arXiv subjects
Publications and source records attributed to Scott Willenbrock.
In honor of Dave Roper's 90th birthday, I present a pedagogical introduction to our modern understanding of unstable particles in Quantum Field Theory, based on the analytic structure of the propagator, with occasional remarks on the Roper resonance. I discuss the mass and decay rate of unstable particles, Breit-Wigner resonance formulae and width, poles and branch cuts, and pole trajectories.
It has been known since the 1950's that an unstable particle is associated with a complex pole in the propagator. This had to be rediscovered twice: in the early 1970's in the context of hadronic resonances, and in the early 1990's in the context of the $Z$ boson. The physical mass of the particle is the real part of the pole in the complex energy plane. In hadronic physics, this replaced the ``Breit-Wigner mass,'' which was found to depend on the parameterization of the ``energy-dependent width.'' In $Z$ physics, it replaced the ``on-shell'' mass, which was found to be gauge dependent. Although the mass defined from the complex pole position has been widely discussed in the literature, it has not yet made its way into quantum field theory textbooks.
We show that the mass and width of an unstable particle are precisely defined by the pole in the complex energy plane, $μ= m - (i/2)Γ$, by identifying the width, $Γ$, with the particle's decay rate and the mass, $m$, with the oscillatory frequency. We find that the physical $Z$ boson mass lies 26 MeV below its quoted value, while the physical $W$ boson mass lies 20 MeV below. We also clarify the various Breit-Wigner formulae that are used to describe a resonance.
We review the effective field theory approach to physics beyond the Standard Model using dimension-six operators. Topics include the choice of operator basis, electroweak boson pair production, precision electroweak physics (including one-loop contributions), and Higgs physics. By measuring the coefficients of dimension-six operators with good accuracy, we can hope to infer some or all of the features of the theory that lies beyond the Standard Model.
We derive bounds on nine dimension-six operators involving electroweak gauge bosons and the Higgs boson from precision electroweak data. Four of these operators contribute at tree level, and five contribute only at one loop. Using the full power of effective field theory, we show that the bounds on the five loop-level operators are much weaker than previously claimed, and thus much weaker than bounds from tree-level processes at high-energy colliders.
The one loop effects of two dimension-six operators on gauge boson self energies are computed within an effective field theory framework. These self energies are translated into effects on precision electroweak observables, and bounds are obtained on the operator coefficients. The effective field theory framework allows for the divergences that arise in the loop calculations to be properly handled, and for unambiguous bounds on the coefficients to be obtained. We find that the coefficients are only weakly bounded, in contrast to previous calculations that obtained much stronger bounds. We argue that the results of these previous calculations are specious.
We study non-standard top quark couplings in the effective field theory approach. All nine dimension-six operators that generate anomalous couplings between the electroweak gauge bosons and the third-generation quarks are included. We calculate their contributions at tree level and one loop to all major precision electroweak observables. The calculations are compared with data to obtain constraints on eight of these operators.
Effective field theory is the ideal framework for discussing top and weak boson properties. We discuss the application of this framework to top physics at both tree level and one loop. We consider weak boson pair production within an effective field theory framework, and argue that one need not be concerned with the violation of unitarity bounds at energies beyond the region where there are data.
We advocate an effective field theory approach to anomalous couplings. The effective field theory approach is the natural way to extend the standard model such that the gauge symmetries are respected. It is general enough to capture any physics beyond the standard model, yet also provides guidance as to the most likely place to see the effects of new physics. The effective field theory approach also clarifies that one need not be concerned with the violation of unitarity in scattering processes at high energy. We apply these ideas to pair production of electroweak vector bosons.
In this review, we summarize tests of standard electroweak (EW) theory at the highest available energies as a precursor to the Large Hadron Collider (LHC) era. Our primary focus is on the published results (as of March 2010) from proton- antiproton collisions at $\sqrt{s}=1.96$ TeV at the Fermilab Tevatron collected using the CDF and D0 detectors. This review is very timely since the LHC scientific program is nearly underway with the first high-energy ($\sqrt{s}=7$ TeV) collisions about to begin. After presenting an overview of the EW sector of the standard model, we provide a summary of current experimental tests of EW theory. These include gauge boson properties and self-couplings, tests of EW physics from top quark sector, and searches for the Higgs boson.
The amplitude for Higgs decay to two photons is calculated in renormalizable and unitary gauges using dimensional regularization at intermediate steps. The result is finite, gauge independent, and in agreement with previously published results. The large Higgs mass limit is examined using the Goldstone-boson equivalence theorem as a check on the use of dimensional regularization and to explain the absence of decoupling.
Diversification return is an incremental return earned by a rebalanced portfolio of assets. The diversification return of a rebalanced portfolio is often incorrectly ascribed to a reduction in variance. We argue that the underlying source of the diversification return is the rebalancing, which forces the investor to sell assets that have appreciated in relative value and buy assets that have declined in relative value, as measured by their weights in the portfolio. In contrast, the incremental return of a buy-and-hold portfolio is driven by the fact that the assets that perform the best become a greater fraction of the portfolio. We use these results to resolve two puzzles associated with the Gorton and Rouwenhorst index of commodity futures, and thereby obtain a clear understanding of the source of the return of that index. Diversification return can be a significant source of return for any rebalanced portfolio of volatile assets.
We present an effective-field-theory calculation of the effect of a dimension-six operator involving the top quark on precision electroweak data via a top-quark loop. We demonstrate the renormalizability, in the modern sense, of the effective field theory. We use the oblique parameter U to bound the coefficient of the operator, and compare with the bound derived from top-quark decay.
We discuss new physics in top-quark interactions, using an effective field theory approach. We consider top-quark decay, single top production, and top-quark pair production. We identify 15 dimension-six operators that contribute to these processes, and we compute the deviation from the Standard Model induced by these operators. The results provide a systematic way of searching for (or obtaining bounds on) physics beyond the Standard Model.
Physics beyond the standard model can affect top-quark physics indirectly. We describe the effective field theory approach to describing such physics, and contrast it with the vertex-function approach that has been pursued previously. We argue that the effective field theory approach has many fundamental advantages and is also simpler.
This is a summary of the talks presented at the International Workshop on Top Quark Physics (top2008) held in Elba, Italy, May 18-24, 2008.
The breaking of SO(10) to SU(3)_C x U(1)_EM can be accomplished by just four Higgs fields: the symmetric rank-two tensor, S(54); a pair of spinors, C(16) and Cbar(16bar); and a vector, T(10). This setup is also able to generate realistic fermion masses. The heavy color triplets in the vector and spinor fields mediate proton decay via dimension-five operators. The experimental bounds on proton decay constrain the structure and size of the Yukawa operators.
We define the collinear factorization scheme, which absorbs only the collinear physics into the parton distribution functions. In order to isolate the collinear physics, we introduce a procedure to combine real and virtual corrections, canceling infrared singularities prior to integration. In the collinear scheme, the factorization scale $μ$ has a simple physical interpretation as a collinear cutoff. We present a method for choosing the factorization scale and apply it to the Drell-Yan process; we find $μ\approx Q/2$, where $Q$ is the vector-boson invariant mass. We show that, for a wide variety of collision energies and $Q$, the radiative corrections are small in the collinear scheme for this choice of factorization scale.