Transcript Physics Expectations at the LHC Sreerup Raychaudhuri Tata Institute of Fundamental Research

Physics Expectations at the LHC
Sreerup Raychaudhuri
Tata Institute of Fundamental Research
Mumbai, India
April 9, 2008
IPM String School 2008, Isfahan, Iran
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…
?
W, Z
quarks
mesons
nuclei
electrons
atoms
cathode rays
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…
Unprecedented
computing
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 mediumsized 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
 c 1
Note (and Apology) on metric choice:

    dx 

Minkowski metric: ds    dx dx  dx
2
0
2
2
1 0 0 0 


0

1
0
0

η
 0 0 1 0 


 0 0 0 1
Particle mass:
p E p m
2
Curvature of a 4-sphere:
2
2
 0
2
Bjorken & Drell
1964
Wick rotation
    
Gauge structure of the Standard Model
All gauge theories have QED as the basic template
LQED    iD  m   14 F F 
D     ieA
F    A   A
: Covariant derivative
: Field-strength tensor
Expands out to:
LQED   F F  i   m  ie    A
1
4

free gauge

free fermion
interaction
e 
LQED   iD  m  F F
1
4

D     ieA
F    A   A
No other renormalizable terms
Invariance under local U(1) gauge transformations:
 ( x)   '( x)  eie ( x ) ( x)
: First kind
A ( x)  A ' ( x)  A ( x)  e  
: Second kind
D  D '  eie ( x ) D
 Conservation of Nöther current & Nöther charge:



 J  0
;
J  e 
Q
0
t
;
Q   d 3 x J 0 ( x)  e
electromagnetic current
electric charge
This gauge symmetry gives its form to the QED
Lagrangian and hence it is solely responsible for
all the observed electromagnetic phenomena…
Hermann Weyl
(1885 – 1955)
Extension of this idea:
the form of strong and weak (nuclear) interactions
are also dictated by gauge symmetries…
Scalar electrodynamics
Charged scalar field :  ( x)   '( x)  e
 ie ( x )
 ( x)
L  LQED   D  D   M  
*

2
*
LsED
Nöther
current
Expands out to:
LsED    *   M 2 *  ie  *   A  e2 * A A
free scalar
seagull
interaction
pair
interaction
e  k1  k2 

ie2 
Non-gauge Interactions
Scalar field allows us to add on two more types of
renormalizable (gauge-invariant) interactions, viz.
4 type
1. Scalar self-interactions:
L  LsED +    
*
2. Yukawa interactions:
2
e1  e2  e  0
L  LQED + LsED +  h1 2   H.c.
Requires at least two differently-charged fermion species
Q. QED works fine. Why do we need a scalar field at all?
The gauge boson (photon) must be massless for gauge invariance
Lmass  12 M A2 A A  12 M A2  A  e     A  e   
Q. Why do we want the photon to have a mass?
Needed in a superconducting medium (not otherwise)
L
1
4
F F

2
A

A0  0 ;  0 A  0
Static limit :
i F ij  M A2 A j


 M A A
1
2

   B   M A2 B
  F   M A2 A
 E0
  B  M A2 A
  2 B  M A2 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…
LsED   D  D          
*

2
*
*
2
  D  D   V ( )
*

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 :

V ( )         
2
*
*

2
V()
0
It is simple to show that
2
0 
2
and arg 0  is arbitrary
Vacuum choice leads to spontaneous breaking of the U(1) gauge symmetry
After choosing the unique vacuum point  = 0 , we are still
free to choose the argument of  …
V()
0
Equivalent to rotation of axes in complex  plane : re-parametrization
Common choice is to set
arg    0 : “unitary” gauge choice
Note that :  ( x) 
1
2
1 ( x)  i2 ( x) 
1
v
0 ( x ) 
 v  i  0 
2
2
1
2
 ( x)
2
v
2
Proper choice of generalized coordinate is to replace :
  0    0 
 v
2
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
1. Gauge boson mass :
L
kinetic
sED
  D  D 
*
   v 
   v 
   
  ie A 

 2 
  2 
    v 
    v 
  
  ie A 

 2 
  2 
1 2 2

 e v A A  ...
2
Gauge boson thus acquires a mass :
M A  e v 
e2  2
2
Short-range
interaction
2. Scalar mass :
  v 
  v 
V ( )    
 

 2 
 2 
 2  2  2
 
 6v   ...
 2 4

2
4
2
Collect quadratic terms
 2  2  2
 
 6
  ...
 2 4 2 

2
4
 2  ...
Scalar thus acquires a real mass :
M 

2
Other scalar (imaginary
part) vanished from the
theory by choice of
“unitary” gauge
3. Fermion mixing :
Lfermion   1  iD 1  m1  1  2  iD 2  m2  2


 h  1 2  H.c.  
v
2
  m1 1 1  m2 2 2 
hv
2
mass terms only
 1 2  H.c.  ...
Break up into chiral components:

1 5
 2 
1 5
 2 
  L  R     L R  R L
Lmass  m1  1L 1R   1R 1L 
 m2  2 L 2 R   2 R 2 L 

hv
2
 1L 2 R   1R 2 L 
mixing term
More convenient in matrix form :
Lmass   1L
 m1
 2 L  hv

 2
hv 
2   1R 
 H.c.


m2   2 R 

Again 1 and 2 are improper choices of coordinates
because they lead to coupled equations of motion
 diagonalise the matrix for (decoupled) eigenstates
 a   1 cos C  2 sin C
 b   1 sin C  2 cos C
fermion mixing
2hv
where tan C 
m1  m2
violation of global U(1) flavor symmetries
Some technical terms:
Peter W. Higgs
(b. 1929)
• 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
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
Murray Gell-Mann
(b. 1929)
Fundamental (gauge) theory
with vector exchange
QCD
QCD : The gauge theory of strong interactions
Each quark carries one of three possible “colors”:
q
q
q
Gauge symmetry is a symmetry under mixing of these
three “colors” :
 q1   U1R U1B U1G  q 
  
 
 q2    U 2 R U 2 B U 2G  q 
 q  U
 q 
U
U
3B
3G  
 3   3R
qi  qi '  U ij q j
U†U  1
det U  1
SU(3)
QCD Lagrangian is constructed on the exact analogy of the
QED Lagrangian :
LQCD  q( x)  iD  mq  q( x) 
1
4
Tr  G  G


D  1   ig S G  ( x)
G     G   G   ig S G  , G 
LQED    iD  m   F F
1
4
D     ieA
F    A   A

Gluons
G   G a Ta
where Ta  λ a
1
2
Gell-Mann
matrices
a  1, 2,...,8
Expands out to:
LQCD  iqi qi  mq qi qi  14    G a   vG a    G a   vG a 
free quark
 ig S qi  Ta ij q j
free gluons
vertex: quark-antiquark-gluon
Similar to QED interaction…
 12 g S f abc    G a   v G a  Gb Gc
3-gluon vertex
 14 g S2 f abc f dec Ga Gb G d G e
4-gluon vertex
Gluon self-interactions are typical of a non-Abelian
(multiple-charge) theory
Ta , Tb   ifabcTc
QCD Feynman rules
gluon propagator
quark propagator
i ij
i ab 
k  mq  i
k 2  i
qqg vertex
ig S   Ta ij
4-gluon vertex
1
3
2
4
3-gluon vertex
igS f a1a2a3  k1  k2  12  cyclic
3


1
2
3


 f a a b f a a b        
1 4
2 3
1 3
2 4
 12 34
ig S2   2  3

  2  4






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
g
(
Q
)
2
S
 S (Q ) 

4
1
bQCD (Q ) 
48 2
2
 S ( 2 )
1  4 S (  2 )bQCD log


2
2
33  2 (Q  mq ) 
q


Q2

2
Since there are only 6 known quark flavors
1
bQCD (Q ) 
48 2
2

 33  12
2
2
0
33  2 (Q  mq )  
2
q

 48
1
Introduce the QCD scale  :    e
2
2
g
(
Q
)
2
S
 S (Q ) 

4
4 bQCD s (  2 )
1
Q2
4 bQCD log 2

As Q2 increases above 2, the QCD coupling decreases…
asymptotic freedom
Politzer-Gross-Wilczek 1973
S (ECM)
Quark confinement :
Free colored states have not been observed in Nature
Conjecture: only color singlets form stable states
V ( x)
x
Open problem :
to obtain a confining potential from the QCD Lagrangian
The gauge theory of electroweak interactions
Weak interaction sector is the most intriguing part of the Standard Model
p
n
u
d
d
e-
-decay : Fermi


u
d
e-
W
-decay : intermediate vector boson
-decay : quark picture
e
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…
Choice of gauge group:
SU(2)  U(1)
Acts on a complex scalar doublet :
Sheldon L. Glashow
(b. 1932)
 1 
 
 2 
 1 '   U11 U12  1 
 
 
 2 '   U 21 U 22  2 
U U 1
†
Electroweak Lagrangian is again constructed on the analogy
of the QED/QCD Lagrangian :
LGSW   D  

†
D   M 2  †
 Tr  W W
1
4


1
4
Tr  B B


g'

D  1   i gW ( x)  2 1B ( x) 


W    W   W  ig  W , W 
B    B   B
σ3
σ1
σ2
W ( x)  W1 ( x)  W2  ( x)  W3 ( x)
2
2
2
SU(2) “charge”  weak isospin
U(1) “charge”  weak hypercharge
Generators of SU(2)
σ3
σ1
σ2
W ( x)  W1 ( x)  W2  ( x)  W3  ( x)
2
2
2
1
1

W ( x)  iW2  ( x)  
W
(
x
)
3
2
2  1

1
1
 W1 ( x)  iW2  ( x) 


W
(
x
)
3

2
2

 

1

 12 W3  ( x)

W
 ( x)
2

 1 
1
 W ( x)  W3  ( x) 
2
 2

gW ( x)  g2' 1B ( x)
g

g'
 g2 W3 ( x)

W
(
x
)

B ( x)

2
2

 g 
g
 W ( x)  W3 ( x)   0
2
 2

 12  gW3 ( x)  g ' B ( x) 

g


W
 ( x)
2



g'
B ( x) 
2
0


1
  gW3 ( x)  g ' B ( x)  
2 
g
2
W ( x)
Mass arises from spontaneous symmetry-breaking and
Higgs mechanism :
L   D  

†
D    V ( )

V ( )         
2
†
†

2
Vacuum at :
Abdus Salam
(1926 – 1996)
 † 
v
2
2

2
4
Steven Weinberg
(b. 1933)
Vacuum manifold has an SO(4) symmetry
v2
2
2
2
2
 Re 1    Im 1    Re 2    Im 2  
2
Choice of vacuum leaves a residual O(2) symmetry
 unbroken U(1)em
0
  v 
 
 2
Shift the vacuum :     
L
kinetic

  D       D     
    †  i gW  g2' 1B  †  

†



     i gW  g2' 1B

  
†

 

Pick out the mass terms and expand…
Lmass  18 g 2 v2W  W



 18 v 2 g 2W3 W3  2 gg 'W3 B  g '2 B  B

g 2 v2 W  W 

8

g 2 v2
8cos2 W
Z   W3 cos W  B sin W
Z  Z
M W  gv
1
2
MW
M Z  cos
W
M  0

g'
tan W 
g
A  W3 sin W  B cos W
After shifting the scalar field:
 1r  i1i   0  2i 1 ( x ) σ1 2 ( x ) σ 2 3 ( x ) σ3 
 ( x)  
   H ( x )  e
 2 r  i2i   2 
Freedom to re-parametrize, i.e. choose the “unitary” gauge
1 ( x)  2 ( x)  2 ( x)  0
 0 
  ( x)   H ( x ) 
 2 
as before…
V ()  
2
4
H 2  ...
massive Higgs boson
not (yet) found
Fermionic sector of the Glashow-Salam-Weinberg model

e
e-
u
d
I
c

-
II
-
III
s
t
b
A little bit of history : Parity violation in weak interactions
• By 1955 it was established that
intrinsic parity P = -1
o , 
have
• 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 parityviolating 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.
LWe 
+
g 


A 

2
A B 1
  e  B   
1 5
2

1 5
2


e W  H.c.

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.
– A form of weak interactions suggested by Marshak &
Sudarshan (1956) and by Feynman and Gell-Mann (1956).
•V
Parity violation is accommodated in the Standard
Model by making the left and right chiral fermions
transform differently under SU(2)…
Doublets :
Singlets :
 eL    L    L 
  
  
 eL    L   L 
 eR
 R
 R
eR
R
R
 cL   t L 
  b 
 sL   L 
uR
cR
tR
dR
sR
bR
 uL 
 
 dL 
 eL 
LL   
Lepton gauge couplings:
 eL 
g
g'

Llepton  2  LL σa LLWa  2 LL  LL B  g ' eR  eR B  H.c.
a 1,2,3
  g2  L  eLW  H.c.  2cosg  L  L Z 
W
 4cosg e   (1  4 sin 2 W   5 )eZ    g sin W  e   eA
W

e

W
 ig2   (1   5 )

e
e
Z
 ig

2

(1

4
sin
W   5 )
4cosW
e
e
Z
ig


(1   5 )
2cosW

ie 
Similarly in the Quark sector…
Lepton masses:
An electron mass term breaks up into combinations of left
and right chiral terms…
e( x ) 
1 5
2
e( x ) 
1 5
2
e( x)  eL ( x)  eR ( x)
Lmass  me e ( x)e( x)
 me  eL  eR  eL  eR 
 me  eL eR  eR eL 
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:
LYukawa  h LL  eR  H.c.
si nglet


 h  L   eL0 eR  H.c.
 h eL

h
2
v
2
eR  H.c.
eL eR 
hv
2
Similarly for the
muon and the
tau masses
eL eR  H.c.
Electron mass term
hv
me 
2

he
me

v
2
Quark Yukawa couplings:
By analogy with the leptons
LYukawa


*

h
'
Q
i


uR  H.c.
 h QL  d R  H.c.
L
2
si nglet
singlet
hv
 md 
2
h'v
 mu 
2
No constraint to restrict to one generation only…
LYukawa  hij QLi d Rj  h 'ij QLi  i 2*  uRj  H.c.
 Yukawa terms +
v
2
hij d Li d Rj 
v
2
h 'ij uLi uRj  H.c.
v
M ij 
hij
2
Kobayashi-Maskawa mechanism:
diagonalization
Lmass  d L sL
 M dd

b L  M sd
 M bd
M ds
M ss
M bs
  
d
L
V
 uL
Physical
states
†
cL
V
†
d
R
V
  
u
L
  
d
L
 M 'uu

tL  M 'cu
 M 'tu
u
L
V
M db   d R 



M sb   sR   H.c.
M bb   bR 
V
M 'uc
M 'cc
M 'tc
†
VRd
M 'ut  u R 



M 'ct   cR   H.c.
M 'tt   t R 
  
u
R
V
†
VRu
v
M 'ij 
h 'ij
2
In terms of the physical states the charged current
interactions are no longer diagonal…
LCC
g

uL
2
cL
g

uL
2
cL
g

uL
2
cL
d L 
  s  W   H.c.
tL
 L 
 bL 
d L 
† 

u
d
tL VL
VL  sL  W  H.c.
 bL 

   
tL

d L 
 K  s  W   H.c.
 L 
 bL 
Cabibbo-Kobayashi-Maskawa
matrix
K  V
u
L
V 
d
L
†
In terms of the physical states the neutral current
interactions remain diagonal…
L
u
NC
g

uL
2
cL
g

uL
2
cL
g

uL
2
cL
u L 

tL  cL  cL  Z 0  H.c.
 t L 
u L 
† 

u
u
tL VL  cL VL  cL  Z 0  H.c.
 t L 
 
 
u L 

tL  cL 1  cL  Z 0  H.c.
 t L 
No Flavor Changing Neutral Currents
CP-violation:
We can take the
hij
v
M ij 
hij
2
v
M 'ij 
h 'ij
2
and the
h 'ij
to be complex
Also complex 
u ,d
complex
L,R
V
 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 event seen at LEP in 1992…
 
Three-jet events in e e pair annihilation
e

q
g
e

q
Gluons exist !!
Hadronic
final states
at different
energies
QCD fits are
amazingly good
P. Schleper, Aachen 2003
pp 
 e, 
 
QCD is tested to at least
O( S2 )
P. Schleper, Aachen 2003
s from QCD fits
Bethke 2002
s global
s from hadr. processses
Very impressive
success of QCD
Limited everywhere by missing higher orders
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 Zpole
‘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  M H  237 GeV
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…