Un scalaire peut en cacher un autre

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On a déjà beaucoup parlé dans ce blog et ailleurs du boson scalaire de Higgs, on a aussi déjà évoqué l'existence hypothétique d'autres particules scalaires qui seraient étroitement associées à ce dernier et dont l'une d'elle est désignée par la lettre σ (sigma). Or il se trouve qu'il existe dans la littérature physique encore une autre particule, désignée par la même lettre et scalaire elle-aussi, mais qui n'est pas ou plus hypothétique car - nous allons le voir dans ce billet - elle a semble-t-il déjà été mise en évidence expérimentalement et cela avant même la découverte du Higgs!  On voit que la situation peut prêter à confusion pour l'intrépide curieux qui chercherait à en savoir d'avantage en parcourant la littérature scientifique. Essayons donc de démêler un peu avec le lecteur cet embrouillamini grâce à un article de Martin Schumacher sur ce sujet, intitulé : Nambu’s Nobel Prize, the σ meson and the mass of visible matter daté du 07/04/2014.

Un prix Nobel qui en rappelle un autre 

The 2013 Nobel Prize in Physics has been awarded to François Englert and Peter Higgs ”for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN’s Large Hadron Collider”. This award followed a related one where one half of the 2008 Nobel Prize in Physics was awarded to Yoichiro Nambu “for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics”. In order to understand the importance of this latter award it is very important to read the Nobel Lecture which was presented by Giovanni Jona-Lasinio, a younger coauthor of the famous Nambu–Jona-Lasinio model [3] published in 1961. This Nobel Lecture having the title “Spontaneous symmetry breaking in particle physics: A case of cross fertilization” describes the way from superconductivity to particle physics which led to the Nambu– Jona-Lasinio (NJL) Lagrangian ...  

In the standard model of particle physics, the NJL model may be regarded as an effective theory for the QCD with respect to generation of the so-called constituent masses. In analogy to different descriptions of superconductivity the NJL model goes over to the linear σ model (LσM) of Gell-Mann and Lévy [4]. In the Nobel Lecture Nambu makes the important statement: ”If this analogy turns out real, the Higgs field might be an effective description of the underlying dynamics.” This Higgs field is the Higgs field of strong interaction represented by the σ meson.

(Partir) du boson de Higgs (pour revenir) au méson sigma (σ)

An explanation of the constituent-quark mass in terms of symmetry breaking mediated by the σ meson remained uncertain as long as the σ meson had not been observed. This, however, has changed dramatically in the last years after the σ meson has been observed as part of the constituent-quark structure via Compton scattering by the nucleon. This experiment was carried out at MAMI (Mainz) and published in 2001 [5,6]. The final interpretation of the results obtained required some further theoretical studies which were published in 2010, 2011 and 2013. Through this experimental and theoretical work the σ meson is by now well investigated and the process of mass generation of constituent quarks well understood ... 

For the Higgs boson the theoretical research started with the work of Goldstone (1961 [10] and 1962 [11] ) where it was shown that spontaneous symmetry breaking leads to massless particles in addition to a heavy particle. This is not a problem for the σ meson where the light π mesons are massless in the chiral limit and have only a small mass as real particles, serving as pseudo-Goldstone bosons. For the Higgs boson these massless Goldstone bosons are strongly unwanted particles because they seem not to be present in nature. Therefore, in a number of papers scenarios were developed leading to symmetry breaking without Goldstone bosons. This essential modification is related to the introduction of massless gauge boson which swallow the Goldsone bosons and in this way generate mass and a longitudinal field component ... 

Les deux sources (essentielles) de la génération de masse des particules quantiques

Nowadays the origin of the theory of spontaneous symmetry breaking is most frequently attributed to the work of Peter Higgs ... But it was Peter Higgs himself who correctly pointed out ... that vacuum expectation values of scalar fields might play a role in breaking of symmetries was first noted by Schwinger. This means that strong and electroweak symmetry breaking both can be traced back to the seminal work of Schwinger ... and that the introduction of the σ meson inspired the electroweak sym- metry breaking, though these two processes take place at completely different scales. The interest in this interplay between the two sectors of symmetry breaking is of importance up to the present. 

Translated into present-day language Schwinger introduced a generic equation between the mass m of a particle and the vacuum expectation value of a scalar field φ₍₀₎ given in the form 

m ∝ g<φ₍₀₎>.                                                           (2)

For the purpose of the present paper we translate Eq. (2) into three related equations, viz. 

 m_l = g_Hll (1/√2) v,                                                       (3)

m⁰_q = g_Hqq (1/√2) v                                                     (4)

and

m^cl_q = g_σqq f ^cl_π .                                                        (5) 

Eqs. (3) and (4) relate the lepton and current-quark masses, respectively, to the elec- troweak vacuum expectation value v of the Higgs field and Eq. (5) the constituent quark mass in the chiral limit (cl), where the effects of the Higgs field are turned off, to the pion decay constant f ^cl_π in the chiral limit. In case of Eqs. (3) and (4) the Higgs-lepton and Higgs-quark coupling constants g_Hll and g_Hqq can be calculated from the known electroweak vacuum expectation value v = 246 GeV and the known lepton mass m_l  and current-quark mass m⁰_q, respectively. In case of Eq. (5) the pion decay constant in the chiral limit is f ^cl_π = 89.8 MeV and g_σqq = 2π/√3 = 3.62 ... 

In (3) – (5) two sources of mass are discussed, viz symmetry breaking mediated by the Higgs field (Eqs. 3 and 4) and spontaneous symmetry breaking mediated by the σ field (Eq. 5). These are the main sources of mass generation. In case of strong interaction there are in addition dynamic effects related to excited states, the interaction of spins and effects due to gluons where the latter effects show up in the form of glueballs and the UA(1) anomaly.

Un boson de Higgs probablement fondamental et un méson sigma indubitablement composite

The discovery of the electroweak Higgs boson has led to models of the vacuum where an overall Higgs field is assumed to exist. For a mass of the Higgs boson of 126 GeV this Higgs field is expected to be elementary, i.e. not composed of fermion-antifermion pairs. The reason for this conclusion is that Higgs bosons composed of t̄t pairs or techniquark- antitechniquark pairs are predicted to have higher masses. In parallel to this, for the strong-interaction counterpart an overall σ field may be assumed to exist in the QCD vacuum which is composed ūu and d̄d pairs forming the structure σ = 1/√2(ūu + d̄d). Then the generation of the mass of the constituent quarks may be understood in terms a q̄q condensate attached to the current quarks. In this condensate the q̄q pairs are ordered to form mesons, like the π meson isospin triplet and the σ meson.

Un méson de 600 MeV pour expliquer la masse des nucléons et un boson de 126 GeV pour comprendre celles de leurs composants

Telle est le résultat étonnant des expériences les plus récentes faites pour comprendre la génération des masses des particules quantiques.  

The most important recent discovery is that the largest part of the electric polarizability and the total diamagnetic polarizability of the nucleon are properties of the σ meson as part of the constituent-quark structure, as expected from the mechanism of chiral symmetry breaking. This view is supported by an experiment on Compton scattering by the proton carried out in the second resonance region, where a large contribution from the σ meson enters into the scattering amplitudes. This experiment led to a determination of the mass of the σ meson of m_σ = 600 ± 70 MeV. From the experimental α_p and predicted differences (α_n − α_p) neutron polarizabilities in the range α_n = 12.0 − 13.4 are predicted ...

Martin Schumacher, Dispersion theory of nucleon Compton scattering and polarizabilities 27/04/2013

Mésons sigma d'hier et d'aujourd'hui (sont-ils les mêmes ?)
(rédaction encore en cours)