Threshold resummation in direct photon production

Nobuo SatoFlorida State University

In collaboration with:J. Owens

Motivation:

I Parton distribution functions (PDFs) - essential ingredients forhadron colliders.

I PDFs cannot be computed from first principles - extracted fromexperimental data.

I The uncertainties in the fitted PDFs are different among the partonspecies.

I In particular, gluon distribution is unconstrained at large x.

I Production of a state with mass m and rapidity y probes PDFs atx ∼ (m/√s)e±y which is relevant for BSM physics.

Motivation:

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

I In the past, the data was used to constrain gluon PDF at largex ≤ 0.6.

I It was removed from global fittings due to inconsistencies betweenthe theory at NLO and the data of various fixed target experiments.

I Recently (1202.1762) d’Enterria and J. Rojo have included isolateddirect photon data to constrain gluon PDF around x ∼ 0.02. Theyshow reduction up to 20%.

Motivation:

10−2 10−10

1

2

3

4

5

6

7

8d

ata/

theo

ry(N

LO

)

0.2 0.4 0.6

WA70√

s = 23.0GeV pp

CDF√

s = 1800.0GeV pp̄

D0√

s = 1960.0GeV pp̄

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 pp̄

data/theory(NLO) vs. xTµR,IF,FF = pTFFs = BFG II

xT

Motivation:

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

I Catani, Mangano, Nason, Oleari, Vogelsang, hep-ph/9903436(direct contribution)

I de Florian, Vogelsang, hep-ph/0506150(direct + jet fragmentation)

Theory of direct photons

At LO:

(a) direct contribution (b) jet fragmentation

p3Tdσ(xT )

dpT=∑a,b,c

fa/A(xa, µIF ) ∗ fb/B(xb, µIF ) ∗Dγ/c(z, µFF ) ∗ Σ̂(x̂T , ...)

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

Theory of direct photonsBeyond LO:

p3Tdσ(xT )

dpT=∑a,b,c

fa/A(xa, µIF ) ∗ fb/B(xb, µIF ) ∗Dγ/c(z, µFF ) ∗ Σ̂(x̂T , ...)

Σ̂(x̂T , ...) ⊃

1 LOαsL

2 αsL αs NLOα2sL

4 α2sL3 α2sL

2 α2sL NNLO...

......

......

αnsL2n αnsL

2n−1 αnsL2n−2 ... NnLO

LL NLL NNLL ...

x̂T = 2pT /z√ŝ

ŝ = xaxbS

L = ln(1− x̂2T ) “Threshold logs”I Resummation: technique to find the exponential representation of

threshold logs.

Theory of direct photons

When are threshold logs important?

p3Tdσ(xT )

dpT=∑a,b,f

∫ 1x2T

dxa

∫ 1x2T

xa

dxb

∫ 1xT√xaxb

dzfa(xa)fb(xb)D(z)Σ̂

(x2T

z2xaxb

)

I x̂T =xT

z√xaxb

⊂ [xT , 1]I Collider: CDF(

√s = 1.8 TeV): xT ⊂ [0.03, 0.11].

I Fixed Target: UA6(√s = 24 GeV): xT ⊂ [0.3, 0.6].

I Threshold logs are more relevant for fixed target experiments.

I Due to PDFs, 〈xa,b〉 is small so that 〈z〉 → 1. This enhances thefragmentation component from threshold logs.

Theory of direct photonsKey observation: D.de Florian,W.Vogelsang (Phys.Rev. D72 (2005))

4.0 4.5 5.0 5.5 6.0 6.5 7.0pT

0.0

0.2

0.4

0.6

0.8

1.0

rati

oFractional Contribution

ratio vs. pTpp→ γ + X√

s = 24.3 GeVPDFs = Cteq6FFs = BFGµR,IF,FF = pT

directdirect+fragment

fragmentdirect+fragment

LO

NLO

NLL

Theory of direct photons

I Resummation is performed in “mellin space”:

fN =

∫ 10

dxxN−1f(x) f(x) =1

2πi

∫ c+i∞c−i∞

dNx−NFN

I The invariant cross section in N-space:

p3Tdσ(N)

dpT=∑a,b,f

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

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

Σ̂NLL(N) = C

(∆aN∆

bN∆

cNJ

dN

∑i

Gi∆(int)i,N

)Σ̂Born(N)

(1)

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/d

3p

(pb

)

Edσ/d3p (pb) vs pT (GeV)UA6 experimentpp→ γ + X√

s = 24.3 GeVPDFs = Cteq6,FFs = BFGII

NLO

NLO + NLL

UA6

ζ = 0.5

ζ = 1.0

ζ = 2.0

Threshold resummation→ sizable scale reduction.

Phenomenology: Gluon constraints

I The current code of NLO+NLL is too slow to be used in global fits.

I An alternative to global fits exist: Bayesian reweighting technique.NNPDF collaboration (1012.0836).

I This technique is suitable for montecarlo based PDFs such asNNPDFs.

I Watt and Thorne (1205.4024) proposed a way to apply thetechnique in PDFs sets such as CTEQ or MSTW.

Phenomenology: Gluon constraintsThe idea:

I random PDFs:

fk = f0 +∑j

(f± − f0)|Rkj | (j = 1..20)

I for each fk compute:

χ2k =∑i

(Di − Tiσi

)2I get weights as:

wK =(χ2k)

12 (Npts−1) ∗ e− 12χ2(k)∑

k(χ2k)

12 (Npts−1) ∗ e− 12χ2(k)

I observables are given as:

〈O〉 =∑k

wkO(fk) σ2 =

∑k

wk(O(fk)− 〈O〉)2

Phenomenology: preliminary

4.0 4.5 5.0 5.5 6.0 6.5pT

10-1

100

101

102

ICS(p

b)

cteq6mE

UA6 pp

Theory : NLO+NLL

µR =µIF =µFF =pT

k−th random PDF setbest k−th random PDF setcentral cteq6mE

UA6(pp)

Phenomenology: preliminary

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.0

0.5

1.0

1.5

2.0

2.5

Rat

ioto〈 gluo

n〉 uw

experimental xT range

unweighted error band

weighted error band

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8x

0.0

0.1

0.2

0.3

0.4

0.5

(σuw−σ

rw)/σ

uwcteq6mEgluon @ Q=10GeVUA6 ppTheory : NLO+NLL

Phenomenology: preliminary

exp/col mode√s (GeV) # pts pT range

WA70 pp 23.0 8 [4.0, 6.5]NA24 pp 23.8 5 [3.0, 6.5]UA6 pp 24.3 9 [4.1, 6.9]UA6 ppb 24.3 10 [4.1, 7.7]E706 pBe 31.5 17 [3.5, 12.0]E706 pp 31.5 8 [3.5, 10.0]E706 pBe 38.7 16 [3.5, 10.0]E706 pp 38.7 9 [3.5, 12.0]R806 pp 63.0 14 [3.5, 12.0]R807 pp 63.0 11 [4.5, 11.0]R110 pp 63.0 7 [4.5, 10.0]

Table : List of fixed target experimental data.

Phenomenology: preliminary

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.0

0.5

1.0

1.5

2.0

Rat

ioto〈 gluo

n〉 uw

experimental xT range

unweighted error band

weighted error band

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9x

0.20.10.00.10.20.30.40.50.60.7

(σuw−σ

rw)/σ

uwcteq6mEgluon @ Q=10GeVTheory : NLO+NLL

Conclusions:

I High-x PDFs important for production of a state with mass m atforward rapidities.

I Threshold resummation improves the theoretical prediction of directphotons at fixed target experiments → potential constrains on gluonPDF at high x.

To do:

I Reweighting studies in other PDFs sets.

I Analysis of the global χ2 after reweighting.

I Develop a faster code for global fitting.

I Compare with scet techniques.