Collinear and TMD densities from Parton Branching Method Ola Lelek 1 - - PowerPoint PPT Presentation

Collinear and TMD densities from Parton Branching Method

Ola Lelek 1 •, Francesco Hautmann 2 , Hannes Jung 1, Voica Radescu 3, Radek Žlebčík 1

1 DESY 2 University of Oxford 3 CERN

Resummation, Evolution, Factorization 2017 Madrid

2

Introduction

Use a Parton Branching (PB) method to:

• solve DGLAP evolution equation to obtain collinear Parton Distribution Functions (PDFs)

But not only! → further advantages:

• obtain Transverse Momentum Dependent (TMD) PDFs

Goal:

• TMD PDF sets for all flavours, all kinetically allowed x, kt, μ2

The project is NOT just an evolution!

• already available in xFitter for determination of PDFs
• TMDlib and TMDplotter web page for easy acces to TMDs and collinear PDFs

and plotting T

• ol
• comparison with measurements through interface with CASCADE and for

example Rivet Details in papers: Phys.Lett. B772 (2017) 446-451 arXiv:1708.03279

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Motivation

• Parton Shower (PS) crucial for obtaining predictions for processes

at high-energy hadron colliders

• pen problem: shower’s transverse momentum kinematics
• One of the approaches to deal with the problem: T

ransverse Momentum Dependent (TMD) formalism based on TMD form of factorization

We want to develop an approach in which transverse momentum kinematics will be treated without any mismatch between matrix element (ME) and PS

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The formalism

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The formalism

T h i s p r

• b

l e m h a s a n i t e r a t i v e s

• l

u t i

• n

a n d a n i n t e r p r e t a t i

• n

i n t e r m s

• f

P a r t

• n

B r a n c h i n g p r

• c

e s s !

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Parton Branching

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Parton Branching

OR

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kt dependence

PB method: for every branching μ is generated and available. How to connect μ with qt,c of the emitted and kt,a of the propagating parton?

kt,a contains the whole history of the evolution. In this method kinematics is treated properly at every branching.

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zM choice

• Partons emitted with a transverse momenta smaller than a certain value

given by a resolution scale can not be resolved → branchings with z >zM are non- resolvable

• Normally treated with the plus prescription but integrals in evolution

equation separately divergent for z → 1 : → solved by a parameter zM : Different choices of zM :

• zM - fixed
• zM - can change dynamically with the scale (resolution scale different for

different scales): Replace qt,c with some minimum q0 :

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NLO comparison with semi analytical methods

Initial distribution: fb0 (x0 , μ0

2 ) - from QCDnum

The evolution performed with parton branching method up to a given scale μ2 . Obtained distribution compared with a pdf calculated at the same scale by semi analytical method (QCDnum) Results for fixed 1 − zM = 10−5 .

Upper plots: collinear pdfs from the parton branching method Lower plots: ratios of the pdfs from a parton branching method and pdfs from QCDnum.

Very good agreement with the results coming from semi analytical methods (QCDnum). More details in: arXiv:1708.03279

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iTMDs: Cross check for different fixed zM

Upper plot: collinear pdfs from the parton branching method Lower plot: ratios of the pdfs from the parton branching method and pdfs from QCDnum.

There is no dependence on zM as long as zM large enough.

Comparison of the results for different fixed zM values (all independent of branching scale).

More details in: arXiv:1708.03279

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iTMDs with dynamic zM

Previous slides: for a fixed value of zM the results the same as from standard evolution (with the same initial conditions). Here: comparison of the PDF from a standard evolution with the PDF from PB with the angular ordering condition to associate kt and μ, with the dynamic zM , for different resolution scales q0 (with the same initial conditions)

• Here starting distribution from HERApdf 2.0 NLO

μ' - scale at which the branching happens q0 - a free parameter describing the resolution scale

Angular ordering with dynamic zM differs from a standard evolution, especially if the q0 large.

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• For collinear PDFs there was no zM dependence (for fixed zM).
• What about zM dependence for TMDs?
• Here the results for fixed zM at NLO

large zM - a lot of soft gluons! qt - ordering: for every zM value we obtain different TMD → not physical behavior, qt - ordering shouldn’t be used For virtuality and angular ordering no zM dependence (suppression of soft gluons because of the(1 − z) term)

TMDs: Cross check for different fixed zM

More details in: arXiv:1708.03279

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TMDs with dynamic zM

Comparison of the TMDs from PB with the angular ordering condition to associate kt and μ, with the dynamic zM , for different resolution scales q0

q0 = 0.1 q0 = 0.01 q0 = 0.5 q0 = 0.1 q0 = 0.01 q0 = 0.5

The same conclusion for virtuality ordering condition to associate kt and μ, with the dynamic zM , for different resolution scales q0

No dependence on q0 parameter in TMD distributions (because of the (1-z) term in the calculation of kt the large z region suppressed)

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TMDs with fixed and dynamic zM

Angular ordering condition to associate kt and μ No difference between fixed and dynamic zM (because of the (1-z) term in calculation of kt)

fixed dynamic

Virtuality ordering condition to associate kt and μ No difference between fixed and dynamic zM (because of the (1-z) term in calculation of kt)

fixed dynamic

Difference in the TMDs from angular ordering and virtuality ordering

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Example of TMDs from PB

From PB method we can obtain TMDs for all flavours at all kinematically allowed x, μ and kt

Results for angular ordering to associate kt and μ , fixed zM

More details in: arXiv:1708.03279

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Procedure of the fit to the F2 data from HERA 1+2

Goal: TMD PDF sets for all flavours, all x, μ2 and kt

More details in talk of Radek Žlebčík,

paper in preparation

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Application of our TMDs to DY

• LO Drell–Yan for qq → Z :
• kt according to TMD (mDY fixed, x1 , x2 change)

TMDs as a manifestation of transverse momentum resummation up to large kt

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Application of our TMDs to DY

• LO Drell–Yan for qq → Z :
• kt according to TMD (mDY fixed, x1 , x2 change)

TMDs as a manifestation of transverse momentum resummation up to large kt

Virtuality ordering and angular ordering condition to associate μ2 and kt both for fixed zM.

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Application of our TMDs to DY

• LO Drell–Yan for qq → Z :
• kt according to TMD (mDY fixed, x1 , x2 change)

TMDs as a manifestation of transverse momentum resummation up to large kt

Virtuality ordering and angular ordering condition to associate μ2 and kt both for fixed zM.

TMD fitted to HERA data reproduces correctly the shape of Z pt spectrum NO tuning/adjustment of parameters is done, all is coming from PDF fit, no free parameters after fit (in contrast to what is being done in MC tuning) transverse momentum originates directly from parton branching difference between angular ordering and virtuality ordering observed also in physical observable

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Application of our TMDs to DY

• LO Drell–Yan for qq → Z :
• kt according to TMD (mDY fixed, x1 , x2 change)

TMDs as a manifestation of transverse momentum resummation up to large kt

TMD fitted to HERA data reproduces correctly the shape of Z pt spectrum NO tuning/adjustment of parameters is done, all is coming from PDF fit, no free parameters after fit (in contrast to what is being done in MC tuning) transverse momentum originates directly from parton branching difference between angular ordering and virtuality ordering observed also in physical observable

Virtuality ordering and angular ordering condition to associate μ2 and kt both for zM changing with the scale μ2 . Results the same as for the fixed zM because TMDs the same.

22

Application of our TMDs to DY

• LO Drell–Yan for qq → Z :
• kt according to TMD (mDY fixed, x1 , x2 change)

TMDs as a manifestation of transverse momentum resummation up to large kt

Virtuality ordering and angular ordering condition to associate μ2 and kt both for zM changing with the scale μ2 . Results the same as for the fixed zM because TMDs the same.

TMD fitted to HERA data reproduces correctly the shape of Z pt spectrum NO tuning/adjustment of parameters is done, all is coming from PDF fit, no free parameters after fit (in contrast to what is being done in MC tuning) transverse momentum originates directly from parton branching difference between angular ordering and virtuality ordering observed also in physical observable

free parameters: intrinsic k t (here gauss with width=1.5 GeV), scale in αs, fit to F2 (including kt dependence of ME)

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Check the sensitivity to intrinsic kt

• Angular ordering to associate scale μ2 with kt ,

Little dependence on intrinsic kt for LHC data. To Do: Check for the low pT data.

Work in progress

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Scale in αs

• Up to now the scale in αs in was the scale of a branching μ2. But the angular ordering

suggests to use αs (μ2 (1-z)2) We compare:

• αs (μ2)
• αs (μ2 (1-z)2)
• αs (μ2 (1-z)2z2)

The scale suggested by angular ordering give a very good description of the Z pT spectrum. Note: no tuning of free parameters here!

Work in progress

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Summary & Conclusions

• Solution of the DGLAP evolution equation with a parton branching

method at NLO was shown.

• it reproduces exactly semi-analytical solution for collinear PDFs (results

consistent with QCDNum)

• extraction of TMD PDFs
• options to study different orderings and different definitions of the

resolution scale for collinear and TMD PDFs available

• TMDs are consistently with angular ordering and virtuality
• rdering but not with qt-ordering
• fit to F2 Hera data at LO and NLO was performed within xFitter, TMDs

sets for all flavours with uncertainties were obtained from the fit

• application in DY measurements: use TMD from PB as an all order qt

resummation.

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Summary & Conclusions

• Solution of the DGLAP evolution equation with a parton branching

method at NLO was shown.

• it reproduces exactly semi-analytical solution for collinear PDFs (results

consistent with QCDNum)

• extraction of TMD PDFs
• options to study different orderings and different definitions of the

resolution scale for collinear and TMD PDFs available

• TMDs are consistently with angular ordering and virtuality
• rdering but not with qt-ordering
• fit to F2 Hera data at LO and NLO was performed within xFitter, TMDs

sets for all flavours with uncertainties were obtained from the fit

• application in DY measurements: use TMD from PB as an all order qt

resummation.

Thank you!