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Related Concept Videos

¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)01:20

¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)

When proton-coupled carbon-13 spectra are simplified by a broadband proton decoupling technique, structural information about the coupled protons is lost. Distortionless enhancement by polarization transfer (DEPT) is a technique that provides information on the number of hydrogens attached to each carbon in a molecule. While the DEPT experiment utilizes complex pulse sequences, the pulse delay and flip angle are specifically manipulated. The resulting signals have different phases depending on...
Electron Paramagnetic Resonance (EPR) Spectroscopy: Organic Radicals01:17

Electron Paramagnetic Resonance (EPR) Spectroscopy: Organic Radicals

Ideally, an unpaired electron shows a single peak in the EPR spectrum due to the transition between the two spin energy states. However, coupling interactions can occur between the spins of the unpaired electron and any neighboring spin-active nuclei. This hyperfine coupling results in hyperfine splitting, where the EPR signal is split into multiplets. The signals split into 2nI + 1 peaks, where n is the number of equivalent nuclei and I is the nuclear spin. These splitting patterns provide...
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
¹³C NMR: ¹H–¹³C Decoupling01:04

¹³C NMR: ¹H–¹³C Decoupling

The probability of having two carbon-13 atoms next to each other is negligible because of the low natural abundance of carbon-13. Consequently, peak splitting due to carbon-carbon spin-spin coupling is not observed in spectra. However, protons up to three sigma bonds away split the carbon signal according to the n+1 rule, resulting in complicated spectra.
A broadband decoupling technique is used to simplify these complex, sometimes overlapping, signals. Broadband decoupling relies on a...
Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...

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Setting Limits on Supersymmetry Using Simplified Models
07:46

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Published on: November 15, 2013

Method for extracting the quark mixing parameter cosalpha via B+/- -->pi(+/-)e(+)e(-)

Grinstein1, Nolte, Rothstein

  • 1Department of Physics,University of California at San Diego, La Jolla, California 92093, USA.

Physical Review Letters
|September 16, 2000
PubMed
Summary

Researchers can determine the weak mixing angle alpha by measuring the B+ meson decay rate into pi+/- and electron-positron pairs. This method leverages interference effects, offering a new way to probe fundamental particle physics.

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Area of Science:

  • High Energy Physics
  • Particle Physics
  • Quantum Chromodynamics

Background:

  • The weak mixing angle (alpha) is a fundamental parameter in the Standard Model of particle physics.
  • Measuring alpha precisely is crucial for testing the Standard Model and searching for new physics.
  • Previous methods for determining alpha have limitations.

Purpose of the Study:

  • To propose a novel method for extracting the weak mixing angle alpha.
  • To investigate the feasibility of using the B+ ---> pi+/- e+e- decay for alpha determination.
  • To analyze the sensitivity of this decay to fundamental parameters.

Main Methods:

  • Analysis of the decay rate for B+ ---> pi+/- e+e-.
  • Interference between long-distance and short-distance contributions to the decay amplitude.
  • Calculation of short-distance contributions using semileptonic form factors.
  • Calculation of long-distance contributions using Ward identities and operator product expansion for invariant lepton pair mass (q^2) > Lambda^2(QCD).

Main Results:

  • The decay rate for B+ ---> pi+/- e+e- is approximately 1x10^-8 |V(td)/0.008|^2 for q^2 >= 2 GeV^2.
  • The differential decay rate (dgamma/dq^2) shows significant sensitivity to cos(alpha) at low q^2.
  • A 50% variation in dgamma/dq^2 is observed for -1 < cos(alpha) < 1 at q^2 = 2 GeV^2.

Conclusions:

  • Measurement of the B+ ---> pi+/- e+e- decay rate provides a viable method to extract the weak mixing angle alpha.
  • The sensitivity to cos(alpha) arises from the interference of different contributing amplitudes.
  • This decay offers a promising channel for precise determination of alpha in future experiments.