W i µ ν = @ µ W i ν − @ ν W i µ − g ✏ ijk W j µ W k q i ψ i γ µ ψ i A µ ν , � − e i g � ψ i γ µ ( g i V − g i A γ 5 ) ψ i Z µ . However, − 2 cos θ W i The local gauge symmetry prevents gauge bosons masses! Pauli’s rejection to the Yang-Mills theory. 9
The Weak force: Quark & Lepton Flavor Transitions Even worse: ``The Left- and right-chiral electrons carry different Weak charges’’ (Lee & Yang) Fermion masses also forbidden by gauge symmetry! Electroweak gauge theory à massless! 10
The Spontaneous Symmetry Breaking “ The Lagrangian of the system may display an symmetry, but the ground state does not respect the same symmetry.” Known Example: Ferromagnetism Above a critical temperature, the system is symmetric, magnetic dipoles randomly oriented. Below a critical temperature, the ground state is a completely ordered configuration in which all dipoles are ordered in some arbitrary direction SO(3) à SO(2) Low temperature super-conductivity is another example! The concept of SSB: profound, common. 11
The Nambu-Goldstone Theorem “If a continuous symmetry of the system is spontaneously broken, then there will appear a massless degree of freedom, called the Nambu-Goldstone boson.” Except the photon, no massless boson (a long-range force carrier) has been seen in Nature! (Recall Pauli’s criticism) The Spontaneous Symmetry Breaking: Brilliant idea & common phenomena, confronts the Nambu-Goldstone theorem! -- A show stopper ? 12
The Higgs Mechanism: The Magic in 1964 “If a LOCAL gauge symmetry is spontaneously broken, then the gauge boson acquires a mass by absorbing the Goldstone mode.” PRL PLB PRL PRL 13 13
An illustrative (original) Model: ¶ ¶ C. Quigg, Gauge Theories of the Strong ... 14
An illustrative (original) Model: ¶ After the EWSB, The gauge field acquires a mass, mixes with the Goldstone boson. Upon diagonalization: 15
the resultant Lagrangian is then: the Higgs boson! • By virtue of a gauge choice - the unitary gauge, the ζ -field disappears in the spectrum: a massless photon “swallowed” the massless NG boson! Degrees of freedom count: Before EWSB: After: 2 (scalar)+2 (gauge pol.); 1 (scalar)+3 (gauge pol.) • Two problems provide cure for each other! massless gauge boson + massless NG boson ➞ massive gauge boson + no NG boson This is truly remarkable! 16
A Few Observations A. The Higgs mechanism ≠ a Higgs boson ! From theoretical point of view, 3 Nambu-Goldstone bosons were all we need! A non-linear realization of the gauge symmetry: τ i τ 3 U = exp { i ω i τ i /v } , D µ U = ∂ µ U + igW i 2 U − ig 0 UB µ µ 2 L = v 2 2 [ D µ U † D µ U ] → v 2 X g 2 W 2 i + g 0 2 B 2 ) 4 ( i The theory is valid to a unitarity bound ~ 2 TeV The existence of a light, weakly coupled Higgs boson carries important message for our understanding & theoretical formulation in & beyond the SM – UV completion / renormalizibility .
B. λ : a “New Force’’ The Higgs potential: V = -µ 2 / ϕ / 2 + λ | ϕ | 4 It represents a weakly coupled new force (a fifth force): • In the SM, λ is a free parameter, now measured: λ = m H 2 / 2v 2 ≈ 0.13 Is it fundamental or induced? • In SUSY, it is related to the gauge couplings tree-level: λ = (g L 2 )/8 ≈ 0.3/4 ß a bit too small 2 + g Y • In composite/strong dynamics, harder to make λ big enough. (due to the loop suppression by design) Already possess challenge to BSM theories.
At higher energies, λ is NOT asymptotically free. It blows up at a high-energy scale (the Landau pole), unless it starts from small (or zero à triviality). For m H = 126 GeV, rather light: 600 The SM can be a consistent perturbative theory up to M pl ! 500 allowing M N , M GUT , … M H [GeV/ c 2 ] 400 Triviality EW 300 Precision Top-Yukawa drags the vacuum 200 126 meta-stable, 100 EW vacuum is absolute minimum New physics below 10 7-11 GeV? 0 3 5 7 9 11 13 15 17 19 The new coupling λ very important! log 10 ! [GeV]
C. Electroweak Super-Conductivity The Higgs potential is of the Landau-Ginsburgh form, but it represents a new fundamental interaction. 20
“... most of the grand underlying principles have been firmly established. An eminent physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals . ” --- Albert Michelson (1894) Michelson–Morley experiments (1887): “the moving-off point for the theoretical aspects of the second scientific revolution” Will History repeat itself (soon)?
Nima Arkani-Hamed (Director of CFHEP, Beijing)
New Era: � Under the Higgs lamp post The “Observation” papers: Now 3600 cites each! Vast scope of topics, from interpretations, explorations in & beyond the SM; applications in astronomy, cosmology, CC; strings/branes, to “Philosophical Perspectives ….”
Question 1: The Nature of EWSB ? In the SM: − µ 2 Φ † Φ + λ ( Φ † Φ ) 2 V ( | Φ | ) = µ 2 H 2 + λ vH 3 + λ 4 H 4 ⇒ Fully determined at the weak scale: √ m H ≈ 126 GeV 2 G F ) − 1 / 2 ≈ 246 GeV v = ( λ ≈ 1 H = 2 µ 2 = 2 λ v 2 m 2 µ ≈ 89 GeV , ⇒ 8 . It is a weakly coupled new force, underwent a 2 nd order phase transition. Is there anything else? 24
Question 1: The Nature of EWSB ? ? All we know: h With new physics near the EW scale: h ( h † h ) + 1 1 à λ hhh = (7/3) λ hhh 2 λ ( h † h ) 2 + 3! Λ 2 ( h † h ) 3 , V ( h ) → m 2 SM ( h † h ) � à λ hhh = (5/3) λ hhh ) → 1 SM 2 λ ( h † h ) 2 log . m 2 λ (h + h) 2 term could be made “-”: leading to EW phase transition strong 1 st order! à O(1) deviation on λ hhh 25
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