Precision Measurementsafter the Higgs Discovery

M.V. ChizhovSofia University, Bulgaria and JINR, Russia

09/06/2014 2

Why do we need the Higgs boson?

( , )x t

0

0 0

( , ), ( , )

( )

( ) ~

( ) ~

A x t A x t

A x

E x A A

H x A

( , )x t

S = ½

S = 1

S = 0

09/06/2014

Harmonic Oscillator(Analytical Mechanics)

2 2

2

[ ( ), ( )]

( ) ( )

2 2

[ ( ), ( )]

theorem of

Emmy Noether,

0 0

const

1915

L q t q t K V

mq t kq t

S L q t q t dt

S q q

E K V

Joseph-Louis Lagrange (Giuseppe Lodovico Lagrangia), 1788

3

q

R > 0R < 0

09/06/2014

Harmonic Oscillator(Scalar Field)

3 4

22

2 2

( ) ( , ) 1: [ , ] [ ] [ ]

2 2

[ , ] [ , ] ; [ , ] [ , ]

q t t xK V

L S L dx td d x

L

L L

0

V[]

Energ

y4

2 2 20 m m

0

2

22

2

2

[ ]0 const

2

[ ] 1( ) ( ) ; 0

2

V

Vx x m

R

09/06/2014

Scalar Potential of Anharmonic Oscillator

242[ ] , 0

2 4V

[ ]V [ ]V

0 0

2 0 0

2

2

22 2 2

0 0

5

09/06/2014

Discrete Z2 Symmetry ofthe Scalar Potential

[ ] [ ]V V

2 0 0 2

2 2 20 0

2 2m

22 4[ ] [ ]

2 4V V

32 42 4

[2 4

2]

4V

2

symmetry

[ ] [ ]V V

broken symmetry

[ ] [ ]V V

6

2 2 , 22

m m

Two Scalar Fields (or Complex Scalar Field) Potential with Broken Symmetry

2

22 2 2 21 2 1 2 1 2[ , ] , 0, 0

2 4V

2 2 2 22 1 2 20 0

0

[ , *]0 ; 0

2 2

V

1 20 0, 0

2 421 2 1 2, * , [ , *]2 2

i iV

Re( )Im( ) 7

2

0

1

0

22 21 2

2

22 1 2

22

1

[ , ]

[

2

, ]0

Vm

Vm

09/06/2014

Continuous U(1) Symmetry of the Potential with Complex Scalar Field

[ ] [e ]iV V 2

2 21 1 2 20 0; ,

21 1

22 22 , , 2

0m m m

2 21

2 4

2 12 2 2 2

1 2 1 1 2[ , ] ( )2 44

(2

)V

1 2 1 2 1 2

broken symmetr

[ , ] [ cos sin , sin

y

cos , ]V V

J. Goldstone, Nuovo Cim. 19 (1961) 154.8

09/06/2014

Goldstone Particle (Theorem)

“if there is continuous symmetry transformation under which the Lagrangian is invariant, then either the vacuum state is also invariant under the transformation, or there must exist spinless particles of zero mass.”Jeffrey Goldstone, Abdus Salam and Steven Weinberg, Phys. Rev. 127 (1962) 965

Re( )

Im( )9

09/06/2014

Examples of Collective Goldstone Bosons

Spin waves in a ferromagnet Phonons in a crystal lattice Superfluidity (Bose condensate,

Боголюбов,1947) Superconductivity (Cooper pairs, 1956;

Боголюбов,1958) Pions in the chiral limit (Nambu, 1961)

2

2

consists of quarks, 938.3MeV / consists of quarks, 939.6MeV /

p

n

p uud m c

n udd m c

2

2

0

2.3MeV /

4.8MeV /

chiral limit lim 0q

u

d

m

u m c

d m c

m

0

2

0 2

2

139.6 MeV /

= 135.0 MeV /2

139.6 MeV /

udm c

dd uum c

m cdu

10

09/06/2014

In Nature there is not a massless spinless colorless particle, which would have had an infinite radius of interaction!Only gravitational and electromagnetic forces have an infinite radius of interaction.

Massless Particles in Nature

1 22

Newton law (1687): N

m mF G

r

11

1 22

0

1Coulomb law (1785):

4

q qF

r

09/06/2014

Gauge Invarianceand Massless Particles

Strenght tensor of electromagnetic field is

invariant under gauge tranformation ( ).1

Therefore, we cannot add the mass term

T

, which is explicitly2

gauge noninvariant.

F A A A

A A х

A А

he photon is massless and transversе!

Am

12

In general case of isospin gauge invariance, for examplebetween proton and neutron from isodoublet, a triplet of gauge vector fields, known as Yang Mills fileds (1954),arises. Therefore, to des

crib

0

masslessHowever, in Nature, besides

e the decay , weshould introdu

the photon, there is no other

ce at least 3 g

massless vector

auge particl

colorless pa

es ,

rticle, which would и .

hav

en peW

W W

e had an infinite radius of intercation.

09/06/2014 13

As Yang relates:

Wolfgang Pauli (1900-1958) was spending

the year in Princeton, and was deeply

interested in symmetries and interactions....

Soon after my seminar began, when I had

written on the blackboard,

(∂ -iB )

Pauli asked, "What is the mass of this field

B ?" I said we did not know. Then I resumed my presentation

but soon Pauli asked the same question again. I said

something to the effect that it was a very complicated problem,

we had worked on it and had come to no definite conclusions. I

still remember his repartee: "That is not sufficient excuse".

An Anecdote by C. N. Yang

09/06/2014

S. L. Glashow, Nucl. Phys. 22 (1961) 579.

Birth of the Standard Model ofElementary Particles SU(2)LU(1) Y

0

Glashow followed the principle: the most important is,the symmetry, while masses can be added by hand. He was the first who realized that the neutral vector boson ofthe triplet is not a photon,

W

0W W

because its interactions violate - parity. To avoid this he added one more neutral vector

field to obtain the particle = sin cos withthe photon properties. In this way he obtained the fol

PB A W B

W0

W W

lowingrelation between the electromagnetic and the weak coupling constants and predicted the existence of a new neutral vector particl

sin= cos sine .

e gZ W B

He was the first who got the limitations on the masses of intermediate bosonsusing Fer 2 2 2 2mi coupling constant sin : 130 GeV. (actually: 40 GeV.)

F W W

W

W WG g M M MM

“Schwinger told me to think about unifying weak and EM. So I did it. For two years ‒ I thought about it.” 14

09/06/2014 15

22

2

sintW

gE

mM

22

2

sinuW

gE

m

M 2

SM

2

SM

4sin

, cos4cos

ZWWs

W

ZWW WW

y g

mg

g

E

y g

M

Unitarity and Z boson

09/06/2014 16

2

2 222

2 2 SM2 2

22 (1 cos )cos

4 3 , where 4 1

cos

Z Wgauge W

W W

Z W

umg

um m

E

m

m

M

22 22 22 2,

2 2 2 2

2 2

4 4

hm s tW W

HW h h W

s m t mg gu

m s m t m m

M

Unitarity and Higgs boson

Not yet tested experimentally… but see the following slide!

09/06/2014 17

Evidence of electroweak W±W±jj production ATLAS-CONF-2014-013 (March 25, 2014), arXiv:1405.6241

SMinc 1.52 0.11 fb SM

VBS 0.95 0.06 fb

expVBS stat syst1.3 0.4 0.2 fb )3.6(

expinc stat syst2.1 0.5 0.3 fb )4.5(

Inclusive mjj QCD+EW region

Enriched VBS region: mjj>500 GeV, |Dyjj|>2.4

09/06/2014

Gauge Invariance and Massive Particles

Schwinger model (1962): two-dimentional quantum electrodynamics, where the photon becomes massive.

Non-relativistic dynamics of the plasma:Philip W. Anderson (1963) – Yang Mills fields acquire the mass due to longitudinal oscillations in plasma (Meissner Ochsenfeld effect).

Am 2

“We conclude, then, that the Goldstone zero-mass difficulty is not a serious one, because we can probably cancel it off against an equal Yang-Mills zero-mass problem.”

18

F. Englert and R. Brout, Phys. Rev. Lett. 13 (1964) 321 (June 26, 1964) P. W. Higgs, Phys. Rev. Lett. 13 (1964) 508 (August 31,

1964) G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Phys. Rev. Lett. 13 (1964) 585 (Octomber 12, 1964)

Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism on one page

19

1

2

2 2

1 2 2 1

22 222 2 2 2

1 2 1 2

11

1 1

2 2

0 1 ,

2 4 0

, , where(

1

4

, ( )2 ( ))

B

F

F F еA еA

mx

B A

G

xxe

mе

L

09/06/2014

Goldstone and Higgs Particles

Jeffrey Goldstone

Peter W. Higgs

Phys. Rev. 145 (1966) 1156H → Z Z

Re( )

Im( )“it is worth noting that an essential feature of this type of theory is the prediction ofincomplete multiplets of scalar and vector bosons.”

Phys. Rev. Lett. 13 (1964) 508

20

09/06/2014

Neither Salam and Ward, who worked at Imperial College in the same group with Guralnik, Hagen and Kibble, nor Glashow, who after Higgs seminar at Harvard on March 16, 1966 said: "that is a nice model, Peter" have realized that they could use this mechanism for generation of masses.

Omitted Opportunities

Glashow (1961) Salam & Ward (1964)

Salam & Ward (Sept 24, 1964→ Nov 15, 1964)(On Monday, October 5, Peter Higgs gave a seminar about his mechanism at Imperial College?) GHK (Oct 12, 1964 → Nov 16, 1964)

“All of us, Brout, Englert and myself, had been going in thewrong direction, looking at hadron symmetries. ” P.W. Higgs

21

0 0

0 0 H HB

H H

W

W

W

SU(2)L U(1)Y

Z 00Im ReH H

Using of EBHGHK mechanism

S. Weinberg (1967) & A. Salam (1968) → Nobel Prize 1979

relation between the masses of intermediate bosons MW =MZ cosW through the mechanism of spontaneous symmetry breaking

09/06/2014 22

2

h

( )12

ff f

hy

fm

Lagrangian ofthe Standard Model

2

Gauge sector

| | ( ) ElectroWeak Symmetry Breaking

Y Flavour sector

SM

i ij j

D F F

D V

L

09/06/2014 23

09/06/2014

Mathematical Foundation ofthe Standard Model (theory)

G. ’t Hooft & M. J. G. Veltman (1972) → Nobel Prize 1999renormalizability of non-abelian gauge theories with broken symmetry is proven

a drawing of their most important discovery 24

Discovery of the weak neutral interactions mediated by Z boson in experiment with bubble chamber Gargamelle at CERN (1973)

Establishment ofthe Standard Model (experiment)

sin2W ~ 0.3-0.5 MW =50-70 GeV MZ =75-80 GeV09/06/2014 25

09/06/2014

Hunt for the Higgs Boson

26

John F. Gunion, Howard E. Haber, Gordon L. Kane, Sally Dawson, The Higgs Hunter's Guide, Upton, NY: Brookhaven Nat. Lab., 1989. - 404 p.

09/06/2014

began work on November 30, 1986 and stopped on September 30, 2011

TeVatron at FNAL

@ 2 ТеВp p27

09/06/2014 28

Tevatron Higgs Exclusion

09/06/2014

Large Electron‒Positron(LEP) collider at CERN

started in August 1989 and ended in late 2000

DELPHI

L3 ALEPH

OPAL

@ 100 200 ГеВe e 29

09/06/2014 30

Direct LEP exclusion

09/06/2014 31

Indirect constraints on Higgs mass

Large Hadron Collider (LHC)

09/06/2014 32

109 interactions per second

1.51011 p

2 1380 bunches

@ 8 TeV !!!

1 Higgs 10 sec

09/06/2014

July 4, 201233

09/06/2014 34

Is it the Higgs, or isn’t Higgs?