======================================================= Description of variables stored for systematics studies ======================================================= By: Johan Alwall, 28/3/2012

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Turn on systematics info with the flag use_syst in the run_card.dat Note that systematics only works with matching (ickkw set to 1)

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Parameters that can be varied after-the-fact (without need to rerun Pythia+detector simulation):

• Central renormalization scale
• Central factorization scale
• PDF choice
• Emission renormalization scale factor
• PDF reweighting scale factor (not available at present)
• QCUT scale

============================================= Variational parameters in reweight.f: =============================================

* Central scale (ren scale): * line 702: scale (asref = alphas(scale))

Event weight given by:

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alpha_s weight: alphas(scale)^{N where}

N=#(QCD vertices) - #(emission alpha_s vertices below)

* Emission alpha_s reweighting: * line 912: qnow = sqrt(q2now)

Event weight given by:

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alphas(alpsfact*qnow)

* PDF reweighting: * line 873 (initial pdf): ipdgcl(idacl(n,i)), xnow(j), q2now (pdgini,xini, q2ini) line 1070 (cont. pdf): ipdgcl(idacl(n,i)), xnow(j), q2now (pdgint,xint, q2int)

etc. (for both sides (1,2))

Event weight given by:

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initial pdf(pdgini,xini,q2ini) *pdf(pdgint,xint,q2int)/pdf(pdgint,xint,q2ini) ... etc. Note: Central fact scale variation corresponds to reweighting the last

scale only on each side

============================================= Variation of QCUT in ME2pythia.f: =============================================

failing criteria in parentheses. line numbers approximate.

SHOWERKT: QCUT line 999: PTSORT(1) (in lhe file) (< QCUT) line 1012 (non-highest mult): shower kt (> QCUT) line 1025 (highest mult): shower kt (> PTSORT(1))

kT-MLM: YCUT=QCUT2 line 1090: NJETS (< NLJETS)

actually Y(NLJETS) (< YCUT)

line 1107 (non-highest mult): Y(NLJETS+1) (> YCUT) if highest mult case: YCUT=PTSORT(1) line 1133: Y(NN) (> YCUT) line 1145: If not clustered, fail line 1176: Y(2) (> YCUT)

So, just need three number for systematic variation of QCUT: SMIN. Fail if < QCUT:

For SHOWERKT: PTSORT(1) For kT-MLM: Y(NLJETS)

SCOMP. Comparison number:

For highest mult: max(QCUT,PTSORT(1)) Otherwise QCUT Perhaps use minimum safe QCUT or 0 instead of QCUT for systematics studies In any case, use max(QCUTcurr,comparison number) for arbitrary QCUTcurr.

SMAX. Fail if > comparison number:

For SHOWERKT: shower kt For kt-MLM: max(Y(NLJETS+1),Y(NN),Y(2))

Note that some events will always fail - I suggest to simply ignore those (as well as requiring minimum safe QCUT = xqcut for SHOWERKT and max(xqcut+10,xqcut*1.3) for kT-MLM).

Event weight given by:

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1 if QCUT < SMIN and SMAX < max(QCUT, SCOMP) otherwise 0

=============================================== Each line in the syst.dat file has the entries: ===============================================

<mgrwt event="event_num"> <rscale>n_qcd ren_scale</rscale> <asrwt>n_alpsem alpsem_scale(1) ... alpsem_scale(n_alpsem)</asrwt> <pdfrwt beam="1">n_pdfrw1 pdf_pdg_code1(1) ... pdf_pdg_code1(n_pdgrw1) \

pdf_x1(1) ... pdf_x1(n_pdfrw1) pdf_q1(1) ... pdf_q1(n_pdfrw1)</pdfwgt>

<pdfrwt beam="2">n_pdfrw2 pdf_pdg_code2(1) ... pdf_pdg_code2(n_pdgrw2) \

pdf_x2(1) ... pdf_x2(n_pdfrw2) pdf_q2(1) ... pdf_q2(n_pdfrw2)</pdfwgt>

<totfact>total_reweight_factor</totfact> <matchscale>SMIN SCOMP SMAX</matchscale> </mgrwt>

Total event weight for event event_num given by:

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alpha_s(scalefact*ren_scale)^{(n_qcd) * # central ren scale alpha_s(alpsfact*alpsem_scale(1)) * # emission ren scale alpha_s(alpsfact*alpsem_scale(2)) * # emission ren scale ... pdf(pdf_pdg_code1(1),pdf_x1(1),pdf_q1(1))* # initial state pdf pdf(pdf_pdg_code1(2),pdf_x1(2),pdf_q1(2))/ pdf(pdf_pdg_code1(2),pdf_x1(2),pdf_q1(2))* # pdf reweighting pdf(pdf_pdg_code1(3),pdf_x1(3),pdf_q1(3))/ pdf(pdf_pdg_code1(3),pdf_x1(3),pdf_q1(2))* # pdf reweighting}

...

pdf(pdf_pdg_code1(n_pdfrw1),pdf_x1(n_pdfrw1),scalefact*pdf_q1(n_pdfrw1))/ pdf(pdf_pdg_code1(n_pdfrw1),pdf_x1(n_pdfrw1),pdf_q1(n_pdfrw1-1))* # Note the central scale reweighting by scalefact above # (if n_pdfrw1 = 1, need to reweight the initial state pdf scale) # Also note that no scale should be larger than the last one (including # scalefact) for that beam. # # Now the same thing for all pdfs in beam 2 (n_pdfrw2) pdf(pdf_pdg_code2(1),pdf_x2(1),pdf_q2(1))* # initial state pdf

...

pdf(pdf_pdg_code2(n_pdfrw2),pdf_x2(n_pdfrw2),scalefact*pdf_q2(n_pdfrw2))/ pdf(pdf_pdg_code2(n_pdfrw2),pdf_x2(n_pdfrw2),pdf_q2(n_pdfrw2-1))* / total_reweight_factor # corr. factor from MG run

• 0 if (QCUT > SMIN or SMAX > max(QCUT, SCOMP)), otherwise 1