scholarly journals Parton distribution functions and benchmark cross sections at next-to-next-to-leading order

2012 ◽  
Vol 86 (5) ◽  
Author(s):  
S. Alekhin ◽  
J. Blümlein ◽  
S. Moch
Keyword(s):  
Cross Sections ◽  
Parton Distribution ◽  
Distribution Functions ◽  
Leading Order ◽  
Parton Distribution Functions

scholarly journals Can $$ \overline{\mathrm{MS}} $$ parton distributions be negative?

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Alessandro Candido ◽  
Stefano Forte ◽  
Felix Hekhorn
Keyword(s):  
Strong Coupling ◽  
Cross Sections ◽  
Parton Distribution ◽  
Distribution Functions ◽  
Leading Order ◽  
Parton Distribution Functions ◽  
Parton Distributions ◽  
Factorization Scheme ◽  
Perturbative Regime

Abstract It is common lore that Parton Distribution Functions (PDFs) in the $$ \overline{\mathrm{MS}} $$ MS ¯ factorization scheme can become negative beyond leading order due to the collinear subtraction which is needed in order to define partonic cross sections. We show that this is in fact not the case and next-to-leading order (NLO) $$ \overline{\mathrm{MS}} $$ MS ¯ PDFs are actually positive in the perturbative regime. In order to prove this, we modify the subtraction prescription, and perform the collinear subtraction in such a way that partonic cross sections remain positive. This defines a factorization scheme in which PDFs are positive. We then show that positivity of the PDFs is preserved when transforming from this scheme to $$ \overline{\mathrm{MS}} $$ MS ¯ , provided only the strong coupling is in the perturbative regime, such that the NLO scheme change is smaller than the LO term.

Parton Distribution Functions

2018 ◽  
Author(s):  
John Campbell ◽  
Joey Huston ◽  
Frank Krauss
Keyword(s):  
Cross Sections ◽  
Parton Distribution ◽  
Distribution Functions ◽  
Data Sets ◽  
Hard Scattering ◽  
Leading Order ◽  
Parton Distribution Functions ◽  
Global Fitting

Parton Distribution Functions (PDFs) are a necessary ingredient in the calculation of cross sections at collider experiments with hadron beams. This chapter explores the techniques of determining the PDFs and their uncertainties, based on global analyses of data sets arising from a variety of hard-scattering processes. PDFs are determined at leading order, next-to-leading order, and next-to-next-to-leading order, with the corresponding orders of hard coefficients and evolution. Differences in the PDFs of different orders, and in their uncertainties, are described. Combinations of PDFs from different global fitting groups are discussed, and several useful tools for comparisons of PDFs are described.

scholarly journals HIGGS PRODUCTION IN ASSOCIATION WITH BOTTOM QUARKS AT HADRON COLLIDERS

2006 ◽  
Vol 21 (02) ◽  
pp. 89-109 ◽  
Author(s):  
S. DAWSON ◽  
C. B. JACKSON ◽  
L. REINA ◽  
D. WACKEROTH
Keyword(s):  
Standard Model ◽  
Cross Sections ◽  
Hadron Collider ◽  
Distribution Functions ◽  
Bottom Quarks ◽  
Final States ◽  
Leading Order ◽  
Hadron Colliders ◽  
Parton Distribution Functions ◽  
Model Case

We review the present status of the QCD corrected cross-sections and kinematic distributions for the production of a Higgs boson in association with bottom quarks at the Fermilab Tevatron and CERN Large Hadron Collider. Results are presented for the Minimal Supersymmetric Standard Model where, for large tan β, these production modes can be greatly enhanced compared to the Standard Model case. The next-to-leading order QCD results are much less sensitive to the renormalization and factorization scales than the lowest order results, but have a significant dependence on the choice of the renormalization scheme for the bottom quark Yukawa coupling. We also investigate the uncertainties coming from the Parton Distribution Functions and find that these uncertainties can be comparable to the uncertainties from the remaining scale dependence of the next-to-leading order results. We present results separately for the different final states depending on the number of bottom quarks identified.

scholarly journals CAN POLARIZED DRELL-YAN SHED MORE LIGHT ON THE PROTON SPIN?

1992 ◽  
Vol 07 (29) ◽  
pp. 2695-2702 ◽  
Author(s):  
PRAKASH MATHEWS ◽  
V. RAVINDRAN
Keyword(s):  
Inelastic Scattering ◽  
Deep Inelastic Scattering ◽  
Parton Distribution ◽  
Factorization Method ◽  
Distribution Functions ◽  
Proton Spin ◽  
Leading Order ◽  
Parton Distribution Functions ◽  
First Moment ◽  
Polarized Deep Inelastic Scattering

We analyze polarized Drell-Yan process using the factorization method and derive operator definitions for polarized parton distribution functions. We demonstrate that a factorization analogous to that in the unpolarized Drell-Yan case holds in this process. We study the leading order gluonic contribution to the first moment of polarized Drell-Yan function and show that it is consistent with the results obtained from polarized deep inelastic scattering.

scholarly journals Measurement of $$W^\pm $$ boson production in Pb+Pb collisions at $$\sqrt{s_{\mathrm{NN}}} = 5.02~\text {Te}\text {V}$$ with the ATLAS detector

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
G. Aad ◽  
◽  
B. Abbott ◽  
D. C. Abbott ◽  
A. Abed Abud ◽  
...  
Keyword(s):  
Cross Sections ◽  
Parton Distribution ◽  
Production Cross ◽  
Charge Asymmetry ◽  
Distribution Functions ◽  
Boson Production ◽  
Parton Distribution Functions ◽  
Absolute Value ◽  
The Absolute ◽  
Thickness Function

AbstractA measurement of $$W^\pm $$W± boson production in Pb+Pb collisions at $$\sqrt{s_\mathrm {NN}} = 5.02~\text {Te}\text {V}$$sNN=5.02Te is reported using data recorded by the ATLAS experiment at the LHC in 2015, corresponding to a total integrated luminosity of $$0.49\;\mathrm {nb^{-1}}$$0.49nb-1. The $$W^\pm $$W± bosons are reconstructed in the electron or muon leptonic decay channels. Production yields of leptonically decaying $$W^\pm $$W± bosons, normalised by the total number of minimum-bias events and the nuclear thickness function, are measured within a fiducial region defined by the detector acceptance and the main kinematic requirements. These normalised yields are measured separately for $$W^+$$W+ and $$W^-$$W- bosons, and are presented as a function of the absolute value of pseudorapidity of the charged lepton and of the collision centrality. The lepton charge asymmetry is also measured as a function of the absolute value of lepton pseudorapidity. In addition, nuclear modification factors are calculated using the $$W^\pm $$W± boson production cross-sections measured in pp collisions. The results are compared with predictions based on next-to-leading-order calculations with CT14 parton distribution functions as well as with predictions obtained with the EPPS16 and nCTEQ15 nuclear parton distribution functions. No dependence of normalised production yields on centrality and a good agreement with predictions are observed for mid-central and central collisions. For peripheral collisions, the data agree with predictions within 1.7 (0.9) standard deviations for $$W^-$$W- ($$W^+$$W+) bosons.

scholarly journals Transverse momentum dependent PDFs at N3LO

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Markus A. Ebert ◽  
Bernhard Mistlberger ◽  
Gherardo Vita
Keyword(s):  
Transverse Momentum ◽  
Cross Sections ◽  
Production Cross ◽  
Gluon Fusion ◽  
Building Blocks ◽  
Distribution Functions ◽  
Leading Order ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Collinear Limit

Abstract We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. Our calculation is based on an expansion of the differential Drell-Yan and gluon fusion Higgs production cross sections about their collinear limit. This method allows us to employ cutting edge multiloop techniques for the computation of cross sections to extract these universal building blocks of the collinear limit of QCD. The corresponding perturbative matching kernels for all channels are expressed in terms of simple harmonic polylogarithms up to weight five. As a byproduct, we confirm a previous computation of the soft function for transverse momentum factorization at N3LO. Our results are the last missing ingredient to extend the qT subtraction methods to N3LO and to obtain resummed qT spectra at N3LL′ accuracy both for gluon as well as for quark initiated processes.

Transverse momentum dependent (TMD) parton distribution functions generated in the modified DGLAP formalism based on the valence-like distributions

2017 ◽  
Vol 32 (19n20) ◽  
pp. 1750121 ◽  
Author(s):  
H. Hosseinkhani ◽  
M. Modarres ◽  
N. Olanj
Keyword(s):  
Transverse Momentum ◽  
Parton Distribution ◽  
Dynamical Variable ◽  
Distribution Functions ◽  
Present Calculation ◽  
Leading Order ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Longitudinal Structure Function ◽  
Wide Range

Transverse momentum dependent (TMD) parton distributions, also referred to as unintegrated parton distribution functions (UPDFs), are produced via the Kimber–Martin–Ryskin (KMR) prescription. The GJR08 set of parton distribution functions (PDFs) which are based on the valence-like distributions is used, at the leading order (LO) and the next-to-leading order (NLO) approximations, as inputs of the KMR formalism. The general and the relative behaviors of the generated TMD PDFs at LO and NLO and their ratios in a wide range of the transverse momentum values, i.e. [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are investigated. It is shown that the properties of the parent valence-like PDFs are imprinted on the daughter TMD PDFs. Imposing the angular ordering constraint (AOC) leads to the dynamical variable limits on the integrals which in turn increase the contributions from the lower scales at lower [Formula: see text]. The results are compared with our previous studies based on the MSTW2008 input PDFs and it is shown that the present calculation gives flatter TMD PDFs. Finally, a comparison of longitudinal structure function [Formula: see text] is made by using the produced TMD PDFs and those that were generated through the MSTW2008-LO PDF from our previous work and the corresponding data from H1 and ZEUS collaborations and a reasonable agreement is found.

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