Roy-Steiner equations for pion-nucleon scattering

In the partonic (or light-front) description of relativistic systems the electromagnetic form factors are expressed in terms of frame-independent charge and magnetization densities in transverse space. This formulation allows one to identify the chiral components of nucleon structure as the peripheral densities at transverse distances b = O(M −1 π ) and compute them in a parametrically controlled manner. A dispersion relation connects the large-distance behavior of the transverse charge and magnetization densities to the spectral functions of the Dirac and Pauli form factors near the two-pion threshold at timelike t = 4M 2 π , which can be computed in relativistic chiral effective field theory. Using the leading-order approximation we (a) derive the asymptotic behavior (Yukawa tail) of the isovector transverse densities in the "chiral" region b = O(M −1 π ) and the "molecular" region b = O(M 2 N /M 3 π ); (b) perform the heavy-baryon expansion of the transverse densities; (c) explain the relative magnitude of the peripheral charge and magnetization densities in a simple mechanical picture; (d) include ∆ isobar intermediate states and study the peripheral transverse densities in the large-N c limit of QCD; (e) quantify the region of transverse distances where the chiral components of the densities are numerically dominant; (f) calculate the chiral divergences of the b 2 -weighted moments of the isovector transverse densities (charge and anomalous magnetic radii) in the limit M π → 0 and determine their spatial support. Our approach provides a concise formulation of the spatial structure of the nucleon's chiral component and offers new insights into basic properties of the chiral expansion. It relates the information extracted from low-t elastic form factors to the generalized parton distributions probed in peripheral high-energy scattering processes.

Section: Jhep01(2014)092mentioning

confidence: 55%

Section: Jhep01(2014)092mentioning

confidence: 99%

Chiral dynamics and peripheral transverse densities

Granados

Weiß

2014

“…In order to render this analogy manifest, we slightly change conventions compared to [26]: we identify here γ * γ * → ππ as the s-channel process instead of γ * π → γ * π. This assignment is slightly unnatural when it comes to constructing dispersion relations for a process with these crossing properties, see [34][35][36][37], but makes the inclusion into the unitarity relation in HLbL more straightforward.…”

Section: Jhep09(2015)074mentioning

confidence: 99%

“…To this end, the Roy-Steiner treatment of [36] can be generalized to the doubly-virtual case. One starts by writing down hyperbolic dispersion relations 37) with hyperbola parameter a [34]. If we invert (2.32) to express the A i in terms of the helicity amplitudes and insert the partial-wave expansion both on the left-and right-hand side of the dispersion relation, we obtain a set of Roy-Steiner equations 38) where i, j ∈ {1, 2, 3, 4, 5}, …”

Section: )mentioning

confidence: 99%

Dispersion relation for hadronic light-by-light scattering: theoretical foundations

Colangelo

Hoferichter

Procura

et al. 2015

197

207

In this paper we make a further step towards a dispersive description of the hadronic light-by-light (HLbL) tensor, which should ultimately lead to a data-driven evaluation of its contribution to (g − 2) µ . We first provide a Lorentz decomposition of the HLbL tensor performed according to the general recipe by Bardeen, Tung, and Tarrach, generalizing and extending our previous approach, which was constructed in terms of a basis of helicity amplitudes. Such a tensor decomposition has several advantages: the role of gauge invariance and crossing symmetry becomes fully transparent; the scalar coefficient functions are free of kinematic singularities and zeros, and thus fulfill a Mandelstam doubledispersive representation; and the explicit relation for the HLbL contribution to (g − 2) µ in terms of the coefficient functions simplifies substantially. We demonstrate explicitly that the dispersive approach defines both the pion-pole and the pion-loop contribution unambiguously and in a model-independent way. The pion loop, dispersively defined as pion-box topology, is proven to coincide exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors.

“…of [93][94][95] will help clarify the situation concerning the phenomenological determination of σ πN [96][97][98].…”

Section: Jhep07(2015)129mentioning

confidence: 99%

Light stops, blind spots, and isospin violation in the MSSM

Crivellin

Hoferichter

Procura

et al. 2015

In the framework of the MSSM, we examine several simplified models where only a few superpartners are light. This allows us to study WIMP-nucleus scattering in terms of a handful of MSSM parameters and thereby scrutinize their impact on dark matter direct-detection experiments. Focusing on spin-independent WIMP-nucleon scattering, we derive simplified, analytic expressions for the Wilson coefficients associated with Higgs and squark exchange. We utilize these results to study the complementarity of constraints due to direct-detection, flavor, and collider experiments. We also identify parameter configurations that produce (almost) vanishing cross sections. In the proximity of these so-called blind spots, we find that the amount of isospin violation may be much larger than typically expected in the MSSM. This feature is a generic property of parameter regions where cross sections are suppressed, and highlights the importance of a careful analysis of the nucleon matrix elements and the associated hadronic uncertainties. This becomes especially relevant once the increased sensitivity of future direct-detection experiments corners the MSSM into these regions of parameter space.