Detector R&D for future Neutrino Experiments with the NuMI Beamline
A report to the Fermilab Director from the Study Group on Future Neutrino Experiments at Fermilab
hep-ex↗
arXiv subjects
R. Shrock
Publications and source records attributed to R. Shrock.
The Potential for Neutrino Physics at Muon Colliders and Dedicated High Current Muon Storage Rings
Conceptual design studies are underway for muon colliders and other high-current muon storage rings that have the potential to become the first true ``neutrino factories''. Muon decays in long straight sections of the storage rings would produce precisely characterized beams of electron and muon type neutrinos of unprecedented intensity. This article reviews the prospects for these facilities to greatly extend our capabilities for neutrino experiments, largely emphasizing the physics of neutrino interactions.
hep-ph↗
Effects of Gauge Interactions on Fermion Masses in Models with Fermion Wavefunctions Separated in Higher Dimensions
We consider models that generate hierarchies via the separation of fermion wavefunctions in higher-dimensional spaces. We calculate the effects of gauge interactions between fermions and show that these are important and could help to explain (i) why the heaviest known fermion is a charge 2/3 quark, rather than a charge -1/3 quark or a lepton, (ii) why this fermion has a mass $m_t$ comparable to the electroweak symmetry breaking scale $M_{ew}$, (iii) the patterns $m_t >> m_b > m_τ$ and $m_c >> m_s > m_μ$, and (iv) the smallness of neutrino masses.
hep-ph↗
Weak and Electromagnetic Nuclear Decay Signatures for Neutrino Reactions in SuperKamiokande
We suggest the study of events in the SuperKamiokande neutrino data due to charged- and neutral-current neutrino reactions followed by weak and/or electromagnetic decays of struck nuclei and fragments thereof. This study could improve the prospects of obtaining evidence for $τ$ production from $ν_μ\to ν_τ$ oscillations and could augment the data sample used to disfavor $ν_μ\to ν_{sterile}$ oscillations.
hep-ph↗
On "Sub-Threshold" Reactions Involving Nuclear Fission
We analyze reactions of several types that are naively below threshold but can proceed because of the release of binding energy from nuclear fission and occasionally the formation of Coulombic bound states. These reactions include (i) photofission with pion production and (ii) charged current neutrino-nucleus reactions that lead to fission and/or formation of a Coulomb bound state of a $μ^-$ with the nucleus of a fission fragment. We comment on the possible experimental observation of these reactions.
nucl-th↗
Physics at a Neutrino Factory
In response to the growing interest in building a Neutrino Factory to produce high intensity beams of electron- and muon-neutrinos and antineutrinos, in October 1999 the Fermilab Directorate initiated two six-month studies. The first study, organized by N. Holtkamp and D. Finley, was to investigate the technical feasibility of an intense neutrino source based on a muon storage ring. This design study has produced a report in which the basic conclusion is that a Neutrino Factory is technically feasible, although it requires an aggressive R&D program. The second study, which is the subject of this report, was to explore the physics potential of a Neutrino Factory as a function of the muon beam energy and intensity, and for oscillation physics, the potential as a function of baseline.
hep-ex↗
T=0 Partition Functions for Potts Antiferromagnets on Lattice Strips with Fully Periodic Boundary Conditions
We present exact calculations of the zero-temperature partition function for the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial) for families of arbitrarily long strip graphs of the square and triangular lattices with width $L_y=4$ and boundary conditions that are doubly periodic or doubly periodic with reversed orientation (i.e. of torus or Klein bottle type). These boundary conditions have the advantage of removing edge effects. In the limit of infinite length, we calculate the exponent of the entropy, $W(q)$ and determine the continuous locus ${\cal B}$ where it is singular. We also give results for toroidal strips involving ``crossing subgraphs''; these make possible a unified treatment of torus and Klein bottle boundary conditions and enable us to prove that for a given strip, the locus ${\cal B}$ is the same for these boundary conditions.
cond-mat.stat-mech↗
Spanning Trees on Graphs and Lattices in d Dimensions
The problem of enumerating spanning trees on graphs and lattices is considered. We obtain bounds on the number of spanning trees $N_{ST}$ and establish inequalities relating the numbers of spanning trees of different graphs or lattices. A general formulation is presented for the enumeration of spanning trees on lattices in $d\geq 2$ dimensions, and is applied to the hypercubic, body-centered cubic, face-centered cubic, and specific planar lattices including the kagomé, diced, 4-8-8 (bathroom-tile), Union Jack, and 3-12-12 lattices. This leads to closed-form expressions for $N_{ST}$ for these lattices of finite sizes. We prove a theorem concerning the classes of graphs and lattices ${\cal L}$ with the property that $N_{ST} \sim \exp(nz_{\cal L})$ as the number of vertices $n \to \infty$, where $z_{\cal L}$ is a finite nonzero constant. This includes the bulk limit of lattices in any spatial dimension, and also sections of lattices whose lengths in some dimensions go to infinity while others are finite. We evaluate $z_{\cal L}$ exactly for the lattices we considered, and discuss the dependence of $z_{\cal L}$ on d and the lattice coordination number. We also establish a relation connecting $z_{\cal L}$ to the free energy of the critical Ising model for planar lattices ${\cal L}$.
cond-mat.stat-mech↗
Ground State Entropy of Potts Antiferromagnets and the Approach to the 2D Thermodynamic Limit
We study the ground state degeneracy per site (exponent of the ground state entropy) $W(Λ,(L_x=\infty) \times L_y,q)$ for the $q$-state Potts antiferromagnet on infinitely long strips with width $L_y$ of 2D lattices $Λ$ with free and periodic boundary conditions in the $y$ direction, denoted FBC$_y$ and PBC$_y$. We show that the approach of $W$ to its 2D thermodynamic limit as $L_y$ increases is quite rapid; for moderate values of $q$ and $L_y \simeq 4$, $W(Λ,(L_x=\infty) \times L_y,q)$ is within about 5 % and ${\cal O}(10^{-3})$ of the 2D value $W(Λ,(L_x=\infty) \times (L_y=\infty),q)$ for FBC$_y$ and PBC$_y$, respectively. The approach of $W$ to the 2D thermodynamic limit is proved to be monotonic (non-monotonic) for FBC$_y$ (PBC$_y$). It is noted that ground state entropy determinations on infinite strips can be used to obtain the central charge for cases with critical ground states.
cond-mat.stat-mech↗
Ground State Entropy in Potts Antiferromagnets and Chromatic Polynomials
We discuss recent results on ground state entropy in Potts antiferromagnets and connections with chromatic polynomials. These include rigorous lower and upper bounds, Monte Carlo measurements, large--$q$ series, exact solutions, and studies of analytic properties. Some related results on Fisher zeros of Potts models are also mentioned.
hep-lat↗
Study of the Potts Model on the Honeycomb and Triangular Lattices: Low-Temperature Series and Partition Function Zeros
We present and analyze low-temperature series and complex-temperature partition function zeros for the $q$-state Potts model with $q=4$ on the honeycomb lattice and $q=3,4$ on the triangular lattice. A discussion is given as to how the locations of the singularities obtained from the series analysis correlate with the complex-temperature phase boundary. Extending our earlier work, we include a similar discussion for the Potts model with $q=3$ on the honeycomb lattice and with $q=3,4$ on the kagomé lattice.
cond-mat.stat-mech↗
Complex-Temperature Singularities in the $d=2$ Ising Model. II. Triangular Lattice
We investigate complex-temperature singularities in the Ising model on the triangular lattice. Extending an earlier analysis of the low-temperature series expansions for the (zero-field) susceptibility $\barχ$ by Guttmann \cite{g75} to include the use of differential approximants, we obtain further evidence in support of his conclusion that the exponent describing the divergence in $χ$ at $u=u_e=-1/3$ (where $u = e^{-4K}$) is $γ_e'=5/4$ and refine his estimate of the critical amplitude. We discuss the remarkable nature of this singularity, at which the spontaneous magnetisation diverges (with exponent $β_e=-1/8$) and show that it lies at the endpoint of a singular line segment constituting part of the natural boundaries of the free energy in the complex $u$ plane. Using exact results, we find that the specific heat has a divergent singularity at $u=-1/3$ with exponent $α_e'=1$, so that the relation $α_e'+2β_e+γ_e'=2$ is satisfied. We also study the singularity at $u=u_s=-1$, where $M$ vanishes (with $β_s=3/8$) and $C$ diverges logarithmically (with $α_s' = α_s = 0$).
hep-lat↗
Complex-Temperature Singularities of the Susceptibility in the $d=2$ Ising Model. I. Square Lattice
We investigate the complex-temperature singularities of the susceptibility of the 2D Ising model on a square lattice. From an analysis of low-temperature series expansions, we find evidence that as one approaches the point $u=u_s=-1$ (where $u=e^{-4K}$) from within the complex extensions of the FM or AFM phases, the susceptibility has a divergent singularity of the form $χ\sim A_s'(1+u)^{-γ_s'}$ with exponent $γ_s'=3/2$. The critical amplitude $A_s'$ is calculated. Other critical exponents are found to be $α_s'=α_s=0$ and $β_s=1/4$, so that the scaling relation $α_s'+2β_s+γ_s'=2$ is satisfied. However, using exact results for $β_s$ on the square, triangular, and honeycomb lattices, we show that universality is violated at this singularity: $β_s$ is lattice-dependent. Finally, from an analysis of spin-spin correlation functions, we demonstrate that the correlation length and hence susceptibility are finite as one approaches the point $u=-1$ from within the symmetric phase. This is confirmed by an explicit study of high-temperature series expansions.
hep-lat↗
Phases in Leptonic Mass Matrices: Higher Order Invariants and Applications to Models
We discuss complex rephasing invariants of charged lepton and neutrino mass matrices and associated theorems which determine in general (i) the number of physically meaningful phases in these matrices and (ii) which elements of these matrices can be rendered real by rephasings. New results are presented on higher order complex invariants and the application of the methods to several models.
hep-ph↗
General Analysis of Phases in Quark Mass Matrices
We give a detailed discussion of our general determination of (i) the number of unremovable, physically meaningful phases in quark mass matrices and (ii) which elements of these matrices can be rendered real by rephasings of fermion fields. The results are applied to several currently viable models. New results are presented for an arbitrary number of fermion generations; these provide further insight into the three-generation case of physical interest.
hep-ph↗
General Determination of Phases in Leptonic Mass Matrices
We construct new invariants and give several theorems which determine in general (i) the number of physically meaningful phases in charged lepton and neutrino mass matrices and (ii) which elements of these matrices can be rendered real by rephasings. We illustrate our results with simple models.
hep-ph↗
General Determination of Phases in Quark Mass Matrices
We construct new invariants and give several theorems which determine in general (i) the number of physically meaningful phases in quark mass matrices and (ii) which elements of these matrices can be rendered real by rephasings. We illustrate our results with simple models.
hep-ph↗
On the Origin of Fermion Masses
We review some recent work on nonperturbative properties of fermions and connections with chiral gauge theories. In particular, we consider one of the ultimate goals of this program: the understanding of the actual fermion mass spectrum. It is pointed out that if quarks and leptons are composite, their masses may be set by the physics of the preons and their interactions in such a manner as to differ considerably from the Yukawa form $m_f \propto v$ (where $v$ is the electroweak symmetry breaking scale) or analogous forms involving $v$. Some ideas of how this might work are given, and some implications are discussed.
hep-ph↗