From Graeme.Watt@cern.ch Wed Feb 15 19:43:03 2012 Date: Thu, 16 Feb 2012 01:42:56 +0100 From: Graeme Watt To: Xiaochao Zheng Subject: Re: MSTW2008 PDFs discontituity? (fwd) Dear Xiaochao, Thanks for the message. The discontinuity at the charm-quark mass, Q^2 = m_c^2 = (1.40 GeV)^2 = 1.96 GeV^2 is a distinctive feature of NNLO evolution in a variable flavour number scheme (VFNS), first implemented in the MRST2006 release [arXiv:0706.0459]. This feature is mentioned in the README file: "Note that the PDFs (and alphaS) are discontinuous at NNLO at the heavy quark thresholds Q^2 = mc^2 and Q^2 = mb^2." The PDFs themselves are not physical quantities and the discontinuity should be cancelled (at least up to higher-order corrections) when the PDFs are convoluted with appropriate coefficient functions in a so-called "general-mass" VFNS to calculate the physical structure functions. You should be able to check this statement explicitly using the structure function code I sent to you. By the way, I've now linked the structure function code directly from http://projects.hepforge.org/mstwpdf/code/code.html following your previous request. Regarding the gamma-Z interference structure functions, there is a public code called QCDNUM (http://mbotje.web.cern.ch/mbotje/qcdnum/Site/QCDNUM17.html) which can calculate structure functions (including the Z contribution) up to NNLO. There are two options explained in Section 2.5 of the manual: the "zero-mass" VFNS appropriate for Q^2 >> m_h^2 where the structure functions will still be discontinuous at Q^2 = m_h^2, and the fixed flavour number scheme (FFNS) where heavy quarks are not included in the PDF evolution so avoiding the discontinuities at Q^2 = m_h^2. If you are interested in the region 1.0 < Q^2 < 3.0 GeV^2 then certainly the FFNS would be more appropriate than the "zero-mass" VFNS. You would then need to use the corresponding 3-flavour MSTW PDFs (http://projects.hepforge.org/mstwpdf/heavyquark/heavyquark.html) instead of the default 5-flavour PDFs. The treatment of heavy-quark contributions to DIS structure functions is unfortunately quite complicated (see https://indico.cern.ch/contributionDisplay.py?contribId=6&confId=168468 for a review talk I gave last Monday on this subject). Best regards, Graeme. On 15 Feb 2012, at 21:58, Xiaochao Zheng wrote: > > Dear Graeme: > > Sorry that I found a mistake in my plotting macro. I have revised the attachment and the email as below: > > Dear Graeme: > > I found the PDF from MSTW2008 code (and earlier codes such as MRST2006) has a slight discontituity in Q2 when called in the NNLO. I have attached plots of quark distributions functions vs. Q^2, for 1.0 > The jump in u and d (both valence and sea) are small in NNLO, and is more apparent in charm. The NLO and LO pdfs do not seem to have the same behavior. > > Are these caused by some artifacts in the MSTW fit? > > Thanks, > > Xiaochao > > --------------------------------------------------------------- > Assistant Professor, Department of Physics, Univ. of Virginia > UVa office (during academic year): > 134 Physics Building, 382 McCormick Rd. > PO Box 400714, Charlottesville, VA 22904-4714 > Phone: 434-243-4032 > > JLab office (during summer months, May-August): > Rm 12/F357, MS 12H5, 12000 Jefferson Ave, Newport News, VA 23606 > Phone: 757-269-5433 > --------------------------------------------------------------- >