Research in QCD factorization

Bowen Wang

Southern Methodist University (Dallas, TX)

Jefferson Lab Newport News, VA

1/12/2015

My research at SMU in 2011-2015 • Ph. D. advisor: Pavel Nadolsky • Ph. D. thesis: The inclusive cross section of neutral

current deep inelastic scattering (DIS) with heavy-quark 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)

2. 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:1212.5344)

My thesis: a three-loop QCD computation for heavy-quark scattering in neutral-current DIS

• To be finished in Spring 2015 • 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

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N3LO_IM

N2LO_GM

Preliminary result in IM N3LO, Q=2 GeV

),( 2

2 QxF h

N3LO Flavor classes

4

FC2, FC20, FC11, FC2g, and FC11g classes

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 . Need to compute coefficient functions with an arbitrary factorization scale.

• The calculation is done recursively using lower order coefficient functions (up to O( ) ) and splitting functions (up to O( ) )

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NNLL/NNLO studies of TMD factorization for

production at hadron colliders

(M. Guzzi, P. M. Nadolsky, B. Wang. arXiv:1309.1393)

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What is TMD factorization

• In Drell-Yan like processes, the produced vector boson recoils against emitted gluons

• At , a fixed-order calculation of distribution contains terms

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.

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)/(ln 22QqT

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Tq

Applications of TMD factorization

• Precision tests of TMD factorization for dependent observables – In hadroproduction, Drell-Yan process, semi-

inclusive 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)

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Our recent work: TMD factorization for Drell-Yan angular distributions

D0, ATLAS published very precise measurements of the angular distribution that probes TMD factorization

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: 9704258

F. Landry, R. Brock, P.M. Nadolsky, C.-P. Yuan, arXiv: 0212159

This calculation provides a very good approximation to the exact NNLL/NNLO calculation from

S. Catani et al, arXiv: 1209.0158, arXiv: 0703012, arXiv:0812.2862

It also implements the nonperturbative contribution according to the approach of

F. Landry et al, arXiv: 0212159

A.V. Konychev, P.M. Nadolsky, arXiv:0506225

10

*

D0 Collaboration, V.M. Abazov et al, 2011, arXiv: 1010.0262 ATLAS Collaboration, G. Aad et al., 2011, arXiv: 1107.2381

Definition of

11

*

is defined as where And In the lab frame, is the difference in azimuthal angle, , between the two lepton candidates. are the pseudorapidities of the negatively and positively charged lepton, respectively.

*

21 and

*

QqT /Tq

** sin)2/tan( acop

acop

2tanhcos 21*

When is small

D0 Collaboration, V.M. Abazov et al, 2011, arXiv: 1010.0262

distribution measured at the Tevatron

12

*

D0 Collaboration, V.M. Abazov et al, 2011, arXiv: 1010.0262 Our 2012 ResBos calculation is an update on the shown ResBos curves. It improves agreement with these data. Focus on 1.0*

Factorization in Collins-Soper-Sterman formalism at small (small )

13

At small the resummed cross section can be written as

where is the Fourier conjugate variable of . can be factorized as

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),,(~

),,(~

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Three regions of

14

sets the momentum scale of calculation. At the nonperturbative effects become important. Tevatron can probe b up to about 1.5 GeV-

1.

b/1

𝑏 ≳ 0.5GeV−1

),(~

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Nonperturbative contribution

15

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),,(~

),,(~

* yQbWyQbWyQbW NPpert

Introduce a nonperturbative factor with “ ” prescription *b

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*

/1 bb

bb

max*max

*max

,

,

bbbb

bbbb

where is the parameter to “freeze” at . Its optimal value was found to be around 1.5 in previous studies.

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Non-perturbative 𝑏 ≳ ΛQCD−1

Nonperturbative contribution

can not be computed perturbatively and is parameterized as

In the vicinity of around , reduces to

with

16

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~

NPW~

GeV6.1

)/(

0

)0(

2,1

Q

eSQx y

in various DY experiments

17

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A. V. Konychev and P. M. Nadolsky, 2005, arXiv: 0507179

Banfi et al. (2009) do not confirm a(M_Z) > 0 at NLL/NLO

Is a non-zero supported by the data?

The evidence for nonperturbative smearing is inconclusive at the NLL+NLO( ) level . Large scale uncertainties appear in the fit. (A. Banfi et al, 2009,2011,2012)

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

18

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Za

FQb bCQCbC 321 ,/,

fits to data

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M. Guzzi, P. M. Nadolsky and B. Wang, 2013, arXiv: 1309.1393

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. 2014)

• New fixed-target data from DY and SIDIS (COMPASS) will probe precisely at low Q

),(~

QbW NP

• The simple parametrization a(Q) b2 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

Modifications

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max

2

1

2

max

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max

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status

• Resummation programs (Legacy & ResBos) are being adapted for producing SIDIS cross sections. – Based on an update of the work by Nadolsky, Stump, Yuan, 2000

• 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)

2. 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:1212.5344)

Backup slides

25

Cross section and structure functions

26

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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 ( )

Marco Guzzi, Pavel M. Nadolsky, Hung-Liang Lai, C.-P. Yuan. arXiv:1108.5112 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, 014032

• 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:0411112 , arXiv:0504242, arXiv:0403192, arXiv:0404111.

• Need a way to approximate massive coefficient functions in order to calculate NNNLO structure functions

28

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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 ,

29

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Status and summary • Status:

– 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

32

Correspondence can be found by reading the ratio of PDFs at the typical momentum fractions

Both figures taken from V. Guzey , M. Guzzi, P. M. Nadolsky, M. Strikman and B. Wang (2012)

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