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14-18 May 2018
Jefferson Lab - CEBAF Center
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First Monte Carlo Global QCD Analysis of Pion Parton Distributions

15 May 2018, 14:20
Auditorium (Jefferson Lab - CEBAF Center)


Jefferson Lab - CEBAF Center


Mr Patrick Barry (North Carolina State University)


Pions have long been associated with being the lightest bound state made of quarks, antiquarks and gluons (partons), as well as being the Goldstone boson produced from the breaking of effective chiral symmetry. In previous works, its parton distribution function (PDF) has been determined only by $\pi A$ Drell-Yan (DY) experiments such as E615 and NA10 done at Fermilab and CERN, respectively. In the DY process, two hadrons collide, with one donating a quark and the other donating an antiquark, eventually producing a dimuon pair. Since the initial annihilation provides enough energy to create a heavy lepton pair, the quark/antiquark must have high momentum. Thus, the DY process can only resolve the high momentum fraction ($x_\pi \gt 0.2$) region of the pion’s parton distribution, which constrains only the valence PDFs. To more accurately determine the pion PDF at lower $x_\pi$, we must include data from leading neutron (LN) electroproduction experiments such as H1 and Zeus done at HERA at DESY. Here, a target proton struck with an electron transforms into a detected neutron, a process which at forward angles, is dominated by the one-pion exchange model. Inherently, the theory has some model dependence (albeit relatively weak) coming from the splitting function’s regularization prescription, of which we test five. This process probes much smaller momentum fraction as $x_\pi \sim 10^{-3}$, where the sea and gluon dominate, providing an unseen constraint on the sea quark and gluon PDFs. In practice, we fit the parton distributions to all existing DY and LN datasets using a Monte Carlo (MC) method based on nested sampling. The method uniquely calculates the likelihood function at various positions in vector space to nest around the global maximum likelihood value. The MC nature allows us to rigorously quantify the uncertainty in the PDFs. We successfully have determined the pion PDFs at both the high-$x_\pi$ and low-$x_\pi$, and in doing so, we obtain a $\chi^2$ of $0.96 – 1.04$ over the five models. The PDFs we obtain reveal that at the input scale, the gluon carries a significant fraction of the pion momentum $\sim 30\%$, which is higher than predicted with only the DY data, and the sea carries $\sim 15\%$ of the momentum fraction of the pion. We can also describe the $\bar{d}-\bar{u}$ asymmetry in the proton by using the determined pion PDF and the same pion splitting functions as used in the LN process.

Primary author

Mr Patrick Barry (North Carolina State University)


Chueng R. Ji (North Carolina State University) Nobuo Sato (UConn) Wally Melnitchouk (Jefferson Lab)

Presentation Materials