Theoretical value of sin(2\beta)

In summary, there is a search for the theoretical value of sin(2\beta) which is different from the experimental value. It is believed that a theoretical value exists based on the choice of the channel B^0\rightarrow J/\psi K^0_S in the BaBar experiment due to its small theoretical error. However, obtaining this value is a challenging task and it is currently not well-understood.
  • #1
Magister
83
0
I am looking for the theoretical value of [itex]sin(2\beta)[/itex] but I just keep finding the experimental one. I supose there is a theoretical value because I have read that they choose in the BaBar experience the channel [itex]B^0\rightarrow J/\psi K^0_S[/itex] because the theoretical error for [itex]sin(2\beta)[/itex] was very small...

Thanks for your replies.
 
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  • #2
Magister said:
I am looking for the theoretical value of [itex]sin(2\beta)[/itex] but I just keep finding the experimental one. I supose there is a theoretical value because I have read that they choose in the BaBar experience the channel [itex]B^0\rightarrow J/\psi K^0_S[/itex] because the theoretical error for [itex]sin(2\beta)[/itex] was very small...

Ahhh... never heard about this argument...
I thought cp phase is an input of SM. I guess it can be infered from existing measurements like K mixing via lattice QCD but that's very hard task.
 
  • #3


The theoretical value of sin(2β) is a mathematical concept that represents the exact value of the sine of twice the angle β. This value is calculated using mathematical equations and principles, and is not dependent on any experimental measurements. It is a fundamental value that is used in various fields of mathematics and physics.

In the context of the BaBar experiment, the choice of the B^0\rightarrow J/\psi K^0_S channel was based on the theoretical value of sin(2β) being very small, meaning that the predicted effects of CP violation in this channel were expected to be small and thus easier to detect. This is because sin(2β) is related to the magnitude of CP violation in certain particle decays, and a small theoretical value implies a smaller effect to be measured.

Experimental measurements, on the other hand, involve collecting and analyzing data from physical experiments. These measurements can sometimes deviate from the theoretical value due to various factors such as experimental errors, uncertainties, and unknown effects. Therefore, it is important to have a theoretical value as a benchmark to compare experimental results to and to understand the underlying physics.

In conclusion, the theoretical value of sin(2β) is an important concept in understanding and predicting CP violation in particle physics. Its small value in the B^0\rightarrow J/\psi K^0_S channel played a significant role in the choice of this channel for the BaBar experiment. However, experimental measurements are also crucial in validating and refining our theoretical understanding of the physical world.
 

Related to Theoretical value of sin(2\beta)

1. What is the theoretical value of sin(2β)?

The theoretical value of sin(2β) is dependent on the angle β in radians. In general, sin(2β) can take on any value between -1 and 1, depending on the specific value of β.

2. Why is sin(2β) important in theoretical research?

Sin(2β) is a trigonometric function that is commonly used in theoretical research, especially in the fields of mathematics, physics, and engineering. It is important because it allows us to model and understand the behavior of oscillating systems, such as waves or pendulums. It also has applications in Fourier analysis, which is used to study periodic phenomena.

3. How is the theoretical value of sin(2β) calculated?

The theoretical value of sin(2β) is calculated using the trigonometric identity sin(2β) = 2sinβcosβ. This means that the value of sin(2β) is equal to twice the value of sinβ multiplied by the value of cosβ. The values of sinβ and cosβ can be determined using a unit circle or a scientific calculator.

4. Can the theoretical value of sin(2β) be negative?

Yes, the theoretical value of sin(2β) can be negative. This occurs when the angle β is in the third or fourth quadrant of the unit circle, where both sinβ and cosβ are negative. In general, sin(2β) can take on any value between -1 and 1, depending on the specific value of β.

5. How is sin(2β) related to other trigonometric functions?

Sin(2β) is related to other trigonometric functions through various identities, such as cos(2β) = 1 - 2sin2β and tan(2β) = 2tanβ / (1 - tan2β). It is also closely related to the Pythagorean identity sin2β + cos2β = 1, which is used to manipulate trigonometric equations.

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