Global analysis of light-hadron fragmentation functions with small-x improvement through soft-gluon logarithm resummation

• Applicant: Professor Dr. Bernd A. Kniehl
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2004 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5434013

• Final Report Year: 2016

Final Report Abstract

The transition of partons into hadrons takes place at an energy scale of the order of 1 GeV and can, therefore, not be treated in QCD perturbation theory. Instead, the hadronization of partons is described by FFs, Da^h (z, µ2). Their values correspond to the probability that the parton a, which is produced at short distance, of order 1/µ, fragments into the hadron h carrying the fraction z of the energy of a. √ the case of e+ e− In annihilation, µ is typically of the order of the center-of-mass energy s. Unfortunately, it is not yet possible to calculate the FFs from first principles, in particular for hadrons with masses smaller than or comparable to the asymptotic scale parameter Λ. However, given their z dependence at some energy scale µ, the evolution with µ may be computed perturbatively in QCD using the timelike DGLAP equations. This allows us to test QCD quantitatively within one experiment observing single hadrons at different values of µ. By the same token, this allows for precise αs determinations. Moreover, the factorization theorem guarantees that the Da^h (z, µ2) functions are independent of the process in which they have been determined and represent a universal property of h. This enables us to make quantitative predictions for other types of experiments as well. We exploited these properties to critically examine the pT distribution of charged hadrons measured by the CDF Collaboration in pp¯ collisions at √s = 1.96 TeV and found a significant deviation, which could subsequently be traced to a problem in the experimental data analysis. We also deepened our understanding of the small-z behaviour of light-hadron FFs. On the one hand, we computed and resummed all the DLs in the gluon coefficient function of inclusive hadron production in e+ e− annihilation. On the other hand, we determined the SL contributions to the timelike DGLAP splitting functions in the MS scheme. Both ingrediences allow us to push the applicability of the theoretical framework underlying global data fits of FFs towards smaller x values and so to exploit a large supply of experimental data that has so far been idle. The first Mellin moment of Da^h (z, µ2 ) carries a physical meaning by itself. In fact, up to corrections of orders beyond our consideration here, it corresponds to the average hadron multiplicity (nh)a of jets initiated by parton a. We elevated the theoretical description of (nh)a to N3LOapprox + NLO + NNLL accuracy, in which the logarithms ln z are resummed through the NNLL level, r+ (Q2) is evaluated approximately at N3LO, and r−(Q2 ) is evaluated NLO. Performing a fit to all available e+ e− data, we thus obtained αs^(5) (mz^2) = 0.1199 ± 0.0026.

Publications

• “Towards a model independent determination of fragmentation functions,” in proceedings of the XIII Advanced Research Workshop on High Energy Spin Physics (DSPIN-09), Dubna, Russia, September 1–5, 2009, p. 45–48
  E. Christova, E. Leader and S. Albino
  
• “Factorization Breaking in High-Transverse- Momentum Charged-Hadron Production at the Tevatron?,” Phys. Rev. Lett. 104 (2010) 242001 (4 pages)
  S. Albino, B. A. Kniehl and G. Kramer
  
• “Hadronization of partons,” Rev. Mod. Phys. 82 (2010) 2489–2556
  S. Albino
  
• “Nonsinglet kaon fragmentation function from e+ e− kaon production,” Phys. Rev. D 81 (2010) 094031 (14 pages)
  S. Albino and E. Christova
  
• “On model independent extraction of the Kaon Fragmentation Functions,” in proceedings of the workshop Advanced Studies Institute on Symmetries and Spin (SPIN-Praha-2010), Prague, Czech Republic, July 18–24, 2010 (6 pages)
  S. Albino, E. Christova and E. Leader
  
• “Fully doublelogarithm-resummed cross sections,” Nucl. Phys. B 851 (2011) 86–103
  S. Albino, P. Bolzoni, B. A. Kniehl and A. Kotikov
  
• “Timelike Small x Resummation for Fragmentation Functions,” in proceedings of the XIX International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2011), Newport News, USA, April 11–15, 2011 (4 pages)
  S. Albino, P. Bolzoni, B. A. Kniehl and A. Kotikov
  
• “A new approach to hadron multiplicity ratio,” in proceedings of the XXth International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2012), Bonn, Germany, March 26–30, 2012 (4 pages)
  P. Bolzoni
  
• “Gluon- and Quark-Jet Multiplicities with NNNLO and NNLL Accuracy,” Phys. Rev. Lett. 109 (2012) 242002 (5 pages)
  P. Bolzoni, B. A. Kniehl and A. V. Kotikov
  
• “Timelike singlelogarithm-resummed splitting functions,” Nucl. Phys. B 855 (2012) 801–814
  S. Albino, P. Bolzoni, B. A. Kniehl and A. V. Kotikov
  
• “Timelike structure functions and hadron multiplicities,” in proceedings of XXI International Baldin Seminar on High Energy Physics Problems: Relativistic Nuclear Physics & Quantum Chromodynamics (ISHEPP 2012), Dubna, Russia, September 10–15, 2012, PoS Baldin-ISHEPP-XXI (2012) 028 (10 pages)
  P. Bolzoni
  
• “Average gluon and quark jet multiplicities at higher orders,” Nucl. Phys. B 875 (2013) 18–44
  P. Bolzoni, B. A. Kniehl and A. V. Kotikov
  
• “α-s from scaling violations of hard parton-to-hadron fragmentation functions,” in Proceedings of the workshop High-precision αs measurements from LHC to FCC-ee, Geneva, Switzerland, October 2–13, 2015, p. 71–79
  B. Kniehl
  
• “Extracting αs from scaling violations in light-hadron fragmentation functions,” Mod. Phys. Lett. A 31 (2016) 1630008 (10 pages)
  B. A. Kniehl