New Physics at a TeV and the LHC - IAccelerator Basics and the LHC

Sreerup Raychaudhuri

Tata Institute of Fundamental Research, Mumbai, India

IPM String School (ISS 2009), Tehran, IranApril 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

Typical scattering experiment

F1

2M

d

d

Two possible designs for a scattering experiment:

1. ‘Fixed’ target experiment

bbb

cm

bbbcm

b

b

b

bcm

b

EEM

EE

EMEMEMmE

MEMm

MEMkE

kME

kMEE

MkE

as 02

as 22

2

2

,0,0,

frame lab in the 0,0,0, and ,0,0,

22

22

222

22

22

As more and more energy is pumped into the beam, more and more energy is lost in the recoil of the target

2. Collider experiment

Full beam energy is available for the process

2

24

0,0,0,2

frame lab in the ,0,0, and ,0,0,

2

22

b

cm

bcm

b

bcm

bb

EE

EEE

EE

kEkE

SLAC 1969

LEP 1991

Tevatron 1994

LHC 2009

How are these high beam energies attained?

E

E

E

E

VE

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

V

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…

1 2

4n nA

L R L

Luminosity cm-2 s-1 Event rate s-1

1,2 number density of bunches

number of crossings per second cross-sectional area of bunches reaction cross section

n

A

As data are gathered over time…

t

dtL0

'L

No of events LdtdtNtt

00

'' LR

Event rate : LR

Integrated luminosity

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

nb-1/s

10 nb-1/s

From the BNL home page

1 2

4n nA

L

How are these high luminosities attained?

1,2 number density of bunches

number of crossings per second cross-sectional area of bunches reaction cross section

n

A

Packing charged particles like 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 : 5 TeV 7 TeV Collision energy : 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: ~ 7 m 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)

barrel radiation sensitive; high efficiency

End-cap radiation hardened; low efficiency

2009,

VXD

EMCHCAL

Ch

CMS Detector

VXD

ECAL

HCAL

Ch

Particle detection at the LHC

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

e

/ /q g /W Z

b/ Ht

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

k

1x k

2kx

Partonic system has an (unknown) longitudinal boost

1 2

1 2

x xx x

Each collision event will have a different we must choose variables which are independent of longitudinal boosts

1. Transverse momentum :2 2

T x yp p p 2 2T TE p m

2. Rapidity :1 log2

z

z

E pyE p

2

1

1 log2

xyx

y

3. Pseudo rapidity : log tan2 if 0y m

4. Angular separation : 2 2R

5. Invariant mass : 2212 1 2M p p

Commonest Variables

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

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

S SN L .

B BN L . exp expN NExperimental results will have errors:

exp standard deviation N

What constitutes a discovery?

Excess/depletion over background : exp BN NAssuming random (Gaussian) fluctuations, the probability that this deviation is just a statistical effect is about :

exp exp

exp exp

exp exp

exp exp

33% if deviation at 67% C.L.

5% if 2 deviation at 95% C.L.

1% if 3 deviation at 99% C.L.

0.01% if 5 deviation at 99.99%

B

B

B

B

N N N

N N N

N N N

N N N

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:

exp expS BN N N N

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 we must have very small exp BN N expSN N≈

Typical new physics bounds arising when experimental cross-sections match with backgrounds :

M

gLarge NS excluded

Small NS allowed

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

S BN N

In this case and

Will be very difficult to observe any signal over the experimental error…

exp BN N exp SN N

Require to reduce the background (without reducing the signal)

«

»

Kinematic Cuts

Fermi’s Golden Rule : 21 M d

F

Phase space integral has to be over all accessible final states

3

32 2i

ii

d pdE

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

(1)

instead of electrons from the process

(2)

pp e e

pp e e From simple energy-sharing arguments, the electron in (1) will have more pT than the electron in (2)

Impose the selection cut : mineT Tp p

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…

what actually matters are : parton distributions luminosity

… actual collisions will happen

between partons…

x f(x)

Parton density functions (PDFs) from the CTEQ-6 Collaboration (C.P. Yuan et al)

4.0x

Trade-off between energy and luminosity…

)TeV 14( ˆˆ.2ˆ

.2

212121

2121212

2211

212

21

xxExxsxxsE

sxxppxxpxpxs

pppps

cmcm

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….

Can find the Higgs boson of the SM (if it exists)Can find a SUSY signal if kinematics permitsCan find a resonant new state

Sure shots :

Less sure :

Can measure Higgs boson couplings

Can determine t quark properties to precision

Can measure SUSY parametersCan discover exotics, e.g. gravitons, monopoles…

How are we so sure?

… next two lectures….