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Scalar Product (Dot Product)01:11

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The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a number, that is, a scalar quantity. Scalar products are used to define work and energy relations. For example, the work that a force (a vector) performs on an object while causing its displacement (a vector) is defined as a scalar product of the force vector with the displacement vector.
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Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of the angle between both the vectors and the direction perpendicular to both the individual vectors. As there are always two directions perpendicular to a given plane, one on each side, the direction of the vector product is governed by the right-hand thumb rule.
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Consider a neutral form of an amine, B, with a partition coefficient, K, in a liquid mixture containing organic and aqueous phases. The pH of the aqueous phase affects the charge on acidic and basic solutes, and the charged form is usually more soluble in the aqueous phase. Suppose the conjugate acid form of the amine is soluble only in the aqueous phase while the base form is soluble in both phases. Then the distribution coefficient, D, can be given as the ratio of amine concentration in the...
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Wood products encompass a broad range of materials crafted from wood strands, veneers, lumber, and even waste wood-like shreds, designed for both structural and nonstructural purposes. Various specialized wood products have been developed to enhance strength, durability, and versatility in building applications.
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Dot Product01:29

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The dot product is an essential concept in mathematics and physics.
In engineering, the dot product of any two vectors is the product of the magnitudes of the vectors and the cosine of the angle between them. It is denoted by a dot symbol between the two vectors.
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Cross Product01:25

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The cross product is a fundamental concept in vector algebra that is a vector operation on two different vectors to obtain a third vector. Unlike the scalar product, the cross product results in a vector quantity perpendicular to both the original vectors.
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Extracting the Top-Quark Width from Nonresonant Production.

Christian Herwig1, Tomáš Ježo2, Benjamin Nachman3

  • 1Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.

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A new method precisely measures the top-quark width (Γt) using data away from resonance peaks. This approach offers improved experimental sensitivity for top-quark physics.

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Area of Science:

  • High Energy Physics
  • Particle Physics
  • Standard Model Physics

Background:

  • The top-quark mass and width (Γt) are precisely calculated in the Standard Model.
  • Current direct measurements of the top-quark width have a large uncertainty of nearly 50%.

Purpose of the Study:

  • To present a novel method for directly measuring the top-quark width.
  • To improve experimental sensitivity in top-quark width extractions.

Main Methods:

  • Utilizing events occurring away from the resonance peak for measurement.
  • Employing an orthogonal dataset to traditional top-quark width extraction techniques.
  • Recasting a recent ATLAS differential cross-section measurement.

Main Results:

  • The study provides the most precise direct measurement of the top-quark width to date.
  • The measured width is Γt = 1.28 ± 0.30 GeV.
  • The expected width measurement was Γt = 1.33 ± 0.29 GeV.

Conclusions:

  • The new method demonstrates potential for significant improvements in experimental sensitivity.
  • This approach offers a valuable alternative for precise top-quark width determination.