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The function that decreases as the input becomes very large provides a clear example of how mathematical functions can behave at extreme values. When the input increases continuously, the output becomes smaller and smaller, getting closer to a particular fixed value. Although the output never actually reaches this value, it moves nearer to it without limit. This behavior is a fundamental concept in understanding how functions behave as the input grows indefinitely. The graphical representation...
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Limit laws provide essential tools for analyzing how functions behave as their input approaches a specific value. These laws are particularly useful when dealing with combinations of functions, provided the individual limits exist. The Sum and Difference Laws state that the limit of the sum or difference of two functions equals the sum or difference of their respective limits:The Product Law asserts that the limit of the product of two functions equals the product of their individual limits:A...
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In calculus, limit laws serve as foundational tools for evaluating the behavior of functions as inputs approach specific values. Among these, the laws concerning quotients, powers, and roots are particularly useful in breaking down complex expressions.The Quotient Law allows the limit of a division between two functions to be calculated by dividing their individual limits, provided the limit of the denominator exists and is not zero. For example,The Power Law states that the limit of a function...
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In the analysis of functions that represent continuous physical phenomena, it is often necessary to determine the output value as the input approaches a specific point. When a combination of algebraic terms defines the function and exhibits no discontinuities or abrupt changes near the point of interest, the limit of the function can be evaluated directly. This process, known as direct substitution, involves replacing the variable in the expression with the value it approaches.Direct...
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Limits on Trigonometric FunctionsThe limits of trigonometric functions play a fundamental role in calculus, particularly in defining derivatives. One of the most important results is:which is important for differentiating trigonometric functions and is widely applied in mathematical analysis and physics.Geometric IntuitionA common approach to proving this result involves analyzing a sector of a unit circle with an angle subtended at the center. Since the arc length is numerically equal to the...
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Understanding the formal definition of a limit is essential for precise mathematical analysis. This concept allows us to rigorously determine how a function behaves near a particular point without relying on ambiguous notions such as "getting close." The ε-δ definition plays a foundational role in calculus, ensuring analytical clarity and logical consistency in limit evaluation.The formal definition states that the limit of a function f(x) as x approaches a is L, written asif for...
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Setting Limits on Supersymmetry Using Simplified Models
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Fastlim: a fast LHC limit calculator.

Michele Papucci1, Kazuki Sakurai2, Andreas Weiler3

  • 1Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48109 USA.

The European Physical Journal. C, Particles and Fields
|March 28, 2015
PubMed
Summary
This summary is machine-generated.

Fastlim is a new tool that calculates limits on new physics models from LHC data without Monte Carlo simulations. It reconstructs visible cross sections for supersymmetric models, aiding in the search for natural SUSY.

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Area of Science:

  • High Energy Physics
  • Particle Physics
  • Computational Physics

Background:

  • Direct searches at the Large Hadron Collider (LHC) aim to detect physics beyond the Standard Model.
  • Interpreting these searches for various theoretical models requires significant computational resources, often involving Monte Carlo simulations.
  • Supersymmetric (SUSY) models are a well-motivated class of extensions to the Standard Model, with specific experimental signatures.

Purpose of the Study:

  • To develop a computational tool, Fastlim, for efficient and accurate calculation of exclusion limits on extensions of the Standard Model.
  • To bypass the need for Monte Carlo event generation in the analysis of LHC direct search data.
  • To provide a user-friendly program for assessing the impact of LHC searches on specific theoretical models, particularly concerning natural SUSY.

Main Methods:

  • Fastlim reconstructs visible cross sections by utilizing pre-calculated efficiency and cross section tables for simplified event topologies.
  • The tool processes model-specific information, including particle spectra and coupling strengths.
  • It calculates normalized visible cross sections and corresponding p-values for each signal region of implemented LHC analyses.

Main Results:

  • The program successfully implements searches relevant to R-parity conserving supersymmetric models.
  • As a demonstration, Fastlim was used to study the sensitivity of ATLAS missing energy searches to natural SUSY models.
  • The tool provides a method to directly compare theoretical model predictions with experimental limits.

Conclusions:

  • Fastlim offers a computationally efficient alternative to Monte Carlo methods for calculating exclusion limits from LHC data.
  • The tool's design facilitates easy integration of external efficiency tables and can be extended to other theoretical frameworks, including R-parity violating and non-SUSY models.
  • Fastlim serves as a valuable resource for phenomenologists and experimentalists seeking to interpret LHC search results in the context of new physics models.