The TMDpdf determination at NLO using parton branching method

Transcription

1 The TMDpdf determination at NLO using parton branching method Radek Žlebčík1 Ola Lelek1, Francesco Hautmann2, Hannes Jung1, Voica Radescu3 1 Deutsches Elektronen-Synchrotron (DESY) 2 University of Oxford 3 CERN REF Madrid, November 14

2 Parton Branching method 1) Introduction to the Parton Branching solution of DGLAP 2) Comparing of the collinear part with QCDnum 3) Extraction of TMDs from HERA DIS data 4) Predictions for in jets events 2

3 Parton Branching Method An analogy to the MC parton showers but is used to solve evolution equation When DGLAP splitings are used the collinear part exactly reproduce semi-analytical DGLAP solution Trace the of each emission and determine the part of PDFs Study diferent kinds of branching dynamics (ordering conditions, resolution condition) and determine their efect on PDFs Diferent flavors have diferent shapes of kt distribution. F. Hautmann, H. Jung, A. Lelek, V. Radescu, R. Zlebcik: Sof-gluon resolution scale in QCD evolution equations [arxiv: ]. 3

4 Evolution Equation We postulate the evolution equation in the form: The Sudakov factor is: The momentum weighted PDF The spliting function for the real emissions The threshold defining the resolvable emission Equation invariant with respect to the rapidity shif The Sudakov factor probability of non-radiating up to scale 4

5 Properties of the equation 1) The momentum sum rule is conserved within evolution for any spliting functions 2) In case when are the standard DGLAP spliting function the solution is identical to DGLAP as soon as is large enough The virtual terms at z=1 are automatically obtained by the unitarity condition (ensured by the Sudakov factors) 5

6 Monte Carlo Solving Method 1) Starting with (for these plots) 2) The position of every next branching (dot) depends only on the previous one and is randomly generated using Sudakov and spliting kernels Higher cut-of causes more sof emissions (dots with similar x) MC evolution paths from the point ploted

7 Dependence of the evolution on The parameter separates resolvable branchings from non-resolvable and virtual one The afects high-x region, no diference if Momentum sum rules still holds irrespectively on Possibility to use like in showers of MC generators. 7

8 The Monte Carlo solution vs QCDNUM LO NLO NNLO The Monte Carlo evolution implemented up to NNLO and cross-checked against the semi-analytical solution of DGLAP The solution s uncertainties are mainly statistical (~ number of generated MC evolutions) 8

9 Parton branching method at NNLO In NNLO VFNS discontinuities both in and PDFs These discontinuities ensure continuity of observables, e.g. Discontinuities in the quark and gluon Sudakov factors NNLO gluon PDF NNLO gluon Sudakov factor 9 M. Buza et al., Eur. Phys. J. C1, 301 (1998), hep-ph/

10 The Transverse Momentum The Parton Branching method allows to study diferent parton shower ordering conditions the bridge between MC parton showers and PDF fits from analytic DGLAP solution Virtuality ordering ( Angular ordering ( ) ) distribution as a probe of the parton shower coherence efects presented in case of angular ordered shower (e.g. in Drell-Yan process) - relative trans. mom. of the emission 10

11 TMD fits using xfiter [arxiv: ] 1) As the Monte Carlo evolution is computationally intense, we employ the linearity of the evolution and calculate only the evolution kernels 2 * 11 functions of 3 variables, values stored on 3D grid 503 2) The evolution kernels allow fast calculation of the TMD for the given initial PDF 3) The TMDs are then employed to calculate the cross sections The algorithm implemented in 11

12 TMD fit of HERA data The HERAPDF like parametrization for 14 free parameters to be fitted 3 parameters constrained by sum rules 2 parameters fixed AUbar = ADbar BUbar = BDbar Fit of HERA DIS NC and CC data at several beam energies ( ) For now, the intrinsic kt distribution at starting scale kept fixed and flavour independent 12

13 TMD fit of HERA data By fiting of 1145 data points Heavy quark masses was obtained (at NLO) 13

14 TMD fit of HERA data 7 distinct HERA data sets fited (2*CC + 5*NC) The resulting PDFs values stored in the grid of The data uncertainties propagated to PDFs by the technique of MC replicas NC, Ep = 920 GeV NC, Ep = 460 GeV CC, Ep = 920 GeV 14

15 virt. ord. angular ord. The TMDs Angular- vs virtuality ordering Flavour dependence of TMDs Angular ord. The kt in case of virtuality ordering higher than for angular ordering condition (especially at high scales) The mean kt of TMD for gluon higher than for quarks The kt of charm generated 15 only via evolution

16 TMD densities Experimental uncertainties of the fited data propagates into kt spectrum of PDF The shape of kt distribution difers between eigenvectors For more information see the TMD library and TMD ploter htp://tmd.hepforge.org htp://tmdploter.desy.de TMDlib and TMDploter: library and ploting tools for transverse-momentum-dependent parton distributions, F. Hautmann et al. arxiv , Eur. Phys. J., C 74(12):3220,

17 Application: Dijet production Events generated by POWHEG 2jets, without including the parton shower Here collinear PDFs used for production The CMS collaboration: Measurement of dijet azimuthal decorrelation in pp collisions at [arxiv: ] between leading and subleading jet Region dominated by sof emission In POWHEG exponentially suppressed via the Sudakov factor

18 Application: Dijet production 1) Events generated by POWHEG 2jets, without including the parton shower 2) The transverse momentum from TMD added to the original POWHEG sample 3) Events analyzed by RIVET The CMS collaboration: Measurement of dijet azimuthal decorrelation in pp collisions at [arxiv: ] 18

19 Application: Dijet production Both angular ordered and rapidity ordered TMDs improve description for The TMD with angular ordering reproduces data quite well for small The TMD with virtuality ordering overestimates data at small (kt part of TMD likely overestimated) The CMS collaboration: Measurement of dijet azimuthal decorrelation in pp collisions at [arxiv: ] 19

20 Application: Dijet production The error band of TMD uncertainties (28 eigenvectors) and statistical uncertainties included Region of high kt in TMD The CMS collaboration: Measurement of dijet azimuthal decorrelation in pp collisions at [arxiv: ] TMD1-recoil jet1 jet3 TMD2-recoil jet2 20

21 Conclusions The developed Parton Branching method solves DGLAP equation at LO, NLO and NNLO collinear accuracy Possibility to study efects of diferent ordering conditions and resolution criteria in the evolution The Parton Branching evolution implemented within xfiter, first TMDs at NLO obtained from HERA inclusive DIS data first predictions for dijet decorrelation and the pt(z) 21

22 Thank you for atention 22