The SM and the Higgs Boson Daniele.Zanzi@cern.ch Is the Higgs boson - - PowerPoint PPT Presentation

The SM and the Higgs Boson

Daniele.Zanzi@cern.ch

Is the Higgs boson responsible for

• ur mass?

Is the Higgs boson responsible for

• ur mass?

NO!!

How ordinary matter gets mass?

Binding energy in nucleons 훥p훥x≥h/2휋 E=mc2

Higgs field gives mass to elementary particles

Higgs field gives mass to elementary particles

Does it matter for us?

Higgs field gives mass to elementary particles

Does it matter for us?

Higgs field gives mass to elementary particles

Can elementary particles have mass without the Higgs field?

Higgs field gives mass to elementary particles

Can elementary particles have mass without the Higgs field? Yes…

QED Electron

QED Electron

Kinetic term Mass term

QED Electron

Kinetic term Mass term

Electron = +

left-handed eL right-handed eR

eL and eR have the same quantum numbers, so they are different (chiral) states

• f the same particle

QED Electron

Kinetic term Mass term

Electron = +

left-handed eL right-handed eR

eL and eR have the same quantum numbers, so they are different (chiral) states

• f the same particle

QED Electron

Kinetic term Mass term

Electron = +

left-handed eL right-handed eR

eL and eR have the same quantum numbers, so they are different (chiral) states

• f the same particle

Electron mass linked to the electron flipping between chiral states

Higgs field gives mass to elementary particles

So, why we need the Higgs field?

Higgs field gives mass to elementary particles

So, why we need the Higgs field? Because of symmetries in Nature…

Standard Model

Standard Model

Interactions among particles driven by symmetries of Nature

Standard Model

Interactions among particles driven by symmetries of Nature Classical mechanics: Symmetry in the system leads to conservation law (Noether’s theorem)

Standard Model

Interactions among particles driven by symmetries of Nature Quantum mechanics: Symmetry in the system leads to charge conservation (quantized charges)

Standard Model

Interactions among particles driven by symmetries of Nature Example: electrical charge conservation

Standard Model

Interactions among particles driven by symmetries of Nature

Global symmetry = charge conservation

Standard Model

Interactions among particles driven by symmetries of Nature

Global symmetry = charge conservation Local symmetry = FORCES Physics of the system unchanged if points are ‘‘connected’’ by a field, the gauge field

Standard Model

SM characterized by the SU(3)⨉SU(2)L⨉U(1)Y gauge symmetry.

(These symmetries are proven experimentally!)

Standard Model

SM characterized by the SU(3)⨉SU(2)L⨉U(1)Y gauge symmetry.

(These symmetries are proven experimentally!) strong force

Standard Model

SM characterized by the SU(3)⨉SU(2)L⨉U(1)Y gauge symmetry.

(These symmetries are proven experimentally!)

e l e c t r

• w

e a k f

• r

c e

Standard Model

SM characterized by the SU(3)⨉SU(2)L⨉U(1)Y gauge symmetry.

(These symmetries are proven experimentally!)

So, why SM particles cannot have masses??

Standard Model

SM characterized by the SU(3)⨉SU(2)L⨉U(1)Y gauge symmetry.

(These symmetries are proven experimentally!)

Electron = +

left-handed eL right-handed eR

Standard Model

SM characterized by the SU(3)⨉SU(2)L⨉U(1)Y gauge symmetry.

(These symmetries are proven experimentally!)

Electron = +

left-handed eL right-handed eR Q

• 1
• 1

Y

• 1
• 2

Standard Model

SM characterized by the SU(3)⨉SU(2)L⨉U(1)Y gauge symmetry.

(These symmetries are proven experimentally!)

Electron = +

left-handed eL right-handed eR Q

• 1
• 1

Y

• 1
• 2

Y= -1

• 2
• 1
• 2

Not allowed by hyper- charge conservation!

Standard Model

SM characterized by the SU(3)⨉SU(2)L⨉U(1)Y gauge symmetry.

(These symmetries are proven experimentally!)

Fermion mass terms are not allowed if the symmetries of SM are to be conserved.

Same argument holds also for the masses of the gauge bosons. In this case the mass terms are not allowed by the preservation of the symmetry under gauge transformations. In a way, the gauge boson are the fields that ‘‘map’’ symmetries under local

• transformations. Since such transformations impact the entire system, these

‘‘’maps’’ need to have an infinite range, hence the carriers need to be massless

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV)

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) In the ground state (vacuum) the field is not null

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) infinite degenerate ground states

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) two possible excitations (quanta): h requires energy ζ doesn’t cost energy h ζ

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) two possible excitations (quanta): h requires energy ζ doesn’t cost energy h ζ Any excitation is equally probable, ie the vacuum has an indefinite number of ζ quanta

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) two possible excitations (quanta): h requires energy ζ doesn’t cost energy h ζ Any excitation is equally probable, ie the vacuum has an indefinite number of ζ quanta Addition/subtraction of a ζ does not change the vacuum (see concept of condensate in

superconductors)

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ

Y= -1 Y= -2

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ

Y= -1 Y= -2

Y= -1

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ

Y= -1 Y= -2

Y= -1

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ

Y= -1 Y= -2

Y= -1

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ Higgs field VEV ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ ζ

Y= -1 Y= -2

Y= -1

Electron acquires mass from the interaction with the Higgs field! Dynamic generation of mass that preserves symmetries of SM

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ Also gauge bosons get mass interacting with Higgs field:

휙 ¡ ¡ 휙 ¡ ¡ Z Higgs field has weak charge, so it can emit a Z boson as electron radiates photons

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ Also gauge bosons get mass interacting with Higgs field:

휙 ¡ ¡ 휙 ¡ ¡ Z Higgs field has weak charge, so it can emit a Z boson as electron radiates photons

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ In the ground state realized in Nature the Higgs fiels has weak charge, but no electrical nor strong charge. So…

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ

Not interacting with Higgs field, massless Interacting with Higgs field, massive

In the ground state realized in Nature the Higgs fiels has weak charge, but no electrical nor strong charge. So…

Here comes the Higgs field

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ

• Symmetries of SM not broken by mass terms
• Not-symmetric ground state ‘‘spontaneously breaks’’ the

symmetries, ie symmetries preserved in Lagrangian, but not visible from the ground state

• Completely consistent theory with a left-over:

Here comes the Higgs boson

Higgs field 휙 is a weak-doublet is a weak-doublet complex scalar field with a Vacuum Expectation Value (VEV) h ζ

• Symmetries of SM not broken by mass terms
• Not-symmetric ground state ‘‘spontaneously breaks’’ the

symmetries, ie symmetries preserved in Lagrangian, but not visible from the ground state

• Completely consistent theory with a left-over: the Higgs

boson, the massive excitation of the Higgs field (like density wave of the Higgs VEV)

Standard Model

Standard Model

Manifest symmetry, no masses Kinetic term for gauge fields Kinetic term for fermions + interactions with gauge fields Interaction between Higgs field and fermions Kinetic term, interaction with gauge fields and potential term of the Higgs field

Standard Model

Hidden symmetry, massive particles Equivalent descriptions of the same system, but from two different point of views

Standard Model

Fermions masses generated by new interactions between fermion and Higgs field ⇒ For each type of fermion, a new parameter ‘‘g’’, the interaction strength, has to be introduced Gauge boson masses determined by the Higgs field interacting via the forces of the SM. The strength of such interactions is known, so that no new parameter is needed Values of gauge boson masses are predicted by the Higgs mechanism!!

Standard Model

• SM with the Higgs field is a consistent theory
• Fundamental particles and force carries get dynamically masses

from the interaction with the Higgs field

• SM highly predictive and in very good agreement with

experimental results

• Value of the gauge boson masses are predicted by the SM!
• What is left to do is to find the Higgs boson…

Higgs Boson

• All its properties are predicted

by the SM

• Only one unknown: its mass
• Interactions of Higgs boson

with other particles determined by Higgs mass

• Strength of coupling of Higgs

boson any other SM particle proportional to the particle mass

[GeV]

H

M

80 100 120 140 160 180 200

Higgs BR + Total Uncert [%]

• 4

10

• 3

10

• 2

10

• 1

10 1

LHC HIGGS XS WG 2013

b b

• µ

µ c c gg

• Z

WW ZZ

LHC & ATLAS

H➝훾훾

H➝ZZ➝4휇

Summary

• SM without the Higgs field cannot describe fundamental massive

particles

• VEV of the Higgs field spontaneously break the SM symmetries and

generate masses

• SM with Higgs field is a consistent and highly predictive theory with
• ne additional particle, the Higgs boson, and one additional unknown,

mH

• Higgs boson is NOT responsible for the mass of fundamental particle,

the Higgs field is!

• Discovery of the Higgs boson is the ultimate proof of the consistency/

predictability of the theory

• After the Higgs discovery, the SM is complete. No compelling need for

new physics

• Yet, many questions are still waiting for answers