arXiv subjects

D. Müller

Publications and source records attributed to D. Müller.

At least 37 records · Page 2Linked to original sources

arXiv2015

Resonant scattering induced thermopower in one-dimensional disordered systems

This study analyzes thermoelectric properties of a one-dimensional random conductor which shows localization effects and simultaneously includes resonant scatterers yielding sharp conductance resonances. These sharp features give rise to a distinct behavior of the Seebeck coefficient in finite systems and incorporate the degree of localization as a means to enhance thermoelectric performance, in principle. The model for non-interacting electrons is discussed within the Landauer-Büttiker formalism such that analytical treatment is possible for a wide range of properties, if a special averaging scheme is applied. The approximations in the averaging procedure are tested with numerical evaluations showing good qualitative agreement, with some limited quantitative disagreement. The validity of low-temperature Mott's formula is determined and a good approximation is developed for the intermediate temperature range. In both regimes the intricate interplay between Anderson localization due to disorder and conductance resonances of the disorder potential is analyzed.

cond-mat.mes-hall↗

arXiv2014

Electron Ion Collider: The Next QCD Frontier - Understanding the glue that binds us all

This White Paper presents the science case of an Electron-Ion Collider (EIC), focused on the structure and interactions of gluon-dominated matter, with the intent to articulate it to the broader nuclear science community. It was commissioned by the managements of Brookhaven National Laboratory (BNL) and Thomas Jefferson National Accelerator Facility (JLab) with the objective of presenting a summary of scientific opportunities and goals of the EIC as a follow-up to the 2007 NSAC Long Range plan. This document is a culmination of a community-wide effort in nuclear science following a series of workshops on EIC physics and, in particular, the focused ten-week program on "Gluons and quark sea at high energies" at the Institute for Nuclear Theory in Fall 2010. It contains a brief description of a few golden physics measurements along with accelerator and detector concepts required to achieve them, and it benefited from inputs from the users' communities of BNL and JLab. This White Paper offers the promise to propel the QCD science program in the U.S., established with the CEBAF accelerator at JLab and the RHIC collider at BNL, to the next QCD frontier.

nucl-ex↗

arXiv2014

Future dynamics in f(R) theories

The $f(R)$ gravity theories provide an alternative way to explain the current cosmic acceleration without invoking dark energy matter component. However, the freedom in the choice of the functional forms of $f(R)$ gives rise to the problem of how to constrain and break the degeneracy among these gravity theories on theoretical and/or observational grounds. In this paper to proceed further with the investigation on the potentialities, difficulties and limitations of $f(R)$ gravity, we examine the question as to whether the future dynamics can be used to break the degeneracy between $f(R)$ gravity theories by investigating the future dynamics of spatially homogeneous and isotropic dust flat models in two $f(R)$ gravity theories, namely the well known $f(R) = R + αR^{n}$ gravity and another by A. Aviles et al., whose motivation comes from the cosmographic approach to $f(R)$ gravity. To this end we perform a detailed numerical study of the future dynamic of these flat model in these theories taking into account the recent constraints on the cosmological parameters made by the Planck team. We show that besides being powerful for discriminating between $f(R)$ gravity theories, the future dynamics technique can also be used to determine the fate of the Universe in the framework of these $f(R)$ gravity theories. Moreover, there emerges from our numerical analysis that if we do not invoke a dark energy component with equation-of-state parameter $ω< -1$ one still has dust flat FLRW solution with a big rip, if gravity deviates from general relativity via $f(R) = R + αR^n $. We also show that FLRW dust solutions with $f''<0$ do not necessarily lead to singularity.

astro-ph.CO↗

arXiv2013

Interactions of Cosmic Rays in the Atmosphere: Growth Curves Revisited

Measurements of cosmic-ray abundances on balloons are affected by interactions in the residual atmosphere above the balloon. Corrections for such interactions are particularly important for observations of rare secondary particles such as boron, antiprotons and positrons. These corrections can either be calculated if the relevant cross sections in the atmosphere are known, or may be empirically determined by extrapolation of the "growth curves", i. e. the individual particle intensities as functions of atmospheric depth. The growth-curve technique is particularly attractive for long-duration balloon flights where the periodic daily altitude variations permit rather precise determinations of the corresponding particle intensity variations. We determine growth curves for nuclei from boron (Z=5) to iron (Z=26), using data from the 2006 Arctic balloon flight of the TRACER detector for cosmic-ray nuclei, and we compare the growth curves with predictions from published cross section values. In general, good agreement is observed. We then study the boron/carbon abundance ratio and derive a simple and energy-independent correction term for this ratio. We emphasize that the growth-curve technique can be developed further to provide highly accurate tests of published interaction cross section values.

astro-ph.HE↗

arXiv2012

The boron-to-carbon abundance ratio and Galactic propagation of cosmic radiation

In two long-duration balloon flights in 2003 and 2006, the TRACER cosmic-ray detector has measured the energy spectra and the absolute intensities of the cosmic-ray nuclei from boron (Z = 5) to iron (Z = 26) up to very high energies. In particular, the second flight has led to results on the energy spectrum of the secondary boron nuclei, and on the boron abundance relative to that of the heavier primary parent nuclei, commonly quantified as the "B/C abundance ratio". The energy dependence of this ratio, now available up to about 2 TeV per amu, provides a measure for the energy dependence of cosmic-ray propagation through the Galaxy, and for the shape of the cosmic-ray source energy spectrum. We use a Leaky-Box approximation of cosmic-ray propagation to obtain constraints on the relevant parameters on the basis of the results of TRACER and of other measurements. This analysis suggests that the source energy spectrum is a relatively soft power law in energy E^{-α}, with spectral exponent α= 2.37 \pm 0.12, and that the propagation path length Λ(E) is described by a power law in energy with exponent δ= 0.53 \pm 0.06, but may assume a constant residual value Λ_0 at high energy. The value of Λ_0 is not well constrained but should be less than about 0.8 g cm^{-2}. Finally, we compare the data with numerical solutions of a diffusive reacceleration model, which also indicates a soft source spectrum.

astro-ph.HE↗

arXiv2011

Energy spectra of primary and secondary cosmic-ray nuclei measured with TRACER

The TRACER cosmic-ray detector, first flown on long-duration balloon (LDB) in 2003 for observations of the major primary cosmic-ray nuclei from oxygen (Z=8) to iron (Z=26), has been upgraded to also measure the energies of the lighter nuclei, including the secondary species boron (Z=5). The instrument was used in another LDB flight in 2006. The properties and performance of the modified detector system are described, and the analysis of the data from the 2006 flight is discussed. The energy spectra of the primary nuclei carbon (Z=6), oxygen, and iron over the range from 1 GeV amu$^{-1}$ to 2 TeV amu$^{-1}$ are reported. The data for oxygen and iron are found to be in good agreement with the results of the previous TRACER flight. The measurement of the energy spectrum of boron also extends into the TeV amu$^{-1}$ region. The relative abundances of the primary nuclei, such as carbon, oxygen, and iron, above $\sim10$ GeV amu$^{-1}$ are independent of energy, while the boron abundance, i.e. the B/C abundance ratio, decreases with energy as expected. However, there is an indication that the previously reported $E^{-0.6}$ dependence of the B/C ratio does not continue to the highest energies.

astro-ph.HE↗

arXiv2007

Towards a fitting procedure for deeply virtual Compton scattering at next-to-leading order and beyond

Combining dispersion and operator product expansion techniques, we derive the conformal partial wave decomposition of the virtual Compton scattering amplitude in terms of complex conformal spin to twist-two accuracy. The perturbation theory predictions for the deeply virtual Compton scattering (DVCS) amplitude are presented in next-to-leading order for both conformal and modified minimal subtraction scheme. Within a conformal subtraction scheme, where we exploit predictive power of conformal symmetry, the radiative corrections are presented up to next-to-next-to-leading order accuracy. Here, because of the trace anomaly, the mixing of conformal moments of generalized parton distributions (GPD) at the three-loop level remains unknown. Within a new proposed parameterization for GPDs, we then study the convergence of perturbation theory and demonstrate that our formalism is suitable for a fitting procedure of DVCS observables.

hep-ph↗

arXiv2007

Fitting DVCS at NLO and beyond

We outline the twist-two analysis of deeply virtual Compton scattering (DVCS)within the conformal partial wave expansion of the amplitude, represented as a Mellin--Barnes integral. The complete next-to-leading order results, including evolution, are obtained in the MS and a conformal factorization scheme. Within the latter, exploiting conformal symmetry, the radiative corrections are evaluated up to next-to-next-to-leading order. Using a new proposed parameterization for GPDs, we study the convergence of perturbation theory and demonstrate for H1 and ZEUS measurements that our formalism is suitable for a fitting procedure of DVCS observables. We comment on a recent claim of a breakdown of collinear factorization and show that a Regge-inspired Q^2 scaling law is ruled out by small x_Bj DVCS data.

hep-ph↗

arXiv2007

Exclusive processes in position space and the pion distribution amplitude

We suggest to carry out lattice calculations of current correlators in position space, sandwiched between the vacuum and a hadron state (e.g. pion), in order to access hadronic light-cone distribution amplitudes (DAs). In this way the renormalization problem for composite lattice operators is avoided altogether, and the connection to the DA is done using perturbation theory in the continuum. As an example, the correlation function of two electromagnetic currents is calculated to the next-to-next-to-leading order accuracy in perturbation theory and including the twist-4 corrections. We argue that this strategy is fully competitive with direct lattice measurements of the moments of the DA, defined as matrix elements of local operators, and offers new insight in the space-time picture of hard exclusive reactions.

hep-ph↗

arXiv2007

Anomalous dimensions of leading twist conformal operators

We extend and develop a method for perturbative calculations of anomalous dimensions and mixing matrices of leading twist conformal primary operators in conformal field theories. Such operators lie on the unitarity bound and hence are conserved (irreducible) in the free theory. The technique relies on the known pattern of breaking of the irreducibility conditions in the interacting theory. We relate the divergence of the conformal operators via the field equations to their descendants involving an extra field and accompanied by an extra power of the coupling constant. The ratio of the two-point functions of descendants and of their primaries determines the anomalous dimension, allowing us to gain an order of perturbation theory. We demonstrate the efficiency of the formalism on the lowest-order analysis of anomalous dimensions and mixing matrices which is required for two-loop calculations of the former. We compare these results to another method based on anomalous conformal Ward identities and constraints from the conformal algebra. It also permits to gain a perturbative order in computations of mixing matrices. We show the complete equivalence of both approaches.

hep-th↗

arXiv2006

Towards Baxter equation in supersymmetric Yang-Mills theories

We perform an explicit two-loop calculation of the dilatation operator acting on single trace Wilson operators built from holomorphic scalar fields and an arbitrary number of covariant derivatives in N=2 and N=4 supersymmetric Yang-Mills theories. We demonstrate that its eigenspectrum exhibits double degeneracy of opposite parity eigenstates which suggests that the two-loop dilatation operator is integrable. Moreover, the two-loop anomalous dimensions in the two theories differ from each other by an overall normalization factor indicating that the phenomenon is not sensitive to the presence of the conformal symmetry. Relying on these findings, we try to uncover integrable structures behind the two-loop dilatation operator using the method of the Baxter Q-operator. We propose a deformed Baxter equation which exactly encodes the spectrum of two-loop anomalous dimensions and argue that it correctly incorporates a peculiar feature of conformal scalar operators -- the conformal SL(2) spin of such operators is modified in higher loops by an amount proportional to their anomalous dimension. From the point of view of spin chains this property implies that the underlying integrable model is ``self-tuned'' -- the all-loop Hamiltonian of the spin chain depends on the total SL(2) spin which in its turn is proportional to the Hamiltonian.

hep-th↗

arXiv2006

Deeply virtual Compton scattering beyond next-to-leading order: the flavor singlet case

We study radiative corrections to deeply virtual Compton scattering in the kinematics of HERA collider experiments to next--to--leading and next--to--next--to--leading order. In the latter case the radiative corrections are evaluated in a special scheme that allows us to employ the predictive power of conformal symmetry. As observed before, the size of next--to--leading order corrections strongly depends on the gluonic input, as gluons start to contribute at this order. Beyond next--to--leading order we find, in contrast, that the corrections for an input scale of few GeV^2 are small enough to justify the uses of perturbation theory. For $ξ> 5 10^{-3}$ the modification of the scale dependence is also small. However, with decreasing $ξ$ it becomes moderate or even large, in particular for the phase.

hep-ph↗

arXiv2005

Integrability of two-loop dilatation operator in gauge theories

We study the two-loop dilatation operator in the noncompact SL(2) sector of QCD and supersymmetric Yang-Mills theories with N=1,2,4 supercharges. The analysis is performed for Wilson operators built from three quark/gaugino fields of the same helicity belonging to the fundamental/adjoint representation of the SU(3)/SU(N_c) gauge group and involving an arbitrary number of covariant derivatives projected onto the light-cone. To one-loop order, the dilatation operator inherits the conformal symmetry of the classical theory and is given in the multi-color limit by a local Hamiltonian of the Heisenberg magnet with the spin operators being generators of the collinear subgroup of full (super)conformal group. Starting from two loops, the dilatation operator depends on the representation of the gauge group and, in addition, receives corrections stemming from the violation of the conformal symmetry. We compute its eigenspectrum and demonstrate that to two-loop order integrability survives the conformal symmetry breaking in the aforementioned gauge theories, but it is violated in QCD by the contribution of nonplanar diagrams. In SYM theories with extended supersymmetry, the N-dependence of the two-loop dilatation operator can be factorized (modulo an additive normalization constant) into a multiplicative c-number. This property makes the eigenspectrum of the two-loop dilatation operator alike in all gauge theories including the maximally supersymmetric theory. Our analysis suggests that integrability is only tied to the planar limit and it is sensitive neither to conformal symmetry nor supersymmetry.

hep-th↗

arXiv2005

Complex conformal spin partial wave expansion of generalized parton distributions and distribution amplitudes

We introduce a new representation of generalized parton distributions and generalized distribution amplitudes that is based on the partial wave decomposition with respect to the complex collinear conformal spin. This decomposition leads us to a versatile parameterization of these non-perturbative functions in terms of conformal moments, which are measurable for integer value on the lattice. This new representation has several advantages: basic properties and crossing relations are automatically implemented, a rather flexible parameterization is possible, the numerical treatment of evolution is simple and analytic approximation of scattering amplitudes can be given. We demonstrate this for simple examples. In particular, phenomenological considerations indicate that the t-dependence of Mellin moments is governed by Regge trajectories. The new representation is vital to push the analysis of deeply virtual Compton scattering to next-to-next-to-leading order.

hep-ph↗

arXiv2005

Generalized Parton Distributions -- theoretical review --

In this talk an introduction to generalized parton distributions is given. Recent developments are shortly reviewed, including non-perturbative calculations, phenomenological aspects and evaluation of higher order perturbative and power corrections.

hep-ph↗

arXiv2004

Integrability in Yang-Mills theory on the light cone beyond leading order

The one-loop dilatation operator in Yang-Mills theory possesses a hidden integrability symmetry in the sector of maximal helicity Wilson operators. We calculate two-loop corrections to the dilatation operator and demonstrate that while integrability is broken for matter in the fundamental representation of the SU(3) gauge group, for the adjoint SU(N_c) matter it survives the conformal symmetry breaking and persists in supersymmetric N=1, N=2 and N=4 Yang-Mills theories.

hep-th↗

arXiv2003

Probing generalized parton distributions with electroproduction of lepton pairs off the nucleon

We evaluate the differential cross section for the electroproduction of lepton pairs off a polarized nucleon target in the generalized Bjorken region to leading power accuracy in hard momentum. We discuss the importance of this process for phenomenology of generalized parton distributions. A special attention is given to the sensitivity of physical observables, i.e., diverse asymmetries, to their dependence on scaling variables that allows to map directly the functional two-dimensional surface of generalized parton distributions.

hep-ph↗

arXiv2003

Next-to-next-to-leading order prediction for the photon-to-pion transition form factor

We evaluate the next-to-next-to-leading order corrections to the hard-scattering amplitude of the photon-to-pion transition form factor. Our approach is based on the predictive power of the conformal operator product expansion, which is valid for a vanishing $β$-function in the so-called conformal scheme. The Wilson--coefficients appearing in the non-forward kinematics are then entirely determined from those of the polarized deep-inelastic scattering known to next-to-next-to-leading accuracy. We propose different schemes to include explicitly also the conformal symmetry breaking term proportional to the $β$-function, and discuss numerical predictions calculated in different kinematical regions. It is demonstrated that the photon-to-pion transition form factor can provide a fundamental testing ground for our QCD understanding of exclusive reactions.

hep-ph↗