Transcript New Physics at a TeV and the LHC

New Physics at a TeV and the LHC - I
Accelerator Basics and the LHC
Sreerup Raychaudhuri
Tata Institute of Fundamental Research,
Mumbai, India
IPM String School (ISS 2009), Tehran, Iran
April 16, 2009
We learn about nuclear and sub-nuclear physics in two ways:
1. Indirect way – from energy levels of nuclear/particle
states (spectroscopy)
2. Direct way – from scattering experiments
d
Typical scattering experiment
1
F
 d
M
2
Two possible designs for a scattering experiment:
1. ‘Fixed’ target experiment
Eb ,0,0, k  and M ,0,0,0
2
2
Ecm  Eb  M ,0,0, k 
2
 Eb  M   k 2
in thelab frame
 Eb2  k 2  M 2  2ME
2 more
2
As more
and
 m  M  energy
2MEb is pumped into the beam,
more and more
energy
is lost in the recoil of the target
2
2
Ecm  m  M  2 MEb  2MEb as Eb  
Ecm
2M

 0 as Eb  
Eb
Eb
2. Collider experiment
Eb ,0,0, k  and Eb ,0,0,k 
2
2
Ecm  2 Eb ,0,0,0
 4E
2
b
in thelab frame

Ecm  2 Eb
Ecm
2
Eb
Full beam energy is available for the process
LHC 2009
Tevatron
1994
LEP 1991
SLAC 1969
How are these high beam energies attained?

E

E

E

E

V
V
E

Cannot make plates too close, for then there will be spark
discharges even with high vacuum; instead we make
voltage high ⇒ use AC voltage instead of DC voltage

E
Cannot use a continuous beam any more;
must send bunches of particles at a time…
…pulsed operation : timing between bunches
must match RF…
Interaction rate will now depend on bunch crossings…
L
n1n2

4 A
Luminosity cm-2 s-1
R L  
Event rate s-1
n1,2  number density of bunches
  number of crossings per second
A  cross-sectional area of bunches
  reaction cross section
Event rate :
R  L 
As data are gathered over time…
t
No of events N 
R
0
t
dt'   L   dt'  L  
0
t
Integrated luminosity
L   L dt'
0
If  Is measured in pb, fb, etc. , L is measured in pb-1, fb-1, etc.
1 pb = 1000 fb
⇒ 1 fb-1 = 1000 pb-1
10 nb-1/s
nb-1/s
From the BNL home page
How are these high luminosities attained?
L
n1n2

4 A
n1,2  number density of bunches
  number of crossings per second
A  cross-sectional area of bunches
  reaction
cross
Packing charged
particles
likesection
electrons and protons
into very small volumes is difficult because of the
strong electrostatic repulsion; requires very strong
focussing magnetic fields from superconducting
electromagnets etc.
Working Principle of a Storage Ring
Re-use the same bunches many many times…
8.6 Km
The LHC is just a
giant storage ring
8.6 Km
Buried 100 m below ground to shield radiation
Section of LHC tunnel showing beam pipe
Some LHC parameters
Beam energy :
Collision energy :
5 TeV  7 TeV
10 TeV  14 TeV
Luminosity :
10 nb-1 s-1 (design)
‘Integrated’ luminosity: 100 fb-1 per year (design)
Bunch crossing rate : 4 107 s-1
Bunch distance:
~7m
Bunch size :
few cm  1 mm, 16 m (collision pt)
No of protons/bunch : 1.1  1011
No of magnets:
9593
Magnet temperature: 1.9 K
Current:
11 700 A
Magnetic field: 8.3 T
Some amusing LHC facts
• LHC will consume as much power as domestic sector in Geneva canton
• LHC budget is comparable to GDP of a small country, e.g. Fiji or Mongolia
• Vacuum is 10 times better than the surface of the Moon
• Magnetic fields of 8.3 Tesla are 100,000 times the Earth’s magnetic field
• Magnets will use 700,000 lit of liquid He and 12,000,000 lit of liquid N
• Total length of cable could stretch from Earth to Sun 5 times
• LHC protons will travel at 0.999999991c
• LHC protons will have energies comparable to that of a flying mosquito
• Protons used in 10 years would be equivalent to only 7.5 g of hydrogen
• LHC beams will together have enough energy to melt 1 tonne of copper
• Data could fill a stack of HD-DVDs 11 Km high (Mt. Everest: 8.8 Km)
2009,
End-cap
barrel
radiation
radiation hardened;
sensitive;
high
low efficiency
efficiency
Ch
HCAL
VXD
EMC
VXD
ECAL
HCAL
Ch
CMS Detector
Particle detection at the LHC

e


q / g /
W /Z
b
t/H
No signals at all ; only missing energy
Track in VXD ; energy deposit in ECAL
Track in VXD ; tracks/deposits in CH
No track in VXD; only deposit in ECAL
Hadronic jets ; signals in all devices
Decay at the interaction vertex itself
Displaced vertices in VXD; deposit in HCAL
Decay at the interaction vertex itself
Everything must be reconstructed only from these effects
Protons not point particles, but conglomerates of
• valence quarks (uud)
• gluons
• sea quarks (u,d,s,c,b,t)
More like two cars crashing and spewing out
parts than like the collision of hard billiard balls…
Choice of Variables
k
x1k
 x2 k
k
Partonic system has an (unknown) longitudinal boost
x1  x2

x1  x2
Each collision event will have a different 
 we must choose variables which
are independent of longitudinal boosts
Commonest Variables
pT 
1. Transverse momentum :
2. Rapidity :
1
E  pz
y  log
2
E  pz
3. Pseudo rapidity :
4. Angular separation :
5. Invariant mass :
p p
2
x
2
y
1
x2
 y  log
2
x1
   log tan

2
M   p1  p2 
pT2  m 2
y
 y if m  0
R   2   2
2
12
ET 
2
Signal and Background
If a certain final state (including phase space
characteristics) is predicted by a theory, the cross-section
for producing that final state is called the signal
NS  L .  S
If it is possible to produce the same final state (including
phase space characteristics) in an older, well-established
theory (e.g. Standard Model), that cross-section is called
a background
NB  L .  B
Experimental results will have errors:
 Nexp  standard deviation 
Nexp   Nexp
What constitutes a discovery?
Excess/depletion over background :
N exp  N B
Assuming random (Gaussian) fluctuations, the probability that this
deviation is just a statistical effect is about :
33% if N exp  N B   N exp
 deviation at 67% C.L.
5% if N exp  N B  2 N exp  deviation at 95% C.L.
1% if N exp  N B  3 N exp  deviation at 99% C.L.
0.01% if N exp  N B  5 N exp  deviation at 99.99% C.L.
Consensus:
3 deviation is exciting;
5 deviation constitutes a discovery;
8 deviation leaves no room for doubt
Limiting the parameter space
Once there is a well-established deviation from the
background, we compare it with the signal:
N S  N B   N exp   N exp 
If the numbers match, we can start claiming a
discovery…
Usually this matching can always be achieved by
tuning the free parameters in the (new) theory…
Comparison essentially serves to constrain the
parameter space of the (new) theory
If
Nexp  NB
we must have very small
NS ≈  Nexp
Typical new physics bounds arising when experimental crosssections match with backgrounds :
g
Large NS
excluded
Small NS
allowed
M
If experimental data are there, this is called an exclusion plot
If the data are projected, this is called a search limit
LHC
If both signal and background are present, the prediction
is that experiment will see the sum of both predictions.
Typical case: background is large; signal is small
NS « N B
In this case
Nexp  NB
and
 Nexp » NS
Will be very difficult to observe any signal over the
experimental error…
Require to reduce the background
(without reducing the signal)
Kinematic Cuts
Fermi’s Golden Rule :
1

F
M
2
d
Phase space integral has to be over all accessible final
3
states
d pi
d 
  2 
i
3
2 Ei
Experimental cross-section may not be able to (wish to)
access all the possible momentum final states
phase space integral must be done with
appropriate kinematic cuts
• acceptance cuts : forced on us by the detector properties.
• selection cuts : chosen to prefer one process over another.

Examples of acceptance cuts:
• minimum pT for the final states :
– very soft particles will not cause showering in ECAL/HCAL
– different cuts for barrel and endcap
• maximum  for the final states :
– no detector coverage in/near beam pipe
• isolation cut on  R for leptonic final states :
– no hadronic deposit within a cone of R = 0.4
– to be sure that the lepton is coming from the
interaction point and not from a hadron semileptonic
decay inside a jet
Will be somewhat different for ATLAS and CMS
Selection cuts can be of different kinds depending on the
process and the purpose for which it is made…
Example of a selection cut:
Suppose we want to select more electrons from the process
 
pp  e e
(1)
instead of electrons from the process
pp  e e 
 
(2)
From simple energy-sharing arguments, the electron in (1) will
have more pT than the electron in (2)
Impose the selection cut :
p p
e
T
min
T
Ensures that the accessible phase space for (2) shrinks without seriously
affecting that of (1) → reflected in the cross-section
A variety of selection cuts can be used to reduce the
background without affecting the signal (much).
Much of the collider physicist’s ingenuity lies in devising a
suitable set of selection cuts to get rid of the
background(s).
Often the background can be reduced really dramatically
– to maybe 1 in 10000…
Nevertheless, often this reduction of
backgrounds to negligible values may also
reduce the already weak signal to less than
one event in the whole running life of LHC!
High luminosity is essential !!
The proton luminosity is not the end of the story…
… actual collisions
will happen
between partons…
 what actually matters are :
parton distributions  luminosity
x f(x)
x  0 .4
Parton density functions (PDFs) from the CTEQ-6 Collaboration
(C.P. Yuan et al)
Trade-off between energy and luminosity…
s   p1  p2   2 p1. p2
2
sˆ  x1 p1  x2 p2   2 x1 x2 p1. p2  x1 x2 s
Eˆ cm  sˆ  x1 x2 s  x1 x2 Ecm  x1 x2  (14 T eV)
2
If x < 0.4, then maximum available energy at
parton level is only about 5 TeV…
But to observe most new physics, high luminosity
demand restricts us to x < 0.1, i.e. 1 – 2 TeV.
LHC probes the TeV scale – but only just…
Physics Goals of the LHC
• to test known
physics,
i.e. SM = QCD + GSW model (H boson)
• to discover new physics,
e.g. dark matter, SUSY, extra dim, new symmetries,
compositeness, …
Q. Why should new physics appear at the TeV scale?
Is this just wishful thinking?
…or do we have solid reasons?
Significance of the TeV energy scale:
• top-down approach :
• GUT or stringy unification must have low energy
consequences; high scale SUSY will have low energy
manifestations, extra dimensions will become accessible
at high enough energies
• bottom-up approach :
• hierarchy problem, neutrino masses, GUT evolution
• aesthetic approach :
• 18 free parameters in the SM
• no QCD-EW unification
• desert scenarios
Capabilities of the LHC
Cannot do a blind search…
All important final states require a trigger
• Huge QCD backgrounds… especially if looking for
hadronic final states
• Cannot see very soft pT jets/leptons/photons
LHC has severe limitations….
Sure shots :
Can determine t quark properties to precision
Can find the Higgs boson of the SM (if it exists)
Can find a SUSY signal if kinematics permits
Can find a resonant new state
Less sure :
Can measure Higgs boson couplings
Can measure SUSY parameters
Can discover exotics, e.g. gravitons, monopoles…
How are we so sure?
… next two lectures….