precision measurements after the higgs discovery
DESCRIPTION
Precision Measurements after the Higgs Discovery. M.V. Chizhov Sofia University, Bulgaria and JINR, Russia. Why do we need the Higgs boson?. S = ½. S = 1. S = 0. Harmonic Oscillator (Analytical M echanics). Joseph-Louis Lagrange ( Giuseppe Lodovico Lagrangia) , 1788. - PowerPoint PPT PresentationTRANSCRIPT
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
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Harmonic Oscillator(Analytical Mechanics)
2 2
2
[ ( ), ( )]
( ) ( ) 2 2
[ ( ), ( )]
theorem ofEmmy Noether,
0 0const
1915
L q t q t K V
mq t kq t
S L q t q t dt
S q qE K V
Joseph-Louis Lagrange (Giuseppe Lodovico Lagrangia), 1788
3
q
R > 0R < 0
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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[]
Ener
gy4
2 2 20 m m
0
2
22
2
2
[ ] 0 const2
[ ] 1( ) ( ) ; 02
V
Vx x mR
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Scalar Potential of Anharmonic Oscillator
242[ ] , 0
2 4V
[ ]V [ ]V
0 0
2 0 0
2
2
22 2 20 0
5
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Discrete Z2 Symmetry ofthe Scalar Potential
[ ] [ ]V V
2 0 0 2
2 2 20 0
2 2m
22 4[ ] [ ]
2 4V V 32 4
2 4
[2 4
2]4
V
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 2
1 2 1 2 1 2[ , ] , 0, 02 4
V
2 2 2 22 1 2 20 00
[ , *] 0 ; 02 2
V
1 20 0, 0
2 421 2 1 2, * , [ , *]2 2i i V
Re( )Im( ) 7
2
0
1
0
22 21 2
2
22 1 2
22
1
[ , ]
[
2
, ] 0
Vm
Vm
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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
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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
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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 cn udd m c
2
2
0
2.3MeV /
4.8MeV /chiral limit lim 0
q
u
d
m
u m cd m c
m
0
2
0 2
2
139.6 MeV /= 135.0 MeV /
2139.6 MeV /
udm c
dd uu m cm c
du
10
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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 22Newton law (1687): N
m mF Gr
11
1 22
0
1Coulomb law (1785): 4
q qFr
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Gauge Invarianceand Massless Particles
Strenght tensor of electromagnetic field is
invariant under gauge tranformation ( ).1Therefore, 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!
A
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
0massless
However, 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
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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
g Em
M2
22
sinuW
g Em
M 2
SM
2
SM
4 sin
, cos4cos
ZWWs
W
ZWW WW
y gmg g
E
y g
M
Unitarity and Z boson
09/06/2014 16
22 22
22 2 SM
2 2
22 (1 cos )cos4 3 , where
4 1cos
Z Wgauge W
W WZ W
umg u
m m
E
mm
M
22 22 22 2,
2 2 2 2
2 2
4 4hm s t
W WH
W h h W
s m t mg g um s m t m m
M
Unitarity and Higgs boson
Not yet tested experimentally… but see the following slide!
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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
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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).
A 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 21 2 1 2
11
1 12 2
0 1 , 2 4 0
, , where(
14
, ( )2 ( ))
B
F
F F еA еA
mx
B A
G
xxe
mе
L
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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 00 0 H H
BH H
WWW
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
2h
( )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
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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 ~ 0.30.5 MW =5070 GeV MZ =7580 GeV09/06/2014 25
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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.
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began work on November 30, 1986 and stopped on September 30, 2011
TeVatron at FNAL
@ 2 ТеВp p27
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Tevatron Higgs Exclusion
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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
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Direct LEP exclusion
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Indirect constraints on Higgs mass
Large Hadron Collider (LHC)
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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?