Physics Expectations at the LHC Tata Institute of Fundamental Research Mumbai, India Sreerup Raychaudhuri II April 10,2008 IPM String School 2008, Isfahan, Iran
Plan of the Lectures • About the LHC • (the six-billion dollar experiment…) • Standard Model of Particle Physics • (what we already know…) • Physics beyond the Standard Model • (what we would like to know…) • Physics Prospects at the LHC • (what we could find in the next few years…)
Part 3 Physics beyond the Standard Model • (what we would like to know…)
Achievements of the Standard Model • Common framework to describe weak, electromagnetic and strong interactions • Mechanism to have short-range interactions for weak force • Common mechanism for generation of mass • Incorporates global and discrete symmetries like quark flavor, lepton number, C, P and T, etc. • ‘Explains’ the origin of flavour violation • Arranges for maximal P violation in weak sector • Accommodates CP violation in CC interactions
What’s wrong with the Standard Model? We haven’t found the Higgs boson… We didn’t look hard enough… Elementary scalars are the simplest reps of the Lorentz group We haven’t found any other elementary scalars Let’s find one first… SM can accommodate more scalar doublets easily Why have only one scalar doublet when there are three fermion doublets?
Can a model with 18 (20) undetermined parameters be a fundamental theory? That’s more of an aesthetic issue … the SM works, doesn’t it?
There’s a desert of 17 orders of magnitude between 102 GeV and 1019 GeV with no new physics • Maybe that’s the way Nature is… • The SM may well be a low-energy effective theory
Folklore: Every time we probed a new energy scale, we discovered new sub-structures and new interactions… Symmetries observed at lower energy scales indicate different arrangement of these substructures… …periodic table… eightfold way… We now have three generations of fermions with repeated properties…
Historical development is not a valid scientific reason… Fermion replication may well be (a) accidental, or (b) a sign of some (broken) global symmetry, e.g. SU(3),S3
The strong interactions are not unified with the electroweak one… All the generators of SU(3)C commute with all the generators of SU(2)LU(1)Y • Unification would require a higher gauge symmetry at higher energies — GUTs • There is no compelling empirical reason to unify strong with electroweak interactions….
Neutrino masses are unnaturally small eV meV eV keV MeV GeV TeV
The Naturalness Argument • If there are very large/small parameters in a quantum theory, there must be a good reason why they are so small…. • In general, there will be large quantum corrections to such parameters in higher orders of perturbation theory, in terms of other parameters which are not so small. • These quantum corrections can cancel out only if there is some underlying symmetry causing them to cancel... The parameter is said to be ‘protected’ by the symmetry. • This applies specially to masses and couplings, which are known to run.
Neutrinos have always been a slight embarrassment in the Standard Model • Earlier they were thought to be massless accommodated in the Standard Model by assuming there is no right-handed neutrino • All that is special about a right-handed neutrino is that it is a gauge singlet • There is as much reason to suppose that gauge singlet fermions exist as there is to suppose that they do not exist • Hence the huge number of models for neutrino mass(es) constructed in the 1980s
The SuperKamiokande Experiment SuperK has changed the scene since neutrinos undergo flavor oscillations they must have nonzero masses But the masses are very very small…. Why?
Are we really bound to answer this question? The mass of the neutrino is not just a mass, it is also the strength of the Yukawa interaction of the neutrino with Higgs bosons…similarly for top quarks… Variation in interaction strength over 11 orders of magnitude is like the difference between weak and electromagnetic interactions does this mean a new type of force between neutrinos and Higgs bosons?
There is an elegant explanation… The Seesaw mechanism: Diagonalise: M ~ 100 TeV Majorana mass:
Many variations of the simplest seesaw mechanism exist many of them proposed to explain the large mixing angle found by SuperK many of them require the right-handed neutrino to have some special properties… Majorana mass…. All require a heavy mass scaleM new physics at scales of TeV or higher… SM is inadequate…
The seesaw argument is pretty but not empirically compelling… • In the SM fermion masses are put in by hand anyway…we do not even try to understand them… • Hierarchy of Yukawa couplings may just be the way Nature is… • Fermion masses get at best logarithmic corrections from high scale physics because of chiral symmetry… naturalness is not such a serious problem…
The Higgs boson mass is not UV stable Umm… er….
A light Higgs boson? • The mass of the Higgs boson is an undetermined parameter in the Standard Model • The scalar self-coupling grows with and becomes non-perturbative around • Electroweak precision data predict a light Higgs with • LEP saw a few candidates around 114 GeV
LEPEWWG 2001 at 68% C.L. Large uncertainties because of the weak dependence on Higgs mass :log MH at 95% C.L.
At the LHC we are almost sure to find a light Higgs boson… • What if we don’t find it? • We will have to find an equally good mechanism to generate masses for all elementary particles • We must explain the radiative corrections to the W-boson self-energy which are precisely measured • We must explain how WW scattering does not violate perturbative unitarity
Sum preserves perturbative unitarity : without H cross-section grows too fast with energy
If we do find it? We must understand why it is so light…
This is not just a piece of theoretical fussiness…. • The Standard Model is a quantum (field) theory • Even tree-level results are just the lowest order in perturbation theory • One-loop predictions are also tested to great accuracy at LEP etc. • It is meaningless to consider only tree-level results, unless we can prove that higher orders give small contributions • Higher order corrections to Higgs boson mass are very large…
The scalar sector of the Standard Model is basically a theory coupled to a (nonAbelian) gauge theory and some fermion multiplets • Higgs boson has quartic self couplings • there are self-energy corrections with quadratic divergences H H H H H is the cutoff for the SM This effect cannot be wished away… H H
The Hierarchy Problem was pointed out by ‘Hooft more than thirty years ago. Over these three decades it has become clear that it cannotbe • ignored(SM is a quantum theory) • removed by renormalisation-type tricks (reappears at next order) • resolved without some new physics (at the electroweak or TeV scale ?)
Q. How can we protect the Higgs boson mass from these large quantum corrections? • Only two ways: • bring down the cutoff to the TeV scale • compositemodels • brane-worlds • introduce some new symmetry into the theory • supersymmetry • little Higgs models new physics at a TeV symmetry must be broken around TeV…
Further Hints of New Physics: • CP-Violation: baryon asymmetry • Cold dark matter: what could it be? • Cosmological constant: > 0 • Modelling is heavily dependent on individual prejudices • Do not indicate the TeV scale per se
Unification of forces has been a cherished goal of scientists from the days of Demokritos They say some things are sweet They say some things are sour But in reality there are only atoms and the void… Early (fanciful) model of unification… Modern Theories of unification: Maxwell (gauge theoretic approach) Einstein (geometric approach) Glashow-Salam-Weinberg
Electroweak unification shows up very nicely in experimental results Deep inelastic scattering data from the HERA collider at DESY, Hamburg
Programme of unification: • Electric + magnetic = electromagnetic • Electromagnetic + weak = electroweak • Electroweak + strong = grand unification • GUT + gravity = super-unification Running coupling constants
U. Amaldi et al 1996 SUSY SU(5)-based one-step grand unification
Positive thinking: • Unification of forces is not just a theoretician’s dream but it is the culmination towards which all fundamental science tends • Supersymmetric SU(5) theories did provide a simple and elegant model for one-step grand unification with SUSY particles at a few TeV… predicts a rather small p • Problems with proton lifetime can be easily resolved by considering SUSY SO(10) GUTs…
DEVIL’S ADVOCATE • Hierarchy problem remains anyway GUT» TeV • Maybe unification of forces occurs in various steps at different energies, the lowest of which may be far beyond a TeV • Maybe unification of couplings occurs only in a (string) theory at the Planck scale • Maybe gauge theories are only effective theories at low energies and when we go higher something completely different happens • Maybe there is no single force in the Universe and Grand Unification is just a dream • In any case, speculating about 16 orders of magnitude is useless without more information
SU(N) • Inspired by superconductivity, quark model and QCD… • Just as mesons are composites of quarks and pion masses are related to QCD scale in a SU(3) gauge theory… • ...so Higgs bosons are composites of techni- fermions and electroweak scale is related to a technicolour scale in a SU(N) gauge theory Idea is simple and elegant ─ implementation is not
How are quark & lepton masses obtained? • Need to relate composite Higgs to fermions… • Extended technicolour (ETC) Symmetry-breaking scale is around 10-100 TeV Generates quark and lepton masses through self-energy corrections with composite Higgs; also predicts heavy technipions around 100 GeV – few TeV
ETC models fail to explain: • small value of mixing • precision data on the S parameter • the large t quark mass • Invention of walking technicolour • TC (Q2) evolves very slowly • small contribution to mixing • small contribution to S parameter
Getting messy… • Large top quark mass is still a problem in ETC models • Invention of topcolour • new (gauge) interaction: leads to formation of condensate Higgs-like particle State of the art: topcolour-assisted ETC Quite a bit of fine-tuning has to be done: still predicts mt ≈ 250 GeV Invention of top-seesaw models
Compositeness is still a very attractive idea • Too complicated to be credible: epicycles? • Too slavish in following QCD? Naïve? • TeV scale interactions may be non-gauge interactions after all Copernican theory ● Sommerfeld atom ●Sakata model
In a supersymmetric theory the bosons and fermions have the same mass and couplings H g2 H H g2 g H H g g Quadratic divergences cancel no hierarchy problem