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Potential Implications of the Higgs Boson. Christopher T. Hill Fermilab Colloquium, Oct. 23, 2013. Electromagnetic force U(1). Quark color force SU(3). Massless Gauge Fields. All Gauge theories are based upon charge conservation. All Gauge theories are based

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## Potential Implications of the Higgs Boson

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**Potential Implicationsof the Higgs Boson**Christopher T. Hill Fermilab Colloquium, Oct. 23, 2013**Electromagnetic**force U(1) Quark color force SU(3) Massless Gauge Fields**All Gauge theories are based**upon charge conservation.**All Gauge theories are based**upon charge conservation. The continuous symmetry that leads, by Noether’s Theorem, to charge conservation is called Local Gauge Invariance**All Gauge theories are based**upon charge conservation. The continuous symmetry that leads, by Noether’s Theorem, to charge conservation is called Local Gauge Invariance Local Gauge Invariance defines the full structure of electrodynamics**Local Gauge Symmetry U(1):**phase of electron’s wave function is strictly unobservable electron = electron + collinear gauge field**Standard Electroweak Model**Weak Force (left-handed fields): SU(2)L x U(1) d nu W e u**Standard Electroweak Model**Weak Force (left-handed fields): SU(2)L x U(1) d What gives rise to the masses of W and Z boson? nu W e u Massive Gauge Fields**Can a gauge field have a**mass and still have gauge symmetry?**Can a gauge field have a**mass and still have gauge symmetry? massless scalar field**Where can we find a massless scalar?**Spontaneous Continuous Symmetry Breaking**U(1) symmetry**Goldstone Theorem Nambu-Goldstone Boson: angular motion with no cost in energy massless mode Higgs Boson: small radial oscillations massive mode**Radius of hat:**v = “VEV” = 175 GeV Curvature in brim: mHiggs**July 4th, 2012**Physicists Find Elusive Particle Seen as Key to Universe**Radius of hat:**v = “VEV” = 175 GeV 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**time light cone +z axis**A massless right-handed fermionsz = +1/2**time momentum spin +z axis**A massless left-handed fermionsz = +1/2**time momentum spin +z axis**Couple electron to the photon**time right-handed right-handed +z axis Chirality is conserved!**Couple electron to the photon**time left-handed left-handed +z axis Chirality is conserved**How do we make a massive electron?**time light cone +z axis**The left-handed and right-handed**electrons have the same electric charge QED is “vectorlike” ergo, no parity violation**A massive fermion oscillates inchirality through spacetime:**right-handed electric charge is conserved m left-handed m right-handed m left-handed spin is conserved m right-handed Chirality is not conserved by mass!**But, only left-handed fermions have**electroweak 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**time left-handed left-handed +z axis**How do we make a massive fermionbut conserve weak charge?**left-handed right-handed mass violates weak charge!!! left-handed right-handed left-handed Mass Violates Electroweak Gauge Symmetry!!!**Couple to a “Higgs boson”**time right-handed Higgs boson left-handed +z axis Weak charge is conserved !**Higgs Boson Condenses in vacuum**time Higgs boson vacuum expectation value = 175 GeV +z axis Weak charge is hidden in vacuum**Fermion Masses in Electroweak Theory**left-handed right-handed left-handed right-handed left-handed Fermion Mass requires Higgs to maintain Electroweak Gauge Symmetry!!!**July 4th, 2012**The Higgs Boson Explains the Masses of Elementary Particles**July 4th, 2012**The Higgs Boson Explains the Masses of Elementary Particles Or Does it?**It was hoped that a fundamental Higgs Mechanism**would explain the origin of electroweak mass**It was hoped that a fundamental Higgs Mechanism**would 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**It was hoped that a fundamental Higgs Mechanism**would 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 But, the Higgs Boson does NOT explain the origin of the electroweak mass-scale: Vweak = 175 GeV**It was hoped that a fundamental Higgs Mechanism**would 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 But, the Higgs Boson does NOT explain the origin of the electroweak mass-scale: Vweak = 175 GeV i.e., what is the origin of the Higgs Boson mass itself?**It was hoped that a fundamental Higgs Mechanism**would 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 But, the Higgs Boson does NOT explain the origin of the electroweak mass-scale: Vweak = 175 GeV i.e., what is the origin of the Higgs Boson mass itself? This is either very sobering, or it presents theoretical opportunities**The world of masslessnessfeatures a symmetry:**Scale Invariance**The world of masslessnessfeatures a symmetry:**Scale Invariance Scale Invariance is (almost) always broken by quantum effects**The world of masslessnessfeatures a symmetry:**Scale Invariance Scale Invariance is (almost) always broken by quantum effects - Feynman Loops h**Scale Symmetry in QCDis broken by quantum loopsand this**gives rise to: The Origin of the Nucleon Mass (most of the visible mass in the Universe)

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