arXiv subjects

Andrew Mullins

Publications and source records attributed to Andrew Mullins.

4 recordsLinked to original sources

arXiv2026

New Limits on $n \rightarrow n'$ Transformation from HFIR Cold Neutron Beam

Hypothetical neutron $n$ to sterile neutron $n'$ transformations would violate baryon number $\mathcal{B}$ and point to the nature of Dark Matter. We performed a new search for $n \rightarrow n'$ using an intense cold neutron beam from the High Flux Isotope Reactor at Oak Ridge National Laboratory. We used a theoretical model that describes the transformation $n \rightarrow n'$ with two parameters: a small mass difference $\Delta{m}$ between the interaction states $n$ and $n'$ and a mixing vacuum angle $\theta_0$. A thin absorbing cadmium wafer was used in the center of the superconducting 6.6 T magnet which provided a large gradient for the non-adiabatic $n \rightarrow n'$ transition. No signal was observed above background in the $^{3}\text{He}$ neutron detector 20 meters downstream of the magnet. This result gives an order of magnitude improvement in the lower limit for the probability $2\theta_0^2$ of the $n \rightarrow n'$ transformation in vacuum in the range of $\Delta{m}$ between $0.1$ neV and $1000$ neV.

hep-ex↗

arXiv2025

Knuth's big-chooser matchbox process: the case of many matchboxes

Banach's matchbox problem considers the setting of two matchboxes that each initially contain the same number of matches. Boxes are chosen with equal probability and a match removed each time. The problem concerns the law of the number of matches remaining in one box once the other box empties. Knuth considered a generalization of this problem whereby `big-choosers' arrive with probability $p$ and remove a match from the box with the most number remaining, and `little-choosers' arrive with probability $1-p$ and remove a match from the box with the least number remaining. In this paper we consider Knuth's generalization for the case of $k$ matchboxes. We determine the generating function for the expected number of matches remaining in $k-1$ matchboxes once a box first empties, a quantity we refer to as the `residue'. Interestingly, this generating function is a quotient whose denominator contains a generating function for a special case of the Raney numbers. The form for this generating function allows us to give an expression for the expected residue in terms of a sum that involves diagonal state return probabilities, where a diagonal state is a configuration in which all matchboxes each contain the same number of matches. We use analytic techniques to determine the asymptotic behaviour of this expected value for all values of $p$, which involves the study of an asymmetric random walk. We also consider the expected value of the order of the first return to a diagonal state and determine its asymptotic behaviour. The coefficients of the diagonal state probability generating function are shown to be related to `manila folder configurations in a filing cabinet', and we make this connection precise. This allows us to use known results for the enumeration of such manila folder configurations to give a closed form expression for the diagonal state return probabilities.

math.CO↗

arXiv2025

First Full Dalitz Plot Measurement in Neutron $\beta$-Decay using the Nab Spectrometer and Implications for New Physics

Precision measurements of observables in neutron $\beta$-decay are used to test the Standard Model description of the weak interaction and search for evidence of new physics. The Nab experiment at the Fundamental Neutron Physics Beamline at the Spallation Neutron Source was constructed to measure correlations in neutron decay by utilizing an asymmetric spectrometer and novel detection system to accurately reconstruct the proton momentum and electron energy for each $\beta$-decay. This work describes the detection of neutron $\beta$-decay products in the Nab spectrometer and presents the first full Dalitz plot representation of the phase space of neutron $\beta$-decay for all electrons >100 keV. In addition, new constraints are placed on a possible excited neutron state, hypothesized to explain the disagreement between the appearance and disappearance neutron lifetime techniques.

nucl-ex↗

arXiv2023

A bump statistic on permutations resulting from the Robinson-Schensted correspondence

In this paper we investigate a permutation statistic that was independently introduced by Romik in 2005. This statistic counts the number of bumps that occur during the execution of the Robinson-Schensted procedure when applied to a given permutation. We provide several interpretations of this bump statistic that include the tableaux shape and also as an extremal problem concerning permutations and increasing subsequences. Several aspects of this bump statistic are investigated from both structural and enumerative viewpoints.

math.CO↗