XI SERC School on Experimental High-Energy Physics National Institute of Science Education and Research 14th November 2017
COLLIDER PHYSICS Lecture I
Sreerup Raychaudhuri TIFR, Mumbai
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Why colliders? Much of our knowledge of subatomic and subnuclear physics comes from scattering experiments. Typical scattering experiment in textbooks is a fixed target experiment…
B T S
B ⇒ beam of incident particles (charged, stable/long-lived) Typically or . Also , heavy ions… T ⇒ target of atoms, nuclei, ions, or other particles S ⇒ screen or detector which converts each particle hit to a signal 3
Energy in centre-of-momentum frame:
If is high enough, then
5 GeV proton mass GeV 100 GeV proton mass GeV 1 TeV proton mass GeV ⇒ Fixed target experiments are okay for low energies, but not for high energies. Gerald O’Neill (1956) proposed the colliding beam design… First 600 MeV collider (Richter, Panofsky) became operative at SLAC (1965)
B X B’ B, B’ ⇒ colliding beams X ⇒ collision point 4
Energy in centre-of-momentum frame:
5 GeV proton mass GeV 100 GeV proton mass GeV 1 TeV proton mass TeV
⇒ very efficient energy conversion for high energies.
Problem: requires two identical beams (if and are different, final states will boost down the beam pipe)
Solution: single beam split into two and made to X ’ collide… Intersecting Storage Rings (CERN 1971) Pulsed operation: pulses enter from A and are M alternately pushed to left and right by an AC… form B and B’ in the two ‘storage’ rings and collide at X
A 5
Making two vacuum rings is difficult and expensive… use a single ring…
X
LHC Ring
X X X
Beams are collimated into narrow pencils and kept apart by magnetic fields… also made to collide at pre-determined points by magnetic deflection… all modern colliders use this design…. 6
Flux and Luminosity In a scattering experiment, intensity of the beam is measured by flux
B A
v
Flux = # of B particles crossing normally-placed unit area per unit time = # of particles in a cylinder of volume
= ( = number density of particles in B, T )
If we get Dimension is [area]-1 x [time]-1 ⇒ unit is cm-2 s-1 Practical unit of area: 1 b = 10-24 cm (b = barn) Practical unit of flux: 1 b-1 s-1 = 1024 cm-2 s-1 (1 nb-1 s-1 = 1033 cm-2 s-1 ) 7
The number per unit time of B particles scattered by T should be proportional to , i.e.
where is the cross-section for scattering. It has units of area and will be measured in barns or sub-multiples. In quantum mechanics, we will calculate as the rate of scattering of one B particle by one T particle, which is given by the Golden Rule of Fermi as
where is a single-particle flux and the phase space element is density of states X four-momentum delta function
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For a collider, we should replace by … ,i.e. a single particle flux becomes, for beams which collide head-on
where the Källen function is
If , then
This is commonly used in high energy electron-positron and hadron colliders, i.e.
In a QFT, is calculated using Feynman diagrams and Feynman rules 9
Modify this in case of pulsed operation… bunches of particles…
Each bunch will contain of the B particles (bunch density). Instantaneous Luminosity ≝ # of particles crossing unit area per unit time which have a chance to interact, i.e.
⇒ # of bunches crossing each other per unit time (bunch crossing frequency) ⇒ area of cross-section of the bunches (⇒ has same units as )
Hence, gives # of scattered particles per unit time Integrated Luminosity ≝ Instantaneous Luminosity X time elapsed
Hence, gives # of scattered particles in given time interval 10
To look for rare processes, i.e. where is small, we require high
1. Increase bunch density and i.e. pack in more particles 2. Increase bunch crossing frequency i.e. reduce bunch separation 3. Decrease bunch area i.e. squeeze the bunches Each of these has its own problems… As the B particles are like charges, they will resist all attempts to increase density. This, then, requires very high magnetic fields, which can be done only with superconducting magnets. The cost goes up enormously with this. Packing charges very closely, or making the bunch separation small, makes it possible for bunches to interact with each other. Beam focusing and cooling becomes more difficult. 11
Synchrotron Radiation In a storage ring, the same bunches keep going around, thus colliding many times – permits a single set of pulses to last a long time. This increases the effective luminosity without taxing the source. However, B particles move in a circular path ⇒ accelerated Being charged, they will emit synchrotron radiation… Radiated power (Panofsky-Phillips § 20-4) in SI units by a B particle
In a circular orbit with radius :
Time for a complete turn :
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Energy radiated per turn by a B particle
In the ultra-relativistic limit and , so that
Putting , we get
Take e.g. the LEP-2 collider, where
Then, due to smallness of
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To go to higher energies, must reduce the synchrotron radiation.
Three ways: 1) Increase e.g. the storage ring girdles the Earth,
Cost is prohibitive… 2) Choose a heavier particle for B, e.g. proton instead of electron
Very efficient and cost friendly, but becomes a hadron collider
3) Avoid the circular design altogether and go for a linear collider 14
Multipurpose Detector
C FC FC HCAL (B)
HCAL (EC) EMC (B) HCAL (EC)
EMC (EC) VXD EMC (EC) beam pipe * EMC (EC) VXD EMC (EC)
HCAL (EC) EMC (B) HCAL (EC)
FC FC HCAL (B) Endcap (50 – 450, 1350 - 1750 C Barrel (450 – 1350)
C : muon chamber F C : forward muon chamber HCAL (B) : hadron calorimeter (barrel) HCAL (EC) : hadron calorimeter (end cap) EMC (B) : e.m. calorimeter (barrel) EMC (EC) : e.m. calorimeter (end cap) VXD : silicon vertex detector (tracker) * inter action point 15
CDF Detector at FNAL 16
VXD : set of silicon strips pixellated with pn junctions Bending of track gives Displaced vertices useful for tagging long-lived particles, e.g. quark
EMC : array of scintillator crystals hooked up to pulse amplifiers Energy deposit left by photons, electrons/positrons,
HCAL : array of optical scintillator fibres with multiplier electronics Energy deposit left by hadrons, i.e. baryons and mesons C : array of proportional wire counters Measures muon energy; bending of track gives 17
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Six Important lessons
1. Only stable, or metastable particles can actually be detected. These include photons, electrons and protons (absolutely stable), muons, neutrons, pions and hyperons (weakly decaying) and possibly exotic particles which are very long-lived.
2. The production and decay of all other particles must be inferred from their decay products.
3. Final state particles which go down the beam pipe will not be detected. Thus energy balance in the longitudinal direction cannot be assumed. 19
4. Neutrinos and similar stable, but very weakly-interacting particles will escape the detector unobserved, but their presence will show up, as in beta decay, as missing transverse energy and momentum.
5. Quarks and gluons will form jets of hadrons, which in turn will cause showering in the HCAL.
6. The four-momentum of photons, electrons, muons and hadronic jets can be measured by a combination of tracking and calorimetry. Everything else has to be inferred from energy-momentum conservation.
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Kinematic Variables 2 → 2 process
Conservation of four-momentum
Collider design
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Mandelstam variables (Lorentz invariants)
satisfying
We have
⇒
i.e.
22 final states
Since , we must have
and so that
⇒ i.e.
( is real because ) i.e.
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Other two Mandelstam variables
where
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3-Momentum conservation
Hence,
i.e.
⇒
Transverse momentum balance Difficult to observe
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If we find that
it means that there was
transverse momentum of invisible particles, so that
We refer to the (minus of sum over visible ) p as the missing and denote it as T .
Usually arises from neutrinos in the Standard Model… 27
Scattering angle:
Under a Lorentz boost along the axis, we have
i.e. the scattering angle changes if the system has a longitudinal boost
However, the azimuthal angle does not change.
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Rapidity:
Under a longitudinal boost (along the axis), we get
If we have two particles, with rapidities and , then we define
Now, under a longitudinal boost
i.e. rapidity differences are invariant under longitudinal boosts 29
Pseudorapidity: In general we have
If , then . Now,
Hence, we can define a pseudorapidity
≝
Rapidity and pseudorapidity are same in the massless case but different in the massive case. ⇒ ⇒ ⇒
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Angular Separation (Cambridge-Aachen):
If we have and , we can obviously define
but this is not invariant under longitudinal boosts.
But if we create
then both are invariant under longitudinal boosts… Add these in quadrature