Research in QCD factorization Bowen Wang Southern Methodist University (Dallas TX) Jefferson Lab Newport News VA 1/1/015
My research at SMU in 011-015 Ph. D. advisor: Pavel Nadolsky Ph. D. thesis: The inclusive cross section of neutral current deep inelastic scattering (DIS) with heavyquark mass effect at approximate NNNLO. Studies of the transverse-momentum-dependent (TMD) factorization. 1. Nonperturbative contributions to a resummed leptonic angular distribution in Drell-Yan process (M. Guzzi P. M. Nadolsky B. Wang. arxiv:1309.1393). NLO computations for TMD factorization in unpolarized SIDIS (P. M. Nadolsky Ted Rogers B. Wang. In progress) 3. Application of TMD factorization in nuclear collisions. (in backup slides) ( V. Guzey M. Guzzi P. M. Nadolsky M. Strikman B. Wang. arxiv:11.5344)
My thesis: a three-loop QCD computation for heavy-quark scattering in neutral-current DIS To be finished in Spring 015 Will document a method to organize N3LO cross sections for NC DIS with heavy-quark mass dependence in the S-ACOT factorization scheme for CTEQ PDF fits 1.5E-01 F h ( x Q ) 1.0E-01 5.0E-0 0.0E+00 Preliminary result in IM N3LO Q= GeV N3LO_IM NLO_GM -5.0E-0 1.E-04 1.E-03 1.E-0 1.E-01 x
N3LO Flavor classes FC FC0 FC11 FCg and FC11g classes 4
An example: mass dependence of FC11 class
Implementation of factorization scale dependence at N3LO The scale uncertainty is significantly reduced near charm production threshold at lower orders compared to calculations which neglects all masses. What about N3LO? The published 3 loop DIS coefficient functions are computed with Q F. Need to compute coefficient functions with an arbitrary factorization scale. The calculation is done recursively using lower order coefficient functions (up to O( S ) ) and 3 splitting functions (up to O( ) ) S
NNLL/NNLO studies of TMD factorization for production at hadron colliders * Z / (M. Guzzi P. M. Nadolsky B. Wang. arxiv:1309.1393)
What is TMD factorization In Drell-Yan like processes the produced vector boson recoils against emitted gluons At q T 0 a fixed-order calculation of q T distribution contains terms n m S ln ( q T / Q ) and diverges. Need a factorization formalism to sum the log terms to all orders with a proper treatment of transverse momentum conservation in multiple gluon emission.
Applications of TMD factorization Precision tests of TMD factorization for dependent observables e e In hadroproduction Drell-Yan process semiinclusive DIS with unpolarized or polarized hadron beams for electroweak precision measurements at the Tevatron and LHC We also applied TMD factorization to obtain better constraints on nuclear PDFs in the Drell- Yan process on heavy nucleus (backup slides) q T 9
Our recent work: TMD factorization for Drell-Yan angular distributions * D0 ATLAS published very precise measurements of the angular distribution that probes TMD factorization D0 Collaboration V.M. Abazov et al 011 arxiv: 1010.06 ATLAS Collaboration G. Aad et al. 011 arxiv: 1107.381 We perform an approximate NNLL/NNLO calculation for this distribution using the Legacy/ResBos resummation programs G. Ladinsky C.-P. Yuan arxiv: 9311341 C. Balazs C.-P. Yuan arxiv: 970458 F. Landry R. Brock P.M. Nadolsky C.-P. Yuan arxiv: 01159 This calculation provides a very good approximation to the exact NNLL/NNLO calculation from S. Catani et al arxiv: 109.0158 arxiv: 070301 arxiv:081.86 It also implements the nonperturbative contribution according to the approach of F. Landry et al arxiv: 01159 A.V. Konychev P.M. Nadolsky arxiv:05065 10
Definition of * When * q T is defined as is small * q T / Q where And * tan( acop acop / )sin * 1 cos tanh In the lab frame is the difference in azimuthal angle between the two lepton candidates. 1 and are the pseudorapidities of the negatively and positively charged lepton respectively. * D0 Collaboration V.M. Abazov et al 011 arxiv: 1010.06 11
* distribution measured at the Tevatron D0 Collaboration V.M. Abazov et al 011 arxiv: 1010.06 Our 01 ResBos calculation is an update on the shown ResBos curves. It improves agreement with these data. Focus on * 0. 1 1
Factorization in Collins-Soper-Sterman q T * formalism at small (small ) At small q T the resummed cross section can be written as d dq AB iqt b e W ( b Q y) dydq AB T b d where is the Fourier conjugate variable of q T. W ~ AB can be factorized as b ~ ~ W AB ( b Q y) ~ W AB ( b Q y) e j S ( b Q) P j / A ( x A b) P j / B ( x B b) H j j 13
Three regions of ~ bw ( b Q) 1/ b sets the momentum scale of calculation. At b 0.5GeV 1 the nonperturbative effects become important. Tevatron can probe b up to about 1.5 GeV - 1. 14
Nonperturbative contribution 1 b Λ QCD Non-perturbative Introduce a nonperturbative factor with b * prescription ~ ~ W( b Q y) W pert ~ NP ( b* Q y) W ( b Q y) b * b b / 1 b max b b b b max max b b * * b b max b max where pert W ~ at be around 1.5 b b is the parameter to freeze. Its optimal value was found to GeV 1 in previous studies. max 15
Nonperturbative contribution W ~ NP can not be computed perturbatively and is parameterized as In the vicinity of Q around M W ~ NP reduces to Z x (0) 1 Q 0 ( Q / 1.6GeV S ) e y with 16
a(q) in various DY experiments Banfi et al. (009) do not confirm a(m_z) > 0 at NLL/NLO A. V. Konychev and P. M. Nadolsky 005 arxiv: 0507179 17
* Is a non-zero supported by the data? a Z The evidence for nonperturbative smearing is inconclusive at the NLL+NLO( ) level. Large scale uncertainties appear in the fit. S (A. Banfi et al 00901101) We performed a more advanced analysis of D0 data by including all non-negligible NNLO ( )corrections Final-state NLO electromagnetic correction Estimates of matching corrections QCD scale dependence quantified by parameters C S 1 bb C Q / Q C3 b F 18
a Z * fits to data M. Guzzi P. M. Nadolsky and B. Wang 013 arxiv: 1309.1393 a Z 0.8 0. 0.11 GeV ( free C 1 3 68% C.L. ) 19
Parameterization of the non-perturbative function in TMD factorization for SIDIS at low Q with P. Nadolsky and T. Rogers in progress
Motivations (John Collins and Ted Rogers. 014) New fixed-target data from DY and SIDIS (COMPASS) will probe precisely at low Q The simple parametrization a(q) b is not sufficient for detailed description of b>1 GeV -1 Fits are performed with new forms of non-perturbative functions that satisfy desired properties in small and large b limits ~ W NP ( b Q)
Modifications b * b 1 b** 1 b / b 1 ( b / b max max ) max b C
status Resummation programs (Legacy & ResBos) are being adapted for producing SIDIS cross sections. Based on an update of the work by Nadolsky Stump Yuan 000 HERAfitter has been set up for fitting TMD predictions to COMPASS SIDIS data. A quick test of the proposed parameterizations in the DY process is planned using a web-based plotter of CSS TMD cross sections developed at SMU.
A summary of my projects The inclusive cross section of neutral current deep inelastic scattering (DIS) with heavy-quark mass effect at approximate NNNLO. (Thesis project) Study of the transverse-momentum-dependent (TMD) factorization. 1. Non-perturbative contribution in TMD factorization for Drell-Yan process. (M. Guzzi P. M. Nadolsky B. Wang. arxiv:1309.1393). Modification of the non-perturbative function for SIDIS. (P. M. Nadolsky Ted Rogers B. Wang. In progress) 3. Application of TMD factorization in nuclear collisions. (in backup slides) ( V. Guzey M. Guzzi P. M. Nadolsky M. Strikman B. Wang. arxiv:11.5344)
Backup slides 5
Cross section and structure functions 6 ) ( ) ( ) ( ) ( / )) ( ) ( ( ) (1 ) ( ] ) (1 [1 4 0 / 1 / 0 1 1 1 1 1 4 Q x C e m Q x C d e Q x F as factorized be can and F F functions structure The xs Q s q P P k P q y q P Q x q Q Q x xf Q x F x y Q x F y Q dxdq d f fs f f fs f N a p a a i N i i p a s h a i N a x N i i
Motivations for the study of quark mass effect in DIS cross sections Provides precision test of the perturbative calculation using QCD factorization theorem. QCD global fit is sensitive to two kinds of mass effect Suppression of cross sections near heavy quark production threshold The mass effect related to the collinear radiation of heavy quarks at large momentum Q is taken into account by evolving parton distribution functions (PDFs).
Status of the calculation of DIS structure functions Recent calculations of structure functions are done to NNLO accuracy ( S ) Marco Guzzi Pavel M. Nadolsky Hung-Liang Lai C.-P. Yuan. arxiv:1108.511 M. Buza Y. Matiounine J. Smith W. L. van Neerven Eur. Phys. J. C1 301 R. S. Thorne R. G. Roberts Phys. Rev. D57 6871 S. Alekhin J. Blumlein S. Klein S. Moch Phys. Rev. D81 01403 Coefficient and splitting functions are calculated to NNNLO in zero mass approximation (neglect quark mass for all flavors) S.A. Larin P. Nogueira T. van Ritbergen J.A.M. Vermaseren. arxiv:9605317 J.A.M. Vermaseren A. Vogt S. Moch.. arxiv:041111 arxiv:05044 arxiv:040319 arxiv:0404111. Need a way to approximate massive coefficient functions in order to calculate NNNLO structure functions 8
A factorization scheme with proper treatment of massive quarks is needed for the calculation Introduce heavy quark mass dependence by replacing Bjorken x with a rescaling variable χ 9 ) ( ) ( 4 1 general more or 4 1 1) ( 0 Q m x Q m x m Q c Q m Q x C h h h k h h h k h h f C F
Status: Status and summary Mass dependence of the diagrams is derived and implemented in the code Implementing scale dependence What I learned in this study Factorization procedure Mass dependence of various diagrams in loop calculations which can be used in future calculations with full mass dependence. Programming experience in numerical calculations
TMD factorization in nuclear collisions
Both figures taken from V. Guzey M. Guzzi P. M. Nadolsky M. Strikman and B. Wang (01) Correspondence can be found by reading the ratio of PDFs at the typical momentum fractions M Q 1 and S T T y e M T Q S T e y 3