Hard Scattering Formalism

2018 ◽  
Author(s):  
John Campbell ◽  
Joey Huston ◽  
Frank Krauss
Keyword(s):  
Form Factor ◽  
Cross Sections ◽  
W Boson ◽  
Production Cross ◽  
Distribution Functions ◽  
Hard Scattering ◽  
Parton Distribution Functions ◽  
Sudakov Form Factor ◽  
State Radiation ◽  
Characteristic Features

The hard scattering formalism is introduced, starting from a physical picture based on the idea of equivalent quanta borrowed from QED, and the notion of characteristic times. Contact to the standard QCD treatment is made after discussing the running coupling and the Altarelli–Parisi equations for the evolution of parton distribution functions, both for QED and QCD. This allows a development of a space-time picture for hard interactions in hadron collisions, integrating hard production cross sections, initial and final state radiation, hadronization, and multiple parton scattering. The production of a W boson at leading and next-to leading order in QCD is used to exemplify characteristic features of fixed-order perturbation theory, and the results are used for some first phenomenological considerations. After that, the analytic resummation of the W boson transverse momentum is introduced, giving rise to the notion of a Sudakov form factor. The probabilistic interpretation of the Sudakov form factor is used to discuss patterns in jet production in electron-positron annihilation.

scholarly journals Heavy-flavor hadro-production with heavy-quark masses renormalized in the $$ \overline{\mathrm{MS}} $$, MSR and on-shell schemes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
M. V. Garzelli ◽  
L. Kemmler ◽  
S. Moch ◽  
O. Zenaiev
Keyword(s):  
Heavy Quark ◽  
Cross Sections ◽  
Top Quark ◽  
Quark Mass ◽  
Production Cross ◽  
Hadron Collider ◽  
Distribution Functions ◽  
Heavy Flavor ◽  
Parton Distribution Functions ◽  
Heavy Quark Mass

Abstract We present predictions for heavy-quark production at the Large Hadron Collider making use of the $$ \overline{\mathrm{MS}} $$ MS ¯ and MSR renormalization schemes for the heavy-quark mass as alternatives to the widely used on-shell renormalization scheme. We compute single and double differential distributions including QCD corrections at next-to-leading order and investigate the renormalization and factorization scale dependence as well as the perturbative convergence in these mass renormalization schemes. The implementation is based on publicly available programs, MCFM and xFitter, extending their capabilities. Our results are applied to extract the top-quark mass using measurements of the total and differential $$ t\overline{t} $$ t t ¯ production cross-sections and to investigate constraints on parton distribution functions, especially on the gluon distribution at low x values, from available LHC data on heavy-flavor hadro-production.

scholarly journals RESUMMATION FOR HEAVY QUARK AND JET CROSS-SECTIONS

2000 ◽  
Vol 15 (09) ◽  
pp. 1245-1296 ◽  
Author(s):  
NIKOLAOS KIDONAKIS
Keyword(s):  
Heavy Quark ◽  
Cross Sections ◽  
W Boson ◽  
Anomalous Dimension ◽  
Production Cross ◽  
Full Range ◽  
Direct Photon ◽  
Boson Production ◽  
Hard Scattering ◽  
W Boson Production

We review the resummation of threshold logarithms for heavy quark, dijet, direct photon, and W boson production cross-sections in hadronic collisions. Beyond leading logarithms the resummed cross-section is sensitive to the color exchange in the hard scattering. The resummation is formulated at next-to-leading logarithmic or higher accuracy in terms of anomalous dimension matrices which describe the factorization of soft gluons from the hard scattering. We give results for the soft anomalous dimension matrices at one loop for the full range of partonic subprocesses involved in heavy quark, dijet, direct photon, and W boson production. We discuss the general diagonalization procedure that can be implemented for the calculation of the resummed cross-sections, and we give numerical results for top quark production at the Fermilab Tevatron. We also present analytical results for the one- and two-loop expansions of the resummed cross-sections.

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.

scholarly journals Precision QCD measurements in DIS at HERA

2016 ◽  
Vol 31 (28) ◽  
pp. 1630025
Author(s):  
Daniel Britzger
Keyword(s):  
Cross Sections ◽  
Production Cross ◽  
Distribution Functions ◽  
Coupling Constants ◽  
Charged Current ◽  
Heavy Flavor ◽  
Parton Distribution Functions ◽  
Quark Masses ◽  
Insight Into

New and recent results on QCD measurements from the H1 and ZEUS experiments at the HERA ep collider are reviewed. The final results on the combined deep-inelastic neutral and charged current cross-sections are presented and their role in the extractions of parton distribution functions (PDFs) is studied. The PDF fits give insight into the compatibility of QCD evolution and heavy flavor schemes with the data as a function of kinematic variables such as the scale Q2. Measurements of jet production cross-sections in ep collisions provide direct proves of QCD and extractions of the strong coupling constants are performed. Charm and beauty cross-section measurements are used for the determination of the heavy quark masses. Their role in PDF fits is investigated. In the regime of diffractive DIS and photoproduction, dijet and prompt photon production cross-sections provide insights into the process of factorization and the nature of the diffractive exchange.

scholarly journals HEAVY QUARK PRODUCTION IN pp COLLISIONS

1995 ◽  
Vol 10 (20n21) ◽  
pp. 2999-3041 ◽  
Author(s):  
P.L. McGAUGHEY ◽  
E. QUACK ◽  
P.V. RUUSKANEN ◽  
R. VOGT ◽  
X.-N. WANG
Keyword(s):  
Heavy Quark ◽  
Cross Sections ◽  
Systematic Study ◽  
Production Cross ◽  
Distribution Functions ◽  
Pp Collisions ◽  
Parton Distribution Functions ◽  
Quark Production ◽  
Heavy Quark Pair ◽  
Existing Data

A systematic study of the inclusive single heavy quark and heavy-quark pair production cross sections in pp collisions is presented for RHIC and LHC energies. We compare with existing data when possible. The dependence of the rates on the renormalization and factorization scales is discussed. Predictions of the cross sections are given for two different sets of parton distribution functions.

scholarly journals DeepXS: fast approximation of MSSM electroweak cross sections at NLO

2020 ◽  
Vol 80 (1) ◽  
Author(s):  
Sydney Otten ◽  
Krzysztof Rolbiecki ◽  
Sascha Caron ◽  
Jong-Soo Kim ◽  
Roberto Ruiz de Austri ◽  
...  
Keyword(s):  
Cross Sections ◽  
Particle Production ◽  
Production Cross ◽  
Hadron Collider ◽  
Distribution Functions ◽  
Monte Carlo Integration ◽  
Leading Order ◽  
Parton Distribution Functions ◽  
Dimensional Parameter ◽  
O 10

AbstractWe present a deep learning solution to the prediction of particle production cross sections over a complicated, high-dimensional parameter space. We demonstrate the applicability by providing state-of-the-art predictions for the production of charginos and neutralinos at the Large Hadron Collider (LHC) at the next-to-leading order in the phenomenological MSSM-19 and explicitly demonstrate the performance for $$pp\rightarrow \tilde{\chi }^+_1\tilde{\chi }^-_1,$$pp→χ~1+χ~1-,$$\tilde{\chi }^0_2\tilde{\chi }^0_2$$χ~20χ~20 and $$\tilde{\chi }^0_2\tilde{\chi }^\pm _1$$χ~20χ~1± as a proof of concept which will be extended to all SUSY electroweak pairs. We obtain errors that are lower than the uncertainty from scale and parton distribution functions with mean absolute percentage errors of well below $$0.5\,\%$$0.5% allowing a safe inference at the next-to-leading order with inference times that improve the Monte Carlo integration procedures that have been available so far by a factor of $$\mathscr {O}(10^7)$$O(107) from $$\mathscr {O}(\mathrm{min})$$O(min) to $$\mathscr {O}(\mu \mathrm{s})$$O(μs) per evaluation.

scholarly journals Trijets in $$k_\mathrm{T}$$-factorisation: matrix elements vs parton shower

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
H. Van Haevermaet ◽  
A. Van Hameren ◽  
P. Kotko ◽  
K. Kutak ◽  
P. Van Mechelen
Keyword(s):  
Cross Sections ◽  
Azimuthal Angle ◽  
Distribution Functions ◽  
Matrix Elements ◽  
Parton Distribution Functions ◽  
Initial State ◽  
Final State ◽  
Proton Proton ◽  
Shell Matrix ◽  
State Radiation

Abstract We study 3-jet event topologies in proton-proton collisions at a centre-of-mass energy of $$\sqrt{s} = 13 \mathrm{\ TeV}$$s=13TeV in a configuration, where one jet is present in the central pseudorapidity region ($$|\eta | < 2.0$$|η|<2.0) while two other jets are in a more forward (same hemisphere) area ($$|\eta | > 2.0$$|η|>2.0). We compare various parton level predictions using: collinear factorisation, $$k_\mathrm{T}$$kT-factorisation with fully off-shell matrix elements and the hybrid framework. We study the influence of different parton distribution functions, initial state radiation, final state radiation, and hadronisation. We focus on differential cross sections as a function of azimuthal angle difference between the leading dijet system and the third jet, which is found to have excellent sensitivity to the physical effects under study.

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.

Sign in / Sign up

Export Citation Format

Share Document