TESLA Technical Design Report Part III: Physics at an e+e- Linear Collider
The TESLA Technical Design Report Part III: Physics at an e+e- Linear Collider
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arXiv subjects
T. Gehrmann
Publications and source records attributed to T. Gehrmann.
Physics at the front-end of a neutrino factory: a quantitative appraisal
We present a quantitative appraisal of the physics potential for neutrino experiments at the front-end of a muon storage ring. We estimate the forseeable accuracy in the determination of several interesting observables, and explore the consequences of these measurements. We discuss the extraction of individual quark and antiquark densities from polarized and unpolarized deep-inelastic scattering. In particular we study the implications for the undertanding of the nucleon spin structure. We assess the determination of alpha_s from scaling violation of structure functions, and from sum rules, and the determination of sin^2(theta_W) from elastic nu-e and deep-inelastic nu-p scattering. We then consider the production of charmed hadrons, and the measurement of their absolute branching ratios. We study the polarization of Lambda baryons produced in the current and target fragmentation regions. Finally, we discuss the sensitivity to physics beyond the Standard Model.
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Two-Loop Master Integrals for $γ^* \to 3$ Jets: The non-planar topologies
The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three on-shell legs. Up to now, only those master integrals corresponding to planar topologies were known. In this paper, we compute the yet outstanding non-planar master integrals by solving differential equations in the external invariants which are fulfilled by these master integrals. We obtain the master integrals as expansions in $\e=(4-d)/2$, where $d$ is the space-time dimension. The fully analytic results are expressed in terms of the two-dimensional harmonic polylogarithms already introduced in the evaluation of the planar topologies.
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Progress on two-loop non-propagator integrals
At variance with fully inclusive quantities, which have been computed already at the two- or three-loop level, most exclusive observables are still known only at one loop, as further progress was hampered up to very recently by the greater computational problems encountered in the study of multi-leg amplitudes beyond one loop. We discuss the progress made lately in the evaluation of two-loop multi-leg integrals, with particular emphasis on two-loop four-point functions.
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Two-Loop Master Integrals for $γ^* \to 3$ Jets: The planar topologies
The calculation of the two-loop corrections to the three jet production rate and to event shapes in electron-positron annihilation requires the computation of a number of up to now unknown two-loop four-point master integrals with one off-shell and three on-shell legs. In this paper, we compute those master integrals which correspond to planar topologies by solving differential equations in the external invariants which are fulfilled by the master integrals. We obtain the master integrals as expansions in $\e=(4-d)/2$, where $d$ is the space-time dimension. The results are expressed in terms of newly introduced two-dimensional harmonic polylogarithms, whose properties are shortly discussed. For all two-dimensional harmonic polylogarithms appearing in the divergent parts of the integrals, expressions in terms of Nielsen's polylogarithms are given. The analytic continuation of our results to other kinematical situations is outlined.
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Using differential equations to compute two-loop box integrals
The calculation of exclusive observables beyond the one-loop level requires elaborate techniques for the computation of multi-leg two-loop integrals. We discuss how the large number of different integrals appearing in actual two-loop calculations can be reduced to a small number of master integrals. An efficient method to compute these master integrals is to derive and solve differential equations in the external invariants for them. As an application of the differential equation method, we compute the ${\cal O}(ε)$-term of a particular combination of on-shell massless planar double box integrals, which appears in the tensor reduction of $2 \to 2$ scattering amplitudes at two loops.
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Differential Equations for Two-Loop Four-Point Functions
At variance with fully inclusive quantities, which have been computed already at the two- or three-loop level, most exclusive observables are still known only at one-loop, as further progress was hampered so far by the greater computational problems encountered in the study of multi-leg amplitudes beyond one loop. We show in this paper how the use of tools already employed in inclusive calculations can be suitably extended to the computation of loop integrals appearing in the virtual corrections to exclusive observables, namely two-loop four-point functions with massless propagators and up to one off-shell leg. We find that multi-leg integrals, in addition to integration-by-parts identities, obey also identities resulting from Lorentz-invariance. The combined set of these identities can be used to reduce the large number of integrals appearing in an actual calculation to a small number of master integrals. We then write down explicitly the differential equations in the external invariants fulfilled by these master integrals, and point out that the equations can be used as an efficient method of evaluating the master integrals themselves. We outline strategies for the solution of the differential equations, and demonstrate the application of the method on several examples.
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The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
The class of the two-loop massless crossed boxes, with light-like external legs, is the final unresolved issue in the program of computing the scattering amplitudes of 2 --> 2 massless particles at next-to-next-to-leading order. In this paper, we describe an algorithm for the tensor reduction of such diagrams. After connecting tensor integrals to scalar ones with arbitrary powers of propagators in higher dimensions, we derive recurrence relations from integration-by-parts and Lorentz-invariance identities, that allow us to write the scalar integrals as a combination of two master crossed boxes plus simpler-topology diagrams. We derive the system of differential equations that the two master integrals satisfy using two different methods, and we use one of these equations to express the second master integral as a function of the first one, already known in the literature. We then give the analytic expansion of the second master integral as a function of epsilon=(4-D)/2, where D is the space-time dimension, up to order O(epsilon^0).
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Measuring $F_L(x,Q^2)/F_2(x,Q^2)$ from Azimuthal Asymmetries in Deep Inelastic Scattering
We demonstrate that the angular distribution of hadrons produced in semi-inclusive deep inelastic final states is related to the inclusive longitudinal structure function. This relation could provide a new method of accessing $F_L(x,Q^2)$ in deep inelastic scattering measurements.
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Summary: Spin Physics
The spin physics parallel sessions at this workshop made a critical review of the physics potential of future experiments on polarized nucleons, with an emphasis on the potential impact of polarized electron-proton collisions at HERA. A summary of the results and discussions from these sessions is presented in this article.
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Azimuthal Asymmetries in Hadronic Final States at HERA
The distribution of hadrons produced in deeply inelastic electron-proton collisions depends on the azimuthal angle between lepton scattering plane and hadron production plane in the photon-proton centre-of-mass frame. In addition to the well known up-down asymmetry induced by the azimuthal dependence of the Born level subprocess, there is also a non-vanishing left-right asymmetry, provided the incoming electron is polarized. This asymmetry is time-reversal-odd and induced by absorptive corrections to the Born level process. We investigate the numerical magnitude of azimuthal asymmetries in semi-inclusive hadron production at HERA with particular emphasis on a possible determination of the time-reversal-odd asymmetry.
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Spin Dependence of Deep Inelastic Diffraction
Using a perturbative model for diffractive interactions, we derive an expression for the polarized diffractive structure function $g_1^D$ in the high energy limit. This structure function is given by the interference of diffractive amplitudes with polarized and unpolarized exchanges. For the polarized exchange we consider both two-gluon and quark-antiquark amplitudes. The polarized diffractive amplitude receives sizable contributions from non-strongly ordered regions in phase space, resulting in a double logarithmic enhancement at small $x$. The resummation of these double logarithmic terms is outlined. We also discuss the transition from our perturbative expression to the nonperturbative region. A first numerical estimate indicates that the perturbative contribution to the spin asymmetry is substantially larger than the nonperturbative one.
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Combined analysis of diffractive and inclusive structure functions in the semiclassical framework
Small-x DIS is described as the scattering of a partonic fluctuation of the photon off a superposition of target color fields. Diffraction occurs if the emerging partonic state is in a color singlet. Introducing a specific model for the averaging over all relevant color field configurations, both diffractive and inclusive parton distributions at some low scale Q_0^2 can be calculated. A conventional DGLAP analysis results in a good description of diffractive and inclusive structure functions at higher values of Q^2.
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Spin physics in deep inelastic scattering: Summary
The problem of our understanding of the spin structure of the nucleon has been with us since the publication of the EMC measurements of the polarised structure function of the proton in 1987. In this talk a review of the results presented in Working Group 6 at this workshop is given.
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Inclusive and Diffractive Structure Functions at Small x
In the semiclassical approach, inclusive and diffractive quark and gluon distributions are expressed in terms of correlation functions of Wilson loops. Each Wilson loop integrates the colour field strength in the area between the trajectories of two fast partons penetrating the proton. We introduce a specific model for averaging over the relevant colour field configurations. Within this model, all parton distributions at some low scale Q_0^2 are given in terms of three parameters. Inclusive and diffractive structure functions at higher values of Q^2 are determined in a leading-order QCD analysis. In both cases, the evolution is driven by a large gluon distribution. A satisfactory description of the structure functions F_2(x,Q^2) and F_2^D(3)(xi,beta,Q^2) is obtained. The observed rise of F_2^D(3) with xi is parametrized by a non-perturbative logarithmic energy dependence, compatible with unitarity. In our analysis, the observed rise of F_2 at small x is largely due to the same effect.
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Physics with Polarized Protons at HERA
The operation of HERA with polarized proton and electron beams will allow to study a wide variety of observables in polarized electron-proton collisions at $\sqrt s=300$ GeV. The physics prospects of this project have been elaborated in detail in a dedicated working group, whose results we summarize in this report. We show that several important and often unique measurements in spin physics could be made at HERA. These include measurements of the polarized structure function $g_1(x,Q^2)$ at low $x$, a direct determination of the polarized gluon distribution $ΔG(x,Q^2)$ for the region $0.002<x<0.2$ from polarized di-jet rates and hadrons with high $p_t$, polarized quark distributions from weak structure functions and semi-inclusive asymmetries, parton distributions in the polarized photon and information on the helicity structure of possible new physics at large $Q^2$. HERA could therefore make a significant contribution to our understanding of spin effects in high energy collisions and to the spin structure of the nucleon.
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Vector Meson Production at a Polarized HERA Collider
A successful interpretation of the cross sections for elastic and inelastic vector meson production can be made if one assumes the underlying dynamics to be governed by hard partonic subprocesses. Extending these partonic approaches to longitudinally polarized electron-proton collisions, we estimate the expected production asymmetries at the HERA collider. The anticipated statistical errors on these asymmetries mostly turn out to be larger than the asymmetries themselves, such that an experimental observation of these asymmetries at HERA looks not feasible.
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QCD Corrections to the Polarized Drell-Yan Process
The results of a recent calculation of the QCD corrections to the longitudinally polarized Drell-Yan process are summarized. In addition to the parity conserving double spin asymmetry which is already accessible in the Drell-Yan production of lepton pairs at fixed target energies, we consider parity violating single spin asymmetries appearing only in the production of massive vector bosons at polarized hadron colliders. The prospects for extracting polarized quark distributions from asymmetries in vector boson production at RHIC are briefly discussed.
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