PHYSICAL REVIEW D 100, 055005 (2019) Phase of confined electroweak force in the early Universe Joshua Berger,1 Andrew J. Long,2,3 and Jessica Turner4 1Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA 2Leinweber Center for Theoretical Physics, University of Michigan, Ann Arbor, Michigan 48109, USA 3Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA 4Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510, USA (Received 18 June 2019; published 6 September 2019) We consider a modified cosmological history in which the presence of beyond-the-Standard-Model 2 physics causes the weak gauge sector, SUð ÞL, to confine before it is Higgsed. Under the assumption of chiral symmetry breaking, quark and lepton weak doublets form condensates that break the global symmetries of the Standard Model, including baryon and lepton number, down to a U(1) subgroup under which only the weak singlet fermions and Higgs boson transform. The weakly coupled gauge group 3 1 2 1 SUð Þc ×Uð ÞY is also broken to an SUð Þc ×Uð ÞQ gauge group. The light states include (pseudo-) Goldstone bosons of the global symmetry breaking, mostly elementary fermions primarily composed of the weak singlet quarks and leptons, and the gauge bosons of the weakly coupled gauge group. We discuss possible signatures from early Universe cosmology including gravitational wave radiation, topological defects, and baryogenesis. DOI: 10.1103/PhysRevD.100.055005 I. INTRODUCTION composite particles and that the predicted low-energy fermion spectrum agrees well with the measured quark Quarks and leptons can interact via the weak force, and lepton masses. However, this scenario is now ruled out mediated by the W- and Z-bosons. The Standard Model of by precision measurements of the electroweak sector [11], elementary particles (SM) describes the electroweak force and it would appear that the weak force is not confining in by a quantum field theory that is constructed from the our present day Universe. gauge group SUð2Þ ×Uð1Þ and is in the Higgs phase L Y Nevertheless, when we study particle physics in a [1–3]. Higgsing screens weak isospin at the weak scale and cosmological context, the system can exist in different leaves only weakly coupled electromagnetic long-range phases at different times, corresponding to different temper- interactions. The theory is weakly coupled in the infrared, atures of the primordial plasma. We explore a scenario in which agrees extremely well with measured quark and which the SUð2Þ weak force was strongly coupled in lepton interactions. By contrast the strong force, which L the early Universe, when the plasma temperature was mediates interactions among the quarks, is strongly coupled T ≫ 100 GeV, but became weakly coupled and Higgsed in the infrared, leading to the confinement of the constitu- well before the epoch of nucleosynthesis, T ∼ MeV. ent quarks into composite states, namely mesons and Although we are unable to access the weak-confined phase baryons. In this article, we study the weak-confined in the laboratory today, e.g., at collider experiments, the Standard Model (WCSM) in which the SUð2Þ component L Universe may contain relics from this period in its cosmic of the electroweak force is strongly coupled and the weak history, such as gravitational waves and the baryon asym- isospin is confined in composite particles. metry of the Universe. Confinement of SUð2Þ was studied in the pioneering L Our work shares some common elements with several work of Abbott, Farhi, and others in the 1980’s [4–7] previous studies of SM exotic phases, their associated (also [8–10]) as an alternative to the SM. Assuming that phase transitions, and their imprints on cosmology. As we confinement occurs without chiral symmetry breaking, they have already mentioned above, SUð2Þ confinement was argued that the known “elementary particles” are actually L studied in Refs. [4–8], and we present a detailed compari- son of our work with theirs in Sec. VI. The authors of Refs. [12,13] studied a variation of the SM in which the Published by the American Physical Society under the terms of Higgs field is absent, and the electroweak force is Higgsed the Creative Commons Attribution 4.0 International license. by the quark chiral condensates, and Ref. [14] points out a Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, dark matter candidate in a related model. Delaying the and DOI. Funded by SCOAP3. electroweak phase transition (EWPT) to coincide with the 2470-0010=2019=100(5)=055005(17) 055005-1 Published by the American Physical Society BERGER, LONG, and TURNER PHYS. REV. D 100, 055005 (2019) chiral phase transition of QCD was studied as a means of remarkable agreement between electroweak-precision generating the baryon asymmetry of the Universe [15–17] theory and measurement. (see also Ref. [18]) and a stochastic background of In general the scalar modulus may have a nonzero gravitational waves [19]. Likewise, an early period of expectation value, hφˆ i, and in this background, the strength 2 QCD confinement, which triggers a first order EWPT, of the SUð ÞL interaction is controlled by the effective was proposed as a possible mechanism of baryogenesis coupling, [20]. Moreover, early QCD phase transitions have been 1 1 φˆ studied in order to open the axion parameter space [21,22]. − h i 2 2 ¼ 2 : ð2:2Þ We will see that SUð ÞL confinement in the WCSM geff g M causes baryon number and lepton number to be sponta- φˆ ≪ 2 ≈ φˆ ∼ 2 neously broken, which is signaled by the formation of If h i M=g then geff g, but if h i M=g then the ≳ φˆ lepton-quark and quark-quark condensates, hlqi and hqqi. weak force is stronger, geff g. The value of h i need not The violation of baryon number is a necessary condition to remain fixed throughout the cosmic history, and we explain the cosmological excess of matter over antimatter, demonstrate this point in the paragraphs below. Thus we and therefore one may expect that the WCSM can naturally will assume that hφˆ i was large in the early Universe, accommodate baryogenesis. However, when we discuss the corresponding to geff >g, but that it evolved to a small ≈ cosmological implications of weak confinement in Sec. V, value, where geff g, at some point before the epoch of big we will see that the viability of baryogenesis remains bang nucleosynthesis. In this way, laboratory probes of the ≈ unclear. weak force only access geff g, whereas cosmological This article is structured as follows. In Sec. II we provide probes of the prenucleosynthesis era may uncover evidence an example of the new physics that could lead to weak for geff >gin the early Universe. confinement in the early Universe. In order to develop As discussed, the effective strength of the weak inter- intuition for confinement in an SU(2) gauge theory, we next action, geff, varies with time through the scalar field study three simplified models in Sec. III. Turning to the modulus, hφˆ i, but it also varies through the cosmological WCSM in Sec. IV, we investigate the symmetry breaking plasma temperature, T. At temperatures T>100 GeV, the 2 pattern, calculate the spectrum of composite particles, and hot Standard Model plasma contains SUð ÞL-charged discuss their interactions. We discuss the possible cosmo- quarks and leptons, which interact via the weak force. logical implications in Sec. V and highlight directions for As the Universe expands and the cosmological plasma future work. We contrast the WCSM with Abbot and cools, these scatterers carry less kinetic energy, and they ’ 2 Farhi s earlier work on SUð ÞL confinement in Sec. VI and probe the weak force at larger-and-larger length scales. This conclude in Sec. VII. scale dependence of the weak force is described by the equations of renormalization group flow, and its effects are captured by treating g as a running coupling that is tiny at II. CONFINEMENT OF THE WEAK FORCE small length scales in the high-energy ultraviolet (UV) 2 What new physics might allow the SUð ÞL weak force to regime and grows bigger at large length scales in the low- confine in the early Universe? In the context of QCD, early energy infrared (IR) regime. In the Standard Model the color confinement has been studied previously in weak force was Higgsed at the electroweak phase transition Refs. [21,22] (see also Ref. [20]), and we can straightfor- when the plasma temperature was T ∼ v ∼ 100 GeV, cor- wardly adapt that mechanism for our purposes. The responding to g2=4π ≪ 1. However, if hφˆ i ∼ M=g2 at early essential idea is to link the strength of the weak force times, then the weak coupling may run to a nonperturba- with the expectation value of a scalar field that experiences 2 4π O 4π ’ tively large value, geff= ¼ ð Þ, while the Higgs field s a phase transition in the early Universe. expectation value remains zero. In that case the Standard Let φˆ ðxÞ be a real scalar field, which we call the 2 Model enters the confined-SUð ÞL phase, which we call modulus field, and suppose that it interacts with the weak the WCSM, and we study the properties of this phase in the force through a dimension-five operator. The relevant remainder of this article. The proposed modification to the Lagrangian is gauge coupling’s running is schematically illustrated in Fig. 1. 1 1 φˆ μν One can imagine several different explanations for the L ¼ − − Tr½WμνW − Vðφˆ Þ; ð2:1Þ 2 g2 M nontrivial dynamics of φˆ .