REFINEMENT OF THE PION PDF IMPLEMENTING DRELL- YAN EXPERIMENTAL - - PowerPoint PPT Presentation
REFINEMENT OF THE PION PDF IMPLEMENTING DRELL- YAN EXPERIMENTAL DATA Patrick B Barry 1 , Nobuo Sato 2 , W. Melnitchouk 3 , Chueng-Ryong Ji 1 pcbarry@ncsu.e .edu North Carolina State University 1 University of Connecticut 2 Thomas Jefferson
Patrick B Barry1, Nobuo Sato2, W. Melnitchouk3, Chueng-Ryong Ji1 pcbarry@ncsu.e .edu North Carolina State University1 University of Connecticut2 Thomas Jefferson National Accelerator Facility3
■ Two hadrons collide
– Do not need to be protons! ■ One donates a quark, other an antiquark ■ Quarks annihilate into a virtual photon ■ Dilepton production ■ Measure differential cross- section of lepton/antilepton pair
■ Cross-section differential in invariant mass of lepton pair, 𝑅", and rapidity, 𝑍 ■ The momentum fractions of the initial hadrons are 𝑦%, 𝑦" ■ Parton distribution functions (PDFs) are 𝑔
( 𝑦, 𝑅"
■ Sum over all partons
■ Parameterize the PDF at 𝑅)
" = 1GeV2 as:
𝑔 𝑦, 𝜈" = 𝑂 ¡𝑦/ 1 − 𝑦1 ■ Definitions: 𝑟3 = 𝑣 53 = 𝑒3; 𝑟7 = 2 ¡𝑣 + 𝑒̅ + 𝑡 ; ■ Use sum rules to fix 𝑂=>, 𝑂
?
■ We fit 𝑏, 𝑐 for the valence, sea, and gluon, and 𝑂 for the sea ■ PDFs are evolved using DGLAP in Mellin space
■ Monte Carlo fitting method ■ Create parameter space to have a uniform prior over a specified range ■ Sample points in parameter space closer and closer to the maximum likelihood ■ Weights produced with each sample based on proximity to maximum likelihood ■ Provides errors without assumption of linear error propagation 𝑊𝑏𝑠 𝒫 ∝ F 𝒫G − 𝐹 𝒫
"
■ Start with random points on line of 0 < 𝑌 < 1. ■ 𝑌 = 0 is the point
likelihood.
■ Start with random points on line of 0 < 𝑌 < 1. ■ 𝑌 = 0 is the point
likelihood. ■ Delete point of lowest likelihood and make it the upper-bound on new sampling boundary
■ Start with random points on line of 0 < 𝑌 < 1. ■ 𝑌 = 0 is the point
likelihood. ■ Delete point of lowest likelihood and make it the upper-bound on new sampling boundary
■ Start with random points on line of 0 < 𝑌 < 1. ■ 𝑌 = 0 is the point
likelihood. ■ Delete point of lowest likelihood and make it the upper-bound on new sampling boundary ■ Keep randomly sampling until a threshold is reached
■ Start with random points on line of 0 < 𝑌 < 1. ■ 𝑌 = 0 is the point
likelihood. ■ Delete point of lowest likelihood and make it the upper-bound on new sampling boundary ■ Keep randomly sampling until a threshold is reached
■ Start with random points on line of 0 < 𝑌 < 1. ■ 𝑌 = 0 is the point
likelihood. ■ Delete point of lowest likelihood and make it the upper-bound on new sampling boundary ■ Keep randomly sampling until a threshold is reached
■ For Drell-Yan, we use E615 and NA10 datasets – 𝜌N beam incident on a Tungsten target – Consider only 0 < 𝑦O < 0.9 and 4.16 < 𝑅 < 8.34 to avoid 𝐾/Ψ and Υ production
Yan
parameters
■ Add in data from HERA (ZEUS & H1) to perform global fit ■ Detect neutrons in coincidence with outgoing electrons: ■ Neutron has most of the energy of the proton ■ Incoming electron barely strikes the surface of the proton, knocking out a pion from the pion cloud ■ Focuses on small 𝑦Z, whereas Drell-Yan focuses on large 𝑦Z
■ Observable in H1 data is 𝐺
" \] ^ 𝑦, 𝑅", 𝑧 = 𝑔Z`a(𝑧) ¡𝐺" Z(𝑦Z, 𝑅")
– Where 𝑔Z`a(𝑧) ¡is the splitting function from the proton, and ¡𝐺"
Z(𝑦Z, 𝑅") is the pion
structure function (depends on pion PDF) ■ Observable in ZEUS is 𝑠 𝑦Z, 𝑅", 𝑧 = 𝑔Z`a 𝑧 𝐺"
Z 𝑦Z, 𝑅"
𝐺
" d 𝑦, 𝑅"
Δ𝑧 – where 𝐺
" d 𝑦, 𝑅" is the proton structure function
■ For Drell-Yan, we use E615 and NA10 datasets – 𝜌N beam incident on a Tungsten target – Consider only 0 < 𝑦O < 0.9 and 4.16 < 𝑅 < 8.34 to avoid 𝐾/Ψ and Υ production ■ For Leading Neutron, we use H1 and ZEUS datasets – We consider cuts on data based on maximum 𝑧 = 𝑦Z/𝑦 values
𝑧-cut of 0.2
𝑧-cut of 0.2
𝑧-cut of 0.2
■ First attempted fit to both high-𝑦Z and low- 𝑦Z regions using Drell-Yan and Leading Neutron data ■ Use of nested sampling algorithm to improve errors ■ Next steps: to include threshold resummation in our calculation
■ Can make a prediction of E866 data for 𝑒̅ − 𝑣 5 = (𝑔Z`a − "
^ 𝑔Zfg``) ⊗ 𝑟
53
Z using our
valence 𝜌 PDF, where 𝑔Z`a and 𝑔Zfg`` are the splitting functions from the proton
0.2 0.4 0.6 0.8 xπ 101 102
2 × 101 3 × 101 4 × 101 6 × 101
Q2
E615 NA10-194GeV NA10-286GeV
4.16" < 𝑅" < 8.34"
large-𝑦i
10−3 10−2 10−1 xπ 101 102 103 Q2
H1 ZEUS
■ For all datasets with overall normalization uncertainty, we fit to within the reported percentage around 1.
LN DY
■ Analogous to the Fourier transform ■ Transform from x-space to Mellin space (exponents of x)
WH WHY??
■ We know how PDFs evolve in scale based on DGLAP:
■ After evolution, invert back into x-space
we do the DGLAP evolution
radius, integrand converges