Leading logarithmic large-x resummation of off-diagonal splitting functions and coefficient functions

We analyze the iterative structure of unfactorized partonic structure functions in the large-x   limit, and derive all-order expressions for the leading-logarithmic off-diagonal splitting functions Pgq$P_{\mathrm{gq}}$ and Pqg$P_{\mathrm{qg}}$ and the corresponding coefficient functions C_?,q$C_{?,\mathrm{q}}$ and C_2,g$C_{2,\mathrm{g}}$ in Higgs- and gauge-boson exchange deep-inelastic scattering. The splitting functions are given in terms of a new function not encountered in perturbative QCD so far, and vanish maximally in the supersymmetric limit CA−CF→0$C_A-C_F\to 0$. The coefficient functions do not vanish in this limit, and are given by simple expressions in terms of the above new function and the well-known leading-logarithmic threshold exponential. Our results also apply to the evolution of parton fragmentation functions and semi-inclusive e⁺e⁻$e^{+}{e}^{-}$ annihilation.     

Invariant-mass distribution of top-quark pairs and top-quark mass determination

In this study, we investigate the invariant-mass distribution of top-quark pairs near the 2m_t threshold, which strongly influences the determination of the top-quark mass m_t. Higher-order non-relativistic corrections lead to large contributions, which are not included in the state-of-the-art theoretical predictions. A factorization formula is derived to resum such corrections to all orders in the strong-coupling, and necessary ingredients are calculated to perform the resummation at next-to-leading power. We combine the resummation with fixed-order results and present phenomenologically relevant numerical results. The resummation effect significantly increases the differential cross-section in the threshold region and makes the theoretical prediction more compatible with experimental data. We estimate that using our prediction in the determination of \begin{document}$m_t $\end{document} will lead to a value closer to the direct measurement result.     

Renormalization and resummation in the O(N) model

In the O(N) model for the large N expansion one needs resummation which makes the renormalization of the model difficult. In the paper it is discussed, how can one perform a consistent perturbation theory at zero as well as at finite temperature with the help of momentum dependent renormalization schemes.     

Temporal breakdown and Borel resummation in the complex Langevin method

We reexamine the Parisi–Klauder conjecture for complex e^iθ/2?⁴$e^{i\theta /2}{?}^4$ measures with a Wick rotation angle 0≤θ/2≤π/2$0\le \theta /2\le \pi /2$ interpolating between Euclidean signature and Lorentzian signature. Our main result is that the asymptotics for short stochastic times t$t$ encapsulates information also about the equilibrium aspects. The moments evaluated with the complex measure and with the real measure defined by the stochastic Langevin equation have the same t→0$t\to 0$ asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t$t$, including their t→∞$t\to \infty$ equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the ‘correct’ result for t$t$ larger than a finite t_c$t_c$. The breakdown time t_c$t_c$ increases powerlike for decreasing strength of the noise’s imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure.     

Lowx physics and structure functions

In this talk I review the behaviour of structure functions at low values of Bjorkenx and discuss the theoretical underpinnings with particular attention to resummation schemes. I present the need for ‘less inclusive’ events to distinguish between various resummation schemes and discuss the various difficulties in differentiating experimentally between different schemes.     

夸克胶子等离子体中的次带头阶得拜屏蔽质量

采用实时有限温度下的QCD,考虑到胶子的衰减率计算了QGP中次领头阶得拜屏蔽质量的贡献,克服了通常计算中的红外发散的困难,且不必引入非微扰的磁屏蔽质量作红外截断.指出了所得结果的正定性和规范无关性并与格点模拟的结果进行了比较.     

Momentum sum rules for fragmentation functions

Momentum sum rules for fragmentation functions are considered. In particular, we give a general proof of the Schäfer–Teryaev sum rule for the transverse momentum dependent Collins function. We also argue that corresponding sum rules for related fragmentation functions do not exist. Our model-independent analysis is supplemented by calculations in a simple field-theoretical model.     

Spin structure of baryon fragmentation functions

The valence part of the quark fragmentation function resulting in the octet of baryons together with their spin structure are parametrised, using a model for the hadronisation and the available experimental data on baryon products in e⁺e^? annihilation and μp deep inelastic scattering. Spin correlations are predicted.     

Modified DGLAP evolution for fragmentation functions in nuclei and QGP

Within the framework of generalized factorization of higher-twist contributions, including modification to splitting functions of both quark and gluon, we get and numerically resolve the medium-modified DGLAP (mDGLAP) evolution equations. With Woods-Saxon nuclear geometry and Hirano 3D ideal hydrodynamic simulations of hot medium, we study the medium modified fragmentation functions (mFF) in DIS and Au+Au collisions in RHIC. Our calculations imply that the parton density in the hot medium produced in RHIC is about 30 times larger than in a cold nucleus.     

Proof of factorization of fragmentation function in non-equilibrium QCD

In this paper, we prove factorization of fragmentation function in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. We use the background field method of QCD in a pure gauge in path integral approach to prove factorization of fragmentation function in non-equilibrium QCD. Our proof is valid in any arbitrary gauge fixing parameter α. This may be relevant to study hadron production from quark-gluon plasma at high energy heavy-ion colliders at RHIC and LHC.     

Soft multihadron production from partonic structure and fragmentation functions

We describe a two-chain model for soft multiparticle production in hadronic collisions. The model is formulated in a parton framework and is consistent with the dual topological scheme for the Pomeron. The sole inputs are valence quark structure functions in the colliding hadrons and parton fragmentation functions, both of which are known from “hard” processes. Our model, which contains no adjustable parameters, reproduces the shape, the energy dependence, and the normalization of inclusive spectra both in the central region and in the fragmentation region. The model provides a natural explanation for the ratio of πp topp cross sections.     

High-energy resummation of direct photon production at hadronic colliders

Direct photon production is an important process at hadron colliders, being relevant both for precision measurement of the gluon density, and as background to Higgs and other new physics searches. Here we explore the implications of recently derived results for high-energy resummation of direct photon production for the interpretation of measurements at the Tevatron and the LHC. The effects of resummation are compared to various sources of theoretical uncertainties like PDFs and scale variations. We show how the high-energy resummation procedure stabilizes the logarithmic enhancement of the cross section at high energy which is present at any fixed order in the perturbative expansion starting at NNLO. The effects of high-energy resummation are found to be negligible at Tevatron, while they enhance the cross section by a few percent for pT?10 GeV$p_T?10\text{GeV}$ at the LHC. Our results imply that the discrepancy at small pT$p_T$ between fixed order NLO and Tevatron data cannot be explained by unresummed high-energy contributions.     

Polarized structure functions of nucleons and nuclei

We determine the quark distributions and structure functions for both unpolarized and polarized DIS of leptons on nucleons and nuclei. The scalar and vector mean fields in the nucleus modify the motions of the quarks inside the nucleons. By taking into account this medium modification, we are able to reproduce the experimental data on the unpolarized EMC effect, and to make predictions for the polarized EMC effect. We discuss examples of nuclei where the polarized EMC effect could be measured. We finally present an extension of our model to describe fragmentation functions.     

Small-scale vorticity filaments and structure functions of the developed turbulence

We develop a theory of turbulence based on the Navier-Stokes equation, without using dimensional or phenomenological considerations. A small scale vortex filament is the main element of the theory. The theory allows to obtain the scaling law and to calculate the scaling exponents of Lagrangian and Eulerian velocity structure functions in the inertial range. The obtained results are shown to be in very good agreement with numerical simulations and experimental data. The introduction of stochasticity into the equations and derivation of scaling exponents are discussed in details. A weak dependence on statistical propositions is demonstrated. The relation of the theory to the multifractal model is discussed.     

Nuclear effects in the structure functions

By using a relativistic framework and accurate nuclear spectral function the structure functions F_2A andF _3A of deep inelastic charged lepton and neutrino scattering are calculated in nuclei and results are presented.     

On the fragmentation functions of heavy quarks into hadrons

An explicit form for the charmed quark fragmentation function D^C_c(z) into hadrons has been obtained with the help of the “reciprocity relation” and the c-quark distribution function in charmed mesons (the function calculated in terms of the Kuti-Weisskopf model). D^C_c(z) turns out to peak mainly at z close to 1. The analysis of new data on muon pair production in neutrino reactions points to such a behaviour of the D^C_c(z) function. The obtained fragmentation function, contrary to those, used earlier, leads to a charmed particle (average) multiplicity in e⁺e^?-annihilation independent of energy.     

On the next-to-next-to-leading order evolution of flavour-singlet fragmentation functions

We present the third-order contributions to the quark-gluon and gluon-quark timelike splitting functions for the evolution of fragmentation functions in perturbative QCD. These quantities have been derived by studying physical evolution kernels for photon- and Higgs-exchange structure functions in deep-inelastic scattering and their counterparts in semi-inclusive annihilation, together with constraints from the momentum sum rule and the supersymmetric limit. For this purpose we have also calculated the second-order coefficient functions for one-hadron inclusive Higgs decay in the heavy-top limit. A numerically tolerable uncertainty remains for the quark-gluon splitting function, which does not affect the endpoint logarithms for small and large momentum fractions. We briefly discuss these limits and illustrate the numerical impact of the third-order corrections. Compact and accurate parametrizations are provided for all third-order timelike splitting functions.     

On the origin of scaling violations in fragmentation functions

We show that the scaling violations observed in the fragmentation functions of neutrino scattering can be mostly of a kinematical origin and not necessarily from a QCDQ ²-evolution. Due to confinement effects, the application of such evolution equations is nontrivial at non-asymptotic energies, but these QCD effects can be taken into account by a dynamical simulation of the parton branching processes followed by a string fragmentation method.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.