We perform a number of improvements to the previous AKK extraction of fragmentation functions for π ± , K ± , p/p, K 0 S and Λ/Λ particles at next-to-leading order. Inclusive hadron production measurements from pp(p) reactions at BRAHMS, CDF, PHENIX and STAR are added to the data sample. We use the charge-sign asymmetry of the produced hadrons in pp reactions to constrain the valence quark fragmentations. Data from e + e − reactions in regions of smaller x and lower √ s are added. Hadron mass effects are treated for all observables and, for each particle, the hadron mass used for the description of the e + e − reaction is fitted. The baryons' fitted masses are found to be only around 1% above their true masses, while the values of the mesons' fitted masses have the correct order of magnitude. Large x resummation is applied in the coefficient functions of the e + e − reactions, and also in the evolution of the fragmentation functions, which in most cases results in a significant reduction of the minimized χ 2 . To further exploit the data, all published normalization errors are incorporated via a correlation matrix.

We present new sets of next-to-leading order fragmentation functions for the production of K 0 S and Λ particles from the gluon and from each of the quarks, obtained by fitting to all relevant data sets from e + e − annihilation. The individual light quark flavour fragmentation functions are constrained phenomenologically for the first time by including in the data the light quark tagging probabilities measured by the OPAL Collaboration.

This chapter of the report of the "Flavor in the era of the LHC" Workshop discusses the theoretical, phenomenological and experimental issues related to flavor phenomena in the charged lepton sector and in flavor conserving CPviolating processes. We review the current experimental limits and the main theoretical models for the flavor structure of fundamental particles. We analyze the phenomenological consequences of the available data, setting constraints on explicit models beyond the standard model, presenting benchmarks for the discovery potential of forthcoming measurements both at the LHC and at low energy, and exploring options for possible future experiments.

We define a general scheme for the evolution of fragmentation functions which resums both soft gluon logarithms and mass singularities in a consistent manner and to any order, and requires no additional theoretical assumptions. Using the Double Logarithmic Approximation and the known perturbative results for the splitting functions, we present our scheme with the complete contribution from the double logarithms, being the largest soft gluon logarithms. We show that the resulting approximation is more complete than the Modified Leading Logarithm Approximation even with the fixed order contribution calculated to leading order only, and find, after using it to fit quark and gluon fragmentation functions to experimental data, that this approximation in our scheme gives a good description of the data from the largest xp values to the peak region in ξ = ln(1/xp), in contrast to other approximations. In addition, we develop a treatment of hadron mass effects which gives additional improvements at large ξ.

We review the description of inclusive single unpolarized light hadron production using fragmentation functions in the framework of the factorization theorem. We summarize the factorization of quantities into perturbatively calculable quantities and these universal fragmentation functions, and then discuss some improvements beyond the standard fixed order approach. We discuss the extraction of fragmentation functions for light charged (π ± , K ± and p/p) and neutral (K 0 S and Λ/Λ) hadrons using these theoretical tools through global fits to experimental data from reactions at various colliders, in particular from accurate e + e − reactions at LEP, and the subsequent successful predictions of other experimental data, such as data gathered at HERA, the Tevatron and RHIC from these fitted fragmentation functions as allowed by factorization universality. These global fits also impose competitive constraints on αs(MZ). Emphasis is placed on the need for accurate data from ep and pp(p) reactions in which the hadron species is identified in order to constrain the separate fragmentation functions of each quark flavour and hadron species. 65 A.1. Twist expansion 66 A.2. The modern approach to factorization 68 A.3. Connection with the older approach to factorization 70 A.4. Treatment of non partonic quarks 71 A.5. Matching conditions 72 3 A.6. Open issues 73 B. Leading order splitting functions 73 C. Mellin space 74 D. Summary of inclusive single hadron production measurements 76 D.1. e + e − reactions 76 D.2. pp(p) reactions 79References 79up to higher twist terms, which are suppressed relative to the overall cross section by a factor O(Λ QCD /E s ) or more. The parton label i = 0 for the gluon, while i = (−)I for (anti)quarks, where I = 1, . . . , 6 corresponds respectively to the flavours d, u, s, c, b and t. The fact that n f = 6 necessarily will be explained below. m i is a renormalization scheme-dependent mass associated with parton i, which will be taken to be its pole mass, and a s = α s /(2π) is the expansion parameter in perturbative series. The dσ i are the equivalent partonic cross sections obtained by replacing the detected hadron h with a real on-shell parton i moving in the same direction but with momentum p h /z, and the sum over unobserved hadrons replaced with a sum over unobserved partons. In e.g. e + e − → h + X, dσ i is completely calculable in perturbation theory, while for processes involving initial state hadrons, such as ep → e + h + X at HERA and pp(p) → h + X at the LHC (RHIC), dσ i will be convolutions of perturbatively calculable quantities with PDFs for each initial state hadron, a result which also follows from the factorization theorem. The dσ i are otherwise perturbatively calculable if all subprocesses with energy scale below some arbitrary factorization scale M f ≫ Λ QCD are factored out of them and into the FFs D h i (and PDFs if applicable) according to the factorization theorem. While the dσ i differ from process to process, the FFs are universal and therefore, through them, measureme...