Off-shell Method Research Articles

Precision Higgs width and couplings with a high energy muon collider

The interpretation of Higgs data is typically based on different assumptions about whether there can be additional decay modes of the Higgs or if any couplings can be bounded by theoretical arguments. Going beyond these assumptions requires either a precision measurement of the Higgs width or an absolute measurement of a coupling to eliminate a flat direction in precision fits that occurs when ghVV/ghVVSM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left|{g}_{hVV}/{g}_{hVV}^{SM}\\right| $$\\end{document} > 1, where V = W±, Z. In this paper we explore how well a high energy muon collider can test Higgs physics without having to make assumptions on the total width of the Higgs. In particular, we investigate off-shell methods for Higgs production used at the LHC and searches for invisible decays of the Higgs to see how powerful they are at a muon collider. We then investigate the theoretical requirements on a model which can exist in such a flat direction. Combining expected Higgs precision with other constraints, the most dangerous flat direction is described by generalized Georgi-Machacek models. We find that by combining direct searches with Higgs precision, a high energy muon collider can robustly test single Higgs precision down to the O.1%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left(.1\\%\\right) $$\\end{document} level without having to assume SM Higgs decays. Furthermore, it allows one to bound new contributions to the width at the sub-percent level as well. Finally, we comment on how even in this difficult flat direction for Higgs precision, a muon collider can robustly test or discover new physics in multiple ways. Expanding beyond simple coupling modifiers/EFTs, there is a large region of parameter space that muon colliders can explore for EWSB that is not probed with only standard Higgs precision observables.

Vanishing of Black Hole Tidal Love Numbers from Scattering Amplitudes.

We extract the black hole (BH) static tidal deformability coefficients (Love numbers) and their spin-0 and spin-1 analogs by comparing on-shell amplitudes for fields to scatter off a spinning BH in the worldline effective field theory and in general relativity. We point out that the general relativity amplitudes due to tidal effects originate entirely from the BH potential region. Thus, they can be separated from gravitational nonlinearities in the wave region, whose proper treatment requires higher order effective field theory loop calculations. In particular, the elastic scattering in the near field approximation is produced exclusively by tidal effects. We find this contribution to vanish identically, which implies that the static Love numbers of Kerr BHs are zero for all types of perturbations. We also reproduce the known behavior of scalar Love numbers for higher-dimensional BHs. Our results are manifestly gauge invariant and coordinate independent, thereby providing a valuable consistency check for the commonly used off-shell methods.

No triangles on the moduli space of maximally supersymmetric gauge theory

Maximally supersymmetric gauge theory in four dimensions has a remarkably simple S-matrix at the origin of its moduli space at both tree and loop level. This leads to the question what, if any, of this structure survives at the complement of this one point. Here this question is studied in detail at one loop for the branch of the moduli space parameterized by a vacuum expectation value for one complex scalar. Motivated by the parallel D-brane picture of spontaneous symmetry breaking a simple relation is demonstrated between the Lagrangian of broken super Yang-Mills theory and that of its higher dimensional unbroken cousin. Using this relation it is proven both through an on- as well as an off-shell method there are no so-called triangle coefficients in the natural basis of one-loop functions at any finite point of the moduli space for the theory under study. The off-shell method yields in addition absence of rational terms in a class of theories on the Coulomb branch which includes the special case of maximal supersymmetry. The results in this article provide direct field theory evidence for a recently proposed exact dual conformal symmetry motivated by the AdS/CFT correspondence.

Off-shell Bethe ansatz equation for osp(2∣1) Gaudin magnets

The semi-classical limit of the algebraic Bethe Ansatz method is used to solve the theory of Gaudin models. Via the off-shell method we find the spectra and eigenvectors of the N-1 independent Gaudin Hamiltonians with symmetry osp(2|1). We also show how the off-shell Gaudin equation solves the trigonometric Knizhnik- Zamolodchikov equation.

Euclidean approach to the entropy for a scalar field in Rindler-like space-times.

The off-shell entropy for a massless scalar field in a $D$-dimensional Rindler-like space-time is investigated within the conical Euclidean approach in the manifold ${C}_{\ensuremath{\beta}}\ifmmode\times\else\texttimes\fi{}{\mathcal{M}}^{N}$, ${C}_{\ensuremath{\beta}}$ being the two-dimensional cone, making use of the $\ensuremath{\zeta}$-function regularization. Because of the presence of conical singularities, it is shown that the relation between the $\ensuremath{\zeta}$ function and the heat kernel is nontrivial and, as first pointed out by Cheeger, requires a separation between small and large eigenvalues of the Laplace operator. As a consequence, in the massless case, the (naive) nonexistence of the Mellin transform is bypassed by Cheeger's analytical continuation of the $\ensuremath{\zeta}$ function on the manifold with conical singularities. Furthermore, the continuous spectrum leads to the introduction of smeared traces. In general, it is pointed out that the presence of the divergences may depend on the smearing function and they arise in removing the smearing cutoff. With a simple choice of the smearing function, horizon divergences in the thermodynamical quantities are recovered and these are similar to the divergences found by means of off-shell methods such as the brick-wall model, the optical conformal transformation techniques, or the canonical path-integral method.

Infrared and mass regularization in AF field theories (II). QCD

We determine the non-leading QCD corrections to deep inelastic (DI) scattering and to the Drell-Yan (DY) process by analysing the order g 2 parton cross sections. Using the insight and the techniques developed in the more simple environment of π 6 3, we regularize and subsequently remove the mass (M), infrared (IR), and ultraviolet (UV) divergences of the (double) cut graphs with the methods exposed in paper I. The QCD calculations are technically more involved. New M divergences are found, IR singularities occur, and overlapping M and IR singularities exist leading to double poles if n-dimensional regularization is used. Gluon gauge invariance must be satisfied. Although the off-shell method leads to gauge-dependent parton cross sections, the correction terms extracted via M factorization remain gauge invariant. The off-shell mass assignment was ill-defined in the past and did not satisfy the double cut rule; we explain the implications. The correction terms are explicitly shown to be independent of any regularization method. Defining the scale-dependent momentum distribution to consist of log Q 2 terms only, their influence in DI scattering is moderate, but considerable in DY massive μμ pair production for Q 2 ⩽ 100 GeV 2.

Bethe-Salpeter Equation

We treat the Bethe-Salpeter equation as a problem in singular integral equations. As such, it has three outstanding features: its algebraic structure, the fixed propagator singularities in the direct channel, and the possible singularities in the potential, which are usually moving singularities. We exploit the algebraic structure in order to give insight into the possible correctness classes for the equation. We give explicit prescriptions for the removal of fixed singularities in a wide class of equations. We show under what circumstances these prescriptions can be adapted to maintain such desirable features as symmetry of the kernel. Moving singularities arise in physically realistic kernels; they are the crossed-channel singularities. The basic mathematics of such singularities is well known and is related to the Riemann-Hilbert problem, but this is useless in off-shell methods because it cannot cope with the integration over the space parts of 4-momenta. Instead, we adopt a method (proposed by one of us elsewhere) based on analyticity in energy variables. The resulting formalism is too complicated to be applied in full generality. We therefore consider the example of the single-particle exchange potential in detail, and show how the moving singularities can be eliminated, exhibiting the resulting equations explicitly in a form to which our theory of fixed singularities can immediately be applied. All our arguments are exact.

Comparison between an Off-Shell Perturbative Method and the On-Shell Dashen-Frautschi Method

An off-shell method of calculating the effects of a small perturbation on the discrete and the continuous spectrum of a two-particle system is developed. The derivation, made in a nonrelativistic context, lends itself to easy extension to some relativistic models. The method, by means of which both short- and long-range perturbations can be handled, is then applied to simple models to test the reliability of the Born approximation to the Dashen-Frautschi (DF) perturbative formula. First the convergence for short-range perturbations is tested. It is found that both perturbative methods are rapidly convergent, unless a virtual state is near the physical threshold. Second, the results are compared: The scattering-length shifts calculated by the DF formula in the Born approximation and by the off-shell formula are of the same order of magnitude for a crude model of $\mathrm{NN}$ interaction. Finally, long-range (Coulomb) perturbations are tested. If in the DF formula we approximate the first-order change in the amplitude by the contribution of the one-photon exchange, the binding-energy shift is different by a factor of ten in magnitude from the corresponding off-shell value. Furthermore, the off-shell value seems less sensitive to the high-energy structure of the form factor than the on-shell value is.