arXiv subjects

Ken Hicks

Publications and source records attributed to Ken Hicks.

3 recordsLinked to original sources

arXiv2021

Series and Product Relations Made from Primes

It is known that the sum of the reciprocal of integers, $\sum_n (1/n)$, and the sum of the reciprocal of primes, $\sum_n (1/p_n)$, both diverge. Here, we study a series made from primes that sums exactly to 1. We also show this sum is simply related to an infinite product over primes. We then generalize the form of the series (and its related product), extending this idea to other number theoretic sets such as twin primes. Evaluating a product made from twin primes gives a new mathematical constant.

math.NT↗

arXiv2007

Pentaquark Searches

Current evidence does not favor the existence of the \thplus pentaquark, which was reported by several groups in the years after 2002. The question naturally arises: how could many groups could have seen fluctuations in their data at the level of 3-5 $σ$ statistical significance? An example of a statistical fluctuation is given and the number of $σ$'s necessary for claims of discovery are examined. Using this guideline, a possible answer to the above question is presented.

hep-ph↗

arXiv2004

Experimental Outlook for the Pentaquark

A critical look is taken at both positive and null evidence for the $Θ^+$ pentaquark. Potential problems with experiments will be discussed and the question of what conclusion can be drawn from both the positive and the null results is examined. First the question of existence of the $Θ^+$ pentaquark is considered, followed by a discussion of new experiments that are either planned or in progress to answer questions about its mass, width and isospin. Finally, indirect evidence for the parity of the $Θ^+$ is examined, and suggestions for experiments to measure its parity directly are given.

hep-ph↗