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.