Physics Expectations at the LHC Sreerup Raychaudhuri Tata

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 2. (the six-billion dollar experiment…) 2. Standard Model of Particle Physics 2. (what we already know…) 3. Physics beyond the Standard Model 3. (what we would like to know…) 4. Physics Prospects at the LHC 1. (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 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 Te. V Energy upgrade to 14 Te. V 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 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: Particle mass: Bjorken & Drell 1964 Wick rotation Curvature of a 4 -sphere:

Gauge structure of the Standard Model All gauge theories have QED as the basic template : Covariant derivative : Field-strength tensor Expands out to: free gauge free fermion interaction

No other renormalizable terms Invariance under local U(1) gauge transformations: : First kind : Second kind Conservation of Nöther current & Nöther charge: 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) the form of strong and weak (nuclear) interactions are also dictated by gauge symmetries… Extension of this idea:

Scalar electrodynamics Charged scalar field : Nöther current Expands out to: free scalar pair interaction seagull interaction

Non-gauge Interactions Scalar field allows us to add on two more types of renormalizable (gauge-invariant) interactions, viz. 1. Scalar self-interactions: 4 type 2. Yukawa interactions: 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 Q. Why do we want the photon to have a mass? Needed in a superconducting medium (not otherwise) Static limit : 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… 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( ) 0 It is simple to show that and 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 : “unitary” gauge choice

Note that : Proper choice of generalized coordinate is to replace : 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 : Gauge boson thus acquires a mass : Short-range interaction

2. Scalar mass : Collect quadratic terms Scalar thus acquires a real mass : Other scalar (imaginary part) vanished from theory by choice of “unitary” gauge

3. Fermion mixing : mass terms only Break up into chiral components: mixing term

More convenient in matrix form : Again 1 and 2 are improper choices of coordinates because they lead to coupled equations of motion diagonalise the matrix for (decoupled) eigenstates fermion mixing where 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” : SU(3)

QCD Lagrangian is constructed on the exact analogy of the QED Lagrangian : Gluons Gell-Mann matrices

Expands out to: free quark free gluons vertex: quark-antiquark-gluon Similar to QED interaction… 3 -gluon vertex 4 -gluon vertex Gluon self-interactions are typical of a non-Abelian (multiple-charge) theory

QCD Feynman rules quark propagator gluon propagator 4 -gluon vertex 1 3 2 4 3 -gluon vertex 1 2 3

QCD coupling g. S is large since the interaction is strong However, it runs at higher energies due to quantum corrections…e. g. vertex corrections… +…

Since there are only 6 known quark flavors Introduce the QCD scale : As Q 2 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 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 ud n u d d e- -decay : Fermi d u u W -decay : intermediate vector boson e -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: Acts on a complex scalar doublet : Sheldon L. Glashow (b. 1932)

Electroweak Lagrangian is again constructed on the analogy of the QED/QCD Lagrangian : SU(2) “charge” weak isospin U(1) “charge” weak hypercharge Generators of SU(2)

Mass arises from spontaneous symmetry-breaking and Higgs mechanism : Vacuum at : Abdus Salam (1926 – 1996) Steven Weinberg (b. 1933) Vacuum manifold has an SO(4) symmetry Choice of vacuum leaves a residual O(2) symmetry unbroken U(1)em

Shift the vacuum : Pick out the mass terms and expand…

After shifting the scalar field: Freedom to re-parametrize, i. e. choose the “unitary” gauge as before… massive Higgs boson not (yet) found

Fermionic sector of the Glashow-Salam-Weinberg model e e- u d I c - 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 Me. V 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. If A = B parity is conserved If A = 0 or B violated = 0, parity is maximally • 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 : Singlets :

Lepton gauge couplings: Similarly in the Quark sector…

Lepton masses: An electron mass term breaks up into combinations of left and right chiral terms… If e. L has T 3 = -1/2 and e. R has T 3 = 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: Similarly for the muon and the tau masses Electron mass term

Quark Yukawa couplings: By analogy with the leptons No constraint to restrict to one generation only…

diagonalization Kobayashi-Maskawa mechanism: Physical states

In terms of the physical states the charged current interactions are no longer diagonal… Cabibbo-Kobayashi-Maskawa matrix

In terms of the physical states the neutral current interactions remain diagonal… No Flavor Changing Neutral Currents

CP-violation: We can take the and the to be complex Also complex 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 pair annihilation Gluons exist !!

Hadronic final states at different energies QCD fits are amazingly good P. Schleper, Aachen 2003

QCD is tested to at least

P. Schleper, Aachen 2003 as from QCD fits Bethke 2002 as global as 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 Ge. V. 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 480 Ge. V at 68% C. L.

CP Violation : fits to the Unitarity Triangle (2006) Area of the triangle ~ sin

The Higgs Boson is the only missing piece…