The Nobel Prize in Physics 2013 the BEH–Mechanism, Interactions With

PoS(CORFU2014)138 http://pos.sissa.it/ . It took another nine months, however, and dedicated 7 − 10 × 3 † ∗ [email protected] Speaker. Talk based on the 2013 physics Nobel prize lecture. Reprinted with the permission of the Nobel Committee for On July 4, 2012, CERNwith announced properties the similar long to awaited thoseparticle discovery physics, expected of the for a Higgs the boson. new missingcollaborations fundamental The link particle discovery of was ATLAS made and the independently Standard CMSpurpose by multichannel Model at two detectors. (SM) the experimental With significance of Large at the Hadronparticle level Collider of was five mainly standard deviations, observed both the decaying new workinghigh into with significance two implies huge channels: that all- two thethe photons probability observed and of signal four background is leptons. fluctuations less conspiring than This to produce efforts from hundreds of scientistspertinent working hard characteristics, to before study CERN additional boldlylong-sought decay announced Higgs channels particle. that and extract the Today we newboson.” believe particle [1]. that An was “Beyond extensive review indeed any of the Higgs reasonable searchesin doubt, prior [2]. it to the is July a 2012 discovery Higgs may be found ∗ † Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c ⃝ Physics. Department of Fundamental Physics, Chalmers UniversitySWEDEN of Technology, S-412 96 Göteborg, E-mail: Lars Brink Proceedings of the Corfu Summer Instituteand 2014 Gravity", "School and Workshops on Elementary3-21 Particle September Physics 2014 Corfu, Greece The Nobel Prize in Physics 2013 The BEH – Mechanism, Interactions withRange Short Forces and Scalar Particles PoS(CORFU2014)138 medal design mark medal design mark ® 8 OCTOBER 2013 8 OCTOBER and the Nobel Prize

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) , , - = 26 (

𝐸𝐸 1

odel (SM) odel of Dirac (Nobel binding them

Paul ics) and that there that there and ics) mous formula ] ] mechanics that works so so works that mechanics

the interaction between the the between interaction the

both working with huge all electricityand magnetism in

two and leptons. photons four . We. knew the building blocks, of five standard deviations, the

: : per from 1931 [3 In a pa that Newtonian the

he could describe could he hat purpose Quantum Electrodynamics (QED) hat Quantum purpose Electrodynamics . It. took another nine months, however, and , , 7 ] - m? 10 common reasons behind different phenomena. We

hat are the are hat the and particles are fundamental what find

ed for the missing link of the Standard M : W : an 3× ed (hencethe name quantummechan ed realis was in ain seemingly perfect way to . Today we believe that “Beyond any reasonable doubt, it is it doubt, reasonable any we “Beyond that Today believe .

, it , had it not, been possible to common find frameworks for

ived ed decaying into two two channels into decaying ed when when we to try understand Nature at smaller and scales. smaller

Dirac equation [4 equation Dirac particle

hydrogen

particle theory and for t observ - Higgs de of physical manifestations physical of de multitu its with us around world he physical at matter is quantis matter at it was believed that all matter could be built up. up. couldbuilt be matter all that was believed it . T . From then on we talk about talk on then we From Field. Electromagnetic of the Theory mical mainly mainly life is but an approximation of the more fundamental quantum mechanics. It ATLAS and CMS at the Large Hadron Collider – the Hadron Collider at andATLAS CMS Large

[1]. An[1]. extensive review of Higgs searches prior to the July 2012 discovery may sought sought

-

– day- s probably always strs probably always Electrodynamics A Dyna every

1933) speculated that the final goal of physics to find the underlying laws of Nature could of could to laws the of Nature underlying goal final physics 1933) find that speculated the on the fundamental question was e beginning of the last century

. One. needed a many 2 th similar simplification occurs

This high significance implies that the probability of background fluctuations conspiring to produce the observed signal less is th dedicated efforts from hundreds of scientists working hard to study additional decay channels decay channels additional study to hard working scientists of hundreds from efforts dedicated was particle that new the announced CERN boldly before characteristics, pertinent extract and indeed the long

Introduction particle a of fundamental new awaited long discovery the announced CERN 4, 2012, July On with properties similar to those expect by two experimental independently was made discovery The Higgs boson. the physics, particle collaborations

purpose multichannel detectors. With significance at the level new particle was was particle new well in well Mankind ha d impossiblewoul be to understand many different phenomena Nature. in The physical development to be discussed here has its origin in 1865 when James Clark of Maxwell unification described his book electromagnetism. Before they were thought of as two different phenomena in Nature. A At be foundbe [2].in Unification of Interactions a Higgs boson.” a Higgs to rationalize want From From of form matter. complex most even the up build that constituents elementary basic are then the between act that interactions fundamental was also realizedwas th Prize, have reached.been Using the particles could be created created could be theory particles invariant a relativistically realized in soon that was it However, and annihilated since mass and energy are connected through Einstein’s fa electron and proton the in force electromagnetic of the mediator the as well as proton the and electron the the photon, and so Quantum 𝑚𝑚𝑚𝑚

PoS(CORFU2014)138 ) 26 (

2 . . ] ] ].

s of zero - Both of Both r. ed for the ed for the , which, a is able theory which the time ies. This is doneby

field, in

𝜇𝜇 finite values to each order in

𝐴𝐴 electron wave function, which , 1965) and Freeman Dyson [8 each he particle an associated

corrections. assign Chadwick (Nobel Prize, 1935) [10

onents.In Hermann 1929 Weyl ] [9

experiments. The parameters are said to

by introducing a local symmetry into the the into symmetry local a introducing by James

to three the

sts were here FeynmanRichard Julian [5], ] proposed that the strong nuclear force is is force nuclear strong the that proposed ] ed quantum rize QED ability of QED was then of that toability was prove gauge QED the vector potential, the the potential, vector - which is explicitly gauge invariant and its six non give the samegive of result in regardless which they order are , ,

uccessfully with uccessfully diagrammatical formulation thatdiagrammatical was formulation to be routinely used 𝜇𝜇 ] (Nobel P s

𝐴𝐴

𝜈𝜈 ) consistent quantum theory could be formulat could be theory quantum consistent ) 𝜕𝜕 𝜕𝜕𝜕𝜕 formulation of of formulation − 𝜈𝜈 . In particular they. showed a systematicthat perturbation expansion 𝐴𝐴

particle that came to be called the neutron. It was soon realized that soon realized was It neutron. the called be to came that particle 𝜇𝜇 𝜕𝜕 e compared s 𝜕𝜕𝜕𝜕 ectric and the magnetic field components. The symmetry is called abelian abelian is called symmetry The components. field magnetic the and ectric = =

μν d a very powerful Itiro Tomonaga [7 is described by a four is by described -

preserved all by the renormalis . A quantum. field theory in which only number a finite of parameters need be gauge invariant invariant gauge ed ki Yukawa (Nobel Prize, 1949) [11 The tokey prove the renormalis describing the free propagation of the particle. The specific quantum field theory

QED n n be written as an expansion in powers of finethe structure constant, α ed to define a finite perturbation expansion is called a renormalis

. field strength F strength field renormalis there are two distinct nuclear forces at play within the nucleus, a weak force that is responsible responsible that is force weak a the nucleus, within play at forces nuclear distinct two are there togethe neutrons the and protons the that binds one strong a and radioactivity the for discovered electrically neutral radiation from the nucleus and could establish that it consisted of of that consisted establish it could and nucleus the from radiation neutral electrically discovered a type new of elementary them act only over a very short range, of the size of the nucleus, hence they have no macroscopic analogue Hide 1935 In mediated by a new particle in analogy with the electromagnetic force. However, the the force. However, the with electromagnetic analogy in new a particle by mediated realized Yukawa range. a short while strong has force a the has range force long electromagnetic the electromagnetic field, and the physical degrees of freedom are carried only by the transverse components. invariance is still performed. symmetryThe leads to redundancyof the time and the longitudinal component

The Strong Interaction paper was Dirac’s published after a year Only [3], Relativistic was developed developed was latein the The1940’s. key physici

Schwinger [6], Sin They showed that a (seemingly electromagnetic interaction could be defined. This means that the amplitude for scattering between electrically charged charged electrically between for scattering amplitude the that means This defined. be could ca particles measure ofthe strength of the electric force. When computing these terms, most of them are found to be infinite. There is, however, a unique way to absorb all the infinit wave of norm the to its and charge its mass, electron the to as them contributions interpreting function. By letting these parameters free,be it is possible to expansion can that the b component has a negative norm relative to the space comp a constructed theory. This symmetry is the local change of the phase of the introduced He field. vector the of transformation a with together (measured), gauged be cannot the components are the el rotation phase two independent since be renormalis Feynman introduce all perturbative the calculations, in Feynman diagrams. To external line then defines the interaction vertices, which are combined with propagators to build diagrams. to diagrams. build propagators combined with are which vertices, interaction the defines then

PoS(CORFU2014)138 ) 26 (

3

-

ld in he

ay. In and a is the

in 1938,

𝑖𝑖𝑖𝑖 𝑎𝑎 𝐶𝐶 ,2,3, 1 = and . . This time the 𝑎𝑎

, this made was

with the doublet doublet with the 𝜇𝜇 𝜕𝜕

𝜕𝜕𝜕𝜕

where is gauge covariant. T ≡ , , scribe the strong nuclear

𝜇𝜇 𝜇𝜇 𝜈𝜈 𝑎𝑎 𝜕𝜕 𝑐𝑐

, 𝐴𝐴 𝑗𝑗 𝐴𝐴 to achieve

𝜓𝜓 𝜇𝜇 and � 𝑏𝑏 showed that a theory involving , 𝐴𝐴

𝑚𝑚

𝑎𝑎 𝜇𝜇 s ’ d discussed a similard discussed idea 𝐴𝐴 −

attempts to such find attempts an alternative 𝑎𝑎𝑎𝑎𝑎𝑎 ) (the) symmetry between the proton ticized, especially by Wolfgang Pauli 𝜇𝜇 𝑖𝑖𝑖𝑖 𝑎𝑎 𝑓𝑓 𝑖𝑖𝑖𝑖 𝐶𝐶 𝑔𝑔

𝐷𝐷

𝑖𝑖𝑖𝑖 𝜇𝜇 +

Mills theory to de theory Mills 𝛾𝛾 +

- ]. 𝜇𝜇 𝑖𝑖 𝑎𝑎 � 𝑖𝑖𝑖𝑖

𝐴𝐴 𝑖𝑖 𝛿𝛿

�

𝜈𝜈 𝜓𝜓 adjoint representation (a) 𝜇𝜇 𝜕𝜕 𝜕𝜕 𝜕𝜕𝜕𝜕

+ − = 𝜈𝜈 𝑎𝑎𝑎𝑎𝑎𝑎 𝜇𝜇 rather different attempt attempt different rather 𝑎𝑎 𝐹𝐹 𝑖𝑖𝑖𝑖

𝐴𝐴 𝐷𝐷

𝑎𝑎 𝜇𝜇 𝜇𝜇𝜇𝜇 and 𝜕𝜕 𝐹𝐹

𝜕𝜕𝜕𝜕 ents describing the proton and neutron. the The gauge 1 4 =

μν −

a like in QED under a local transformation but also also but which behaves transformation local a under QED in like uld perhaps needed.be Many F = A new

𝐿𝐿

part

two compon two unique. The freedom whichis symmetry (gauge) group to use and which il Powell (Nobel Prize, 1950) [12 Powell Prize, il (Nobel

range force of strong the interactions believed to the be fundamental force. - the particle came to be called was not discovered until after the Wor after Second until called be was to came not the discovered particle . Apart from the introduction of this derivative instead of the ordinary ordinary of the instead derivative this of introduction the from Apart . with theory there are three gauge fields (vector fields) (i) as of the matter fields to choose. the of matter fields

field strengthfield Ning Yang (Nobel Prize, 1957) and Robert Mills [13] constructed 1957) non a Mills and [13] who Prize, Robert Yang Ning (Nobel

i - Mills - Gordan coefficient connecting the connecting coefficient Gordan - satisfactorily led the physics community to doubt the relevance of relativistic quantum quantum of doubtrelativistic to relevance the community the led physics satisfactorily Abelian Gauge Theory

Proliferation of Elementary Particles - Non War, inWar, 1947, by Cec Lagrangian constructed asis Lagrangian Clebsch were were made in the following years. However, the great experimental developments of the 1950 success of QED was an accident; in order to describe the other forces forces other the describe to order in fieldtheories. accident; an Perhaps was QED the of success some alternative formalism wo force This was a was new approachThis very attractive but soon was it cri 1954 by by 1954 Chen where D is the covariant derivative (Nobel Prize, 1945), since the theory force. No a massless mediating particle the contains vector and, particle as suchwas above, asuch known noted a mediate would long rangeparticle force instead of the short Yukawa’s theory had been successful to predict a new particle but the attempts to make it into a into it make to attempts the but particle new a predict to successful been had theory Yukawa’s failed. theory field quantum force is the force mediated strong particles, by interactions massless electromagnetic the while that, must be mediated by massive particles. The mass then gives a natural scale for the range of the force. The pion

spinor field ψ transformation now is a local transformation between twothe components. The transfor mation of vector the field has one representation The The failureof the Yukawa field theory and the Yang abelian gauge field theory based on the isospin group isospin SU(2 the on based field theory gauge abelian and the neutron). The Swedish physicist Oskar Klein [14] ha but the outbreak of the war and the emphasis on other problems made this idea fade aw the Yang a gauge covariant of transforming as thea gauge part adjoint SU(2) representation corresponding derivative, the Lagrangian consistssimply of free the parts for vector the fields and spinors. the This construction is representations

PoS(CORFU2014)138 ) 26 (

4 auge before able so able so s known at able but as able but . In. 1961 he also known to known also 60, many new many new 60,

were extremely –

renormalis - al Ne’eman also put

Mann exten [21], ding nd Robert Schrieffer , - pions, have a lifetime of are needed

Mann proposed that the the that proposed Mann - . The proliferation of new was not renormalis

abelian gauge theory with gauge - range forces. The idea was tempting, e Theoreme heory - t model for all the interactions. Similar the all interactions. for model

the strong interaction . This. theory was non , like, the charged The

s discovery Yang the was by Dao Tsung and ’ 1969). He realized that in order to find a a find to order in that realized He 1969).

as up to build the all possible particle aying by s. Others came to be called flavour.) Yuv came flavour.) to called be

23 - urthermore interaction the weak was theory) was formulated for the weak interactions by to a theory describe unified of weak interactions and

lived particles were also found to follow this symmetry symmetry this to follow found also particles were lived by theby weak nuclear force A - -

) to) classify the particles stable under the influence of the V e [23]. Alsoe [23]. Feynman and Gell able. F abelian gauge field theory, commonly was it that gauge fieldbut theory, abelian believed Schwinger proposed a non -

aking and the Goldston 1979) [24] extended Schwinger’s idea and constructed a g a constructed and idea Schwinger’s extended [24] 1979) ,

, abelian theories lead to long lead theories abelian - range forcesrange of the weak interactions obtainedwere introducingby named after John Bardeen, Leon Cooper a - Mann (Nobel Prize, structur - SU(2) x U(1)

A

wed that, in order to understand the basic laws of Nature, the the laws basic of understandto basic the Nature, in order wed that, - s. They decay Mann and George the ZweigWith concept. the [17,quark introduced 18] 10 ll- - , while, non 10 Symmetry Bre

to were not renormalis and the V the and

6 [15]. (The new quantum number -

papers published were

SU(2) A lived with a lifetime of the order of 10 - - V ematic description of all these particles, new quantum numbers only nucleons and pions must be incomplete. When the new particle accelerators at CERN CERN at in accelerators new particle When the incomplete. be and pions must nucleons only Geneva and Brookhaven in the USA were brought into operation in 1959 particles were discovered. Most ofthem dec short

typically 10 typically elementary particles sho of order to to this Nature of The plethora bring known. be physicist also must blocks building Gells Murray wa particles syst SU(3group symmetry the introduced strong force forward the same idea [16]. The short Gell and [20], by and Sudarshan Feynman George and Marshak Robert earlier ideas of Enrico Fermi (Nobel Prize, 1938) [22] Lee (NobelLee Prize, 1957) [19] that parity is broken thein weak interactions. Shortly thereafter, an effective quantum field theory (the help of three quarks and their antiparticles it w pattern. In 1964 Ge that time. There was, however, still dynamical no theory the for quarks. The Weak Interaction The great theoretical development thein late 1950 the quantum corrections could not be trusted, but since the coupling strength of the weak force force weak the of strength coupling the since but trusted, could be not corrections quantum the veryis smallthe firstterm often is a good precision enough. great with This described theory and was clearly experiments of anmultitude embryo of a correct theory. In fact, already the group group underlying theory could be could non a theory be underlying have a short range a short have such theories theory based on the group group the on based theory electromagnetism. The short explicit masses for three of the four vector particles. vector four of for the three masses explicit however, and and however, survived, it it but was onlypursued by number a small of 1961 physicists. In Prize (Nobel Glashow Sheldon results were obtained Abdus by were results three years Ward [25]. later Salam J.C. and Spontaneous Another remarkable development came around 1960 when Yôichirô Nambu (Nobel Prize 2008) shown He [27]. had previously physics [26] to particle superconductivity from ideas extended state ( ground BCS the that we shall see shall it later step thewe a unified towards was first

PoS(CORFU2014)138 ) 26 (

5 , , , to, 2 0 𝜇𝜇 ngian ass the ass the symmetry t the most most t the after earlier

, U(1) a . . This Lagrangian

with a Lagra

) 2 , ie., d that a gauge theory theory ad that gauge 𝜑𝜑 𝜑𝜑

𝑖𝑖 𝑖𝑖𝑖𝑖 relativistic since it has a + - 𝑒𝑒

1 it it spontaneouslyis broken is positive

: on 𝜑𝜑 0 ( ⟶

,

2 2 1 ) √ 𝜑𝜑 𝜑𝜑 , ,

= φ � 𝜑𝜑 ticle physics the breaking of a local (

0 6 𝜆𝜆 − 𝜑𝜑

� 𝜑𝜑

studied a quantum field theory studied a forfield hypothetical quantum 2 0 𝜇𝜇

− [27] 𝜑𝜑

bu 𝜇𝜇 broken gauge symmetry. This means that, while the 𝜕𝜕

and the coupling constant 𝜆𝜆 constant coupling the and

, � 𝜑𝜑

𝜇𝜇 𝜕𝜕 that the theory in this case is n

, = 𝐿𝐿 a complex massive scalar field massive 𝜑𝜑 a complex Jeffrey Goldstone [29] pointed out that an alternative way to break way break to an alternative that out [29] pointed Goldstone Jeffrey

, by Philip Andersonby (Nobel Prize, 1977) and [28] others had fallen short Then the potential looks like a “Mexican hat” . . that of that

ntaneously is toscalara the with is ntaneously the of introduce numbers quantum field

, 1972), hasspontaneously e is the complex conjugate of 𝜑𝜑 of conjugate complex the is

� 𝜑𝜑 give risegive to length small scales if the local symmetry is spontaneously broken and tohence

ermi surface. In his paper of 1960 Nam F assumed He type. symmetry. symmetry is gauge This global chiral not with the and of fermions fields of to condensate a value expectation a by giving vacuum that underlying Hamiltonian is invariant with respect to the choice of the electromagnetic gauge, the of explanation original the of validity the on s doubt some cast fact This not. is state ground BCS the Meissner effect within the BCS theory, which, though well motivated on physical grounds, Nambu gauge finally not explicitly doubtswas invariant. these toput rest be abe negative number d then show that there is a bound state of the fermions, which he interpreted as the interpreted he which fermions, of athe state bound is show that there he could then and the If the interactions. detailing without principles general follows from result This pion. fermions m a small the By massless. giving the must be pion exact, is symmetry slightly is a Note is this pion that violated symmetry development given the and mass. small came four years before the quark hypothesis.

of providing a fully rigorous theory. In the language of par of the language In theory. rigorous fully a providing of where important contributions gauge symmetry, when a normal metal becomes superconducting, gives rise to a finite mass for the but nothing is scale length conjugate The superconductor. the inside field photon the showe superconductivity from example This depth. penetration London could thoughrange Note forces. short Nambu’sSoon after work Nobel Priz Nobel

density of the form is invariant under a global rotation of the phase of the field as in QED, although not QED, Suppose the although local of a now in the chooses as that square one. one mass,

important one was vacuum and to give it a vacuum expectation value. He studied some different cases bu different some He studied value. expectation vacuum a it give to and vacuum the symmetry spo

PoS(CORFU2014)138 ) 26 (

6

- .

= . 𝑣𝑣 2 2 . In. was was � | 2 𝜑𝜑 2 1979), ′

𝜑𝜑 a vacuum it was not was it +

o avoid the the o avoid 2 𝜑𝜑 1

′ but for | t function and 𝜑𝜑 �

0 = 0 = Goldstone mode is is Goldstone mode poin 𝜆𝜆 φ 24 - -

were understoodwere

with Glashow, −

� 2 2 ′ 𝜑𝜑 a massless one. It is rather rather is It one. a massless , + is 2 the potential is like a harmonic 2 )

1 2 1 ′ 𝜑𝜑 ′

𝜑𝜑 � , ie., he gave the field 𝜑𝜑 �

( 𝑣𝑣 1

′ 0 + 𝜑𝜑 6 𝜆𝜆 ′ was taken upwas in a subsequent paper by 𝑣𝑣

of magnetism from 1928 [30], + 𝜑𝜑

, 6 0 .

𝜆𝜆 to the two together two to the 𝜑𝜑 =

which is − � , 𝜑𝜑 𝜑𝜑

2 ′ 2 0 , , where m is the mass of the propagating modes. ity ofity a massless whenparticle the symmetry was 𝜇𝜇 2 𝜑𝜑

as

𝜇𝜇 m ′ + 𝜕𝜕 2 𝜑𝜑 ′ 𝜑𝜑

𝑖𝑖 𝜑𝜑

𝜕𝜕

𝜇𝜇

𝜕𝜕 � 𝜑𝜑

Schwinger [32] asked the question aif massive vector field 1 2 𝑖𝑖

𝜕𝜕 it is flat. The massless particle came to be called the Nambu

Heisenberg’s theory theory Heisenberg’s +

) = 2 he phenomenon of spontaneous breaking of a symmetry of the Hamiltonian 1 𝐻𝐻 ′ complex field 𝜑𝜑

describes a massive field, while 𝜑𝜑 2 0

over the three space directions, does not occur for 1 𝜇𝜇 ′ 2 new a + 1 in cases of spontaneous symmetry breaking, the Nambu in cases symmetry breaking, spontaneous of ′

, while thewhile onemassive was not given a name see yet. that will get We one it will 𝜑𝜑

how general the conclusion above is conclusion how general the , 𝜇𝜇 𝜕𝜕 Goldstone [31]. They showed under very general assumptions that a in Lorentz 1

′ There are an infinite number of degenerate minima all lying on acircle of radius

s a linear dispersion between energy and momentum at low momenta. ut a gauge theory for the strong interactions and hence it was natural to think about about think to natural was it hence and interactions strong the theory for gauge a ut

.

𝜑𝜑

2 0 0 𝜇𝜇 𝜇𝜇 𝜆𝜆 3 𝜕𝜕 the valley of the Mexican hat), where in the direction

( ffort parallel to Goldstone’s, to Goldstone’s, parallel ffort − 1 2 en introduced en introduced

= = 2 is clear that the lowest thelowest that value clear is 𝐿𝐿 t 𝑣𝑣 obvious from the potential that this should happen. We now expand around the minimum (one point in expectation value. The explicit symmetry between the two field components is now broken and The alluded have later to breaking of called was above). we spontaneousway (as tobe this now is Lagrangian

We see that the field 𝜑𝜑 I where the sum over i runs

Goldstone boson Goldstone necess the found hence Goldstone Nambu, Like Althoughmassless t particle. known before, for example from in the sequel. It should be pointed out that the symmetry is still present in the theory although it any longer. not linearly realized the is Only statevacuum the symmetry. breaks broken spontaneously. From the arguments above it above that From looks it quite the it spontaneously. arguments ishard t seen broken potential while in the direction 2

He th He condensed matter condensed until now that the full consequences of spontaneous symmetry breaking spontaneous of symmetry the consequences full that now until manifested a The question of together with together Abdus Salam and Steven Weinberg (Nobel Prize a theory at strong coupling. Such a occur Such could to coupling. scenario at strong theory due a possibly corrections. quantum a two and investigated framework a general in question the discussed He always comesalways with together a massless His scalar. idea a that was massless gauge at boson weak He was invariance. gauge the breaking without coupling at a can strong mass get coupling thinking abo invariant theory a spontaneous ofinvariant breaking a symmetry necessitates a massless the in particle spectrum. This came to be called Goldstone’s theorem Precursors anIn e wrote terms it in of an unknown function of

PoS(CORFU2014)138 ) 26 (

7

in a up a

1980) would would

raham , Ab

tuation up up tuation , of a massive of a massive the media to

We conclude, then, would valid be t theory. They set

same

potential relation from the from relation potential from March 1964 -

the same phenomenon

[34] arged plasma. Anderson followed followed Anderson plasma. arged

show how

concluded by saying ” saying concluded by He could then show how terms can cancel can terms cancel how show then could He

with no no with scalar massless mode, or particle

. .” ) that one could indeed have massive vector vector have massive indeed could that one

that in a relativistically invariant theory the

and ,0,0 0 1, ( but it did not did it but ed by Walter Gilbert (Nobel Prize in chemistry tressed

= , 𝜇𝜇 𝑛𝑛 st particle in the plasma with its own potential he could could he own its potential with plasma the in st particle mass problem

- and the cancellation cannot occur. This was the si the was This occur. cannot cancellation the and , 𝜇𝜇 took up the question if one if question the up took Anderson comment of the by inspired

, Mills zero Mills massless mode massless - discussed Nambu’s treatment of superconductivity and showed that that and showed superconductivity of treatment Nambu’s discussed

mass difficulty is not a serious one, because we can probably cancel it it cancel probably can we because one, a serious not is difficulty mass not pursued much by particle physicists, who instead tried to to even tried instead who physicists, by particle much not pursued - that as plasmon longitudinal is interpreted of an usually the attribute the

the flaw in the argument and stated that the stated that and argument the in flaw the

inally

relativistic setting. - ivistically invariant theory. Anderson showed

s ideas were ’ rguments were immediately criticis y with a spontaneouslyy with symmetry broken relativistic version of the of arguments version Goldstone, Salam Weinberg. and Abdus relativistic by then They - sidestep Goldstone’s to sidestep theorem able ould be in a relativistically invarian work in a relat in work that Goldstone zero the also there one could interpret the result as a massive vector field. a as result massive one the could interpret there also vector boson. He f He boson. vector a was This very important forward showing step particles without having a longitudinal mode would not be possible to separate from the third component the third to separate from mode would possible be not longitudinal to summer the of 1964 when the breakthrough finally came. each other leading to the absence of a massless pole. In the relativistic case there is only one one only there is case relativistic the In pole. a massless of absence to leading the other each vector at hand, the momentum, 𝑘𝑘 [35]. He showed that the arguments of Klein and Lee could be given a seemingly relativistic form introducingby a vector constant

off against an equal Yang equal an against off equations of motion and on other the hand considering dielectric the response of an external field. By introducing a te a as propagates it that found He field. total the compute and two in ways current the describe a of This frequency. example indeed an was a mass with a particle plasma for to related the field theor plasma while the transverse of real photons the modifications modes as are interpreted propagating the in plasma. He further s He checked the commutation relations for the currents and found situations where the massless massless the where situations found currents and the for relations commutation the checked He wouldcase disappear and would a have one This massive not a was cas e. a general proof but framework in which to discuss the problem. A definite model was missing. 1962In P.W. Anderson [33] another in important development took Schwinger’s up problem a ch of namely that model, a specific in it discussed and Schwinger’s analysis on by one the hand considering currentthe Anderson pointed out

Their a relativistic theory. Anderson although in non a although further strengthen Goldstone’s theorem. However in a paper Klein and Benjamin Lee W. w non argued through and it also should that a mode. in case followed this scalar massless there be they Finally

PoS(CORFU2014)138 ) 26 (

8

1

𝜑𝜑 term that that term

dashed line is - . . say that They point function for - der to find

. Goldstone field and vice vice and field Goldstone - 𝜇𝜇 𝐴𝐴

the expectation value, just just value, expectation the .

� 𝜇𝜇 . This. the is keyobservation. 1 𝜈𝜈 𝐴𝐴 dashed line is the insertion of

𝑞𝑞

𝜑𝜑 2 - ,

2

𝑞𝑞 𝜇𝜇 𝜇𝜇 𝑞𝑞 > 𝐴𝐴

1 𝜇𝜇 This is a completely is of This new type −

𝜑𝜑 𝐴𝐴 .

1 𝜇𝜇𝜇𝜇 𝜑𝜑 < ∗

𝑔𝑔 � 2 𝜑𝜑

2 𝑒𝑒 2 2

𝑒𝑒 and the short

> − , gauge invariant theory with a massive vector Goldstone particle massless 2 - 1 2 − 𝜑𝜑 𝜑𝜑

𝜑𝜑

𝜇𝜇 point function to lowest or to lowest function point . Hence. they gave ⃗ < 𝜇𝜇 � � 𝜕𝜕 �

2 ⃖ 𝜕𝜕

. field vector the to couplings the by affected not is 2

∗ 𝜇𝜇 √ 𝑒𝑒

𝑖𝑖 𝐴𝐴 𝜑𝜑 /

4 t it 𝜇𝜇 They started with an Abelian gauge theory coupled to a a to coupled theory gauge Abelian an with started They ) > >

𝐴𝐴

1 1 2 tha 2𝜋𝜋 𝜑𝜑 𝑖𝑖𝑖𝑖 𝜑𝜑 ( √

Englert and Brout [36] motivated by the work of Schwinger Schwinger of work the by motivated [36] Brout and Englert < = <

see =

, f the remaining field 𝜑𝜑

) 𝑖𝑖𝑖𝑖𝑖𝑖 =

𝑞𝑞 −𝑒𝑒 𝐻𝐻 ( Goldstone particle 𝜑𝜑 particle Goldstone becomes the Nambu > -

= 2 𝜇𝜇𝜇𝜇 ∗ ′ Π 𝜑𝜑 𝑡𝑡 𝜑𝜑 They then broke the symmetry by giving a vacuum expectation value 𝑛𝑛 . 𝑖𝑖 ) < 𝐻𝐻 2 = 𝜑𝜑

𝑖𝑖 > , and, one can 2 + - the two could now compute 𝜑𝜑 𝜑𝜑 1 𝜑𝜑

( 2 1 √ Effect and the Scalar Particle - =

𝜑𝜑 estorder namely the terms rm versa, while the second term is a pure mass term for the vector field orderIn to keep gauge invariance both terms are necessary. Previous attempts had had only the second term. a FeynmanIn diagram language the relevant terms to the photon propagator are firstThe term comes from the first one theexpression in above, where the long Nambu the of propagator the to the field as < as field the to diagram, while the second diagram comes from the second term, ie. from a new mass an interaction. like treated is the vacuum expectation value o This expression is gauge invariant and shows that the vector field has acquired a mass of the Englert and Brout The firstThe term a is coupling where a vector field goes over to the Nambu where In a paperIn submitted on June 26 The BEH models. specific in problem the studied

is orthogonal to orthogonal is like Goldstone had done and used the results from Goldstone, Abdus Salam and Weinberg that that and Weinberg Salam Abdus Goldstone, from results and the done used had Goldstone like the other field component The solution of to the a The having relativisticproblem particle and hence a force short with came range in the summer of 1964, first a paper in by Higgs. Peter by papers two in later month a and and Brout Robert Englert François Hamiltonian complete the specify not They did scalar electrodynamics. i.e. field, scalar complex in wrote they the which scalar the and field vector the on involving both terms concentrated but the fo They did not further comment on this particle but concentrated on the two the on concentrated but particle this comment on further did not They it to contributions new two are now there that Hamiltonian the from clear is It field. vector the to low

PoS(CORFU2014)138 ) 26 (

9

, , 2 𝜑𝜑 ould where 0, potential potential He could could He

= . 1 𝜈𝜈

𝜑𝜑 𝐴𝐴 ∆

𝜈𝜈 𝑛𝑛

, , with the scalars 𝜇𝜇 𝜕𝜕 vanishing vacuum

- 𝜇𝜇

Abelian gauge theory 𝑛𝑛 -

, − 𝜇𝜇 Goldstone mode is there 𝐵𝐵 𝜇𝜇 -

𝐴𝐴 𝜈𝜈

𝜕𝜕 𝜇𝜇

al massless scalars. dstone mode

two non 𝜕𝜕

−

0, 𝜈𝜈 Gol Nambu - 𝐵𝐵

0, = Introducing the specific 𝜇𝜇 𝜇𝜇 derived an explicit explicit an derived Higgs that fact e 𝜕𝜕 =

𝐵𝐵 having 2 𝜇𝜇

= 𝜑𝜑 𝜕𝜕

∆

𝜇𝜇𝜇𝜇

]

𝐺𝐺 particle.

)

2

0 abelian case, namelyabelian SU(3) case,

0,

-

𝜑𝜑

(

=

′′ , 1 𝜇𝜇 𝑉𝑉

𝜑𝜑 𝐵𝐵 2

∆ 0 2

) 𝜇𝜇 0 𝜕𝜕 4𝜑𝜑 1 𝜑𝜑

htforward to see Feynman using diagrams. − 𝑒𝑒 − ) ( 𝜇𝜇 0 𝜕𝜕 + 𝜑𝜑

appears. He then showed how one gets in this case the 𝑒𝑒 𝜇𝜇

Goldstone’s theorem can be violated. theorem can howbe Goldstone’s relativistic treatment superconductivity. of treatment relativistic ( µ 𝜇𝜇𝜇𝜇 here is a is there case Gilbert’s that out where pointed [37] Higgs Peter 𝜕𝜕 -

[ , 𝐺𝐺 . He then studied the equations of motion for small oscillations oscillations small for motion of equations the studied then He .

− 0 𝜈𝜈 𝜇𝜇 𝜕𝜕 𝜑𝜑

𝐴𝐴

=

= which is straig

> , 𝜇𝜇 linear terms. He then pointed out that the remaining scalar field 𝐵𝐵 2 𝜑𝜑 bare massbare the of scalar hasparticle led to the name “Higgs asparticle”, but we < e the and could conclude that also in this case the mechanism works, ie. via spontaneous breaking of case this also the that mechanism could ie. conclude of in and works, spontaneousvia breaking gauge symmetry one and the gets vector physic massive no particles concluded mechanism also showing the that is They a condensate by used towhen works break symmetry as in Nambu’sthe non but it gets absorbed into the third component of a massive vector field. A key was to use use to was A key field. vector a of massive component third the into absorbed gets it but diagram result The given techniques. Feynman to was argued order they first but w it that toorders all through go a non for problem same the studied Brout and Englert analysis this After July 27 submitted on a paper In where he used a gauge transformation to absorb the Nambu

criticism does not apply, namely in a gauge theory. For such a theory one must choose a gauge a gauge choose must For one theory. a theory such a gauge namely in does not apply, criticism one the a typical Coulomband is gauge as can which be written formabove. The Goldstone theorem holds in the sense that the

precisely the constant vector n vector constant the precisely around vacuum this and introduced a new variable satisfies the of equation satisfies motion then readthen off equations the of motion as which he correctly interpreted as the gauge invariant equations of motion for a massive vector that clear could was but be it it analysis linear The was atlevel the particle. performed augmented non with - shows thewhich mass bare remaining scalar the of used Goldstone by one gets the mass he got for the field. Th expression for seenhave the particle also is a consequence of the mechanism of Englert and Brout. non the to generalization the sketched also Higgs expressions of Klein and Lee, and and Englert model as same the Higgs [38] 31 studied August on submitted paper second a In and and with Englert Goldstone in field comparison scalar the on indices (Heswitched Brout. and Brout Englert Like did andBrout.) it the completely not called scalar he V potential specify assumedbut that it was that such the symmetry is spontaneously broken by a vacuum valu expectation forming an octet. He pointed out the possibility of the out an He octet. possibility pointed forming

PoS(CORFU2014)138 ) 26 ( 10

- a 0

for

= 3

𝐼𝐼

theoretic ator for a - ive vector very importantvery and isospin

0 known. It came to be be to came It known.

= the authors behind the the behind authors the

, 𝑌𝑌 hough that this paper was physicists there at the time

just like the propag the like just ut and Englert together with with together Englert and ut

2 Hagen and T.W.B. Kibble [40] 𝑞𝑞

. Bro

𝜈𝜈 erturbation theory using a Bethe 2 𝑞𝑞 2

𝜇𝜇 𝑚𝑚 .

𝑚𝑚 𝑞𝑞

𝜈𝜈

𝑞𝑞 2 2 −

− 𝑞𝑞 𝜇𝜇 2 𝑚𝑚 𝑞𝑞

𝑞𝑞 𝜇𝜇𝜇𝜇

𝑔𝑔 − −

2 n the West. They set up a field sighted sentence, where he pointed out that if if that out pointed he where sighted sentence, = 𝑞𝑞 𝜇𝜇𝜇𝜇 -

) 𝑔𝑔

𝑞𝑞 (

= Goldstone mode only interacts with virtual particles particles virtual with interacts only mode Goldstone s. ) 𝜇𝜇𝜇𝜇 - 𝑞𝑞 Δ (

𝜇𝜇𝜇𝜇 the propagator goes like like 1/ goes propagator the , Δ

∞ → 𝜇𝜇 ability that to come. was ability

with a scalar bound state and computed in a in computed abelian and state gauge bound scalar theory a with - these papers. They showed carefully and in detail how Goldstone’s theorem is

d for a non 9]. They had to struggle for about a year to get permission to get about year a for to struggle had They to9]. submit their paper to year old undergraduates, Alexander Migdal and Alexander Polyakov, who found a Polyakov, who found Alexander and Migdal Alexander old undergraduates, year - ation values which be chosenmay to be the two hypercharge quite isolated but Nambu’s, but isolated quite Schwinger’s and Goldstone’s work was

F. Thiry [41] pointed out that the propagator for the massive vector particle has the form has the particle vector massive the for propagator the that out pointed [41] F. Thiry massless vectormassless particle. For a massive vector anwith particle explicit breaking of the gauge like looks the propagator symmetry with much worse divergence properties in the UV limit. This result would be In the ultraviolet limit when 𝑞𝑞 Even though there was little excitement about the papers at the time the at papers the about excitement little was there though Even the proof the of renormalis the expect

members of the octet. He concluded with a far a with He concluded octet. the of members mechanism did continue to on it. work a paperIn from 1966 It is clear in retrospect that now all was there to construct a viable unified model for the the for model unified viable a construct to there was all that now retrospect in clear is It electroweak theory but it should take some further time. there is a mechanism for the weak interactions of this kind it could lead to mass to lead could it this of kind interactions weak for the a mechanism is there while can the massless.photon particles remain Further contributions theoremGoldstone’s was also discussed in the Soviet Union. The were M. two 19 two [3 solution journal, since the leading scientists of the time in the Soviet Union did not support their work. their support not did Union Soviet the in time the of scientists leading the since journal, The paper could submitted finally be in November ofclear 1965. It is t completely independent of the development i spontaneously broken version of the model to orders all in p the model of version broken spontaneously framework Nambu that the find to equation Salpeter and therefore is unobservable. Their paper was hence an independent confirmation of the Brout’s and Englert’s of second mechanism In a paper submitted on October 12, 1964, G.S. Guralnik, C.R discussed whatdiscussed essentiallywas same the model as the one by Englert and Brout byand Higgs. They also cite violated and reached the same as the reached and conclusions the violated previous authors.

PoS(CORFU2014)138 ) 26 ( 11

for

now e the The result unity break only

. particles. He particles.

abelian gaugeabelian 0 tially the same same the tially ad done done ad much Z 1999)

. the In next few years merical predictions merical and the

- abelian case more in detail ,W - + able such theory with massive of the vector particle. This is in

Prize to both, Prize point couplings to couplings point produc 2 - ld. This This done ld. dividingwas by the

transform differently. this In way ,

) renormalisable Nobel

for W the

⋯

.

2 + renormalis . The model was a remarkably attractive model attractive a remarkably .was The ) ′ 0 0 .

𝜑𝜑 asses 𝜑𝜑 𝜑𝜑 2

2 𝜑𝜑 is in fact stressed that it would to that possible be stressed

+ + ′ 𝜇𝜇 point coupling. point ability and the Standard Model Glashow and Salam and Ward h Abdus Salam [45] presented essen

- ry

𝐴𝐴 𝜑𝜑 . . 1

( (

𝜇𝜇

𝜇𝜇 𝜇𝜇 𝐴𝐴 like proportional to the m to the proportional 𝐴𝐴 𝐴𝐴

𝜇𝜇 𝜇𝜇 𝐴𝐴 𝐴𝐴

2 𝑚𝑚 possibility to have a the as in the work of Goldstone. Then the coupling looks like the coupling Then Goldstone. of the work in as l parts and having the two having and parts l parts SU(2) x U(1) ′ abelian gauge theo - 𝜑𝜑 mechanism to provide m - pendence of thethree

a bit early for the physics community. There was a general mistrust in in community. physics mistrust a general There the was for a bit early lert an Hed Brout. finally is a constantis number. expanding By the square and normalizing correctly the

0 Salam Model, Renormalis - 𝜑𝜑 uld stay By massless. introducing masses this way Weinberg that could show the

into their chira

used the BEH masses to leptons by coupling them to to coupling the leptonsmasses by scalar fie

icle from the vector particle are d point coupling where a fermion emits a scalar particle is proportional to the mass, fermion is scalar a proportional emits coupling fermion where particle a point - Weinberg expression will look like look will expression Introduce the shifted field field shifted the Introduce earlier andearlier

which shows the mass de Remember that Higgs also published a longer version of of results also a longer version he scattering his in [42], studied Higgs where 1966 published the three that result He out important the pointed processes.

lepton fields lepton proposal but came also came but proposal quantum field theory and in fact easy to see. coupling the tofactConsider easy see. original introduce co neutrinos the on later important become to was which fact a later year a half Symposium about Nobel a in model three a subgroup the of gauge andgroup theories have bothwith massive and massless vector Also Higgs discussed his second had particles. in that paper. The 1967In Steven Weinberg [44] finally tied the pieces together. He set up a non- the on based theory group Also Kibble came back to the problem in a paper in 1967 [43] where he showed carefully how the and non also the discussed gauge invariant he indeed results are than in the work of Eng scalar part vector particles. vector The breakthrough came in 1971 Gerhard when ‘t Hooft presented [46] first his proof that a non broken spontaneously he completedhe s proof the full Veltman Martinu with [47] ( gauge all works of for Veltman ‘t and Hooft proof theory. The electroweak the on focused came as a bomb. Finally one had a theory that could give precise nu precise give could that a theory had one Finally as a bomb. came comm physics particle the of attention the of most and processes scattering various

PoS(CORFU2014)138 ) 26 ( 12

is

to the the to

thanks tothanks started at started at

Mann [57] - n QED the er SU(2) x U(1) ). This model has abelian gauge theory Salam model. (Nobel pened and Gross and - -

very attractive one. We one. attractive very

a ed on the gauge symmetry like constituents with the like constituents gauge group

bas

zero when the energy goes to , he last remaining piece has been was ons This came to calledbe Quantum . . born suggested

have this property. (Nobel Prize ly rks in a triplet in rks representation interacting d remarkable scaling properties the in been

ber. 1967 In new experiments were particles [48] thewith masses predicted from

0 1984) slybroken, which of the two mechanisms that

, or strong the interacti but with quarks with integer charges. Before that the one with a fundamental particle or the one with and the Z the and

e coupling constante goes to - - quantum num quantum

,W (Nobel Prize to Jerome Friedman, Henry Kendall and Richard

+ rified with exquisite precision. T abelian gauge theories could - . . The possibility of having qua , with the symmetry spontaneously to SU(3) symmetry broken the with x, U(1 Now the road fora theory for the strong interactions was o

. is chosen by Nature. new a to look particle, for been scalar choice has favourite The

, 1990). The experimental results also showe

2004) ,

, site is true. However in 1973 David Gross and Frank Wilczek [54] and David Politzer [55]

the correct one. The Nobel Prizeto Glashow, Abdus Salam and Weinbergwas given in 1979. The experimental discovery of the W theories and many gauge groups would give the same results to leading order in the in order to leading results the same give would groups many gauge and theories perturbation expansions. Since the effective weak coupling is very small of years some took it original the that settle to indeed experiments dedicated

the model came 1983in further strengthening the belief thein Weinberg Prize to Carlo andRubbia Simon van der Meer The idea of having a gauge also f a gauge having theory of idea The have seen how Yang and Mills and Schwinger but also Englert, Brout, Higgs, Migdal and Brout, Higgs, Migdal and also seen Englert, how Schwinger and but Yang Mills have had such Polyakov had second Inideas. of the half the it that 1960’s clear became a theory such Han 1965 Nambu and the quarks. [49] suggestedIn a non involve should based on the gauge group SU(3) be can should which quarks that parastatistics had satisfy Greenberg [50] suggested O.W. interpreted as they if have an SU(3) quantum of numbers quantum quarks [51] to was now [52]. idea Bjorken The James theoretical of results earlier limit proving asymptotic argued [53] Symanzik Kurt 1970 and in scaling, include could a theory physical how understand that only theories where the effectiv infinity could have this property. The theory should be “asymptotically free”. Few believed that that was i It known this could property. have field theory quantum ordinary an oppo non indeed that reported Taylor ering ering scatt processes. inelastic The deeply in protons off scattered were electrons where SLAC, - point from if scattered the as photons be could interpreted results three Wilczek [56] suggested that the correct theory was a theory with an SU(3) colour gauge group an with theory a was theory correct that the suggested [56] Wilczek with quarks the in triplet representation (“three colours”) (QCD) ChromoDynamics and Gell Fritzsch Harald by before year the discussed had been particle vector a with models. all to attempt catalogue possible an in (SM) Physics for Particle had Model now Standard The to show how the symmetry the spontaneou was how to show suggested had Brout and Englert SU(3) x SU(2) x U(1) the lastin thirty years been ve composite answ the know now We settled. be question this could found was one until not but an unprecedented effort by thousands of experimental particle physicists. particle experimental of by thousands effort unprecedented an

PoS(CORFU2014)138 ) 26 ( 13

his The

for the coupling - rland 1984, in . It is given by owerful particle . Unfortunately,. The discovery had . . ], and the specialised particle is too- smallis electro the

H ng theng beams around the irmation of the validity of t Which of these two had Nature Nature two of had these Which

. as the correct gauge symmetry 2

bendi is too large the self too Higgs large is /c

would be much larger than 1 TeV much be larger would H

U(1) H × GeV The vacuumThe expectation value v

, ) . 𝑣𝑣 246

] in addition to hundreds of beam focusing focusing of beam hundreds to addition in

SU(2) 𝜆𝜆 2

≈ (Note a that slightly different normalisation is he ultimatehe conf

29 . . � – 2

H

/ : : 1

= F − and t )

𝐻𝐻 G

𝐹𝐹 ome is studied by (at the moment) seven experiments: e Planck scale. This the is scale where the SM breaks 58], CMS [59] and ALICE [60 𝑚𝑚

𝐺𝐺

]. 2 1 √ ( , excluding other speculations. Aremained, puzzle speculations. other , excluding however:

= below th below

new field would be a new fundamental particle, now commonly a commonly would field new fundamental now be particle, new the experimental discovery of this new

𝑣𝑣

Λ a

–

The LHC protons accelerating is to of capable energies of 7 TeV.

particle is, on the other hand, fixed within the Standard Model by the conducting 8.3T dipole magnets, magnets, dipole 8.3T conducting stable the and Higgs potential ahas second (global) minimum to which effect order in to spontaneously break the gauge symmetry to U(1). As we - - weak segment and MoEDAL [6 era dates back to two workshops, which took place in Switze in took place which two to workshops, dates back era - - mined constantFermi Higgs (BEH) theory does not predict the mass of the particle the of mass the not predict does theory Higgs (BEH) coupling parameter, notis predicted the by theory but must determinedbe - - by a precise measurement of m

self 1232 super

the SM as the correct theory with theory correct the as SM the purpose complexes ATLAS [ -

Englert – -

, the is unknown, the unknown, mass is Higgs cannot the of boson a lower upper be predicted but an and

λ λ generating mechanism the original paper by Goldstone [ Goldstone by paper than original in the

Brout

LHC the of start The circumference of the LHC. atcollide four ions and as lead to such protons of heavy beams circulating allows design LHC the points outc where collision interaction the general LHCb, TOTEM, LHCf gauge field of the Higgs experimentally deter

Since (or Higgs for (or short), Higgs boson Higgs the called where The physical manifestation of divergesat some energy scale mental Hunt for the Higgs Boson The Higgs Experi the Hunt for mental LargeThe Hadron Collider (LHC) at CERN is at thepresent most world’s p has It accelerator. been in thebuilt 27 longkm tunnel that housed (thepreviously LEP Large incorporates and Collider) Positron Electron yearthe following the discovery of the weak force carriers W and Z established

magnets the Universe will eventually repair. If, on the other hand, m weak vacuum is meta used bound can be determined indirectly from theoretical arguments. If m experimentally describing its its electro describing - mass the down and new physics must enter. Furthermore, if m The SM uses the BEH seenhave before there are two different ways to implement this. chosen? chosen? [62]

PoS(CORFU2014)138 ) 26 ( 14

, is 0 or a 𝐻𝐻 ) ) at the the at

− → 𝑒𝑒

+ − 1993). His 𝑒𝑒 𝑒𝑒 then

– + or . 40 TeV). 40. This

+ a machine with

− 𝑒𝑒

𝜇𝜇

+

𝜇𝜇 mass energy close to - of positron collider had yet collider had positron -

].

elected to aim for

the U.S., Japan, Canada, India and

0 lepton pair (like C. Llewellyn Smith, Llewellyn andC. finally was - 𝐻𝐻

+ a year before before started a year LHC runs. physics energy electron-

g ∗ anti Rubbia, Director General of of during General CERN Director Rubbia, - 𝑍𝑍

→

2009; . 0 𝑍𝑍 mentioned further [63 known technology used most recently most used technology known in competition – strahlun

- irector for Future Accelerators (1990 (1990 Accelerators for Future irector → unity an accelerator to achieve beam energies the in TeV , which operated at a centre a at operated which , − 1 𝑒𝑒 ing + + positron collider like LEP, i.e. the reaction - 𝑒𝑒 exceed called Higgs called omponents of colliding beams) are proportional to fermion the are proportional of beams) colliding omponents - 𝑊𝑊 ) decaying into a lepton a into decaying ) 1993, and by successor by and his 1993, +

Super Collider (SSC) project was eventually discontinued in 1993 due due 1993 in discontinued eventually (SSC) project was Collider Super . The reaction cross section for this process involves the triple boson the triple involves forprocess this section cross reaction The .

Z* – LAS and CMS. In the addition to addition the In LAS CMS. and � 𝑊𝑊 𝑞𝑞 𝑞𝑞 the commissioning of SLC, LEP and the Tevatron were only sensitive to → and the predicted Yukawa couplings to the fundamental fermions (quarks fermions fundamental the to couplings Yukawa predicted the and 𝑊𝑊

its attention to the LHC project and to the two two the to and project LHC the to USA Since has turned attention then its boson ( boson was supported not only by CERN member states. In 1997, USA agreed to to USA agreed 1997, In states. CERN member by only not supported was + earches at LEP and the Tevatron s

conducting 1989 and hence Associate D Associate and 1989 hence 𝑊𝑊

and at the Tevatron in the USA. No high- –

quark pair, - Super particle anti - well on relying collider, hadron a was

mass, was was the soinstead mass, -

rchers engage in AT 0 ia also made significant contributions, making the LHC a world project. world a the LHC making contributions, significant made also ia 𝑍𝑍

called called - theoretically allowed the at reasons: least two for challenging are searches Higgs Experimental range mass large is and leptons the essential leptons and i.e. c mass and hence small (except perhaps for the top quark). For this reason, the probability for for the reason, probability For this top the for quark). perhaps (except small hence and mass an at electron detection Higgs direct

LHC projectThe 1700 than more Today, experiments. and the machine $ the to M 531 contributing participate, resea range “unitarity” would threatened be with, for instance, the (perturbatively determined) probability for the process 1984,In the only realistic alternative for Higgs Higgs searches prior to Higgs masses below a few andGeV not be will with the virtual Z- tiny. The most important process at LEP process important most The tiny. the quark successor, L. Evans, was responsible for the LHC project during the critical construction and and construction critical the during project the LHC for responsible was Evans, L. successor, commissioning phase. S. Meyers followed him in CERN Russ an energy reach at least twice that achievable the in planned LHC/LEP tunnel (i.e so been been built and those the in planning stage aimed at energies on the order 0.1 TeV. So, while – U.S. the LHC, the for go to decided Europe

to escalating costs. to escalating them. to massively contributed and and CMS ATLAS collaborations enthusiastically was supported by project LHC The 1989 period critical the approved CERNby Council 1994. in The accelerator design based on superconducting magnet CERN for Director Technical Brianti, G. of leadership the out under worked was technology 1981 during

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t of for of deviations Summary fits 7: Figure the ratios of the measured couplings to SM predictions expected to reflect such deviations as as such deviations reflect to expected SM to predictions of couplings measured the ratios the exist. may

that data is consistent with the SM expectation 0 expectation SM the with consistent is data that if there is no deviation from SM from deviation no is there if (twiki.cern.ch/twiki/bin/view/CMSPublic/Hig13005Twiki#Test_of_Fermion_and_Vector_B oson) the to analyses precisely Higgs determine results spin, from Updated aiming more its boson at confer reported continuously, and are its couplings properties production to manuscripts Physics two collaboration submitted ATLAS the year, In July this publications. Letters [75, B 79] of about 25 fb luminosity channels high confidence. Fig. 8 (logarithm of the ratio of likelihoods) used to distinguish between the two two 0 hypotheses the between to distinguish used likelihoods) of ratio the of (logarithm whereas in the updated updated is favouredis over J

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– and scalar new particles. someIn of these theories,

- + symmetric 0 unless “unnatural” cancellations occur. Therefore,

these models see [62]. all tone for particle physics and a tremendous success for the the for tremendous a success and physics tone for particle eaking can be achieved without introducing fundamental fundamental introducing without achieved can be eaking ld mimic the Higgs. In addition symmetry br

precisely measure the Higgs boson self

For a discussion a For of

to wait for the presently discussed High Luminosity LHC (HL LHC Luminosity discussed High forpresently the to wait .

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- H the existence of five Higgs bosons, three neutral and two charged. The lightest of lightest The two charged. and three neutral Higgs bosons, five of existence the [79 Theorists believe that the SM that the a most is but probably low believe Theorists . . The lightest scalar in these models alsoresembles the SM Higgs. yetIn o m

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) accordance with SM expectations with accordance (fig. 1). Super minimal form to the SM similar couplings should Higgs have neutrals the collaboration

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extensions of the SM are proposed, keeping the successful features of the SM but at the same time introducing “new physics” in a way, which stabilises m alternative is “Little Higgs” models where new strong interactions are introduced at the scal the are at introduced new interactions where strong Higgs” models is “Little alternative tens Outlook are particle discovered newly the of that properties the confirm date to measurements All - BEH the by predicted boson scalar fundamental the for expected those with consistent mechanism. The discovery is a miles Standard Model. However, far from closing the book it opens a number of new exciting possibilities: scalar fields but with composite scalar or pseudo scalar composite or with but scalar fields models more complete theory. this If tonotwere so, the corrections quantum Higgs mechanical mass drive would Higgs extra space dimensions beyond the standard 3+1 spacetime standard 3+1 the beyond dimensions space extra of addition a composite light scalar cou light a composite To discriminate between these theories one would particles particles measurem challengingbe even then since the Higgs pair production cross section is small

PoS(CORFU2014)138 ) 26 ( 23

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