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Linear vs. non-linear QCD evolution: from HERA data to LHC phenomenology

  • Regular Article - Theoretical Physics
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Abstract

The very precise combined HERA data provides a testing ground in which the relevance of novel QCD regimes, other than the successful linear DGLAP evolution, in small-x inclusive DIS data can be ascertained. We present a study of the dependence of the AAMQS fits, based on the running coupling BK non-linear evolution equations (rcBK), on the fitted dataset. This allows for the identification of the kinematical region where rcBK accurately describes the data, and thus for the determination of its applicability boundary. We compare the rcBK results with NNLO DGLAP fits, obtained with the NNPDF methodology with analogous kinematical cuts. Further, we explore the impact on LHC phenomenology of applying stringent kinematical cuts to the low-x HERA data in a DGLAP fit.

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Notes

  1. The BK equation written here assumes translational invariance of the dipole amplitude \(\mathcal {N}\). Also, some constant factors have been absorbed in the evolution kernel \(\mathcal{K}\), see e.g. [22] for precise definitions.

  2. It is indeed straightforward to check that the non-linear term in Eq. (1) prevents the dipole scattering amplitude to grow above unity, provided the initial condition is unitary itself, i.e. \(\mathcal{N}\leq1\).

  3. The photon wave function \(\varPsi_{T,L}^{f}\) in Eq. (3) peaks at r∼2/Q.

  4. In the NNPDF analysis the full information on the correlated systematics is taken into account into the definition of the χ 2, and the normalization uncertainties are included following the t 0 prescription [38]. Let us recall that non negligible differences are expected if the systematic uncertainties are added in quadrature to the statistical error, and that the χ 2 will be artificially about 15 % lower in the latter approximation [23].

  5. The distances defined to compare PDFs in the NNPDF framework are defined in Appendix B of Ref. [37]. They should not be confused with the relative and statistical distances, Eqs. (6) and (7), introduced later in this work.

  6. In the AAMQS approach the χ 2 is calculated as \(\chi^{2}=\sum_{i}\frac{(\sigma_{\mathrm {r,th}}-\sigma_{\mathrm{r,exp}})^{2}}{\Delta\sigma_{\mathrm {r,exp}}^{2}}\), where \(\Delta\sigma_{\mathrm{r,exp}}^{2}\) is the total experimental error obtained adding in quadrature all experimental uncertainties, and thus neglects the effects of correlations.

  7. In the context of future DIS facilities, the physics that can be probed at low x within the DGLAP framework has been studied in [44, 45].

  8. Of course such deviations from fixed order DGLAP might also contaminate extractions of the strong coupling constant from global PDF analyses, in which the HERA data play an important role [46].

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Acknowledgements

The research of J.L.A. is supported by a fellowship from the Théorie LHC France initiative funded by the IN2P3. J.R. is grateful to S. Forte for discussions. The research of J.R. has been supported by a Marie Curie Intra-European Fellowship of the European Community’s 7th Framework Programme under contract number PIEF-GA-2010-272515. J.G.M. acknowledge the support of Fundação para a Ciência e a Tecnologia (Portugal) under project CERN/FP/116379/2010. The work of P.Q.A. is funded by the French ANR under contract ANR-09-BLAN-0060.

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Authors and Affiliations

  1. IPNO, Université Paris-Sud, CNRS/IN2P3, 91406, Orsay, France

    J. L. Albacete

  2. IPhT, CEA/Saclay, 91191, Gif-sur-Yvette cedex, France

    J. L. Albacete

  3. CENTRA, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    J. G. Milhano

  4. Physics Department, Theory Unit, CERN, 1211, Genève 23, Switzerland

    J. G. Milhano & J. Rojo

  5. LPTHE, UPMC Univ. Paris 6 and CNRS UMR7589, Paris, France

    P. Quiroga-Arias

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  1. J. L. Albacete
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  2. J. G. Milhano
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  3. P. Quiroga-Arias
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  4. J. Rojo
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Correspondence to P. Quiroga-Arias.

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Albacete, J.L., Milhano, J.G., Quiroga-Arias, P. et al. Linear vs. non-linear QCD evolution: from HERA data to LHC phenomenology. Eur. Phys. J. C 72, 2131 (2012). https://doi.org/10.1140/epjc/s10052-012-2131-x

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