Simplified ACOT scheme with Massive Phase Space (S-ACOT-MPS)

Transcription

1 Simplified ACO scheme with Massive Phase Space (S-ACO-MPS) Keping Xie Department of Physics, Southern Methodist University, Dallas, X CEQ JLAB Parton Distributions as a Bridge from Low to High Energies November, 2018 Based on the work with J. Camell (Fermilab) and P. Nadolsky (SMU) 18xx.xxxxx. 1 / 18

2 What is S-ACO-MPS? Simplified-ACO scheme with Massive Phase Space: A QCD factorization approach for heavy-quark scattering at hadron-hadron colliders at (N)NLO in α s. 9 dσ/dp [fb/gev]13ev LHCb data NF=4 cross section Flavor-excitation Subtraction SACO-MPS SACO-MPS Ratio to data / 18

3 Heavy-Flavor Production in DIS 3-flavor O (α s 2 ) NLO α s 2 ln 2 ( ) 4-flavor O (α s ) NLO F 2 c (x,q) F 2 c (x,q) NLO NLO Q 2 Q 2 Figure: Expected uncertainty of Fixed Flavor Number Scheme for the Heavy-Flavor structure function in DIS. ung et. al. JPG2002. Q m Q, m Q matters, Q(x, µ) 0, Flavor Creation (N f scheme). Q m Q, m Q 0, Q(x, µ) matters, Flavor Excitation (N f + 1 scheme). Aivazis-Collins-Olness-ung [PRD1994] introduce an asymptotic subtraction (SB) term to get rid of the double-counting between Flavor Creation and Flavor Excitation, which switches from N f to N f + 1 scheme (Variable Flavor Number Scheme). Q m Q, SB FE, return back to N f scheme. Q m Q, SB FC, switch to N f + 1 scheme. FC + FE SB (1) 3 / 18

4 ACO series Simplified-ACO scheme [J. Collins PRD1998, M. Kramer et. al. PRD2000] treats heavy-quark as massless in Flavor Excitation. Drawback: instability of the cancellation between SB and FE around the switching point. he S-ACO-χ sheme [W. ung et.al. JPG2002] introduces rescaling variable χ = x(1 + 4m 2 Q /Q2 ) to capture the mass threshold effect. It stabilizes the perturbative convergence near the switching point by enforcing energy-momentum conservation in all scattering contributions. he S-ACO-MPS [K. Xie et. al. 18xx.xxxxx] scheme extends the S-ACO-χ method to hadron-hadron collisions. 4 / 18

5 heavy-quark production at colliders Lots of related experimental data such as D,B mesons at LHCb, b-quark jets at UA1, D0, CDF, ALAS, and CMS. Forward heavy-quark productions at the LHCb are sensitive to gluon-pdf at small-x, because of x 1,2 m 2 +p 2 s e ±y [PROSA arxiv: ]. Physical observable: p Q p Q m Q, N f Fixed Flavor Number Scheme [P. Nason et. al. NPB1989, W. Beenakker NPB1991], p Q m Q, Zero-Mass Scheme (N f + 1), p Q m Q, General-Mass Variable Flavor Number Scheme. Existing GM-VFNS s for heavy-quark hadroproduction FONLL [M. Cacciari et. al., hep-ph/ , hep-ph/02134], GM-VFNS code [B. Kneihl et. al. hep-ph/04289, ], S-ACO-MPS [K. Xie et. al. 18xx.xxxxx]. 5 / 18

6 FFNS calculations In FFNS for b production, we should take N f = 4 in both α s and PDF running. he heavy-quark running in the virtual loops is missing. No Flavor Excitation contributions as no heavy-flavor PDF. If Using N f = 5 PDF in MCFM, MadGraph_aMC@NLO, POWHEG, N f = 5 in the α s running, e.g. reading directly from LHAPDF; No FE contributions, equivalent to N f = 4 in the PDFs. 6 / 18

7 GM-VFNS s: Adding the Flavor Excitation terms and subtracting the double-counted terms (FC+FE-SB). Figure: Representative diagrams for Flavor Creation, Flavor Excitation and SuBtraction terms.hick (thin) lines indicate massive (massless) quark propagators. he dot means convolution. Ideally, we have p Q m Q, SB FE, FC dominates (FFNS), p Q m Q, SB FC, FE takes over (ZMS). 7 / 18

8 Comparisons with 2 existing codes FONLL resums logarithms as fragmentation functions and subtracts the massless limit of fixed-order where only log terms retained [M. Cacciari et. al., hep-ph/ , hep-ph/02134]. FONLL = FO + (RS FOM0) G(m,p ). (2) he matching function is tuned to keep lim m/p 0 G(m,p ) = 1. GM-VFNS code [B. Kneihl et. al. hep-ph/04289, ], σ = FC + FE σ, where lim m 0 σ m = σ 0 + σ. (3) he subtraction term σ is logarithms, equivalent to FOM0. S-ACO-MPS scheme is equivalent to GM-VFNS, except the subtraction term is calculated with the convolution of splitting function [J. Collins PRD1998, M. Kramer et. al. PRD200], SB = ˆσ gq P Q g g(x) (4) We introduce the massive phase space to capture the threshold effect in FE and SB by following the idea S-ACO-χ scheme[w. ung et.al. JPG2002]. 8 / 18

9 NLO cross section: massless vs. massive phase space. he matching instability is tamed by the massive phase space. FONLL deals it with a tuned a tuned matching function G(m,p ) GM-VFNS has to impose a cut p Q > m Q. 9 dσ/dp [fb/gev]7ev FC 0FE 0SB mfe msb 9 dσ/dp [fb/gev]7ev data FC FE SB FC+FE-SB Ratio to FC Ratio to data Figure: he FC is calculated with MCFM, which is cross-checked with MadGraph_aMC@NLO and FONLL online web. he B ± is corrected back to the b-quark with fragmentation ratio f(b B ± ) = [PDG2016]. 9 / 18

10 S-ACO-MPS vs. LHCb data: the p b distribution 9 b dσ/dp [fb/gev]7ev MC unc. PDF unc. Scale unc. m b unc. data b dσ/dp [fb/gev]13ev MC unc. PDF unc. Scale unc. m b unc. data Ratio Ratio Figure: We choose C14 PDF. he scale and m b uncertainties are calculated by varying µ R = µ F = (1/2,1,2) p 2 + m2 Q and m b = 4.75 ± 0.25 GeV. / 18

11 NLO scale uncertainties are large. α s (µ R ) is large and varies drastically around µ R m Q, Heavy-flavor PDF Q(x, µ F ) starts to be generated perturbatively at µ F = m Q. We can introduce the ratio observables R E1 /E 2 (X) = σ(x,e 1) σ(x,e 2 ), in which theoretical uncertainties cancel significantly [M. Mangano ]. R(13 ev/7 ev) LHCb 2.0 < y < Data FONLL p [GeV/c] Figure: LHCb measurements of D 0 production at 7 ev [ ], and the cross section ratio R(13eV/7eV) of B ± p distribution [ ]. 11 / 18

12 S-ACO-MPS vs. LHCb data: the ratio R(13eV/7eV) heoretical uncertainties cancel, especially the scale uncertainty b b dσ/dp (13eV) dσ/dp (7eV) MC unc. PDF unc. Scale unc. unc. m b data PDF unc Scale unc m b unc tot unc / 18

13 NLO vs. LHCb data: double-differential cross section d 2 σ/dp dy[fb/gev] 7eV 2.0<y< <y<3.0( ) <y<3.5( ) <y<4.0( ) <y<4.5( ) Figure: Double differential cross section for 7 ev. Yellow bands are the total theoretical uncertainties, added in quadrature. Good overall agreement. 13 / 18

14 13 ev case d 2 σ/dp dy[fb/gev] 13eV 2.0<y< <y<3.0( ) <y<3.5( ) <y<4.0( ) <y<4.5( ) Figure: Double differential cross section for 13 ev. 14 / 18

15 NLO vs. LHCb data: ratios of double-diff. cross sections d σ/dp dy(13ev) 2 d σ/dp dy(7ev) 4.0<y<4.5(+8) 3.5<y<4.0(+6) 3.0<y<3.5(+4) 2.5<y<3.0(+2) 2.0<y< / 18

16 C14 Hessian profiling with epump [C. Schmidt et. al ]. LHCbBX(w): C14 PDF updated with wight 1() LHCb B ± data. Caveat: We treat the systematic errors as uncorrelated, since we do not have the full correlated uncertainties. 2.0 g(x,q) at Q =5.0 GeV 90%C.L. 2.0 g(x,q) at Q =5.0 GeV 90%C.L. PDF Ratio to C14nn C14nn LHCbBX/C14nn LHCbBX w /C14nn x Error bands of g(x,q) C14nn LHCbBX LHCbBX w x We observe the impact on gluon PDF, but still mild, because C14 PDF describe the data very well, he experimental uncertainties are still large. 16 / 18

17 PROSA15 PDFs fitting 7 ev LHCb charm data [ ], compatible with C14HERA2NLO N f = 3. Figures: Bo-ing Wang Next rounds of LHCb measurements may help constrain the small-x gluon. 17 / 18

18 Summary We develop S-ACO-MPS scheme calculations to the heavy-flavor hadroproduction. Contributions to inclusive heavy quark from both Flavor Creation and Flavor Excitation; he double-counted term from gluon splitting is subtracted; We introduce massive phase space to capture the threshold effect. We obtain good cancellations behaviors in both asymptotic limits: p m Q, the SB cancels the FE terms, p m Q, the SB cancels the FC terms. Our calculations agree well with the LHCb B ± measurements. With theoretical uncertainties cancel significantly, the ratio observables impact the gluon-pdf in the small-x region. he precise data in next rounds can potentially provide strong constraints. Implementation in MCFM can be easily extended to NNLO, and applied to other heavy-quark processes, such as H/V + Q. 18 / 18