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## Physics Expectations at the LHC

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**Physics Expectations at the LHC**Tata Institute of Fundamental Research Mumbai, India Sreerup Raychaudhuri April 9, 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 1**The Large Hadron Collider • (the biggest science experiment ever…)**Energy timeline…**? W, Z quarks mesons nuclei electrons atoms Reach Planck scale in 2243? cathode rays**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+**The CMS detector weighs 1950 tonnes**(= weight of 5 Jumbo jets …)**About**1 000 000 000 such events per second… Unprecedentedcomputing 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 Kby mid-June 2008 First collisions will start around mid-August 2008 By October-November 2008 collision energy should reach 10 TeV Energy upgrade to 14 TeV by early 2009 Higgs boson discovery (?) by 2011**Interesting factoids about LHC:**• LHC when running will consume as much power as a medium- sized 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 12,000,000 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: • Quark model • Non-Abelian gauge theory • strong and electroweak sectors • Scalar4 theory with Yukawa interactions • Parity violation in the weak sector • CP violation in the weak sector**Note (and Apology) on metric choice:**Minkowski metric: Bjorken & Drell 1964 Particle mass: 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: interaction free fermion free gauge**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) Extension of this idea: the form of strong and weak (nuclear) interactions are also dictated by gauge symmetries…**Scalar electrodynamics**Charged scalar field : Nöther current Expands out to: seagull interaction free scalar pair interaction**Non-gauge Interactions**Scalar field allows us to add on two more types of renormalizable (gauge-invariant) interactions, viz. 4 type 1. Scalar self-interactions: 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: • Generates mass for the gauge boson • Generates real mass for the scalar • 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 the theory by choice of “unitary” gauge**3. Fermion mixing :**mass terms only Break up into chiral components: mixing term**where**More convenient in matrix form : Again 1and 2are improper choices of coordinates because they lead to coupled equations of motion diagonalise the matrix for (decoupled) eigenstates fermion mixing violation of global U(1) flavor symmetries**Peter W. Higgs (b. 1929)**Some technical terms: • Generation of gauge boson masses by a self-interacting tachyonic scalar fieldAnderson-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”: qqq 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**3 1 1 2 4 2 3 gluon propagator quark propagator 4-gluon vertex 3-gluon vertex**QCD coupling gS 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 Q2 increases above 2, the QCD coupling decreases… asymptotic freedom Politzer-Gross-Wilczek 1973**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