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Spin–Spin Coupling Constant: Overview01:08

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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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¹H NMR: Long-Range Coupling01:27

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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
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In a beam of charged particles created by a heated cathode, the particles move at different speeds. However, many applications need a beam with uniform particle speeds. An arrangement known as a velocity selector uses electric and magnetic fields to pick particles with a particular speed from the beam.
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NMR Spectroscopy: Spin–Spin Coupling01:08

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The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
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Spin–Spin Coupling: One-Bond Coupling01:17

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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Future Circular Collider (FCC-ee) experiments can precisely measure Higgs self-coupling. This study shows FCC-ee

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Area of Science:

  • High Energy Physics
  • Particle Physics
  • Standard Model Physics

Background:

  • Probing Higgs self-coupling is crucial for understanding the Standard Model.
  • New physics beyond the Standard Model can modify Higgs self-coupling.
  • Next-to-leading order (NLO) calculations are required for precise predictions.

Purpose of the Study:

  • To determine the sensitivity of FCC-ee to Higgs self-coupling modifications (δκλ).
  • To perform a global analysis including various experimental data and theoretical effects.
  • To assess the potential of FCC-ee compared to other colliders like the High-Luminosity LHC (HL-LHC).

Main Methods:

  • Utilizing the Standard Model Effective Field Theory (SMEFT) framework.
  • Incorporating flavor, LEP, LHC, and FCC-ee observables in a global analysis.
  • Applying one-loop renormalization group evolution for NLO effects.
  • Including finite NLO contributions to electroweak precision and ZH observables.

Main Results:

  • FCC-ee offers significant sensitivity to Higgs self-coupling modifications.
  • A global analysis incorporating diverse observables and NLO effects is performed.
  • Flavor considerations are integrated into the analysis, highlighting their importance.

Conclusions:

  • FCC-ee has the potential to provide superior sensitivity to Higgs self-coupling compared to HL-LHC.
  • The study demonstrates the importance of global analyses for precise measurements.
  • This research paves the way for future precision Higgs physics at FCC-ee.