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

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 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. ◮ Recently (1202.1762) d’Enterria and J. Rojo have included isolated direct photon data to constrain gluon PDF around x ∼ 0 . 02 . They show reduction up to 20%.

Motivation: 8 WA70 √ s = 23 . 0GeV pp CDF √ s = 1800 . 0GeV p¯ data / theory(NLO) vs . x T p 7 D0 √ s = 1960 . 0GeV p¯ µ R , IF , FF = p T p E706 √ s = 31 . 5GeV pp FFs = BFG II E706 √ s = 38 . 7GeV pp 6 PHENIX √ s = 200 . 0GeV pp data / theory(NLO) R110 √ s = 63 . 0GeV pp 5 R806 √ s = 63 . 0GeV pp R807 √ s = 63 . 0GeV pp UA6 √ s = 24 . 3GeV pp 4 UA6 √ s = 24 . 3GeV p¯ p 3 2 1 0 0 . 2 0 . 4 0 . 6 10 − 2 10 − 1 x T

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 dσ ( x T ) � f a/A ( x a , µ IF ) ∗ f b/B ( x b , µ IF ) ∗ D γ/c ( z, µ F F ) ∗ ˆ p 3 = Σ(ˆ x T , ... ) T dp T a,b,c ◮ Direct contribution: D γ/γ = δ (1 − z ) ◮ Jet fragmentation: D γ/c ∼ α em /α S

Theory of direct photons Beyond LO: dσ ( x T ) � f a/A ( x a , µ IF ) ∗ f b/B ( x b , µ IF ) ∗ D γ/c ( z, µ F F ) ∗ ˆ p 3 = Σ(ˆ x T , ... ) T dp T a,b,c 1 LO α s L 2 α s L α s NLO α 2 s L 4 α 2 s L 3 α 2 s L 2 α 2 s L NNLO ˆ Σ(ˆ x T , ... ) ⊃ . . . . . . . . . . . . . . . α n s L 2 n α n s L 2 n − 1 α n s L 2 n − 2 N n LO ... LL NLL NNLL ... √ ˆ x T = 2 p T /z ˆ s ˆ s = x a x b S x 2 L = ln(1 − ˆ T ) “Threshold logs” ◮ Resummation: technique to find the exponential representation of threshold logs.

Theory of direct photons When are threshold logs important? � 1 � 1 � 1 x 2 � � dσ ( x T ) p 3 � dzf a ( x a ) f b ( x b ) D ( z )ˆ T = dx a dx b Σ T z 2 x a x b dp T x 2 xT x 2 T a,b,f T xa √ xaxb ◮ ˆ x T x T = z √ x a x b ⊂ [ x T , 1] ◮ Collider: CDF( √ s = 1 . 8 TeV): x T ⊂ [0 . 03 , 0 . 11] . ◮ Fixed Target: UA6( √ s = 24 GeV): x T ⊂ [0 . 3 , 0 . 6] . ◮ Threshold logs are more relevant for fixed target experiments. ◮ Due to PDFs, � x a,b � is small so that � z � → 1 . This enhances the fragmentation component from threshold logs.

Theory of direct photons Key observation: D.de Florian,W.Vogelsang (Phys.Rev. D72 (2005)) Fractional Contribution 1 . 0 direct direct+fragment fragment direct+fragment 0 . 8 LO NLO 0 . 6 NLL ratio 0 . 4 ratio vs . p T pp → γ + X √ s = 24 . 3 GeV 0 . 2 PDFs = Cteq6 FFs = BFG µ R , IF , FF = p T 0 . 0 4 . 0 4 . 5 5 . 0 5 . 5 6 . 0 6 . 5 7 . 0 p T

Theory of direct photons ◮ Resummation is performed in “mellin space”: � 1 � c + i ∞ 1 dxx N − 1 f ( x ) dNx − N F N f N = f ( x ) = 2 πi 0 c − i ∞ ◮ The invariant cross section in N-space: dσ ( N ) � f a/A ( N + 1) f b/B ( N + 1) D γ/c (2 N + 3)ˆ p 3 = Σ( N ) T dp T a,b,f ◮ The resummed partonic cross section in N-space is given by: � � G i ∆ ( int ) Σ NLL ( N ) = C ˆ ∆ a N ∆ b N ∆ c N J d � Σ Born ( N ) ˆ N i,N i (1)

Phenomenology NLO 10 2 NLO + NLL UA6 ζ = 0 . 5 10 1 ζ = 1 . 0 Ed σ/ d 3 p (pb) ζ = 2 . 0 10 0 Ed σ/ d 3 p (pb) vs p T (GeV) UA6 experiment 10 − 1 pp → γ + X √ s = 24 . 3 GeV PDFs = Cteq6 , FFs = BFGII 10 − 2 4 . 0 4 . 5 5 . 0 5 . 5 6 . 0 6 . 5 7 . 0 p T (GeV) Threshold resummation → sizable scale reduction.

Phenomenology: Gluon constraints ◮ The current code of NLO+NLL is too slow to be used in global fits. ◮ An alternative to global fits exist: Bayesian reweighting technique. NNPDF collaboration (1012.0836). ◮ This technique is suitable for montecarlo based PDFs such as NNPDFs. ◮ Watt and Thorne (1205.4024) proposed a way to apply the technique in PDFs sets such as CTEQ or MSTW.

Phenomenology: Gluon constraints The idea: ◮ random PDFs: � f k = f 0 + ( f ± − f 0 ) | R kj | ( j = 1 .. 20) j ◮ for each f k compute: � 2 � D i − T i � χ 2 k = σ i i ◮ get weights as: 2 ( N pts − 1) ∗ e − 1 1 2 χ 2 ( k ) ( χ 2 k ) w K = 2 ( N pts − 1) ∗ e − 1 1 k ( χ 2 2 χ 2 ( k ) � k ) ◮ observables are given as: σ 2 = � � w k ( O ( f k ) − � O � ) 2 � O � = w k O ( f k ) k k

Phenomenology: preliminary cteq6mE UA6 pp 10 2 Theory : NLO +NLL µ R = µ IF = µ FF =p T ICS(pb) 10 1 10 0 k − th random PDF set best k − th random PDF set central cteq6mE 10 -1 UA6(pp) 4.0 4.5 5.0 5.5 6.0 6.5 p T

Phenomenology: preliminary 2.5 cteq6mE gluon @ Q =10GeV 2.0 uw � UA6 pp gluon 1.5 Theory : NLO +NLL � 1.0 Ratio to 0.5 experimental x T range unweighted error band 0.0 weighted error band 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ( σ uw − σ rw ) /σ uw 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 x

Phenomenology: preliminary √ s (GeV) exp/col mode # pts p T 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 2.0 cteq6mE gluon @ Q =10GeV uw 1.5 � Theory : NLO +NLL gluon 1.0 � Ratio to 0.5 experimental x T range unweighted error band weighted error band 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ( σ uw − σ rw ) /σ uw 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x

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 at high x . To do: ◮ Reweighting studies in other PDFs sets. ◮ Analysis of the global χ 2 after reweighting. ◮ Develop a faster code for global fitting. ◮ Compare with scet techniques.