<p>We investigate the impact of preheating on baryogenesis in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-Higgs inflation. In this scenario, the inclusion of a dimension-six operator <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mi>R</mi><mo>/</mo><msup><mi mathvariant="normal">Λ</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow><msub><mi>B</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msub><msup><mover accent="true"><mi>B</mi><mo stretchy="false">˜</mo></mover><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math> abundantly generates helical hypermagnetic fields during inflation, leading to a baryon asymmetric Universe at the electroweak crossover. Focusing on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-like regime, we first derive the relevant dynamics of preheating using a doubly covariant formalism. We find that preheating can happen for the Higgs, transverse gauge, and Goldstone bosons, however, it is dependent on the value of the nonminimal coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ξ</mi><mi>H</mi></msub></math> between the Standard Model Higgs field and the Ricci scalar. We identify the preheating temperature to determine the appropriate scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> for driving baryogenesis, which is around <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Λ</mi><mo>∼</mo><mn>2.2</mn><mo stretchy="false">(</mo><mn>2.6</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup><msub><mrow><mi>M</mi></mrow><mrow><mi mathvariant="normal">P</mi></mrow></msub></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ξ</mi><mi>H</mi></msub><mo>∼</mo><mn>1</mn><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math>. Our results represent the most accurate estimation of the scale of gravity induced baryogenesis in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-Higgs inflation to date. Areas for further improvement are identified.</p>

France

Yann Cado

United Kingdom

Christoph Englert

India

Tanmoy Modak

Spain

Mariano Quirós

Implication of preheating on gravity assisted baryogenesis in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>R</mi><mn>2</mn></msup></math>-Higgs inflation

With the Large Hadron Collider (LHC) running, we should probe electroweak baryogenesis (EWBG) while probing <math><mrow><mi>C</mi><mi>P</mi></mrow></math> violation (<math><mi>C</mi><mi>P</mi><mi>V</mi></math>) with electron electric dipole moment (eEDM). Rooted in the flavor structure of the Standard Model (SM), the general two Higgs doublet model (g2HDM) with a second set of Yukawa couplings can deliver EWBG while surviving eEDM. We point out a chiral-enhanced top-bottom interference effect that makes <math><mi>b</mi><mo>→</mo><mi>s</mi><mi>γ</mi></math> decay an exquisite window on EWBG and eEDM, and illustrate the importance of the <math><mi>Δ</mi><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math> observable at Belle II.

Taiwan

Wei-Shu Hou

United States

Girish Kumar

Germany

Probing baryogenesis with radiative beauty decay and electron electric dipole moment

We study a search for the charged Higgs boson via e + e  −  → H + H  −  →   <math> <mover> <mi>c</mi> <mo>¯</mo> </mover> <mi>b</mi> <mover> <mi>c</mi> <mo>¯</mo> </mover> <mi>b</mi> </math>  $$ \overline{c}b\overline{c}b $$  at the 500 GeV ILC. In a general two Higgs doublet model without Z 2 symmetry, extra Yukawa couplings ρ  tt  and ρ  tc  can drive baryogenesis, but searches at the HL-LHC may still go empty-handed if the couplings are relatively weak. Taking   <math> <msub> <mi>m</mi> <msup> <mi>H</mi> <mo>+</mo> </msup> </msub> </math>  $$ {m}_{H^{+}} $$  ≃ m  H  ≃ m  A  ≃ 200 GeV, with ρ  tt , ρ  tc  ∼ 0.1 and no h(125)-H mixing, H + →   <math> <mi>c</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ c\overline{b} $$  decay is dominant, and the   <math> <mover> <mi>c</mi> <mo>¯</mo> </mover> <mi>b</mi> <mover> <mi>c</mi> <mo>¯</mo> </mover> <mi>b</mi> </math>  $$ \overline{c}b\overline{c}b $$  final state is likely overwhelmed by QCD background at the LHC. We show that the electroweak production of H + H  −  at the ILC is discoverable with integrated luminosity of 1 ab −1. Furthermore, we show that   <math> <msub> <mi>m</mi> <msup> <mi>H</mi> <mo>+</mo> </msup> </msub> </math>  $$ {m}_{H^{+}} $$  can be extracted by requiring the two pairs of b and light jets be roughly equal in mass, without assuming the mass value. Thus, ILC can probe low mass Higgs bosons in multijet final states to complement HL-LHC in the future.

Rishabh Jain

Searching for Charged Higgs Bosons via e + e  −  → H + H  −  →   <math> <mover> <mi>c</mi> <mo>¯</mo> </mover> <mi>b</mi> <mover> <mi>c</mi> <mo>¯</mo> </mover> <mi>b</mi> </math>  $$ \overline{c}b\overline{c}b $$  at Linear Colliders

We study  $$R^2$$  <math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math>  -Higgs inflation in a model with two Higgs doublets in which the Higgs sector of the Standard Model is extended by an additional Higgs doublet, thereby four scalar fields are involved in the inflationary evolutions. We first derive the set of equations required to follow the inflationary dynamics in this two Higgs doublet model, allowing a nonminimal coupling between the Higgs-squared and the Ricci scalar R, as well as the  $$R^2$$  <math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math>   term in the covariant formalism. By numerically solving the system of equations, we find that, in parameter space where a successful  $$R^2$$  <math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math>  -Higgs inflation are realized and consistent with low energy constraints, the inflationary dynamics can be effectively described by a single slow-roll formalism even though four fields are involved in the model. We also argue that the parameter space favored by  $$R^2$$  <math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math>  -Higgs inflation requires nearly degenerate masses for  $$m_{\mathsf {H}}$$  <math> <msub> <mi>m</mi> <mi>H</mi> </msub> </math>  ,  $$m_A$$  <math> <msub> <mi>m</mi> <mi>A</mi> </msub> </math>   and  $$m_{{\mathsf {H}}^{\pm }}$$  <math> <msub> <mi>m</mi> <msup> <mrow> <mi>H</mi> </mrow> <mo>±</mo> </msup> </msub> </math>  , where  $${\mathsf {H}}$$  <math> <mi>H</mi> </math>  , A, and  $${\mathsf {H}}^{\pm }$$  <math> <msup> <mrow> <mi>H</mi> </mrow> <mo>±</mo> </msup> </math>   are the extra CP even, CP odd, and charged Higgs bosons in the general two Higgs doublet model taking renormalization group evolutions of the parameters into account. Discovery of such heavy scalars at the Large Hadron Collider (LHC) are possible if they are in the sub-TeV mass range. Indirect evidences may also emerge at the LHCb and Belle-II experiments, however, to probe the quasi degenerate mass spectra one would likely require high luminosity LHC or future lepton colliders such as the International Linear Collider and the Future Circular Collider.

South Korea

Sung Lee

Japan

Kin-ya Oda

Tomo Takahashi

The  $$R^2$$  <math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math>  -Higgs inflation with two Higgs doublets

Recent progress on muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> measurement prompts one to take it even more seriously. In the general two Higgs doublet model that allows extra Yukawa couplings, we take a simplified approach of single enhanced coupling. We fix the charged lepton flavor violating coupling, <math><msub><mi>ρ</mi><mrow><mi>τ</mi><mi>μ</mi></mrow></msub><mo>=</mo><msub><mi>ρ</mi><mrow><mi>μ</mi><mi>τ</mi></mrow></msub></math>, via the one-loop mechanism, for illustrative masses of the heavy scalar <math><mi>H</mi></math> and pseudoscalar <math><mi>A</mi></math>, where we assume <math><msub><mi>m</mi><mi>A</mi></msub><mo>=</mo><msub><mi>m</mi><msup><mi>H</mi><mo>+</mo></msup></msub></math>. Since extra top Yukawa couplings are plausibly the largest, we turn on <math><msub><mi>ρ</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub></math> and find that LHC search for <math><mi>g</mi><mi>g</mi><mo>→</mo><mi>H</mi><mo>,</mo><mi>A</mi><mo>→</mo><mi>τ</mi><mi>μ</mi></math> gives a more stringent bound than from <math><mi>τ</mi><mo>→</mo><mi>μ</mi><mi>γ</mi></math> with the two-loop mechanism. Turning on a second extra top Yukawa coupling, <math><msub><mi>ρ</mi><mrow><mi>t</mi><mi>c</mi></mrow></msub></math>, can loosen the bound on <math><msub><mi>ρ</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub></math>, but LHC constraints can again be more stringent than from <math><mi>B</mi><mo>→</mo><mi>D</mi><mi>μ</mi><mi>ν</mi></math> versus <math><mi>D</mi><mi>e</mi><mi>ν</mi></math> universality. This means that evidence for <math><mi>H</mi><mo>,</mo><mi>A</mi><mo>→</mo><mi>τ</mi><mi>μ</mi></math> may yet emerge with full LHC Run 2 data, while direct search for <math><msup><mi>τ</mi><mo>±</mo></msup><msup><mi>μ</mi><mo>∓</mo></msup><mi>b</mi><msup><mi>W</mi><mo>+</mo></msup></math> or <math><mi>t</mi><mover><mi>c</mi><mo>¯</mo></mover><mi>b</mi><msup><mi>W</mi><mo>+</mo></msup></math> (plus conjugate) may also bear fruit.

Chung Kao

Collider prospects for the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> in a general two-Higgs-doublet model

We study the complementarity between the Large Hadron Collider (LHC) and future lepton colliders in probing electroweak baryogenesis induced by an additional bottom Yukawa coupling <math><msub><mrow><mi>ρ</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow></msub></math>. The context is general two Higgs doublet model (g2HDM) where such additional bottom Yukawa coupling can account for the observed baryon asymmetry of the Universe if <math><mtext>Im</mtext><mo>(</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow></msub><mo>)</mo><mo>≳</mo><mn>0.058</mn></math>. We find that LHC would probe the nominal <math><mtext>Im</mtext><mo>(</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow></msub><mo>)</mo></math> required for baryogenesis to some extent via <math><mi>b</mi><mi>g</mi><mo>→</mo><mi>b</mi><mi>A</mi><mo>→</mo><mi>b</mi><mi>Z</mi><mi>h</mi></math> process if <math><mn>300</mn><mspace width="0.25em"></mspace><mtext>GeV</mtext><mo>≲</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>≲</mo><mn>450</mn></math> GeV, where A is the CP-odd scalar in g2HDM. We show that future electron positron collider such as International Linear Collider with 500 GeV and 1 TeV collision energies may offer unique probe for the nominal <math><mtext>Im</mtext><mo>(</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow></msub><mo>)</mo></math> via <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>Z</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>→</mo><mi>A</mi><mi>H</mi></math> process followed by <math><mi>A</mi><mo>,</mo><mi>H</mi><mo>→</mo><mi>b</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> decays in four b-jets signature. For complementarity we also study the resonant diHiggs productions, which may give an insight into strong first-order electroweak phase transition, via <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>Z</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>→</mo><mi>A</mi><mi>H</mi><mo>→</mo><mi>A</mi><mi>h</mi><mi>h</mi></math> process in six b-jets signature. We find that 1 TeV collision energy with <math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo><mspace width="0.25em"></mspace><msup><mrow><mtext>ab</mtext></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> integrated luminosity could offer an ideal environment for the discovery.

Vietnam

Eibun Senaha

Electroweak baryogenesis via bottom transport: Complementarity between LHC and future lepton collider probes

A correction to this paper has been published:  https://doi.org/10.1140/epjc/s10052-020-08450-5

Erratum to: Echoes of 2HDM inflation at the collider experiments

We study the prospect for discovering the <math><mi>c</mi><mi>g</mi><mo>→</mo><mi>b</mi><msup><mi>H</mi><mo>+</mo></msup><mo>→</mo><mi>b</mi><mi>A</mi><msup><mi>W</mi><mo>+</mo></msup></math> process at the LHC. Induced by the top-flavor changing neutral Higgs coupling <math><msub><mi>ρ</mi><mrow><mi>t</mi><mi>c</mi></mrow></msub></math>, the process may emerge if <math><msub><mi>m</mi><msup><mi>H</mi><mo>+</mo></msup></msub><mo>&gt;</mo><msub><mi>m</mi><mi>A</mi></msub><mo>+</mo><msub><mi>m</mi><msup><mi>W</mi><mo>+</mo></msup></msub></math>, where <math><msup><mi>H</mi><mo>+</mo></msup></math> and <math><mi>A</mi></math> are charged and <math><mi>C</mi><mi>P</mi></math>-odd Higgs bosons in the general two Higgs doublet model (g2HDM). We show that the <math><mi>c</mi><mi>g</mi><mo>→</mo><mi>b</mi><msup><mi>H</mi><mo>+</mo></msup><mo>→</mo><mi>b</mi><mi>A</mi><msup><mi>W</mi><mo>+</mo></msup></math> process can be discovered at LHC run 3, while the full run 2 data at hand can constrain the parameter space significantly by searching for the same-sign dilepton final state. The process has unique implications on the hint of <math><mi>g</mi><mi>g</mi><mo>→</mo><mi>A</mi><mo>→</mo><mi>t</mi><mover><mi>t</mi><mo>¯</mo></mover></math> excess at <math><msub><mi>m</mi><mi>A</mi></msub><mo>≈</mo><mn>400</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> reported by CMS. When combined with other existing constraints, the <math><mi>c</mi><mi>g</mi><mo>→</mo><mi>b</mi><msup><mi>H</mi><mo>+</mo></msup><mo>→</mo><mi>b</mi><mi>A</mi><msup><mi>W</mi><mo>+</mo></msup></math> process can essentially rule out the g2HDM explanation of such an excess.

Prospect and implications of <math><mi>c</mi><mi>g</mi><mo>→</mo><mi>b</mi><msup><mi>H</mi><mo>+</mo></msup><mo>→</mo><mi>b</mi><mi>A</mi><msup><mi>W</mi><mo>+</mo></msup></math> production at the LHC

We suggest searching for the charged Higgs boson at the Large Hadron Collider (LHC) via <math><mrow><mi>c</mi><mi>g</mi><mo>→</mo><mi>b</mi><msup><mrow><mi>H</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><mi>b</mi><mi>t</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math>. In the general two Higgs doublet model, extra top Yukawa couplings <math><msub><mi>ρ</mi><mrow><mi>t</mi><mi>c</mi></mrow></msub></math> and <math><msub><mi>ρ</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub></math> can drive the disappearance of antimatter from the Universe, while <math><mover><mi>c</mi><mo>¯</mo></mover><mi>b</mi><msup><mi>H</mi><mo>+</mo></msup></math> and <math><mover><mi>t</mi><mo>¯</mo></mover><mi>b</mi><msup><mi>H</mi><mo>+</mo></msup></math> couple with strength <math><msub><mi>ρ</mi><mrow><mi>t</mi><mi>c</mi></mrow></msub><msub><mi>V</mi><mrow><mi>t</mi><mi>b</mi></mrow></msub></math> and <math><msub><mi>ρ</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><msub><mi>V</mi><mrow><mi>t</mi><mi>b</mi></mrow></msub></math>, respectively. For <math><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mi>t</mi><mi>c</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>∼</mo><mn>0.5</mn></mrow></math>, and <math><mrow><msub><mrow><mi>m</mi></mrow><mrow><msup><mrow><mi>H</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></msub><mo>∼</mo><mn>300</mn><mi>–</mi><mn>500</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>, evidence could emerge from LHC run 2 data at hand and discovery by adding run 3 data in the near future.

Dilip Kumar Ghosh

Sub-TeV <math><msup><mi>H</mi><mo>+</mo></msup></math> Boson Production as Probe of Extra Top Yukawa Couplings

We study the prospect of probing electroweak baryogenesis driven by an extra bottom Yukawa coupling ρ  bb  in a general two Higgs doublet model via electric dipole moment (EDM) measurements and at the collider experiments. The parameter space receives meaningful constraints from 125 GeV Higgs h boson signal strength measurements as well as several heavy Higgs boson searches at the Large Hadron Collider (LHC). In addition, we show that the asymmetry of the CP asymmetry of inclusive B → X  s  γ decay would provide complementary probe. A discovery is possible at the LHC via bg → bA → bZh process if |ρ  bb | ∼ 0.15 and 250 GeV≲ m  A  ≲ 350 GeV, where A is CP odd scalar. For m  A  &gt; 2m  t  threshold, where m  t  is the top quark mass, one may also discover bg → bA →   <math> <mi>bt</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> </math>  $$ bt\overline{t} $$  at the high luminosity LHC run if an extra top Yukawa coupling |ρ  tt | ∼ 0.5, though it may suffer from systematic uncertainties. For completeness we study gg →   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>A</mi> </math>  $$ t\overline{t}A $$  →   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ t\overline{t}b\overline{b} $$  but find it not promising.