Theoretical physics to face the challenge of LHC lecture notes of the les houc

Experiments in high energy physicsVIII 1958 The many body problem IX 1959 The theory of neutral and ionized gases X 1960 Elementary particles and dispersion relations XI 1961 Low tempera

Theoretical Physics to Face the Challenge of LHC

Ecole de Physique des Houches

Session XCVII, 1–26 August 2011

Theoretical Physics to Face the

Challenge of LHC

Edited by Laurent Baulieu, Karim Benakli, Michael R Douglas,

and Leticia F Cugliandolo

3

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´Ecole de Physique des HouchesService inter-universitaire commun

`

a l’Universit´e Joseph Fourier de Grenoble

et `a l’Institut National Polytechnique de GrenobleSubventionn´e par l’Universit´e Joseph Fourier de Grenoble,

le Centre National de la Recherche Scientifique,

le Commissariat `a l’ ´Energie Atomique

Directeur:

Leticia F Cugliandolo, Sorbonne Universit´es, Universit´e Pierre et Marie Curie,Laboratoire de Physique Th´eorique et Hautes Energies, CNRS UMR 7589, Paris,France

Directeurs scientifiques de la session XCVII:

Laurent Baulieu, Sorbonne Universit´es, Universit´e Pierre et Marie Curie, Laboratoire

de Physique Th´eorique et Hautes Energies, CNRS UMR 7589, Paris, FranceKarim Benakli, Sorbonne Universit´es, Universit´e Pierre et Marie Curie, Laboratoire

de Physique Th´eorique et Hautes Energies, CNRS UMR 7589, Paris, FranceMichael R Douglas, Department of Physics and Astronomy, Rutgers University, USABruno Mansouli´e, Institut de Recherches sur les lois Fondamentales de l’Univers,CEA Saclay, France

Eliezer Rabinovici, Racah Institute of Physics, Hebrew University, Jerusalem, IsraelLeticia F Cugliandolo, Sorbonne Universit´es, Universit´e Pierre et Marie Curie,Laboratoire de Physique Th´eorique et Hautes Energies, CNRS UMR 7589, Paris,France

Previous sessions

I 1951 Quantum mechanics Quantum field theory

II 1952 Quantum mechanics Statistical mechanics Nuclear physicsIII 1953 Quantum mechanics Solid state physics Statistical mechanics

Elementary particle physics

IV 1954 Quantum mechanics Collision theory Nucleon-nucleon

inter-action Quantum electrodynamics

V 1955 Quantum mechanics Non equilibrium phenomena Nuclear

reac-tions Interaction of a nucleus with atomic and molecular fields

VI 1956 Quantum perturbation theory Low temperature physics

Quan-tum theory of solids FerromagnetismVII 1957 Scattering theory Recent developments in field theory Nuclear

and strong interactions Experiments in high energy physicsVIII 1958 The many body problem

IX 1959 The theory of neutral and ionized gases

X 1960 Elementary particles and dispersion relations

XI 1961 Low temperature physics

XII 1962 Geophysics; the earths environment

XIII 1963 Relativity groups and topology

XIV 1964 Quantum optics and electronics

XV 1965 High energy physics

XVI 1966 High energy astrophysics

XVII 1967 Many body physics

XVIII 1968 Nuclear physics

XIX 1969 Physical problems in biological systems

XX 1970 Statistical mechanics and quantum field theory

XXI 1971 Particle physics

XXII 1972 Plasma physics

XXIII 1972 Black holes

XXIV 1973 Fluids dynamics

XXV 1973 Molecular fluids

XXVI 1974 Atomic and molecular physics and the interstellar matterXXVII 1975 Frontiers in laser spectroscopy

XXVIII 1975 Methods in field theory

XXIX 1976 Weak and electromagnetic interactions at high energy

XXX 1977 Nuclear physics with heavy ions and mesons

XXXI 1978 Ill condensed matter

XXXII 1979 Membranes and intercellular communication

XXXIII 1979 Physical cosmology

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Previous sessions vii

XXXIV 1980 Laser plasma interaction

XXXV 1980 Physics of defects

XXXVI 1981 Chaotic behavior of deterministic systems

XXXVII 1981 Gauge theories in high energy physics

XXXVIII 1982 New trends in atomic physics

XXXIX 1982 Recent advances in field theory and statistical mechanics

XL 1983 Relativity, groups and topology

XLI 1983 Birth and infancy of stars

XLII 1984 Cellular and molecular aspects of developmental biologyXLIII 1984 Critical phenomena, random systems, gauge theories

XLIV 1985 Architecture of fundamental interactions at short distancesXLV 1985 Signal processing

XLVI 1986 Chance and matter

XLVII 1986 Astrophysical fluid dynamics

XLVIII 1988 Liquids at interfaces

XLIX 1988 Fields, strings and critical phenomena

L 1988 Oceanographic and geophysical tomography

LI 1989 Liquids, freezing and glass transition

LII 1989 Chaos and quantum physics

LIII 1990 Fundamental systems in quantum optics

LV 1991 Particles in the nineties

LVI 1991 Strongly interacting fermions and high Tc superconductivityLVII 1992 Gravitation and quantizations

LVIII 1992 Progress in picture processing

LIX 1993 Computational fluid dynamics

LX 1993 Cosmology and large scale structure

LXI 1994 Mesoscopic quantum physics

LXII 1994 Fluctuating geometries in statistical mechanics and quantum

field theoryLXIII 1995 Quantum fluctuations

LXIV 1995 Quantum symmetries

LXV 1996 From cell to brain

LXVI 1996 Trends in nuclear physics, 100 years later

LXVII 1997 Modeling the earths climate and its variability

LXVIII 1997 Probing the Standard Model of particle interactions

LXIX 1998 Topological aspects of low dimensional systems

LXX 1998 Infrared space astronomy, today and tomorrow

LXXI 1999 The primordial universe

LXXII 1999 Coherent atomic matter waves

LXXIII 2000 Atomic clusters and nanoparticles

LXXIV 2000 New trends in turbulence

LXXV 2001 Physics of bio-molecules and cells

LXXVI 2001 Unity from duality: Gravity, gauge theory and strings

viii Previous sessions

LXXVII 2002 Slow relaxations and nonequilibrium dynamics in condensed

matterLXXVIII 2002 Accretion discs, jets and high energy phenomena in astrophysicsLXXIX 2003 Quantum entanglement and information processing

LXXX 2003 Methods and models in neurophysics

LXXXI 2004 Nanophysics: Coherence and transport

LXXXII 2004 Multiple aspects of DNA and RNA

LXXXIII 2005 Mathematical statistical physics

LXXXIV 2005 Particle physics beyond the Standard Model

LXXXV 2006 Complex systems

LXXXVI 2006 Particle physics and cosmology: the fabric of spacetime

LXXXVII 2007 String theory and the real world: from particle physics to

astrophysicsLXXXVIII 2007 Dynamos

LXXXIX 2008 Exact methods in low-dimensional statistical physics and

quan-tum computing

XC 2008 Long-range interacting systems

XCI 2009 Ultracold gases and quantum information

XCII 2009 New trends in the physics and mechanics of biological systemsXCIII 2009 Modern perspectives in lattice QCD: quantum field theory and

high performance computingXCIV 2010 Many-body physics with ultra-cold gases

XCV 2010 Quantum theory from small to large scales

XCVI 2011 Quantum machines: measurement control of engineered quantum

systemsXCVII 2011 Theoretical physics to face the challenge of LHC

Special Issue 2012 Advanced data assimilation for geosciences

Publishers

– Session VIII: Dunod, Wiley, Methuen

– Sessions IX and X: Herman, Wiley

– Session XI: Gordon and Breach, Presses Universitaires

– Sessions XII–XXV: Gordon and Breach

– Sessions XXVI–LXVIII: North Holland

– Session LXIX–LXXVIII: EDP Sciences, Springer

– Session LXXIX–LXXXVIII: Elsevier

– Session LXXXIX– : Oxford University Press

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Every Les Houches Summer School has its own distinct character The objective ofthe August 2011 session “Theoretical physics to face the challenge of LHC” was todescribe, to an audience of advanced graduate students and postdoctoral fellows, theareas in high-energy physics in which profound new experimental results are hopefully

on the verge of being discovered at LHC at CERN This was to be done with theexpectation that contact with new fundamental theories on the nature of fundamen-tal forces and the structure of spacetime will be made The students benefited fromlectures by, and interacted with, many of the leaders in the field

The school was held in a summer of tense anticipation Exciting new resultsfrom high-energy colliders were in the air, whether about the long anticipated dis-covery of the Higgs particle or about a “divine” surprise, evidence for the existence ofsupersymmetry in nature

For some years, the community of theorists had split into several components:those doing phenomenology, those dealing with highly theoretical problems, and sometrying to explore if it was possible to bridge the two In this school, we celebrated thereunification of these groups—at least for a few years

The talks given by experimentalists accurately pointed out how intensively and howprecisely the newborn collider has verified all theoretical predictions that were at thefrontline of the revolutionary experimental discoveries of the 1970s, 1980s, and 1990s.They detailed many of the ingenious and pioneering techniques developed at CERN forthe detection and data analysis of several billions of proton–proton collisions Duringthe entire period of the school, the students received daily news about the progress ofthese searches A trip to the CERN facilities was organized, with visits to the LHC andATLAS detector control rooms, as well as the CMS detector coordination room andthe Cosmic Antimatter Detector control room coordinated with the space laboratory.The talks given by theoreticians were about many of the attempts to go beyondthe Standard Model that yield beautiful new physical insights yet to be observedexperimentally

The students were very active during the talks and had interesting interactions.The organizers and speakers encouraged them to pose unrestricted questions duringand after the lectures In addition, we had a “Wisdom Tree” session during whichMichael Douglas, Juan Maldacena, and Bruno Mansouli´e shared their thoughts onany subject the students desired We also held the traditional “Gong Show” in whichevery participant could speak about his or her work for three minutes The cocktail

of theorists and experimentalists proved to be most interesting

More precisely, the topics covered in the school were as follows

In the first morning, Jean Iliopoulos and Luis Alvarez-Gaum´e gave an introduction

to the school Jean Iliopoulos recalled the historical path taking us from the Standard

Massimo Giovanozzi gave an account of how the accelerator had been sioned, how the setback caused by a hardware failure was overcome, how the LHCfunctioned in the Summer of 2011, and what were the plans for its future upgrade.Dan Green took us from the accelerator to the giant detectors surrounding it Hedescribed the requirements for the detectors and the different choices made in theirdesign.

commis-Bruno Mansouli´e guided the audience along the way from the registration of theevents in the detectors to their analysis He explained the difficulties involved in correctidentification of the signals

Yves Sirois and Louis Fayard discussed the available LHC data and their cations for the Higgs boson searches at CMS and ATLAS, respectively, while KarlJakobs summarized the constraints derived on new physics

impli-Michelangelo Mangano explained the methods needed to compute the expectedbackgrounds without whose detailed knowledge one could not extract the newdiscoveries

Nima Arkani-Hamed and David Kosower explained new techniques recently oped to perform in a more efficient way the calculations of amplitudes, in particularfor the underlying QCD processes

devel-Gia Dvali described how unitarity is realized in effective field theories in particlephysics and its implication for graviton scattering

Juan Maldacena reviewed our theoretical knowledge on quantum gravity He scribed how the amazing correspondence between field theories on the boundary andgravity theories in a bulk with a negative cosmological constant arises This comesunder the umbrella of AdS/CFT He outlined the state of the art in the field, which

de-is a very concrete realization of the concept of holography

Jan de Boer went into the details of basic examples of AdS/CFT duality

Yaron Oz explained how to obtain hydrodynamics equations from the study ofblack hole solutions and described the emergence of an amazing correspondencebetween features of gravity and fluids

Gian Giudice discussed the most popular supersymmetric extension of theStandard Model

Gerard ’t Hooft unveiled his ideas for addressing the black hole physics informationparadox He described several consequences of the spontaneous breaking of a localconformal invariance and how this helps to obtain concrete complementarity mapsbetween different sets of observables in the presence of a black hole

Zohar Komargodski described the possible definition of a c-function and his proof

of the associated a-theorem

Alex Pomarol described the implementation of electroweak symmetry-breakingmechanisms in different extensions of the Standard Model

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Preface xi

Karim Benakli described in detail the basics of supersymmetry breaking

Luis Ib´a˜nez reviewed the implementation of the phenomenologically viable symmetric extensions of the Standard Model in string theory

super-Michael Douglas discussed the problems of classifying the possible models andestimating their frequency in the landscape of string vacua

Laurent Baulieu explained the use of a twisted supersymmetry algebra insupergravity and its consequences

Eliezer Rabinovici described his work with Jos´e Luis Barb´on on various types ofbig crunches using the AdS/CFT correspondence, and the surprising result that somebig crunches can be equivalently described by a nontrivial infrared theory living on asingularity-free de Sitter space

Gabriele Veneziano summarized some 25 years of work on the energy collisions of particles, strings, and branes He discussed different regimes inthese processes, recovering physical expectations (e.g., gravitational deflection andtidal excitation) at large distance and exposing new phenomena when the string lengthexceeds the gravitational radius of the collision’s energy He also presented recentattempts to approach the short-distance regime where black hole formation is expected

transplanckian-to occur

Daniel Zwanziger explained formal aspect of the Gribov problem in QCD.Altogether, it is the general feeling of the organizers, lecturers, and students thatthe School was a success, striking the right balance between the exciting physics that

is currently coming out of LHC, while covering important recent developments in thetheory of elementary particles

More than one of the speakers reminisced on their days as students and postdocs

in Les Houches, and were grateful for this chance to return at the moment where LHC

is starting to unveil a yet-unknown domain of energy We were happy to have thechance to maintain such a longstanding tradition, and are confident that our studentswill make important contributions in the coming era We hope some of them will havethe chance to return as lecturers in their turn

As organizers, we express our gratitude to the local staff of the Les Houches Schoolfor their help, as well as to the funding agencies (CEA, CERN, CNRS, EuropeanScience Foundation, IN2P3, and the Les Houches School of Physics) that made possiblethe organization of this event

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and future upgrades

5.3 The final-state evolution of quarks and gluons 119

6.3 The N = 4 super Yang–Mills/AdS5× S5 example 152

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8.5 Holographic hydrodynamics: the fluid/gravity correspondence 194

10.3 Local conformal invariance and the stress–energy–momentum tensor 21710.4 Local conformal symmetry in canonical quantum gravity 22010.5 Local conformal invariance and the Weyl curvature 225

13.2 Type II orientifolds: intersections and magnetic fluxes 294

14 The string landscape and low-energy supersymmetry

14.2 Low-energy supersymmetry and current constraints 321

twisted supersymmetric fields

15.2 N = 1, d = 4 supergravity in the new minimal scheme 34215.3 Self-dual decomposition of the supergravity action 345

15.5 The supergravity curvatures in the U(2) ⊂ SO(4)-invariant

15.6 The 1.5-order formalism with SU(2)-covariant curvatures 35115.7 Vector supersymmetry and nonvanishing torsion 35615.8 Matter and vector multiplets coupled to supergravity 358

Appendix A: The BSRT symmetry from horizontality conditions 361

Appendix C: The action of γ matrices on twisted spinors 363Appendix D: Algebra closure on the fields of matter and vector multiplets 364

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Contents xvii

16 AdS crunches, CFT falls, and cosmological complexity

16.3 Facing the CFT crunch time is complementary 375

17.2 Gravitational collapse criteria: a brief review 400

17.4 The small-angle regime: deflection angle

17.5 The string-gravity regime: a precocious black hole behaviour? 40617.6 The strong-gravity regime: towards the large-angle/collapse phase? 40717.7 High-energy string–brane collisions: an easier problem? 410

List of participants xix

IBA ˜NEZ Luis

Departamento de F´ısica Te´orica, and Instituto de F´ısica Te´orica, UniversidadAut´onoma de Madrid, Spain

Department of Physics, University of California at Santa Barbara, USA

BERASALUCE-GONZ ´ALEZ Mikel

Insituto de F´ısica Te´orica, Universidad Aut´onoma de Madrid, Spain

Department of Physics, University of Crete, Greece

DE ADELHART Toorop Reinier

The National Institute for Nuclear Physics and High Energy Physics, Amsterdam,The Netherlands

FRELLESVIG Hjalte Axel

Niels Bohr Institute, Copenhagen, Denmark

GIANNUZZI Floriana

Dipartimento di Fisica, Universit`a di Bari and INFN, Italy

GUDNASON Sven Bjarke

High Energy Physics Group, The Hebrew University, Jerusalem, Israel

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List of participants xxi

Academy of Sciences, Czech Republic

LOU Hou Keong

Department of Physics, Princeton University, New Jersey, USA

xxii List of participants

SALAS Hern´andezClara

Instituto de F´ısica Te´orica, Universidad Aut´noma de Madrid/CSIC, Spain

Physics Department, New York University, USA

TAN Hai Siong

Physics Department, University of California at Berkeley, USA

Theoretical Physics to Face the Challenge of LHC Edited by L Baulieu, K Benakli, M R Douglas,

B Mansouli´ e, E Rabinovici, and L F Cugliandolo c Oxford University Press 2015.

Published in 2015 by Oxford University Press.

Introduction 3

The Large Hadron Collider (LHC) is the most complex scientific instrument ever builtfor particle physics research It will for the first time give access to the TeV energyscale To achieve this, a number of technological innovations have been necessary.The two counter-rotating proton beams are guided and focused by superconductingmagnets with a novel two-in-one structure to save cost and allow the machine to beinstalled in an existing tunnel The very high field of more than 8 T in the dipoles canonly be achieved by cooling them below the transition temperature of liquid helium

to the superfluid state More than 80 tons of superfluid helium is needed to cool thewhole machine In its first year of operation, it has been shown to behave in a veryreliable and predictable way Single-bunch currents 30% above the design value havealready been achieved, and the luminosity has increased by five orders of magnitude

in the first 200 days of operation

In this chapter, a brief description of the design principles of the major systems isgiven and some of the results of commissioning and first operation discussed

The LHC is a two-ring superconducting hadron accelerator and collider installed in theexisting 26.7 km tunnel that was constructed between 1984 and 1989 for the CERNLarge Electron Positron (LEP) collider The LEP tunnel has eight straight sectionsand eight arcs and lies between 45 and 170 m below the surface on a plane inclined

at 1.4%, sloping towards Lake L´eman Approximately 90% of its length is in molasserock, which has excellent characteristics for this application, and 10% is in limestoneunder the Jura mountain There are two transfer tunnels, each approximately 2.5 km

in length, linking the LHC to the CERN accelerator complex that acts as injector.Full use has been made of the existing civil engineering structures, but modificationsand additions have also been needed Broadly speaking, the underground and surfacestructures at Points 1 and 5 for ATLAS and CMS, respectively, are new, while thosefor ALICE and LHCb, at Points 2 and 8, respectively, were originally built for LEP.The approval of the LHC project was given by the CERN Council in December

1994 At that time, the plan was to build a machine in two stages, starting with acentre-of-mass energy of 10 TeV, to be upgraded later to 14 TeV However, during1995–96, intense negotiations secured substantial contributions to the project fromnonmember states, and in December 1996, the CERN Council approved construction

of the 14 TeV machine in a single stage

The LHC design depends on some basic principles linked with the latest technology.Since it is a particle–particle collider, there are two rings with counter-rotating beams,unlike particle–antiparticle colliders, which can have both beams sharing the samering The tunnel in the arcs has a finished internal diameter of 3.7 m, which makes itextremely difficult to install two completely separate proton rings This hard limit onspace led to the adoption of the twin-bore magnet design that was proposed by JohnBlewett at the Brookhaven Laboratory in 1971 At that time, it was known as the

“two-in-one” superconducting magnet design [1] and was put forward as a cost-savingmeasure [2, 3], but in the case of the LHC, the overriding reason for adopting thissolution was the lack of space in the tunnel

4 The Large Hadron Collider

In the later part of the twentieth century, it became clear that higher energies couldonly be reached through better technologies, principally through superconductivity.The first use of superconducting magnets in an operational collider was in the ISR,but always at 4–4.5 K [4] However, research was moving towards operation at 2 K andlower, to take advantage of the increased temperature margins and the enhanced heattransfer at the solid–liquid interface and in the bulk liquid [5] The French TokamakTore II Supra demonstrated this new technology [6, 7], which was then proposed forthe LHC [8] and brought from the preliminary study to the final concept design andvalidation in six years [9]

In a chapter of this length, it is impossible to describe in detail all the differentsystems needed to operate the LHC Instead, we concentrate on the principal newtechnologies developed for the machine A detailed description of the machine as builtcan be found in the LHC Design Report [10], which is in three volumes This chapterends with a brief description of commissioning and the first year of operation

where σeventis the cross section for the event under study and L the machine

luminos-ity The machine luminosity depends only on the beam parameters and can be writtenfor a Gaussian beam distribution as

L = N

2

b n b frevγr

where N b is the number of particles per bunch, n b the number of bunches per beam,

frev the revolution frequency, γ r the relativistic gamma factor, ε n the normalized

transverse beam emittance, β ∗ the beta function at the collision point, and F the

geometric luminosity reduction factor due to the crossing angle at the interaction

point (IP) F is given by

where θ c is the full crossing angle at the IP, σ z the root mean square (RMS) bunch

length, and σ ∗the transverse RMS beam size at the IP The expression (1.3) assumes

round beams, with σ z << β, and equal beam parameters for both beams The

explor-ation of rare events in the LHC collisions therefore requires both high beam energiesand high beam intensities

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Main machine layout and performance 5

The LHC has two high-luminosity experiments, ATLAS [11] and CMS [12], both

aiming at a peak luminosity of L = 1034cm−2s−1 for proton operation There are

also two low-luminosity experiments: LHCB [13] for B physics, aiming at a peak luminosity of L = 1032cm−2s−1, and TOTEM [14] for the detection of protons from

elastic scattering at small angles, aiming at a peak luminosity of L = 2 ×1029cm−2s−1with 156 bunches In addition to the proton beams, the LHC will also be operatedwith ion beams The LHC has one dedicated ion experiment, ALICE [15], aiming at

a peak luminosity of L = 1027cm−2s−1 for nominal lead–lead ion operation

The high beam intensity required for a luminosity of L = 1034cm−2s−1 excludesthe use of antiproton beams, and hence excludes the particle–antiparticle colliderconfiguration of a common vacuum and magnet system for both circulating beams,

as used for example in the Tevatron To collide two counter-rotating proton beamsrequires opposite magnetic dipole fields in both rings The LHC is therefore designed as

a proton–proton collider with separate magnet fields and vacuum chambers in the mainarcs and with common sections only at the insertion regions where the experimentaldetectors are located The two beams share an approximately 130-m-long commonbeam pipe along the interaction regions (IRs)

As already mentioned, there is not enough room for two separate rings of magnets

in the LEP/LHC tunnel, and so the LHC uses twin-bore magnets consisting of twosets of coils and beam channels within the same mechanical structure and cryostat.The peak beam energy depends on the integrated dipole field around the storagering, which implies a peak dipole field of 8.33 T for the 7 TeV energy This can only

be achieved with “affordable” niobium–titanium (NbTi) superconductor by loweringthe temperature to 1.9 K, below the phase transition of helium from a normal to asuperfluid state

Beam–beam limit

When the beams collide, a proton in one beam is affected by the electromagneticfield of the other beam The maximum particle density per bunch is limited by thenonlinearity of this beam–beam interaction, the strength of which is measured by thelinear tune shift, given by

implies that the linear beam–beam tune shift for each IP should satisfy ξ < 0.005.

Maximum dipole field and magnet quench limits

The maximum beam energy that can be reached in the LHC is limited by the peakdipole field in the storage ring The nominal field is 8.33 T, corresponding to an energy

6 The Large Hadron Collider

of 7 TeV Operating at this very high field level requires that the magnets be cooled

in a bath of superfluid helium at 1.9 K

Energy stored in the circulating beams and in the magnetic fields

A total beam current of 0.584 A corresponds to a stored energy of approximately

362 MJ In addition to the energy stored in the circulating beams, the LHC magnetsystem has a stored electromagnetic energy of approximately 600 MJ, yielding a totalstored energy of more than 1 GJ This stored energy must be absorbed safely at theend of each run or in the case of a malfunction or an emergency The beam dumpingsystem and the magnet system therefore provide additional limits for the maximumattainable beam energies and intensities

Heat load

Although synchrotron radiation in hadron storage rings is small compared with thatgenerated in electron rings, it can still impose practical limits on the maximum at-tainable beam intensities if the radiation has to be absorbed by the cryogenic system

In addition to the synchrotron-radiation heat load, the LHC cryogenic system mustabsorb the heat deposition from luminosity-induced losses, impedance-induced losses(resistive wall effect), and electron-cloud bombardment

Field quality and dynamic aperture

Field quality errors compromise the particle stability in the storage ring, and henceloss-free operation requires a high field quality A characterizing feature of supercon-ducting magnets is the decay of persistent currents and their “snap back” at thebeginning of the ramp Achieving small beam losses therefore requires tight control

of the magnetic field errors during magnet production and during machine operation.Assuming fixed limits for the beam losses (set by the quench levels of the supercon-ducting magnets), the accuracy of the field quality correction during operation andits limitation on machine performance can be estimated

Collective beam instabilities

The interaction of the charged particles in each beam with each other via magnetic fields and the conducting boundaries of the vacuum system can result incollective beam instabilities Generally speaking, the collective effects are a function

electro-of the vacuum system geometry and its surface properties They are usually tional to the beam currents and can therefore limit the maximum attainable beamintensities

The basic layout of the LHC follows the LEP tunnel geometry (see Fig 1.1) The LHChas eight arcs and eight straight sections Each straight section is approximately 528 mlong and can serve as an experimental or utility insertion The two high-luminosity

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Main machine layout and performance 7

Dump

Cleaning Cleaning

RF and future

Fig 1.1 Schematic layout of the LHC (Beam 1 clockwise; Beam 2 anticlockwise).

experimental insertions are located at diametrically opposite straight sections: the LAS experiment is located at Point 1 and the CMS experiment at Point 5 Two moreexperimental insertions are located at Points 2 and 8, which also include the injec-tion systems for Beams 1 and 2, respectively The injection kick occurs in the verticalplane, with the two beams arriving at the LHC from below the LHC reference plane.The beams cross from one magnet bore to the other at four locations The remainingfour straight sections do not have beam crossings Insertions at Points 3 and 7 eachcontain two collimation systems The insertion at Point 4 contains two radiofrequency(RF) accelerating systems: one independent system for each LHC beam The straightsection at Point 6 contains the beam dump insertion, where the two beams can besafely extracted from the machine if needed Each beam features an independent abortsystem

AT-The arcs of the LHC lattice are made of 23 regular arc cells AT-The arc cells are106.9 m long and are made out of two 53.45-m-long half cells, each of which containsone 5.355-m-long cold mass (6.63-m-long cryostat), a short straight section (SSS)

8 The Large Hadron Collider

assembly, and three 14.3-m-long dipole magnets The LHC arc cell has been optimizedfor a maximum integrated dipole field along the arc with a minimum number of magnetinterconnections and with the smallest possible beam envelopes

The two apertures of Ring 1 and Ring 2 are separated by 194 mm The twocoils in the dipole magnets are powered in series, and all dipole magnets of one arcform one electrical circuit The quadrupoles of each arc form two electrical circuits:all focusing quadrupoles in Beams 1 and 2 are powered in series, and all defocusingquadrupoles in Beams 1 and 2 are powered in series The optics of Beam 1 and Beam

2 in the arc cells are therefore strictly coupled via the powering of the main magneticelements

A dispersion suppressor (DS) is located at the transition between an LHC arc and

a straight section, yielding a total of 16 DS sections The aim of the DS is threefold:

• Adapt the LHC reference orbit to the geometry of the LEP tunnel

• Cancel the horizontal dispersion arising in the arc and generated by theseparation/recombination dipole magnets and the crossing angle bumps

• Facilitate matching the insertion optics to the periodic optics of the arc

Interaction regions 1 and 5 house the high-luminosity experiments of the LHC andare identical in terms of hardware and optics, except that the crossing angle is in the

vertical plane at Point 1 and in the horizontal plane at Point 5 The small β-function

values at the IPs are generated between quadrupole triplets that leave ±23 m free

space about the IP In this region, the two rings share the same vacuum chamber,

the same low-β triplet magnets, and the D1 separation dipole magnets The

remain-ing matchremain-ing section and the DS consist of twin-bore magnets with separate beampipes for each ring From the IP up to the DS insertion, the layout comprises thefollowing:

• A 31-m-long superconducting low-β triplet assembly, operated at a temperature

of 1.9 K and providing a nominal gradient of 205 T/m

• A pair of separation/recombination dipoles separated by approximately 88 m

• The D1 dipole located next to the triplet magnets, which has a single bore andconsists of six 3.4-m-long conventional warm magnet modules yielding a nominalfield of 1.38 T

• The following D2 dipole, which is a 9.45-m-long twin-bore superconducting dipolemagnet, operating at a cryogenic temperature of 4.5 K with a nominal field of3.8 T The bore separation in the D2 magnet is 188 mm and is thus slightlysmaller than the arc bore separation

• Four matching quadrupole magnets The first quadrupole following the ation dipole magnets, Q4, is a wide-aperture magnet operating at a cryogenictemperature of 4.5 K and yielding a nominal gradient of 160 T/m The remainingthree quadrupole magnets are normal-aperture quadrupole magnets, operating at

separ-a cryogenic tempersepar-ature of 1.9 K with separ-a nominsepar-al grsepar-adient of 200 T/m

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Main machine layout and performance 9

Fig 1.2 Schematic layout of the right side of IR1 (distances in m).

The straight section of IR2 (see Fig 1.3) houses the injection elements for Ring 1,

as well as the ion beam experiment ALICE During injection, the optics must satisfythe special constraints imposed by the beam injection for Ring 1, and the geometricalacceptance in the interaction region must be large enough to accommodate both beams

in the common part of the ring, with a beam separation of at least 10σ.

The IR3 insertion houses the momentum-cleaning systems (capturing off-momentumparticles) of both beams, while IR7 houses the betatron-cleaning systems (to controlthe beam halo) of both beams Particles with a large momentum offset are scattered

by the primary collimator in IR3 and particles with large betatron amplitudes arescattered by the primary collimator in IR7 In both cases, the scattered particles areabsorbed by secondary collimators Figures 1.4 and 1.5 show the right sides of IR3and IR7, respectively

Fig 1.3 Schematic layout of the matching section on the left side of IR2 (distances in m).

Fig 1.4 Schematic layout of the matching section on the right side of IR3 (distances in m).

10 The Large Hadron Collider

Fig 1.5 Schematic layout of the matching section on the right side of IR7 (distances in m).

In IR7, the layout of the long straight section between Q7L and Q7R is symmetric with respect to the IP This allows a symmetrical installation for thecollimators of the two beams and minimizes the space conflicts in the insertion Start-ing from Q7 left, the superconducting quadrupole Q6 is followed by a dogleg structuremade of two sets of MBW warm single-bore wide-aperture dipole magnets (two warmmodules each) The dogleg dipole magnets are labelled D3 and D4 in the LHC se-quence, with D3 being the dipole closer to the IP The primary collimators are locatedbetween the D4 and D3 magnets, allowing neutral particles produced in the jaws topoint out of the beam line and most charged particles to be swept away The inter-beam distance between the dogleg assemblies left and right from the IP is 224 mm, i.e

mirror-30 mm larger than in the arc This increased beam separation allows a substantiallyhigher gradient in the Q4 and Q5 quadrupoles, which are not superconducting because

of the heavy irradiation from the collimators The space between Q5 left and rightfrom the IP is used to house the secondary collimators at appropriate phase advanceswith respect to the primary collimators

IR4 (see Fig 1.6) houses the RF and feedback systems, as well as some of the LHCbeam instrumentation The RF equipment is installed in the old ALEPH (LEP) cavern,which provides a large space for the power supplies and klystrons In order to providethe transverse space for two independent RF systems for Beam 1 and Beam 2, theseparation must be increased to 420 mm This is achieved by two pairs of doglegdipole magnets labelled D3 and D4 in the LHC sequence, with D3 being the dipolemagnets closer to the IP In contrast to IR3 and IR7, the dogleg magnets in IR4 aresuperconducting, since the radiation levels are low

Fig 1.6 Schematic layout of the matching section on the right side of IR4 (distances in m).

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Main machine layout and performance 11

IR6 (see Fig 1.7) houses the beam abort systems for Beams 1 and 2 Beam abort fromthe LHC is done by kicking the circulating beam horizontally into an iron septummagnet, which deflects the beam in the vertical direction away from the machinecomponents to absorbers in a separate tunnel Each ring has its own system, and bothare installed in IR6 To minimize the length of the kicker and of the septum, large

drift spaces are provided Matching the β-functions between the ends of the left and

right DS requires only four independently powered quadrupoles In each DS, up tosix quadrupoles can be used for matching The total of 16 quadrupoles is more than

sufficient to match the β-functions and the dispersion and to adjust the phases There

are, however, other constraints to be taken into account concerning apertures insidethe insertion

Special detection devices protect the extraction septum and the LHC machineagainst losses during the abort process The TCDS absorber is located in front of theextraction septum and the TCDQ in front of the Q4 quadrupole magnet downstream

of the septum magnet

IR8 houses the LHCb experiment and the injection elements for Beam 2 The small

β-function values at the IP are generated with the help of a triplet quadrupole assemblythat leaves±23 m of free space around the IP In this region, the two rings share the

same vacuum chamber, the same low-β triplet magnets, and the D1 separation dipole

magnet The remaining matching section and the DS consist of twin-bore magnetswith separate beam pipes for each ring From the IP up to the DS insertion, thelayout comprises the following:

• Three warm dipole magnets to compensate the deflection generated by the LHCbspectrometer magnet

• A 31-m-long superconducting low-β triplet assembly operated at 1.9 K and

providing a nominal gradient of 205 T/m

• A pair of separation/recombination dipole magnets separated by approximately

54 m The D1 dipole located next to the triplet magnets is a 9.45-m-longsingle-bore superconducting magnet The following D2 dipole is a 9.45-m-long

Fig 1.7 Schematic layout of the matching section on the right side of IR6 (distances in m).

12 The Large Hadron Collider

Fig 1.8 Schematic layout of the matching section on the right side of IR8 (distances in m).

double-bore superconducting dipole magnet Both magnets are operated at 4.5 K.The bore separation in the D2 magnet is 188 mm, and is thus slightly smallerthan the arc bore separation

• Four matching quadrupole magnets The first quadrupole following the ation dipole magnets, Q4, is a wide-aperture magnet operating at 4.5 K andyielding a nominal gradient of 160 T/m The remaining three matching-sectionquadrupole magnets are normal-aperture quadrupole magnets operating at 1.9 Kwith a nominal gradient of 200 T/m

separ-• The injection elements for Beam 2 on the right side of IP8 In order to providesufficient space for the spectrometer magnet of the LHCb experiment, the beamcollision point is shifted by 15 half RF wavelengths (3.5 times the nominal bunchspacing≈ 11.25 m) towards IP7 This shift of the collision point has to be com-

pensated before the beam returns to the DS sections and requires a nonsymmetricmagnet layout in the matching section

The LHC relies on superconducting magnets that are at the edge of present ogy Other large superconducting accelerators (Tevatron-FNAL, HERA-DESY, andRHIC-BNL) all use classical NbTi superconductors, cooled by supercritical helium attemperatures slightly above 4.2 K, with fields below or around 5 T The LHC magnetsystem, while still making use of the well-proven technology based on NbTi Ruther-ford cables, cools the magnets to a temperature below 2 K, using superfluid helium,and operates at fields above 8 T Since the electromagnetic forces increase with thesquare of the field, the structures restraining the conductor motion must be mech-anically much stronger than in earlier designs In addition, space limitations in thetunnel and the need to keep costs down have led to the adoption of the “two-in-one”

technol-or “twin-btechnol-ore” design ftechnol-or almost all of the LHC superconducting magnets The in-one design accommodates the windings for the two beam channels in a commoncold mass and cryostat, with magnetic flux circulating in the opposite sense throughthe two channels

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Magnets 13

The transverse cross section of the coils in the LHC 56-mm-aperture dipole magnet(Fig 1.9) shows two layers of different cables distributed in six blocks The cable used

in the inner layer has 28 strands, each having a diameter of 1.065 mm, while the cable

in the outer layer is formed from 36 strands, each of 0.825 mm diameter

The filament size chosen is 7 µm for the strand of the inner layer cable and 6 µmfor the strand of the outer layer cable They are optimized to reduce the effects of thepersistent currents on the sextupole field component at injection The residual errorsare corrected by small sextupole and decapole magnets located at the end of eachdipole

The LHC ring accommodates 1232 main dipoles: 1104 in the arc and 128 in the

DS regions They all have the same basic design The geometric and interconnectioncharacteristics have been targeted to be suitable for the DS region, which is moredemanding than the arc The cryodipoles are a critical part of the machine, both fromthe machine performance point of view and in terms of cost Figure 1.10 shows thecross section of the cryodipole

The successful operation of the LHC requires that the main dipole magnets havepractically identical characteristics The relative variations of the integrated fieldand the field shape imperfections must not exceed ∼ 10 −4, and their reproducibility

must be better than 10−4 after magnet testing and during magnet operation Thereproducibility of the integrated field strength requires close control of coil diameterand length and of the stacking factor of the laminated magnetic yokes, and possiblyfine tuning of the length ratio between the magnetic and nonmagnetic parts of theyoke The structural stability of the cold mass assembly is achieved by using very rigidcollars, and by opposing the electromagnetic forces acting at the interfaces between

Fig 1.9 Conductor distribution in the dipole coil cross section (X axis in mm on left) Picture

of cables and strand on right

14 The Large Hadron Collider

Alignment target Main quadripole bus-bars Heat-exchanger pipe Superinsulation Superconducting coils Beam pipe

Vacuum vessel Beam screen Auxiliary bus-bars Thermal shield (55−75 K) Nonmagnetic collars Iron yoke (cold mass, 1.9 K) Dipole bus-bars

Support post Shrinking cylinder / He I-vessel

Fig 1.10 Cross section of cryodipole (lengths in mm).

the collared coils and the magnetic yoke with the forces set up by the shrinkingcylinder A prestress between coils and retaining structure (collars, iron lamination,and shrinking cylinder) is also built in Because of the larger thermal contractioncoefficient of the shrinking cylinder and austenitic steel collars with respect to the yokesteel, the force distribution inside the cold mass changes during cool down from roomtemperature to 1.9 K

The vacuum vessel consists of a long cylindrical standard tube with an outer diameter

of 914 mm (36 inches) and a wall thickness of 12 mm It is made from alloyed carbon steel The vessel has stainless steel end flanges for vacuum-tight connectionvia elastomer seals to adjacent units Three support regions feature circumferentialreinforcement rings Upper reinforcing angles support alignment fixtures An ISO-standard flanged port is located azimuthally on the wall of the vessel at one end Innormal operation, the vessel will be under vacuum In case of a cryogenic leak, thepressure can rise to 0.14 MPa absolute, and a sudden local cooling of the vessel wall

low-to about 230 K may occur The steel selected for the vacuum vessel wall is tested low-todemonstrate adequate energy absorption during a standard Charpy test at−50 ◦C A

front view of the cryodipole is shown in Fig 1.11

In the main dipoles, the magnetic field is up in one aperture and down in theother In straight sections 2 and 8, the beams are separated into two apertures withspecial superconducting dipoles D1 with a single aperture and D2 with two apertures,where the field direction is identical for both Such special dipoles are also used in the

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MLI: 50–55 K

Bottom tray assembly

Fig 1.11 LHC dipole cryomagnet assembly.

RF insertion at Point 4, where the beams are separated further to make way for thecavities All these special dipoles were designed and built in the USA at BrookhavenLaboratory

Figure 1.12 shows a perspective view and Fig 1.13 illustrates the cross section of anSSS The cold masses of the arc SSSs contain the main quadrupole magnets (MQ) and

Vacuum barrier Helium vessel

{inertia tube}

Vacuum vessel

Machine interconnect

LHS−SSS reference drawing

Auxiliary bus-bar tube

Octupole MO BPM

technical service module

Lattice quadrupole

MQ Thermal shield

Multilayer insulation

Support post

Beam vacuum pumping manifold

Corrector MSCB

16 The Large Hadron Collider

Alignment target Main quadrupole bus-bars Heat-exchanger pipe Superinsulation Superconducting coils Beam pipe Inertia tube / He II-vessel Iron yoke

Thermal shield Auxiliary bus-bars Austenitic steel collars Beam screen Instrumentation wires Filler piece Dipole bus-bars Support post Vacuum vessel

Fig 1.13 Cross section of SSS at quadrupole cold mass inside cryostat.

various corrector magnets On the upstream end, these can be octupoles (MO), tuningquadrupoles (MQT), or skew quadrupole correctors (MQS) On the downstream end,the combined sextupole–dipole correctors (MSCB) are installed

Because of the lower electromagnetic forces than in the dipoles, the two apertures

do not need to be combined, but are assembled in separate annular collaring systems

The insertion magnets are superconducting or normally conducting and are used inthe eight insertion regions of the LHC Four of these insertions are dedicated to experi-ments, while the others are used for major collider systems (one for the RF, two forbeam cleaning, and one for beam dumping) The various functions of the insertionsare fulfilled by a variety of magnets, most based on the technology of NbTi super-conductors cooled by superfluid helium at 1.9 K A number of standalone magnets inthe matching sections and beam separation sections are cooled to 4.5 K, while in theradiation areas, specialized normally conducting magnets are installed

The tuning of the LHC insertions is provided by the individually powered quadrupoles

in the matching and DS sections The matching sections consist of standalone rupoles arranged in four half-cells, but the number and parameters of the magnetsare specific for each insertion Apart from the cleaning insertions, where specializednormally conducting quadrupoles are used in the high-radiation areas, all matching

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Radiofrequency systems 17

quadrupoles are superconducting magnets Most of them are cooled to 4.5 K, exceptthe Q7 quadrupoles, which are the first magnets in the continuous arc cryostat andare cooled to 1.9 K

CERN has developed two superconducting quadrupoles for the matching sections:the MQM quadrupole, featuring a 56-mm-aperture coil, which is also used in the DSsections, and the MQY quadrupole, with an enlarged, 70 mm, coil aperture Both quad-rupoles use narrow cables, so that the nominal current is less than 6 kA, substantiallysimplifying the warm and cold powering circuits Each aperture is powered separately,but a common return is used, so that a three-wire bus-bar system is sufficient for fullcontrol of the apertures

In the cleaning insertions IR3 and IR7, each of the matching quadrupoles Q4 andQ5 consists of a group of six normally conducting MQW magnets This choice isdictated by the high radiation levels due to scattered particles from the collimationsystem, and therefore the use of superconducting magnets is not possible It featurestwo apertures in a common yoke (2-in-1), which is atypical for normally conductingquadrupole magnets, but is needed because of transverse space constraints in thetunnel The two apertures may be powered in series in a standard focusing/defocusingconfiguration (MQWA), or alternatively in a focusing/focusing configuration (MQWB)

to correct asymmetries of the magnet In a functional group of six magnets, five areconfigured as MQWA, corrected by one configured as MQWB

The low-β triplet is composed of four single-aperture quadrupoles with a coil aperture

of 70 mm These magnets are cooled with superfluid helium at 1.9 K using an externalheat-exchanger system capable of extracting up to 10 W/m of power deposited in thecoils by the secondary particles emanating from the proton collisions Two types ofquadrupoles are used in the triplet: 6.6-m-long MQXA magnets designed and devel-oped by KEK, Japan and 5.7-m-long MQXB magnets designed and built by Fermilab,USA The magnets are powered in series with 7 kA, with an additional inner loop of

5 kA for the MQXB magnets Together with the orbit correctors MCBX, skew

quadru-poles MQSX, and multipole spool pieces supplied by CERN, the low-β quadruquadru-poles are

completed in their cold masses and cryostated by Fermilab The cryogenic feed-boxes(DFBX), providing a link to the cryogenic distribution line and power converters, aredesigned and built by Lawrence Berkeley National Laboratory, USA Alongside the

LHC main dipoles, the high-gradient wide-aperture low-β quadrupoles are the most

demanding magnets in the collider They must operate reliably at 215 T/m, sustainextremely high heat loads in the coils and high radiation dose during their lifetime,and have a very good field quality within the 63 mm aperture of the cold bore

The injected beam is captured, accelerated, and stored using a 400 MHz ducting cavity system, and the longitudinal injection errors is damped using the same