Science & Technology

My Deep Research About Higgs’ Boson

What is the Higgs boson?

It is an elementary and indivisible particle that, for now, only exists in theory. It was described in 1964 by three groups of physicists, including the British Peter Higgs, who gave it its name.

Why should it exist?

The Higgs boson is the last particle that remains to be discovered to confirm the standard model, which classifies the types of indivisible particles that exist in the universe into two: fermions and bosons. The former are minimum units that, when joined together, form the protons, neutrons and electrons of an atom. Bosons, in turn, transmit forces that hold matter together. For now, the 16 particles that make up the standard model have been observed. All, except two types of bosons, have mass although it is not known why. Particle number 17, the Higgs boson, is the alleged responsible.

How does the boson work?

The origin of the mass of the particles is not due to the boson, but to the associated field. When the different particles pass through it, it offers each resistance. A quark finds more resistance than an electron, for example, because it interacts more with the Higgs field. To find the Higgs boson is to prove that the associated field exists. This would explain how elementary particles obtained their mass fractions of a second after the Big Bang, which in turn allowed them to compose a universe with matter, planets and life.

When will it meet?

Maybe never. The LHC is the only machine that can find it. His method is to collide hadrons. These subatomic particles are composed of quarks, elementary particles described in the standard model. The hadrons join together to form protons and the LHC shoots them at almost the speed of light to generate miniature big bangs. Other elementary particles arise from these impacts. The vast majority has already been discovered and its properties fit perfectly with what was predicted in the standard model. By the end of 2020 the LHC will have accumulated some 1,000 billion collisions. Among all of them there will be a few that will allow us to say whether the higgs exist or not. It will be the beginning of a new challenge, since it will be necessary to find out if the properties of this new particle are what are expected of it.

Why is it called ‘god particle’?

If there is an issue that causes more interest than the Higgs boson is his nickname. It is due to Leon Lederman’s informative book The God particle: if the universe is the question, what is the answer? Higgs himself explained that Lederman is not to blame for the nickname, which outrages many scientists and fans for their religious connotations. Lederman wanted to call it the damn particle (goddamn ‘, in English), something his editor didn’t like, which shortened the term to’ god ‘.

The Higgs boson is a massive hypothetical elementary particle whose existence is predicted by the standard model of particle physics. It plays an important role in explaining the origin of the mass of other elementary particles, in particular the difference between the photon (without mass) and the bosons W and Z (relatively heavy). Elemental particles with mass and the difference between electromagnetic interaction (caused by photons) and weak force (caused by bosons W and Z) are critical in many aspects of the microscopic (and thus macroscopic) structure of matter. With this, if the particle exists, the Higgs boson would have a huge effect on physics and the world today.

To date, the accumulation of the empirical data analyzed and published is insufficient to fully confirm the existence of the Higgs boson. Although it is the only elementary particle of the standard model that has not been experimentally observed so far, on December 13, 2011 the European Center for Nuclear Research (thanks to experiments in the Large Hadron Collider) has delimited the region in the which would be located as well as the quantification of its mass at approximately 126 Gigaelectrovolts (GeV), noting that the data is insufficient to claim the discovery of the particle.

The Higgs mechanism, which gives mass to the boson vector, was theoretically raised in 1964 by Peter Higgs, François Englert and Robert Brout (who worked on the ideas of Philip Anderson), and independently by GS Guralnik, CR Hagen and TWB Kibble. Higgs – in a comment added to a letter addressed to the Physical Review – proposed that the existence of a massive scalar particle could be a proof of theory. Steven Weinberg and Abdus Salam were the first to apply the Higgs mechanism to the spontaneous rupture of electrodevil symmetry. The electroweak theory predicts a neutral particle whose mass is not very far from that of bosons W and Z.

APS JJ Sakurai Award – Kibble, Guralnik, Hagen, Englert, Brout.

Theoretical overview

The particle called the Higgs boson is a quantum of one of the components of the Higgs field. In an empty space, the Higgs field acquires an expected value of vacuum (VEV) other than zero that remains constant over time and everywhere in the universe. The VEV of a Higgs field is constant and equal to 246 GeV. The existence of a non-zero VEV is of fundamental importance: it gives a mass to each elementary particle, including the same Higgs boson. In particular, the spontaneous acquisition of a non-zero VEV breaks the electroweak Gaugian symmetry, a phenomenon known as the Higgs mechanism. This is the simple mechanism capable of giving mass to a gauge boson that is also compatible with gauge field theory.

In the standard model, a Higgs field consists of two neutral and two charged fields. The two charged components and one of the neutral are Goldstone bosons, which have no mass and become, respectively, the third polarization longitudinal components of the W and Z (massive) bosons. The quantum of the remaining neutral components corresponds to the massive Higgs bosons. A Higgs field is a scalar field, the Higgs boson has a zero spin and has no intrinsic angular momentum. The Higgs boson is also its own antiparticle and has CPT symmetry.

The standard model does not predict the mass value of the Higgs boson. If the mass of this boson is between 115 and 180 GeV, then the standard model can be valid at all energy scales up to the Planck scale (1016TeV). Many theories are waiting for a new physics beyond the standard model that could arise at TeV scales, based on the shortcomings of the standard model. The highest possible mass scale allowed in the Higgs boson (or in some spontaneous rupture of electrodevil symmetry) is one TeV; after that point the standard model becomes inconsistent without such a mechanism because the uniqueness is violated in certain dispersal processes. Many scientific theory models predict that the Higgs particle can have a mass solely slightly on top of this experimental limits, at concerning a hundred and twenty GeV or less.

Experimental research

To date, the Higgs boson has not been experimentally observed, despite the efforts of large research laboratories such as CERN or Fermilab. The non-observation of clear evidence allows an experimental minimum mass value of 114.4 GeV to be estimated for the Higgs boson of the standard model, with a 95% confidence level.[6] Experimentally, a small number of inconclusive events have been recorded in the LEP collider at CERN. These have been interpreted as results of the Higgs bosons, but the evidence is inconclusive.[7] It is expected that the Large Hadron Collider, already built-in CERN, can confirm or deny the existence of this boson. The 27 km circumference ring (called Large Hadron Collider) was lit on September 10,2008, as planned, but a failure in the cooling system that must keep the magnets at an approximate temperature of -271.3° C stopped the experiment, until November 20, 2009, when it was turned on again, from 450 GeV to 2.23 TeV . But it was turned off to make adjustments, and on March 30 it was turned on again, although at a power of 7 TeV. Of course, it will not be until 2016 when it works at full capacity.

The search for the Higgs boson is also the objective of certain experiments of the Tevatron in Fermilab

Alternatives to the Higgs mechanism for the spontaneous rupture of electrodevil symmetry

Since the years in which the Higgs boson was proposed, there have been many alternative mechanisms. All other alternatives use a dynamics that interacts strongly to produce an expected value of the vacuum that breaks the electroweak symmetry. A partial list of these alternative mechanisms is:

Technicolor is the kind of model that tries to mimic the dynamics of strong force as a way to break the electrodevil symmetry.

The Abbott-Farhi model of composition of the vector bosons W and Z.

Higgs Field

The Higgs Field is a quantum field, which, according to a hypothesis of the standard model of particle physics exposed by physicist Peter Higgs, would permeate the entire universe, and whose effect would be that the particles behave as endowed with mass, due to to the associated interaction of elementary particles, with the Higgs boson, whose existence has not yet been directly tested and that by interaction with itself would also “acquire” mass. The Large Hadron Collider is expected to test the Higgs hypothesis.

Higgs mechanism

The Higgs mechanism, devised by Peter Higgs among others, is one of the possible mechanisms to produce the spontaneous rupture of electroweak symmetry in an invariant Gauge Theory. It allowed to establish, the unification between the electromagnetic theory and the weak nuclear theory, which was called Unified Field Theory giving Nobel Prize in 1979 to Steven Weinberg, Sheldon Lee Glashow and Abdus Salam

This mechanism is also known as the Brout – Englert – Higgs mechanism, Higgs – Brout – Englert – Guralnik – Hagen – Kibble mechanism, or Anderson – Higgs mechanism. In 1964, it was initially proposed by Robert Brout and François Englert, and independently by Peter Higgs and Gerald Guralnik, CR Hagen, and Tom Kibble. It was inspired by the BCS Theory of Superconductivity Symmetry Breaking based on the Ginzburg-Landau Theory, the works of the structure of the void of Yoichiro Nambu, and the ideas of Philip Anderson according to which superconductivity could be relevant in relativity, electromagnetism and other classical phenomena. The mechanism name of Higgs was given by Gerardus’ t Hooft in 1971. The three original articles of Guralnik, Hagen, Kibble, Higgs, Brout,

Fields and particles

The second half of the 20th century was a time of discovery of new elementary particles, new forces and, above all, new fields. The space can be filled with a wide variety of invisible influences that have all kinds of effects on ordinary matter. Of all the new fields that were discovered, the one that has more to teach us about the landscape is the Higgs field. There is a general relationship between particles and fields. For each type of nature particle there is a field and for each type of field there is a particle. Thus fields and particles bear the same name. The electromagnetic field could be called photon field. The electron has a field, so do the quark, the gluon and each member of the cast of characters of the Standard model, including the Higgs particle.

The Higgs Field

In the conception of the Standard Model of particle physics, the Higgs boson as well as other bosons (already found experimentally) and linked in this theory, are interpreted from the Goldstone Boson where each part of the symmetry break generates a field, for the which elements that live in this field are their respective bosons. There are theories created from the fear of the non-existence of the Higgs boson where its appearance is not necessary. The Higgs field is the mathematical entity where it exists, its interpretation with the theory is the product of it with the other fields that comes out of the mechanism of rupture, this product gives us the coupling and interaction of it, with this interaction with the other fields let the characteristic of mass generator.

Mathematical formulation

We introduce an additional field? that breaks the symmetry SU (2) L × U (1) Y? U (1) em. Due to the conditions required by the theory, it will be a double (of SU (2) L) of complex scalar fields (Higgs double):

\ Phi (x) = {\ left (\ begin {matrix} \ phi ^ + \\ \ phi ^ 0 \ end {matrix} \ right)} = \ frac {1} {\ sqrt {2}} {\ left (\ begin {matrix} \ phi_1 + \ mathrm {i} \ phi_2 \\ \ phi_3 + \ mathrm {i} \ phi_4 \ end {matrix} \ right)}

 Higgs doublets


The total number of inputs (dimensional number of the vector) of Higgs is not determined by theory and could be any. However, the minimum version of the SM has only one of these doublets.

The system will then be described by a Lagrangian of the form:

\ mathcal {L} _ {SBS} = (\ mathcal {D} _ \ mu \ Phi) ^ {\ dagger} (\ mathcal {D} ^ \ mu \ Phi) - V (\ Phi)

such that:

V (\ Phi) = \ mu ^ 2 \ Phi ^ {\ dagger} \ Phi - \ lambda (\ Phi ^ {\ dagger} \ Phi) ^ 2

where V (phi) is the renormalizable potential (and therefore that maintains the gauge invariance) easier. For spontaneous symmetry rupture to occur, it is necessary that the expected value of the Higgs field in a vacuum be non-zero. For lambda greater than 0, if mu 2  less than 0, the potential has infinite non-zero solutions (see figure 1), in which only the Higgs field norm is defined:

| \ Phi | ^ 2 = \ Phi ^ {\ dagger} \ Phi = - \ frac {\ mu ^ 2} {2 \ lambda} = \ frac {\ upsilon ^ 2} {2}

Fundamental state

The ground state is therefore degenerate and does not respect the symmetry of SU (2) L  × U (1) Y . However, it does retain the symmetry of the group U (1) em . The cup value? Indicates the scale of energy at which the electroweak symmetry breaks. The rupture SU (2) L  × U (1) and  Phi U (1) em occurs when a specific vacuum state is selected. The usual choice is one that makes Phi 3 non-zero:

Particle spectrum

The resulting physical particle spectrum is constructed by making small oscillations around the vacuum, which can be parameterized in the form:

where the vector  and the scalar h (x) are small fields corresponding to the four real degrees of freedom of the field . The three fields are the null-mass Goldstone bosons, which appear when a continuous symmetry is broken by the fundamental state (Goldstone theorem).

At this point we still have 4 gauge bosons (W ? (X) and B ? (X)) and 4 scalars (  yh (x)), all without mass, which is equivalent to 12 degrees of freedom (It should be noted that a vector boson of zero mass has two degrees of freedom, while a massive vector boson acquires a new degree of freedom due to the possibility of having longitudinal polarization:12=4[vector bosons without mass]×2+[scalars without mass]). PW Higgs was the first to realize that Goldstone’s theorem is not applicable to gauge theories, or at least it can be circumvented by a convenient selection of representation. So, just choose a transformation:

so that:

\ vec {\ xi} (x)

whereby the three fields of non-physical Higgs disappear . We must apply these transformations on the sum of the Lagrangians for bosons and fermions:

\ mathcal {L} = \ mathcal {L} _ {bos.} + \ mathcal {L} {ferm.} + \ mathcal {L} _ {SBS}

At the end of the process, three of the four gauge bosons acquire mass by absorbing each of the three degrees of freedom removed from the Higgs field, thanks to the couplings between the gauge bosons and the Phi field present in the kinetic component of the Lagrangiana SBS :

(\ mathcal {D} _ \ mu \ Phi) ^ {\ dagger} (\ mathcal {D} ^ \ mu \ Phi) = \ frac {\ upsilon ^ 2} {8} [\ mathrm {g} ^ 2 ( W_ {1 \ mu} ^ 2 + W_ {2 \ mu} ^ 2) + (\ mathrm {g} W_ {3 \ mu} - \ mathrm {g} ^ \ prime B_ \ mu) ^ 2]

On the other hand, the vacuum of the theory must be electrically neutral, which is why there is no coupling between the photon and the Higgs field, h (x), so that it maintains a null mass. In the end, we get three massive gauge bosons (W ± ?, Z µ ), a gauge boson without mass (A ? ) And a scalar with mass (h), so we still have 12 degrees of freedom (in the same way as before :12=3[massive vector bosons]×3+1[vector boson without mass]×2+1[scalar]). The physical states of the gauge bosons are then expressed as a function of the original states and the angle of electrodeble mixture? W :

 \ begin {matrix} \ mathrm {W} ^ \ pm_ \ mu & = & \ frac {1} {\ sqrt {2}} (\ mathrm {W} _ \ mu ^ 1 \ mp \ mathrm {W} _ \ mu ^ 2) \ qquad \ \ \ \ \ \\ \ mathrm {Z} _ \ mu & = & \ cos {\ theta_ \ mathrm {W}} \ mathrm {W} _ \ mu ^ 3 - \ sin {\ theta_ \ mathrm {W}} \ mathrm {B} _ \ mu \\ \ mathrm {A} _ \ mu & = & \ sin {\ theta_ \ mathrm {W}} \ mathrm {W} _ \ mu ^ 3 + \ cos {\ theta_ \ mathrm {W}} \ mathrm {B} _ \ mu \ end {matrix}

Mixing angle

The mixing angle? W , is defined as a function of the weak coupling constants, g , and electromagnetic,  , according to:

\ tan {\ theta_ \ mathrm {W}} \ equiv \ frac {\ mathrm {g} ^ \ prime} {\ mathrm {g}}

The predictions of the masses of the bosons at tree level are:

 \ begin {matrix} \ mathrm {M_W} & = & \ frac {1} {2} \ mathrm {g} \ upsilon \ qquad \ \ \ \ \ \ \\ & & \\ \ mathrm {M_Z} & = & \ frac {1} {2} \ upsilon \ sqrt {\ mathrm {g} ^ 2 + {\ mathrm {g} ^ \ prime} ^ 2} \ end {matrix}

where ( e is the electric charge of the electron):

 \ begin {matrix} \ mathrm {g} & = & \ frac {e} {\ sin {\ theta_ \ mathrm {W}}} \\ \ mathrm {g} ^ \ prime & = & \ frac {e} { \ cos {\ theta_ \ mathrm {W}}} \ end {matrix}

 Higgs boson mass

The mass of the Higgs boson is expressed as a function of? and of the value of the symmetry break scale,?, such as:

\ mathrm {m_H ^ 2} = 2 \ lambda \ upsilon ^ 2

The measure of the partial width of the decay:

\ mu \ rightarrow \ nu_ \ mu \ bar {\ nu_ \ mathrm {e}} \ mathrm {e}

at low energies in the SM it allows to calculate the Fermi constant, G F , with great precision. And since:

\ upsilon = (\ sqrt {2} \ mathrm {G_F}) ^ {- \ frac {1} {2}}

you get a value of? =246 GeV. Notwithstanding the value of? it is unknown and therefore the mass of the Higgs boson in the SM is a free parameter of the theory.

 Boson gauges and fermions

Similarly to the case of gauge bosons, fermions acquire mass through so-called Yukawa couplings, which are introduced through a series of new terms in Lagrangiana:

{\ mathcal L} _ {YW} = \ lambda _ {\ mathrm {e}} \ bar {\ ell} _L \ Phi \ mathrm {e} _R + \ lambda _ {\ mathrm {u}} \ bar {\ mathrm { q}} _ L \ tilde {\ Phi} \ mathrm {u} _R + \ lambda _ {\ mathrm {d}} \ bar {\ mathrm {q}} _ L \ Phi \ mathrm {d} _R + \ mbox {hc + 2nd and 3rd families}

where:

 \ begin {matrix} \ ell_L & = & {\ left (\ begin {matrix} \ mathrm {e} \\ \ nu_ \ mathrm {e} \ end {matrix} \ right)} _ L, {\ left (\ begin {matrix} \ mu \\ \ nu_ \ mu \ end {matrix} \ right)} _ L, {\ left (\ begin {matrix} \ tau \\ \ nu_ \ tau \ end {matrix} \ right)} _ L \ \ & & \\ \ mathrm {q} _L & = & {\ left (\ begin {matrix} \ mathrm {u} \\ \ mathrm {d} \ end {matrix} \ right)} _ L, {\ left ( \ begin {matrix} \ mathrm {c} \\ \ mathrm {s} \ end {matrix} \ right)} _ L, {\ left (\ begin {matrix} \ mathrm {t} \\ \ mathrm {b} \ end {matrix} \ right)} _ L \ end {matrix}

In the same way as before, the transformation is applied to the levógira part of the fermions, while the dextrógira part is not transformed:

 \ ell'_L = U (\ xi) \ ell_L; \ qquad \ \ \ \ mathrm {e} '_ R = \ mathrm {e} _R
 \ mathrm {q} '_ L = U (\ xi) q_L; \ qquad \ \ \ \ mathrm {u}' _ R = \ mathrm {u} _R; ~ \ mathrm {d} '_ R = \ mathrm {d}

And finally the masses of the fermions are obtained according to:

 \ begin {matrix} \ mathrm {m} _ {\ mathrm {e}} & = & \ lambda_ \ mathrm {e} \ frac {\ upsilon} {\ sqrt {2}} \\ \ mathrm {m} _ { \ mathrm {u}} & = & \ lambda_ \ mathrm {u} \ frac {\ upsilon} {\ sqrt {2}} \\ \ mathrm {m} _ {\ mathrm {d}} & = & \ lambda_ \ mathrm {d} \ frac {\ upsilon} {\ sqrt {2}} \\ ... \ end {matrix}

It is convenient to note at this point that the determination of the Higgs boson mass does not directly explain the fermionic masses since they depend on the new constants? e ? u ? d ,… On the other hand, the value of the Higgs boson couplings with the different fermions and bosons is also deduced, which are proportional to the gauge coupling constants and the mass of each particle.

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