Recent progress in Regge limit Agust´ ın Sabio Vera Universidad Aut´ onoma de Madrid, Instituto de F´ ısica Te´ orica UAM/CSIC Hadron Structure & QCD, GATCHINA, RUSIA, June 30 - July 4, 2014 Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 1 / 16
BFKL is a beautiful theory At very high energies new degrees of freedom arise Present in QCD, SUSY and gravity They allow to calculate many processes to all orders � s In the limit s ≫ t , Q 2 we have α s ( Q ) log � ∼ O (1) . t These dominate the amplitudes and must be resummed to all orders. Kinematic origin: where y A − y B is the difference in rapidity of particles A and B. Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 2 / 16
s log n ( s ) ∼ α n s ( y A − y B ) n . When s → ∞ we should resum α n � y A � y 1 � y n − 1 ∞ � σ LL C LL ( k i ) α n = dy 1 dy 2 . . . dy n tot n s y B y B y B n =0 ∞ C LL ( k i ) � s ( y A − y B ) n n α n = n ! � �� � n =0 LL LL BFKL formalism allows us to calculate the coefficients C LL ( k i ). n Real physics starts at NLL: sensitive to the running & choice of energy scale: ∞ C LL ( k i ) � n ( y A − y B − B ) n � � n α s − A α 2 σ tot = s n ! n =1 � � ∞ B C LL ( k i ) + ( n − 1) A C LL n − 1 ( k i ) � n s ( y A − y B ) n − 1 = σ LL α n tot − ( n − 1)! � �� � n =1 NLL besides, quarks enter the game ... Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 3 / 16
LHC phenomenology : examples with a cut Production of Jets, W, Z y Drell-Yan in different topologies: Production of quark pairs & Higgs in different topologies: Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 4 / 16
LHC phenomenology : examples without a cut Diffractive production in different topologies: Gap = region in the detector without hadronic activity. Clear signal. Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 5 / 16
• Need to find at least one observable where ”pure” BFKL at NLO fits the data and all other approaches fail. • From there we can introduce corrections: Lower the p T : Treatment of the running in the infrared Asymmetric scales: Collinear corrections Larger energies: Non-linearities • We need two ingredients: △ NLO Coupling of Pomeron to external system. Lipatov high energy effective action is very useful for this: We have used it to obtain [ Chachamis, Hentschinski, Madrigal, SV ]: NLO gluon Regge trajectory NLO Mueller-Navelet vertex NLO Mueller-Tang vertex. △ Exact solution to the NLO gluon Green function with access to all its exclusive information. Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 6 / 16
Monte Carlo for ”pure” NLO BFKL Effective Feynman rules: Simplest case, minijet production at LL. Gluon Regge trajectory: log q 2 q ) = − α s N c ω ( � λ 2 π Modified propagators in the t -channel: � � ω ( t i ) s i = e ω ( t i )( y i − y i +1 ) s 0 � 1 − λ 2 � � 2 − λ 2 � � α s N c � 2 � k 2 � k 2 θ θ δ (2) � � d 2 � d 2 � � k A + � k 1 + � k 2 − � k 1 k 2 k B π k 2 π k 2 π 1 2 � Y � y 1 dy 2 e ω ( � k A ) ( Y − y 1 ) e ω ( � k A + � k 1 ) ( y 1 − y 2 ) e ω ( � k A + � k 1 + � k 2 ) y 2 × dy 1 0 0 Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 7 / 16
� d 2 � k A d 2 � k B φ A ( Q 1 ,� k A ) φ B ( Q 2 ,� f ( � k A ,� σ ( Q 1 , Q 2 , Y ) = k B ) k B , Y ) � �� � � �� � PROCESS − DEPENDENT UNIVERSAL � � � k A ,� f k B , Y = � � i − λ 2 � n � k 2 ∞ δ (2) � � α s N c θ � � e ω ( � k A ) Y � k A − � d 2 � = + k B k i π k 2 π i n =1 i =1 � � � � y i − 1 n � dy i e ( ω ( � k A + � i l =1 � k l ) − ω ( � k A + � i − 1 l =1 � k l )) y i δ (2) � � k l − � × k A + k B 0 l =1 This is not a model of BFKL, it is full NLO BFKL at cross section level Agreement with all known analytic results at NLO in QCD and N=4 SUSY (singlet and adjoint) Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 8 / 16
Number of emissions? The area is the gluon Green function [Chachamis,ASV] [PLB709 2012] Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 9 / 16
Gluon | p T | in a given rapidity bin? [Chachamis, ASV][PLB717 2012] [...+Salas][PRD87 2013][...+Murdaca, Caporale, Madrigal][PLB724 2013] Modifications of BFKL (non-perturbative or saturation) suppress IR diffusion. This is the same effect as momentum transfer in elastic non-forward amplitudes. Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 10 / 16
� � � k A ,� Growth with energy? = f k B , Y Forward LO BFKL Singlet Green function (q = 0) f n (k A = 15 GeV, k B = 30 GeV, Y, α = 0.2) 0.01 n = 0 1 2 0.001 0.0001 1e-05 0 1 2 3 4 5 6 Y Different growth for different components in the azimuthal angle: � � � � � 2 π | � k A | , | � � k A ,� d θ f n k B | , Y = 2 π f k B , Y cos ( n θ ) 0 n = 0 grows and n > 0 decrease with Y VERY IMPORTANT: this happens only in BFKL dynamics We can use it to distinguish BFKL from other approaches Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 11 / 16
BFKL CCFM All CCFM projections grow, not in BFKL. [Chachamis,Deak,ASV,Stephens][NPB849 2011] Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 12 / 16
In BFKL cross sections � d 2 k a d 2 k b φ A ( Q 1 , k a ) φ B ( Q 2 , k b ) f ( k a , k b , Y ) σ ( Q 1 , Q 2 , Y ) = LO NLO N 2 LO N 3 LO N 4 LO f (k a , k b = 20, � = 0.2, Y = 3) 0.001 Bessel 0.0001 1e-05 0.1 1 10 k a / k b collinear regions important if impact factors allow for asymmetric scales. To remain in strict BFKL domain we need “delta-like” impact factors φ A , B & Q 1 ≃ Q 2 . Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 13 / 16
DIS data: F 2 ( x , Q 2 ) ≃ x − λ Hadron-Pomeron coupling based on NLL BFKL 0.5 Combined HERA data Real cuts: Λ = 0.21 GeV, Q 0 = 0.27 GeV, δ = 6.9 Smooth cuts: Λ = 0.21 GeV, Q 0 = 0.27 GeV, δ = 6.9 0.45 0.4 0.35 0.3 λ 0.25 0.2 0.15 0.1 1 10 100 Q 2 (GeV 2 ) Transition from Hard to Soft Pomeron well described. But it is NLL BFKL plus many other things - It is too inclusive [Hentschinski,ASV,Salas][PRL110, PRD87 2013] Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 14 / 16
Observable proposed in [ASV][NPB746 2006] [ASV,Schwennsen][NPB 2007,PRD77 2008] as perfect to capture BFKL dynamics C 1 = < cos (2 θ ) > C 2 < cos ( θ ) > Conformal observable: [Angioni,Chachamis,Madrigal,ASV][PRL107 2011] There should be no contribution from n = 0 component Predictions at LO and NLO are very similar for this observable Confirmation of this idea in 2013 [Caporale,Murdaca,ASV,Salas][NPB 875 2013] . Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 15 / 16
Recent progress in Regge limit Rich phenomenology, all ingredients are ready. New observables? Workshops Series in Madrid on MRK (October 2012, February 2014) Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 16 / 16
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