Parton densities with Parton Branching method and applications

Transcription

1 Parton densities with Parton Branching method and applications Radek Žlebčík1 Armando Bermudez Martinez1, Francesco Hautmann2, Hannes Jung1, Ola Lelek1, Voica Radescu3 1 Deutsches Elektronen-Synchrotron (DESY) 2 University of Oxford 3 CERN March 21st Moriond 2018

2 What are TMD? TMD = Transverse Momentum Dependent parton distributions At very small transverse momenta Typically for small qt in DY production or semi-inclusive DIS, e.g CSS At very small x unintegrated PDFs Essentially only gluon densities, e.g. CCFM, BFKL etc. New approach covering all flavour and and wide range of x and kt Parton Branching method Flavour dependence! F. Hautmann, H. Jung, A. Lelek, V. Radescu, R. Zlebcik, JHEP 1801 (2018) 070 [arxiv: ]. F. Hautmann, H. Jung, A. Lelek, V. Radescu, R. Zlebcik, Phys.Let. B772 (2017) [arxiv: ]. 2

3 Why TMD? Dijet decorrelation, The CMS collaboration: Measurement of dijet azimuthal decorrelation in pp collisions at 8 TeV [arxiv: ] NLO-dijet (Powheg) w/o PS cannot describe small Δφ region NLO-dijet (Powheg) convoluted with TMDs describes both low and Δφ 3

4 Evolution Equation We use the evolution equation in the form: The Sudakov factor (no emission probability): The momentum weighted PDF The spliting function for the real emissions Freedom to choose renormalization scale Freedom to choose threshold for resolvable emissions 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) No need to calculate them 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 affects high-x region, small differences 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 consistency check LO NLO NNLO The simplest scenario where and can be compared with semi-analytical solution of DGLAP Method verified against QCDNUM up to NNLO The solution s uncertainties are mainly statistical (~ number of generated MC evolutions) 8

9 The Transverse Momentum The Parton Branching method allows to assign pt to every branching and study different parton shower ordering conditions the bridge between MC parton showers and PDF fits using analytic DGLAP solution Virtuality ordering ( ) Angular ordering ( ) - relative trans. mom. of the emission The angular ordering treats correctly color coherence effects used in following TMDs 9

10 The evolution equation and fit The described MC technique solves the following evolution equation (of the Fredholm type) Two alternative fit variants tested PB NLO fit1 PB NLO fit2 Ordering variable (factorization scale) Angle Angle Argument of αs (renormalization scale) Angle PT Implemented in xfiter The resolutions threshold zm Fiting reduced DIS cross-section HERAPDF-like parametrization of the PDFs at starting scale 10

11 Fit to HERA DIS data Fit 1 with (same value as HERAPDF 2.0) Fit 2 with At higher scales PDFs from both variants start to be identical 11

12 Fit to HERA DIS data Differences between fit1 and fit2 at small kt Introducing in fit2 increases the emission rate at higher z (near sof resum. region) the kt increases 12

13 Application 1: DY pt spectrum Using DY production at LO to probe pt spectrum TMDs convoluted with hard matrix element 13

14 Application 1: DY pt spectrum Using DY production at LO to probe pt spectrum ATLAS Collaboration Eur. Phys. J. C76 (2016), 291 [arxiv: ] TMD with angular ordering and TMD with angular ordering and Beter description of low pt region The intrinsic kt also plays a role for small transverse momenta 14

15 Application 2: Dijet production Angular decorrelation of leading jets sensitive to the extra radiation The CMS collaboration: Azimuthal correlations for inclusie 2-jet, 3-jet, and 4-jet events in pp at [arxiv: ] between leading and subleading jet 15

16 Application 2: Dijet production 1) Events generated by POWHEG 2jets, without including the parton shower 2) The transverse momentum of partons entering hard process generated according to TMDs 3) The TMD based ISR + FSR generated using CASCADE MC The CMS collaboration: Azimuthal correlations for inclusie 2-jet, 3-jet, and 4-jet events in pp at [arxiv: ] 16

17 Application 2: Dijet production Both fit1 and fit2 TMDs agree with the data, agreement seen over the whole pt range The Powheg with Pythia8 showers gives slightly higher angular decorrelation than in data The CMS collaboration: Azimuthal correlations for inclusie 2-jet, 3-jet, and 4-jet events in pp at [arxiv: ] 17

18 Conclusions Transverse momenta of the interacting partons important for precision physics need for TMDs The developed Parton Branching method solves DGLAP-like equations up to NNLO collinear accuracy freedom in choosing ordering condition and renormalization scale The method implemented in xfiter allows to determine kt distributions of all partonic flavours two TMD sets with unc. extracted by fiting of HERA DIS data Many phenomenological applications for LHC processes demonstrated on pt(z) distribution and dijet decorrelation 18