Threshold resummation in direct photon production Nobuo Sato - - PowerPoint PPT Presentation

Threshold resummation in direct photon production

Nobuo Sato

Florida State University In collaboration with:

• J. Owens
• D. Westmark

Motivation:

◮ Parton distribution functions (PDFs) - essential ingredients for

hadron colliders.

◮ PDFs cannot be computed from first principles - extracted from

experimental data.

◮ The uncertainties in the fitted PDFs are different among the parton

species.

◮ In particular, gluon distribution is highly unconstrained at large x! ◮ Production of a state with mass m and rapidity y probes PDFs at

x ∼ (m/√s)e±y which is relevant for BSM physics.

Motivation:

How to constrain gluon PDF at large x? → Single inclusive direct photon production at fixed target experiments.

◮ In the past, the data was used to constrain gluon PDF at large

x ≤ 0.6.

◮ It was removed from global fittings due to inconsistencies between

the theory at NLO and the data of various fixed target experiments.

Motivation:

10−2 10−1 1 2 3 4 5 6

data/theory(NLO)

0.2 0.4 0.6

WA70 √s = 23.0GeV pp CDF √s = 1800.0GeV p¯ p D0 √s = 1960.0GeV p¯ p E706 √s = 31.5GeV pp E706 √s = 38.7GeV pp PHENIX √s = 200.0GeV pp R110 √s = 63.0GeV pp R806 √s = 63.0GeV pp R807 √s = 63.0GeV pp UA6 √s = 24.3GeV pp UA6 √s = 24.3GeV p¯ p

data/theory(NLO) vs. xT µR,IF,FF = 0.5 ∗ pT FFs = BFG II xT

Motivation:

Can we improve theory at NLO? → threshold resummation for single inclusive direct photon production.

◮ Catani, Mangano, Nason, Oleari, Vogelsang, hep-ph/9903436

(direct contribution)

◮ de Florian, Vogelsang, hep-ph/0506150

(direct + jet fragmentation)

Theory of direct photons

At LO:

(a) direct contribution (b) jet fragmentation

p3

T

dσ(xT ) dpT =

• a,b,c

fa/A(xa, µIF ) ∗ fb/B(xb, µIF ) ∗ Dγ/c(z, µF F ) ∗ ˆ Σ(ˆ xT , ...)

◮ Direct contribution: Dγ/γ = δ(1 − z) ◮ Jet fragmentation: Dγ/c ∼ αem/αS

Theory of direct photons

Beyond LO: p3

T

dσ(xT ) dpT =

• a,b,c

fa/A(xa, µIF ) ∗ fb/B(xb, µIF ) ∗ Dγ/c(z, µF F ) ∗ ˆ Σ(ˆ xT , ...) 1 LO αsL2 αsL αs NLO α2

sL4

α2

sL3

α2

sL2

α2

sL

NNLO . . . . . . . . . . . . . . . αn

s L2n

αn

s L2n−1

αn

s L2n−2

... NnLO LL NLL NNLL ... ˆ xT = 2pT /z √ ˆ s ˆ s = xaxbS L = ln(1 − ˆ x2

T ) “Threshold logs” ◮ Resummation: technique to find the exponential representation of

threshold logs.

Theory of direct photons

When are threshold logs important? p3

T

dσ(xT ) dpT =

• a,b,f

1

x2

T

dxa 1

x2 T xa

dxb 1

xT √xaxb

dzfa(xa)fb(xb)D(z)Σ

• x2

T

z2xaxb

• ˆ

xT = 2pT /z √ ˆ s ˆ s = xaxbS L = ln(1 − ˆ x2

T )

ˆ xT =

xT z√xaxb = [xT , 1]

xT = 2pT / √ S CDF:(collider) √ S = 1.8 TeV xT = [0.03, 0.11] UA6:(fixed target) √ S = 24 GeV xT = [0.3, 0.6]

◮ Threshold logs are more relevant for fixed target experiments. ◮ Due to trigger bias effect z → 1 which leads to enhancement of

fragmentation component from theshold logs.

Theory of direct photons

Key observation: D.de Florian,W.Vogelsang (Phys.Rev. D72 (2005))

4.0 4.5 5.0 5.5 6.0 6.5 7.0

pT

0.0 0.2 0.4 0.6 0.8 1.0

ratio

Fractional Contribution

ratio vs. pT pp → γ + X √s = 24.3 GeV PDFs = Cteq6 FFs = BFG µR,IF,FF = pT

direct direct+fragment fragment direct+fragment

LO NLO NLL

Theory of direct photons

◮ Resummation is performed in “mellin space”:

fN = 1 dxxN−1f(x) f(x) = 1 2πi c+i∞

c−i∞

dNx−NFN

◮ The invariant cross section in N-space:

p3

T

dσ(N) dpT =

• a,b,f

fa/A(N + 1)fb/B(N + 1)Dγ/c(2N + 3)ˆ Σ(N)

◮ The resummed partonic cross section in N-space is given by:

ˆ ΣNLL(N) = CeS[ln(N+1)] ˆ ΣBorn(N) eS(ln(N)) = ∆a

N∆b N∆c NJd N

• i

Gi∆(int)

i,N

Phenomenology

4.0 4.5 5.0 5.5 6.0 6.5 7.0

pT (GeV)

10−2 10−1 100 101 102

Edσ/d3p (pb) Edσ/d3p (pb) vs pT (GeV) UA6 experiment pp → γ + X √s = 24.3 GeV PDFs = Cteq6, FFs = BFGII NLO NLO + NLL UA6 ζ = 0.5 ζ = 1.0 ζ = 2.0

Phenomenology: χ2

DOF profile

23.0 23.75 24.3 24.3 31.5 31.5 38.7 38.7 63.0 63.0 63.0 200.0 546.0 630.0 630.0 630.0 1800.0 1960.0 630.0 1800.0 1960.0 7000.0 7000.0 5 10 15 20 25

χ2

DOF

χ2

DOF vs

√ S µR = µIF = µFF = 0.5 ∗ pT NLO NLO+NLL

Phenomenology: χ2

DOF profile

23.0 23.75 24.3 24.3 31.5 31.5 38.7 38.7 63.0 63.0 63.0 200.0 546.0 630.0 630.0 630.0 1800.0 1960.0 630.0 1800.0 1960.0 7000.0 7000.0 5 10 15 20 25

χ2

DOF

χ2

DOF vs

√ S µR = µIF = µFF = 1.0 ∗ pT NLO NLO+NLL

Phenomenology: χ2

DOF profile

23.0 23.75 24.3 24.3 31.5 31.5 38.7 38.7 63.0 63.0 63.0 200.0 546.0 630.0 630.0 630.0 1800.0 1960.0 630.0 1800.0 1960.0 7000.0 7000.0 5 10 15 20 25

χ2

DOF

χ2

DOF vs

√ S µR = µIF = µFF = 2.0 ∗ pT NLO NLO+NLL

Phenomenology: Optimal normalization

23.0 23.75 24.3 24.3 31.5 31.5 38.7 38.7 63.0 63.0 63.0 200.0 546.0 630.0 630.0 630.0 1800.0 1960.0 630.0 1800.0 1960.0 7000.0 7000.0 1 2 3 4 5 6

Optimal Normalization Optimal Normalization vs √ S µR = µIF = µFF = 0.5 ∗ pT NLO NLO+NLL

Phenomenology: Optimal normalization

23.0 23.75 24.3 24.3 31.5 31.5 38.7 38.7 63.0 63.0 63.0 200.0 546.0 630.0 630.0 630.0 1800.0 1960.0 630.0 1800.0 1960.0 7000.0 7000.0 1 2 3 4 5 6

Optimal Normalization Optimal Normalization vs √ S µR = µIF = µFF = 1.0 ∗ pT NLO NLO+NLL

Phenomenology: Optimal normalization

23.0 23.75 24.3 24.3 31.5 31.5 38.7 38.7 63.0 63.0 63.0 200.0 546.0 630.0 630.0 630.0 1800.0 1960.0 630.0 1800.0 1960.0 7000.0 7000.0 1 2 3 4 5 6

Optimal Normalization Optimal Normalization vs √ S µR = µIF = µFF = 2.0 ∗ pT NLO NLO+NLL

Phenomenology: Gluon constraints

◮ Bayesian reweighting technique. Watt and Thorne (1205.4024),

NNPDF collaboration (1012.0836)

◮ The idea:

◮ Compute cross section for the available data sets using an ensemble

• f N random PDFs: {PDFK}.

◮ Compute the χ2

DOF(k) of the combined data sets for each member

PDFK in the ensemble.

◮ Compute weights as:

wK = N e− 1

2 χ2 DOF(k)

• k e− 1

2 χ2 DOF(k)

◮ The new constrained PDFs and its uncertainty can be written as:

PDF (x, Q) = 1 N

• k

wkPDF(x, Q)k δ PDF (x, Q) =

• 1

N

• k

wk(PDF(x, Q)k − PDF (x, Q))2

Phenomenology: Gluon constraints (preliminary)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

x

0.6 0.8 1.0 1.2 1.4

Ratio to CTEQ6 Gluon(x, Q = 10.0 GeV) eigen directions reweighted

Conclusions:

◮ High-x PDFs important for production of a state with mass m at

forward rapidities.

◮ Threshold resummation improves the theoretical prediction of direct

photons at fixed target experiments → potential constrains on gluon PDF up to x ∼ 0.6. To do:

◮ Constrain PDFs with threshold resummation in DIS and lepton-pair

production (D. Westmark).

◮ Compare our results with SCET calculations by Becher and Schwarts

(only resummation of direct part).