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Physics Expectations at the LHC

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

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Physics Expectations at the LHC

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  1. Physics Expectations at the LHC Tata Institute of Fundamental Research Mumbai, India Sreerup Raychaudhuri April 9, 2008 IPM String School 2008, Isfahan, Iran

  2. 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…)

  3. Part 1 The Large Hadron Collider • (the biggest science experiment ever…)

  4. Energy timeline… ? W, Z quarks mesons nuclei electrons atoms Reach Planck scale in 2243? cathode rays

  5. 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+

  6. 8.6 Km

  7. Working Principle of a Collider Machine

  8. 8.6 Km

  9. Buried 100 m below ground to shield radiation

  10. Section of LHC tunnel showing pipe carrying liquid He

  11. ATLAS Detector

  12. The CMS detector weighs 1950 tonnes (= weight of 5 Jumbo jets …)

  13. Typical LHC Event

  14. About 1 000 000 000 such events per second… Unprecedentedcomputing challenge… Worldwide distribution of analysts Gb/s data transfer rates

  15. Actual Gb/s transfer rates as monitored by BARC, India during a test run in 2006

  16. 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

  17. 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

  18. 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…

  19. Part 2 Standard Model of Particle Physics • (what we already know…)

  20. 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 • Scalar4 theory with Yukawa interactions • Parity violation in the weak sector • CP violation in the weak sector

  21. Note (and Apology) on metric choice: Minkowski metric: Bjorken & Drell 1964 Particle mass: Wick rotation Curvature of a 4-sphere:

  22. 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

  23. 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

  24. 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…

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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 1. Gauge boson mass : Gauge boson thus acquires a mass : Short-range interaction

  33. 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

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

  35. 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

  36. Peter W. Higgs (b. 1929) Some technical terms: • 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

  37. 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

  38. 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

  39. 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)

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

  41. 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

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

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

  44. 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

  45. S (ECM)

  46. 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

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