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Register a new userFragmentation with a Cut on Thrust: Predictions for B-factories
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When high-energy single-hadron production takes place inside an identified jet, there are important correlations between the fragmentation and phase-space cuts. For example, when one-hadron yields are measured in on-resonance B-factory data, a cut on the thrust event shape T is required to remove the large b-quark contribution. This leads to a dijet final state restriction for the light-quark fragmentation process. Here we complete our analysis of unpolarized fragmentation of (light) quarks and gluons to a light hadron h with energy fraction z in e+ e- -> dijet + h at the center-of-mass energy Q=10.58 GeV. In addition to the next-to-next-to-leading order resummation of logarithms of 1-T, we include the next-to-leading order (NLO) nonsingular O(1-T) contribution to the cross section, the resummation of threshold logarithms of 1-z, and the leading nonperturbative contribution to the soft function. Our results for the correlations between fragmentation and the thrust cut are presented in a way that can be directly tested against B-factory data. These correlations are also observed in Pythia, but are surprisingly smaller at NLO.
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In e+e- event shapes studies at LEP, two different measurements were sometimes performed: a calorimetric measurement using both charged and neutral particles, and a track-based measurement using just charged particles. Whereas calorimetric measurements are infrared and collinear safe and therefore calculable in perturbative QCD, track-based measurements necessarily depend on non-perturbative hadronization effects. On the other hand, track-based measurements typically have smaller experimental uncertainties. In this paper, we present the first calculation of the event shape track thrust and compare to measurements performed at ALEPH and DELPHI. This calculation is made possible through the recently developed formalism of track functions, which are non-perturbative objects describing how energetic partons fragment into charged hadrons. By incorporating track functions into soft-collinear effective theory, we calculate the distribution for track thrust with next-to-leading logarithmic resummation. Due to a partial cancellation between non-perturbative parameters, the distributions for calorimeter thrust and track thrust are remarkably similar, a feature also seen in LEP data.
We derive the transverse momentum dependent (TMD) factorization and resummation formula of the unpolarized transverse momentum distribution ($j_T$) for the single hadron production with the thrust axis in electron-positron collision. Two different kinematic regions are considered, including small transverse momentum limit $j_T ll Q$, and joint transverse momentum and threshold limit $j_T ll Q(1-z_h) ll Q$, where $Q$ and $z_h$ are the hard scattering energy and the observed hadron momentum fraction. Using effective theory methods, we resum logarithms $ln(Q/j_T)$ and $ln(1-z_h)$ to all orders. In the end we present the differential cross sections and Gaussian widths calculated for the inclusive charged pion production and find that our results are consistent with the measurements reported by the Belle collaboration.
Recently the LHCb collaboration has measured both longitudinal and transverse momentum distribution of hadrons produced inside $Z$-tagged jets in proton-proton collisions at the Large Hadron Collider. These distributions are commonly referred to as jet fragmentation functions and are characterized by the longitudinal momentum fraction $z_h$ of the jet carried by the hadron and the transverse momentum $j_perp$ with respect to the jet direction. We derive a QCD formalism within Soft-Collinear Effective Theory to describe these distributions and find that the $z_h$-dependence provides information on standard collinear fragmentation functions, while $j_perp$-dependence probes transverse momentum dependent (TMD) fragmentation functions. We perform theoretical calculations and compare our results with the LHCb data. We find good agreement for the intermediate $z_h$ region. For $j_perp$-dependence, we suggest binning in both $z_h$ and $j_perp$, which would lead to a more direct probing of TMD fragmentation functions.
We address the propagation and hadronization of a struck quark by studying the gauge invariance of the color-averaged cut quark propagator, and by relating this to the single inclusive quark fragmentation correlator by means of new sum rules. Using suitable Wilson lines, we provide a gauge-invariant definition for the mass of the color-averaged dressed quark and decompose this into the sum of a current and an interaction-dependent component. The latter, which we argue is an order parameter for dynamical chiral symmetry breaking, also appears in the sum rule for the twist-3 $tilde{E}$ fragmentation function, providing a specific experimental way to probe the dynamical generation of mass in Quantum Chromo Dynamics.
The first direct observation of time-reversal (T) violation in the $Bbar{B}$ system has been reported by the BaBar collaboration, employing the method of Ba$tilde {rm n}!$uls and Bernabeu. Given this, we generalize their analysis of the time-dependent T-violating asymmetry ($A_{T}$) to consider different choices of CP tags for which the dominant amplitudes have the same weak phase. As one application, we find that it is possible to measure departures from the universality of $sin(2beta)$ directly. If $sin(2beta)$ is universal, as in the Standard Model, the method permits the direct determination of penguin effects in these channels. Our method, although no longer a strict test of T, can yield tests of the $sin(2beta)$ universality, or, alternatively, of penguin effects, of much improved precision even with existing data sets.
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