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A Pedagogical Introduction to Electroweak Baryogenesis

Graham Albert White

Chapter 1

Introduction

The origin of the baryon asymmetry of the Universe (BAU) is one of the deepestshort-comings of our understanding of particle physics, as it cannot be explainedwithin the Standard Model. For instance, one cannot simply set the baryonasymmetry as an initial condition as this would be washed out by inflation1. Onthe other hand, coinciding estimates of the baryon asymmetry using differenttechniques are a triumph of modern cosmology. The baryon asymmetry can beestimated by the deuterium abundance and from the cosmic microwave background(CMB), where the relative sizes of Doppler peaks in the temperature anisotropy aresensitive to the BAU. These two methods give the overlapping estimates of thebaryon to entropy ratio2 [2–4]

= − ¯ ≈ =± ×

± ×± ×

−

−

−

⎧⎨⎪

⎩⎪Y

n ns

ns

(7.3 2.5) 10 , BBN

(9.2 1.1) 10 , WMAP

(8.59 0.11) 10 , Planck.

(1.1)BB B B

11

11

11

This remarkable overlap in the estimates of the BAU from light element abundances(particularly deuterium) and baryon acoustic oscillations are shown in figure 1.1 andfigure 1.2 respectively. Reproducing this estimate using particle physics makes one ofthe three pillars of the Standard Model of particle cosmology, the other two beinginflation [5] and dark matter [6]. Like inflation and dark matter, it requires at leastsome additions to the Standard Model. Furthermore, like the other two pillars of theStandard Model of particle cosmology, there are a very large variety of models toexplain this peculiar fact about our Universe. Two of the most elegant explanations

1For a recent attempted exception to this, albeit a fine-tuned one, see [1].2 Sometimes the baryon asymmetry is compared to the photon density, ≈γn n Y/ 7.04B B, rather than theentropy. However during the early Universe many particles are expected to be in thermal equilibrium makingYB more convenient.

doi:10.1088/978-1-6817-4457-5ch1 1-1 ª Morgan & Claypool Publishers 2016

are leptogenesis [9] and the Affleck–Dine mechanism [10]. Unfortunately both tendto be well out of reach of the particle colliders of today and of the foreseeable future.

The focus of this review will be electroweak baryogenesis, which is the term forany mechanism that produces the matter–antimatter asymmetry during the electro-weak phase transition. Such a scenario requires physics beyond the Standard Modelthat must couple relatively strongly to Standard Model particles and have massesthat are not too far above the weak scale. Therefore, unlike Affleck–Dine baryo-genesis or leptogenesis, electroweak baryogenesis has the tantalizing prospect ofbeing tested, at least indirectly, by weak and TeV scale searches at the large hadroncollider (LHC).

Apart from testability, electroweak baryogenesis has the attractive feature thatcoincides the breaking of the symmetry between particles and anti-particles with thespontaneous breaking of the one symmetry we know to be broken—electroweaksymmetry. Unfortunately the literature on this exciting subject is somewhat opaqueto newcomers. There are some very nice pedagogical introductions to small parts ofthe theoretical foundations of baryogenesis scattered throughout the literature if onedigs hard enough3. However, the study of baryogenesis is arguably too decoupled

Figure 1.1. The abundances predicted by the Standard Model of Big Bang nucleosynthesis (BBN) [7] for4He, D, 3He, and 7Li. Here the bands show the range for the 95% confidence level and the boxes indicatethe light element abundances—the smaller boxes show σ2.75 statistical errors; the larger boxes σ2.75 statisticaland systematic errors. The wide band indicates the BBN concordance range, whereas the vertical narrowband indicates the baryon asymmetry measured via the CMB given at the 95% confidence level. Reproducedfrom [2].

3 For recent reviews see [11–14].

A Pedagogical Introduction to Electroweak Baryogenesis

1-2

from the rest of high energy physics given its promising phenomenologicalimplications and the fundamental nature of the question it attempts to answer.Furthermore, the techniques one needs to learn to research in the field of electro-weak baryogenesis have a large cross-over with other calculations in particlecosmology—including other models of producing the baryon asymmetry such asleptogenesis.

This primer will therefore give a mostly self-contained introduction to the field ofelectroweak baryogenesis, assuming the reader has a graduate level knowledge of

Figure 1.2. Ω − ΩΛM constraints due to CMB, baryon acoustic oscillations, and Supernova CosmologyProject Union2.1 SN constraints including SN systematic errors. Reproduced from [8].

A Pedagogical Introduction to Electroweak Baryogenesis

1-3

particle physics, including dimensional regularization, some basic path integraltechniques, the computation of amplitudes at tree and loop level, the StandardModel Lagrangian, and Big Bang cosmology, as well as a rudimentary knowledge ofeffective field theory and the minimal supersymmetric Standard Model (MSSM),4

which we will use as a pedagogical tool where appropriate. There are of course manycandidates for producing the BAU, but it is my hope that the theoretical foundationsgiven in this book should make learning such mechanisms significantly moretractable.

References[1] Krnjaic G 2016 Can the baryon asymmetry arise from initial conditions? arXiv: 1606.05344[2] Eidelman S et al 2004 (Particle Data Group Collaboration) Review of Particle Physics Phys.

Lett. B 592 1[3] Spergel D N et al 2003 (WMAP Collaboration) First year wilkinson microwave anisotropy

Probe (WMAP) observations: determination of cosmological parameters Astrophys. J. Suppl.148 A16

[4] Ade P A R et al 2014 Planck 2013 results. XVI. cosmological parameters Astron. Astrophys.571 A16

[5] Bassett B A, Tsujikawa S and Wands D 2006 Inflation dynamics and reheating Rev. Mod.Phys. 78 2

[6] Feng J L 2010 Dark matter candidates from particle physics and methods of detection Annu.Rev. Astron. Astrophys. 48 495–545

[7] Cyburt R H et al 2008 An update on the big bang nucleosynthesis prediction for 7Li: theproblem worsens J. Cosmol. Astropart. Phys. JCAP11(2008)012

[8] Suzuki N et al 2012 The Hubble Space Telescope Cluster Supernova Survey. V. Improvingthe dark-energy constraints above z > 1 and building an early-type-hosted supernova sample756 85

[9] Fukugita M and Yanagida T 1986 Baryogenesis without grand unification Phys. Lett. B174 1

[10] Affleck I and Dine M 1985 A new mechanism for baryogenesis Nucl. Phys. B 249 361[11] Morrissey D E and Ramsey-Musolf M J 2010 Electroweak baryogenesis New J. Phys. 14 12[12] Cline J M 2012 Baryogenesis arXiv: 0609145(hep-ph)[13] Riotto A and Trodden M 1999 Recent progress in baryogenesis Annu. Rev. Nucl. Part.

Sci. 49 46[14] Trodden M 1999 Electroweak baryogenesis Rev. Mod. Phys. 71 5[15] Kuroda M 1999 Complete lagrangian of MSSM arXiv: 9902340(hep-ph)[16] Csaki C 1996 Theminimal supersymmetric standardmodel (MSSM)Mod. Phys. Lett.A 11.08

599–613

4 If you lack knowledge of the MSSM see [15,16] for an introduction.

A Pedagogical Introduction to Electroweak Baryogenesis

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