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Physics Expectations at the LHC. Tata Institute of Fundamental Research Mumbai, India. Sreerup Raychaudhuri. April 9, 2008. IPM String School 2008, Isfahan, Iran. Plan of the Lectures. About the LHC (the six-billion dollar experiment…) Standard Model of Particle Physics - PowerPoint PPT Presentation
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Physics Expectations at the LHC
Sreerup Raychaudhuri
IPM String School 2008, Isfahan, Iran
Tata Institute of Fundamental ResearchMumbai, India
April 9, 2008
Plan of the Lectures
1. About the LHC
(the six-billion dollar experiment…)
2. Standard Model of Particle Physics
(what we already know…)
3. Physics beyond the Standard Model
(what we would like to know…)
4. Physics Prospects at the LHC
(what we could find in the next few years…)
Part 1
The Large Hadron Collider
(the biggest science experiment ever…)
Energy timeline…
atoms
electronsnuclei
quarks
W, Z
cathode rays
?
mesons
Reach Planck scale in 2243?
LHC is the Biggest and most Expensive
Science Experiment ever attempted
Price Tag: US $ 6.1 billion (Viking missions US $ 0.93 b)
No of scientists: 7000+
8.6 Km
Working Principle of a Collider Machine
8.6 Km
Buried 100 m below ground to shield radiation
Section of LHC tunnel showing pipe carrying liquid He
ATLAS Detector
The CMS detector weighs 1950 tonnes
(= weight of 5 Jumbo jets …)
Typical LHC Event
About
1 000 000 000
such events per second…
Unprecedentedcomputing challenge…
Worldwide distribution of analysts
Gb/s data transfer rates
Actual Gb/s transfer rates as monitored by BARC, India during a test run in 2006
LHC Timeline
First LHC studies were done in 1982
Project was approved in 1994 ; final decision in 1996
Construction started in 2002
LHC is expected to start-up in summer 2008
All the components are already in place
The detectors are being calibrated with cosmic rays particles
Cooling all sectors down to 1.9 K by mid-June 2008
First collisions will start around mid-August 2008
By October-November 2008 collision energy should reach 10 TeV
Energy upgrade to 14 TeV by early 2009
Higgs boson discovery (?) by 2011
Interesting factoids about LHC:• LHC when running will consume as much power as a medium-
sized European town
• LHC budget is comparable to the GDP of a small country, e.g. Fiji or Mongolia
• LHC vacuum is 100 times more tenuous then the medium in which typical communications satellites move
• LHC magnetic fields of 8.4 Tesla are 100,000 times the Earth’s
• LHC magnets will use 700,000 litres of liquid Helium and 12,000,000 litres of liquid Nitrogen
• LHC protons will have energies comparable to that of a flying mosquito
• LHC optical grid at 1.5 Gb/s could eventually make the Internet 300 times faster
What is this tremendous effort for?
What does the LHC hope to achieve?
Is success guaranteed?
We shall try to address, if not fully answer, these questions…
Part 2
Standard Model of Particle Physics
(what we already know…)
The Standard Model is a (partially) combined model of strong and electroweak interactions
Gravity is ignored…
Major ingredients:
1. Quark model
2. Non-Abelian gauge theory
• strong and electroweak sectors
3. Scalar 4 theory with Yukawa interactions
4. Parity violation in the weak sector
5. CP violation in the weak sector
Note (and Apology) on metric choice:
Minkowski metric: 2 22 0ds dx dx dx dx
Particle mass: 2 2 2 2p E p m
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
η
Curvature of a 4-sphere: 0
Bjorken & Drell 1964
Wick rotation
1c
Gauge structure of the Standard Model
All gauge theories have QED as the basic template
1QED 4
iD m F F
D ieA
F A A
L: Covariant derivative
: Field-strength tensor
Expands out to:
1QED 4
F F i m Aei
L
free gauge free fermion interaction
e
Invariance under local U(1) gauge transformations:
( )( ) '( ) ( )
( ) ' ( ) ( )
ie xx x e x
A x A x A x e
: First kind
: Second kind
1QED 4
iD m F F L D ieA
F A A
( )' i xeD D e D
Conservation of Nöther current & Nöther charge:
3 0
0 ;
0 ; ( )
J J e
QQ d x J x e
t
electromagnetic current
electric charge
No other renormalizable terms
Hermann Weyl (1885 – 1955)
This gauge symmetry gives its form to the QED Lagrangian and hence it is solely responsible for all the observed electromagnetic phenomena…
Extension of this idea: the form of strong and weak (nuclear) interactions are also dictated by gauge symmetries…
Scalar electrodynamicsCharged scalar field :
( )( ) '( ) ( )i xex x e x
* 2 *QED D D M
L L
Expands out to:
* 2 * * 2 *sED M ie A e A A
�
L
sEDL
free scalar pair interaction
seagull interaction
1 2e k k
2ie
Nöther current
Non-gauge InteractionsScalar field allows us to add on two more types of
renormalizable (gauge-invariant) interactions, viz.
1. Scalar self-interactions:
2*sED +LL
2. Yukawa interactions:
QED sED 1 2 H.c.h + +L L L
Requires at least two differently-charged fermion species
4 type
1 2 0e e e
Q. QED works fine. Why do we need a scalar field at all?
The gauge boson (photon) must be massless for gauge invariance
1 12 2mass 2 2A AM A A M A e A e
L
Q. Why do we want the photon to have a mass?
Needed in a superconducting medium (not otherwise)
1 1 24 2 AF F M A A
L 2AF M A
Static limit : 0 00 ; 0 0A A E
2 2 ij ji A AF M A B M A
2 2 2 A AB M B B M B
Skin effect
A self-interacting scalar field can generate a mass for the photon in a renormalizable and ‘gauge-invariant’ way.
Trick is to utilize the scalar self-interaction…
* *2D
*E
*
2
s
( )
D D
D D V
L
For real the (x) field is tachyonic
improper choice of generalised coordinates
need to re-define coordinates
Ginzburg & Landau 1950
Physical vacuum corresponds to the minimum of the potential :
22 * *( )V
V()
0
It is simple to show that and is arbitrary2
0 2
0arg
Vacuum choice leads to spontaneous breaking of the U(1) gauge symmetry
V()
0
After choosing the unique vacuum point = 0 , we are still free to choose the argument of …
Equivalent to rotation of axes in complex plane : re-parametrization
Common choice is to set : “unitary” gauge choice arg 0
Proper choice of generalized coordinate is to replace :
002
v
Note that : 1 11 22 2
( ) ( ) ( ) ( )x x i x x
0
1( ) 0
2 2
vx v i
2
2v
This shifting breaks the gauge symmetry spontaneously…
Consequences:
1. Generates mass for the gauge boson
2. Generates real mass for the scalar
3. Causes fermions to mix through their Yukawa coupling
*kineticsED
v v
2 2
v v
2 2
D D
ie A
ie A
L1. Gauge boson mass :
2 21v ...
2e A A
Gauge boson thus acquires a mass :
2 2
v2A
eM e
Short-range interaction
2. Scalar mass :2 4
2
22 2
2 22
22
v v
2 2
6v ...2 4
6 ...2 4 2
...4
( )V
Collect quadratic terms
Scalar thus acquires a real mass :
2M
Other scalar (imaginary part) vanished from the theory by choice of “unitary” gauge
3. Fermion mixing :
fermion 1 1 1 1 2 2 2 2
1 2
1 1 1 2 2 2 1 2
v2
v2
H.c.
H.c. ...h
iD m iD m
h
m m
L
mass terms only
Break up into chiral components:
1 15 52 2 L R
L R R L
mass 1 1 1 1 1
2 2 2 2 2
1 2 1 2v2
L R R L
L R R L
L R R Lh
m
m
L
mixing term
More convenient in matrix form :
1 1mass 1 2
22
v2
v2
H.c.
RL L
R
h
h
m
m
L
Again 1 and 2 are improper choices of coordinates
because they lead to coupled equations of motion
diagonalise the matrix for (decoupled) eigenstates
1 2
1 2
cos sin
sin cosa C C
b C C
where1 2
2 vtan C
h
m m
fermion mixing
violation of global U(1) flavor symmetries
Some technical terms:
• Generation of gauge boson masses by a self-interacting tachyonic scalar field
Anderson-Higgs Mechanism
• Residual massive scalar field Higgs Boson
• Imaginary part of scalar Goldstone Boson
• Fermion mixing from Yukawa interactions and spontaneous symmetry-breaking
Kobayashi-Maskawa Mechanism
• Fermion mixing angle C Cabibbo Angle
Peter W. Higgs (b. 1929)
Application of gauge theoretic ideas to strong and (weak) nuclear interactions :
Traditional picture of nucleus… Rutherford-Curie-Chadwick
Coulombic repulsion is overcome by strong nuclear interaction within a range of ~ 1 fm ; beyond 1 fm the repulsion causes instability and radioactive decay…
Weizäcker’s semi-empirical mass formula
Yukawa picture : exchange of mesons
This is only an effective picture since protons and neutrons (also pions) are composites made up of quarks and gluons…
Effective (Yukawa) theory with scalar exchange
Fundamental (gauge) theory with vector exchange
QCD
Murray Gell-Mann (b. 1929)
QCD : The gauge theory of strong interactions
Each quark carries one of three possible “colors”:
q q qGauge symmetry is a symmetry under mixing of these three “colors” :
1 1 1 1
2 2 2 2
3 3 3 3
R
R
R
B
B
GB
G
G
q U U U
q U U U
q U U U
q
q
q
'i i ij jq q U q
†
det 1
U U 1
U
SU(3)
1QCD 4
( ) ( ) Tr
( )
,
q
S
S
x i m x
ig x
ig
q D q G G
D 1 G
G G G G G
L
1QED 4
iD m F F
D ieA
F A A
L
QCD Lagrangian is constructed on the exact analogy of the QED Lagrangian :
1
2
where
a a
a a
G
G T
T λ
Gell-Mann matrices
Gluons
1,2,...,8a
Expands out to:
1QCD 4
1
2
1 24
v aai i q i i a v a
S i a jij
S abc a v a b c
S abc dec a b d e
iq q m q q G G G G
ig q T q
g f G G G G
g f f G G G G
Lfree quark free gluons
vertex: quark-antiquark-gluon
3-gluon vertex
4-gluon vertex
Similar to QED interaction…
Gluon self-interactions are typical of a non-Abelian (multiple-charge) theory ,a b abc cT T if T
QCD Feynman rules
ij
q
i
k m i
quark propagator gluon propagator
2
abi
k i
1 2 3 1 23
1 2 cyclicS a a aig f k k
1
2
3
3-gluon vertex
S a ijig T
qqg vertex
4-gluon vertex
1
2
3
4
1 2 3 4 1 4 2 3 1 3 2 4
2 2 3
2 4
a a b a a b
S
f f
ig
QCD coupling gS is large since the interaction is strong
However, it runs at higher energies due to quantum corrections…e.g. vertex corrections…
2 2 22
22
QCD 2
( ) ( )( )
41 4 ( ) log
S SS
S
g QQ
Qb
2 2 2QCD 2
1( ) 33 2 ( )
48 qq
b Q Q m
+ …
Since there are only 6 known quark flavors
2 22
2
QCD 2
( ) 1( )
44 log
SS
g QQ
Qb
Introduce the QCD scale :
2 2 2QCD 2 2
1 33 12( ) 33 2 ( ) 0
48 48qq
b Q Q m
2QCD
1
4 ( )sbe
As Q2 increases above 2, the QCD coupling decreases…
asymptotic freedom Politzer-Gross-Wilczek 1973
S
(EC
M)
Quark confinement :
Free colored states have not been observed in Nature
Conjecture: only color singlets form stable states
x
( )V x
Open problem : to obtain a confining potential from the QCD Lagrangian
Weak interaction sector is the most intriguing part of the Standard Model
The gauge theory of electroweak interactions
n
p
e-
e-udd
u d u
-decay : Fermi
-decay : quark picture
e-
d
u
W--decay : intermediate vector boson
Interaction must be of short-range nature, i.e. W bosons must be massive
To accommodate charged gauge bosons, we must have a non-Abelian theory…
Sheldon L. Glashow (b. 1932)
Choice of gauge group: SU(2) U(1)Acts on a complex scalar doublet :
1
2
† U U 11 11 12 1
2 21 22 2
'
'
U U
U U
† 2 †GSW
1 1
4 4
'2
Tr Tr
( ) ( )
,
g
M
B B
i g x B x
ig
B B B
D D
W W
D 1 W 1
W W W W W
L
Electroweak Lagrangian is again constructed on the analogy of the QED/QCD Lagrangian :
31 21 2 3( ) ( ) ( ) ( )
2 2 2x W x W x W x
σσ σW
Generators of SU(2)SU(2) “charge” weak isospin
U(1) “charge” weak hypercharge
31 21 2 3
1 13 1 22 2
1 11 2 32 2
1 132 2
1 1322
( ) ( ) ( ) ( )2 2 2
( ) ( ) ( )
( ) ( ) ( )
( ) ( )
( ) ( )
x W x W x W x
W x W x iW x
W x iW x W x
W x W x
W x W x
σσ σW
'
2
'32 2 2
'3 222
132 2
1322
( ) ( )
( ) ( ) ( ) 0
0 ( )( ) ( )
( ) ' ( ) ( )
( ) ( ) ' ( )
g
g g g
gg g
g
g
g x B x
W x W x B x
B xW x W x
gW x g B x W x
W x gW x g B x
W 1
Mass arises from spontaneous symmetry-breaking and Higgs mechanism :
†
22 † †
( )
( )
V
V
D DL
Vacuum at :
2 2v†42
Vacuum manifold has an SO(4) symmetry
2
2 2 2 2
1 1 2 2
vRe Im Re Im
2
Choice of vacuum leaves a residual O(2) symmetry unbroken U(1)em
Abdus Salam (1926 – 1996)
Steven Weinberg (b. 1933)
†kinetic
†'† †2
'
2
g
g
i g B
i g B
D D
W 1
W 1
L
Shift the vacuum :
2
v
0
Pick out the mass terms and expand…
1 2 2
mass 8
1 2 2 23 3 38
2 22 2
2
vv8 8cos
v
v 2 ' '
W
gg
g W W
g W W gg W B g B B
W W Z Z
L
3 cos sinW WZ W B 3 sin cosW WA W B
'tan W
g
g
1
2
cos
v
0
W
MWZ
W
M g
M
M
After shifting the scalar field:
1 1 2 2 3 3( ) ( ) ( )1 1 2
2 2 2
( )
0( )
ix x xr i
r iH x
ix e
i
σ σ σ
Freedom to re-parametrize, i.e. choose the “unitary” gauge
1 2 2( ) ( ) ( ) 0x x x
2
( )
0( ) H xx
22 ...
4( ) HV
as before…
massive Higgs boson
not (yet) found
Fermionic sector of the Glashow-Salam-Weinberg model
e-e -
u d
sc
-
b
tI
IIIII
A little bit of history : Parity violation in weak interactions
• By 1955 it was established that o , have
intrinsic parity P = -1
• Cosmic ray experiments had found two particles, both having mass 498 MeV and decay lifetime 12.4 ns, of which one decayed to
+ + o (P = +1 state)
and one decayed to
+ + - + + (P = -1 state)
• Yang and Lee (1956) conjectured that (a) both are decay modes of the same particle – the K+ (b) P is violated in weak interactions (c) 3 is parity-conserving decay; 2 is parity-violating decay
• The 1957 Co-60 experiment of Wu, Amblers et al established that P-violation does indeed happen in weak interactions
• Did not establish the extent of P-violation, e.g.
+
1 15 52 2
H.c.2We
ge e WA B
L
1A B If A = B parity is conserved
If A = 0 or B = 0, parity is maximally
violated
• Goldhaber et al, later in 1957, proved that for inverse -decay, B = 0.
• V – A form of weak interactions suggested by Marshak &
Sudarshan (1956) and by Feynman and Gell-Mann (1956).
Parity violation is accommodated in the Standard Model by making the left and right chiral fermions transform differently under SU(2)…
Doublets :
eL
Le
L
L
L
L
L
L
u
d
L
L
c
s
L
L
t
b
Re
Singlets :
R R
Ru
RdRc
RsRt
Rb
eR R R
Lepton gauge couplings:
1,2,3
2
'lepton 2 2
2cos2
54cossin sin
' H.c.
H.c.
( 1 4 )
a
W W
g ga L L R R
g gL L L L
W
g
W
aL L
g
L L gL L
e W Z
e eZ e eA
W B Be e
σL
eLL
L
Le
52(1 )ig e
W
52cos(1 )
W
ig
Z
2
54cossin(1 4 )
WW
ig
eZ
e ie
e
e
Similarly in the Quark sector…
Lepton masses:
An electron mass term breaks up into combinations of left and right chiral terms…
1 15 52 2
( ) ( ) ( ) ( ) ( )L Re x e x e x e x e x
mass ( ) ( )e
e L R L R
e L R R L
m e x e x
m e e e e
m e e e e
L
If eL has T3 = -1/2 and eR has T3 = 0, this mass term is not gauge invariant…
Hence the requirement of parity-violation and electroweak gauge symmetry make all Standard Model fermions massless… massive
Lepton Yukawa couplings:
single
Yukaw
t
a H.c.L Rh L e
L
0
2 2
v
2
v
H.c.
H.c.
H.c.
L L R
L R
L R L Rh h
h e e
h e e
e e e e
Electron mass term
v
2e
hm
v2e eh m
Similarly for the muon and the tau masses
Quark Yukawa couplings:
single
Yukaw
t
a H.c.L RhQ d
L
By analogy with the leptons
*2
singlet
' H.c.L Rh Q i u
v
2d
hm ' v
2u
hm
No constraint to restrict to one generation only…
*Yukawa 2
v v
2 2Yukawa terms
' H.c.
+ ' H.c.
ij i j ij i j
ij i j
L R L R
ij iR RjL L
h Q d h Q i u
h d d h u u
L
mass H.c.
' ' '
' ' ' H.c.
' ' '
dd ds db R
L L sd ss sb RL
bd bs bb R
uu uc ut R
L L L cu cc ct R
tu tc tt R
M M M d
d s b M M M s
M M M b
M M M u
u c t M M M c
M M M t
L
†d dR RV V †d d
L LV V
†u uR RV V †u u
L LV V
Kobayashi-Maskawa mechanism: v
2ij ijM h
v' '
2ij ijM h
diag
onal
izat
ion
Physical states
In terms of the physical states the charged current interactions are no longer diagonal…
†
CC H.c.2
H.c.2
H.c.2
u
L
L L
dL
L L
L
L
L L L L
L
L
L L L L
L
L
dg
u c t s W
b
dg
u c t sV W
b
dg
u c t s W
V
b
K
L
Cabibbo-Kobayashi-Maskawa matrix †u d
L LV VK
In terms of the physical states the neutral current interactions remain diagonal…
0NC
0†
0
H.c.2
H.c.2
H.c.2
u
Lu
L L L L
L
L
L L Lu
L L L
L
L
L L L L
L
ug
u c t c ZLt
ug
u c t c ZLt
ug
u c t c ZLt
V V
c
c
c
1
L
No Flavor Changing Neutral
Currents
CP-violation:
We can take the and the to be complex ijh 'ijhv
2ij ijM h
v' '
2ij ijM h
Also complex complex
,,u dL RV
CKM matrix K can also be complex
CP is violated
Note that there is no explanation for the CP violating phases; they are just accommodated… like parity violation…
Experimental tests:
Hundreds of tests till date … cross-sections, decay widths, branching fractions,…
QCD tests: DIS results, three-jet events,
line-shape fits, parton-density fits, etc.
Electroweak tests: Neutral currents, W,Z discovery,
precision tests at LEP and SLD, HERA, Tevatron, Babar and BELLE, …
Everything agrees with Standard Model within experimental errors…
QCD tests:
Three-jet events in pair annihilatione e
e q
qe
Gluons exist !!
Three-jet event seen at LEP in 1992…
g
Hadronic final states at different energies
P. Schleper, Aachen 2003
QCD fits are amazingly good
pp ,e
QCD is tested to at least 2( )SO
s globalBethke 2002
s from QCD fits
s from hadr. processses
Very impressive success of QCD
Limited everywhere by missing higher orders
P. Schleper, Aachen 2003
Electroweak precision tests:
The LEP Collider at CERN, Geneva (1991-2001) was a electron-positron collider running at an energy between 90 – 210 GeV.
Precision electroweak tests at LEP have established the Standard Model results to accuracy of (for some variables) 1 in 100,000…
Z-boson parameters
Light neutrino species:
Weinberg angle:
Universality of gauge couplings is tested at per mille level
Altarelli and Grünewald, Phys. Rep. 2004
‘Measurement’ is the direct result from the LEP data at the Z-pole
‘SM fit’ is a minimum 2 -fit to all the LEP observables using all the SM variables….
… including the mass of the Higgs boson
Altarelli and Grünewald, Phys. Rep. 2004
Altarelli and Grünewald, Phys. Rep. 2004
Dependence of loop corrections on MH is always logarithmic
114 GeV 237 GeVHM at 68% C.L.
480 GeV
CP Violation : fits to the Unitarity Triangle (2006)
Area of the triangle ~ sin
The Higgs Boson is the only missing piece…
