Recent progress in Regge limit Agust n Sabio Vera Universidad Aut - - PowerPoint PPT Presentation

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Recent progress in Regge limit Agust n Sabio Vera Universidad Aut - - PowerPoint PPT Presentation

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Recent progress in Regge limit Agust n Sabio Vera Universidad Aut onoma de Madrid, Instituto de F sica Te orica UAM/CSIC Hadron Structure & QCD, GATCHINA, RUSIA, June 30 - July 4, 2014 Agust n Sabio Vera (UAM, IFT)

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Recent progress in Regge limit

Agust´ ın Sabio Vera

Universidad Aut´

  • noma de Madrid, Instituto de F´

ısica Te´

  • rica 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

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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 In the limit s ≫ t, Q2 we have αs(Q) log s

t

  • ∼ O(1) .

These dominate the amplitudes and must be resummed to all orders. Kinematic origin: where yA − yB 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

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When s → ∞ we should resum αn

s logn (s) ∼ αn s (yA − yB)n .

σLL

tot

=

∞

  • n=0

CLL

n

(ki) αn

s

yA

yB

dy1 y1

yB

dy2 . . . yn−1

yB

dyn =

∞

  • n=0

CLL

n

(ki) n! αn

s (yA − yB)n

  • LL

LL BFKL formalism allows us to calculate the coefficients CLL

n

(ki). Real physics starts at NLL: sensitive to the running & choice of energy scale: σtot =

∞

  • n=1

CLL

n

(ki) n!

  • αs − Aα2

s

n (yA − yB − B)n = σLL

tot − ∞

  • n=1
  • B CLL

n

(ki) + (n − 1) A CLL

n−1 (ki)

  • (n − 1)!

αn

s (yA − yB)n−1

  • NLL

besides, quarks enter the game ...

Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 3 / 16

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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

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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

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  • 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 pT: 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

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Monte Carlo for ”pure” NLO BFKL Effective Feynman rules: Simplest case, minijet production at LL. Gluon Regge trajectory: ω ( q) = − αsNc

π

log q2

λ2

Modified propagators in the t-channel:

  • si

s0

ω(ti) = eω(ti)(yi−yi+1) αsNc π 2 d2 k1 θ

  • k2

1 − λ2

πk2

1

  • d2

k2 θ

  • k2

2 − λ2

πk2

2

δ(2)

  • kA +

k1 + k2 − kB

  • ×

Y dy1 y1 dy2eω(

kA)(Y −y1)eω( kA+ k1)(y1−y2)eω( kA+ k1+ k2)y2

Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 7 / 16

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σ(Q1, Q2, Y ) =

  • d2

kAd2 kB φA(Q1, kA) φB(Q2, kB)

  • PROCESS−DEPENDENT

f ( kA, kB, Y )

  • UNIVERSAL

f

  • kA,

kB, Y

  • =

= eω(

kA)Y

  • δ(2)
  • kA −

kB

  • +

∞

  • n=1

n

  • i=1

αsNc π

  • d2

ki θ

  • k2

i − λ2

πk2

i

× yi−1 dyie(ω(

kA+i

l=1

kl)−ω( kA+i−1

l=1

kl))yiδ(2)

  • kA +

n

  • l=1
  • kl −

kB 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

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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

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Gluon |pT| 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

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Growth with energy? f

  • kA,

kB, Y

  • =

1e-05 0.0001 0.001 0.01 1 2 3 4 5 6

fn (kA = 15 GeV, kB = 30 GeV, Y, α = 0.2)

Y Forward LO BFKL Singlet Green function (q = 0)

n = 0 1 2

Different growth for different components in the azimuthal angle: fn

  • |

kA|, | kB|, Y

  • =

2π

dθ 2πf

  • kA,

kB, Y

  • cos (nθ)

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

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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

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In BFKL cross sections σ(Q1, Q2, Y ) =

  • d2kad2kb φA(Q1, ka) φB(Q2, kb) f (ka, kb, Y )

1e-05 0.0001 0.001 0.1 1 10

f (ka, kb = 20, = 0.2, Y = 3) ka / kb

LO NLO N2LO N3LO N4LO Bessel

collinear regions important if impact factors allow for asymmetric scales. To remain in strict BFKL domain we need “delta-like” impact factors φA,B & Q1 ≃ Q2.

Agust´ ın Sabio Vera (UAM, IFT) Recent progress in Regge limit April 15, 2014 13 / 16

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DIS data: F2(x, Q2) ≃ x−λ Hadron-Pomeron coupling based on NLL BFKL

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 1 10 100 λ Q2 (GeV2) Combined HERA data Real cuts: Λ = 0.21 GeV, Q0 = 0.27 GeV, δ = 6.9 Smooth cuts: Λ = 0.21 GeV, Q0 = 0.27 GeV, δ = 6.9

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

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Observable proposed in [ASV][NPB746 2006] [ASV,Schwennsen][NPB 2007,PRD77 2008] as perfect to capture BFKL dynamics

C2 C1 = <cos (2θ)> <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

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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