Probing high energy effects in multijet production

Transcription

1 Probing high energy effects in multijet production David Gordo Gómez Instituto de Física Teórica UAM/CSIC Madrid, Spain in collaboration with F. Caporale, F. Celiberto, G. Chachamis, A. Sabio Vera based on Nuclear Physics B 910 (2016) Eur.Phys.J. C77 (2017) no.1, 5 Phys.Rev. D95 (2017) no.7, REF2017 November 13 th - 16 th, 2017 Madrid, Spain

2 David Gordo Gómez Probing high energy effects in multijet production 2 / 27 Outline 1 Introduction Motivation Mueller Navelet jets 2 Multi-jet production A new way to probe BFKL Three-jet at partonic level Three-jet at hadronic level Three-jet at hadronic level. NLLA Ongoing project 3 Conclusions & Outlook

3 David Gordo Gómez Probing high energy effects in multijet production 3 / 27 Motivation High energy limit The high energy limit studies a limited part of the phase space, but allow us to compute things otherwise impractical Purely theoretical CFT s AdS/CFT Special Functions Integrability Methods Spin Chains

4 Motivation High energy limit Why bother at all? Phenomenology Mueller-Navelet jets Muellet-Tang jets DIS at small x And now, for the time being, forget that you've heard about BFKL, Pomeron With the advent of LHC we have access to higher energies: opportunity to test pqcd in the high-energy limit and the applicability region of BFKL resummation. David Gordo Gómez Probing high energy effects in multijet production 4 / 27

5 David Gordo Gómez Probing high energy effects in multijet production 5 / 27 Mueller Navelet jets Warming up: Mueller Navelet jets p 1 x 1 k J,1 It has been a playground for BFKL tests since it was proposed in [ A. H. Mueller, H. Navelet (1987)] x 2 k J,2 At =0, no minijet radiation in the rapidity interval. Exact correlation dσ δ 2 ( kj,1 + kj,2 ) At large the BFKL approach predicts decorrelations (minijets) p 2 Picture from [D. Colferai, F. Schwennsen, L. Szymanowski, S. Wallon (2010)] Key observable: correlation in the azimuthal angle of the 2 tagged jets.

6 David Gordo Gómez Probing high energy effects in multijet production 6 / 27 Mueller Navelet jets Warming up: Mueller Navelet jets p 1 p 2 x 1 k J,1 x 2 k J,2 Picture from [D. Colferai, F. Schwennsen, L. Szymanowski, S. Wallon (2010)] [ dσ = 1 dx 1 dx 2 d kj,1 d kj,2 dθ 1 dθ 2 (2π) 2...large jet transverse momenta: k 2 J,1 k 2 J,2 Λ 2 QCD DGLAP evolution. pqcd applicable....large rapidity interval between jets: = ln x 1 x 2 s kj,1 kj,2 BFKL resummation effects α 1 LLA BFKL: (α s log s Q 2 ) q terms NLLA BFKL: α s (α s log s Q 2 ) q terms All orders result in perturbation thery! C 0 + n=1 2 cos(nθ) C n ]

7 Mueller Navelet jets Mueller Navelet jets Mueller-Navelet jets Mueller-Navelet jets NLLA predictions against LHC data quite successful for large rapidities. [B. Ducloué, L. Szymanowski, S. Wallon (2014)] David Gordo Gómez Probing high energy effects in multijet production 7 / 27

8 David Gordo Gómez Probing high energy effects in multijet production 8 / 27 Mueller Navelet jets Mueller Navelet jets The observed sensitivity to the implementation of the colour-coherence effects in the DGLAP MC generators and the reasonable data-theory agreement shown by the NLL BFKL analytical calculations at large Dy, may be considered as indications that the kinematical domain of the present study lies in between the regions described by the DGLAP and BFKL approaches. Possible manifestations of BFKL signatures are expected to be more pronounced at increasing collision energies. But at the studied energy, the data can be described within both BFKL and DGLAP approaches. We do not have a clear BFKL signature.

9 David Gordo Gómez Probing high energy effects in multijet production 9 / 27 Mueller Navelet jets Mueller Navelet jets Big dependence on high order corrections in C 0 due to collinear contamination, better to define ratios. [ A. Sabio Vera, F. Schwennsen (2007)] Focusing in azimuthal angle correlations is more fruitful than the usual growth with energy behaviour. Including more jets allow us to study azimuthal correlations and its dependence on transverse momentum. Less inclusive observables! Multi-jet production!

10 David Gordo Gómez Probing high energy effects in multijet production 10 / 27 A new way to probe BFKL Three- and four-jet production p1 p1 x1 ka, ϑa, A x1 ka, θa, A k1, ϑ1, y1 kj, θj, yj k2, ϑ2, y2 x2 kb, θb, B x2 kb, ϑb, B p2 p2 [F. Caporale, G. Chachamis, B. Murdaca, A. Sabio Vera (2015)] [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (2016) (2017)] [F. Caporale, F.G. Celiberto., G. Chachamis, A. Sabio Vera (2016)] [F. Caporale, F.G. Celiberto, G. Chachamis, D. G.G., A. Sabio Vera (2016)]

11 David Gordo Gómez Probing high energy effects in multijet production 11 / 27 Three-jet at partonic level An event with three tagged jets kb kj φ 1 φ 2 ka Beam axis kb 2 Π ΘB B < y J < A kj ΘJ Rapidity B yj A B 2 ka A ΘA 0 Azimuthal Angle

12 David Gordo Gómez Probing high energy effects in multijet production 12 / 27 Three-jet at partonic level The three-jet partonic cross section Starting point: differential partonic cross-section (no PDFs) d 3 ˆσ 3 jet = ᾱs ( ) d 2 p A d 2 p B δ (2) p A + kj p B dk J dθ J dy J πk ( J ) ) ϕ ka, p A, A y J ϕ ( p B, kb, y J B p1 x1 x2 ka, θa, A kj, θj, yj kb, θb, B Multi-Regge kinematics rapidity ordering: B < y J < A k J lie above the experimental resolution scale ϕ is the BFKL gluon Green function (LLA or NLLA) ᾱ s = α s N c /π p2

13 David Gordo Gómez Probing high energy effects in multijet production 13 / 27 Three-jet at partonic level Generalized azimuthal correlations - partonic level Prescription: integrate over all angles after using the projections on the two azimuthal angle differences indicated below......to define: 2π 2π 2π dθ A dθ B dθ J cos (M (θ A θ J π)) cos (N (θ J θ B π)) d3 ˆσ 3 jet dk J dθ J dy J N ( ) = NL (k ) L 1 ᾱ s 2 2 J dp 2 ( N L 2π p 2) 2 dθ ( 1)M+N cos (Mθ) cos ((N L)θ) L=0 0 0 ( ) N p 2 + kj p 2 kj 2 cos θ φ M ( k 2 A, p 2, A y J ) φn ( p 2 + k 2 J + 2 p 2 k 2 J cos θ, k2 B, y J B ) Main observables: generalized azimuthal correlation ratios (w/o the 0 component) R MN PQ = C MN C PR = cos(m(θ A θ J π)) cos(n(θ J θ B π)) cos(p(θ A θ J π)) cos(q(θ J θ B π))

14 David Gordo Gómez Probing high energy effects in multijet production 14 / 27 Three-jet at hadronic level Next step: hadronic level predictions Introduce PDFs and running of the strong coupling: dσ 3 jet = dk A d A dθ A dk B d B dθ B dk J dy J dθ J 8π 3 C F ᾱ s (µ R ) 3 x JA x JB NC 3 d 2 p k A k B k A d 2 p B δ (2) ( ) p A + kj p B J ( ) N C f g (x C JA, µ F ) + f r (x JA, µ F ) F r=q, q ( ) N C f g (x C JB, µ F ) + f s (x JB, µ F ) F s=q, q ( ) ) ϕ ka, p A, A y J ϕ ( p B, kb, y J B Match the LHC kinematical cuts (integrate dσ 3 jet on k T and rapidities A, B ): GeV k A 60 GeV; 35 GeV k B 60 GeV; symmetric cuts GeV k A 60 GeV; 50 GeV k B 60 GeV; asymmetric cuts = A B fixed; y J = ( A + B )/2.Maximize rapidity differences among tagged jets s = 7, 13 TeV

15 2 60 kj GeV Introduction Multi-jet production Conclusions & Outlook Three-jet at hadronic level 4 R vs for three different k J bins 6 k min A = 35 GeV, k min B = 35 GeV, k max A = k max B 4 = 60 GeV (symmetric) s = 13 TeV; k B min = 35 GeV kj GeV kj GeV kj GeV R R [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (2016)] is the rapidity difference between the most forward/backward jet; y J = A + B David Gordo Gómez Probing high energy effects in multijet minproduction 15 / 27

16 Three-jet at hadronic level R vs for three different k 6 J bins k min A = 35 GeV, k min B = 50 GeV, k max A = k max B = 60 GeV (asymmetric) s = 13 TeV; k B min = 50 GeV 20 kj GeV kj GeV kj GeV R kj GeV kj GeV kj GeV [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (2016)] is the rapidity difference between the most forward/backward jet; y J = A + B 2. s = 13 TeV; k min B = 50 GeV David Gordo Gómez Probing high energy effects in multijet production 16 / 27

17 David Gordo Gómez Probing high energy effects in multijet production 17 / 27 Three-jet at hadronic level R12 23 vs = A B, s and kb min k J bins for three s = 7 TeV; k B min = 35 GeV s = 7 TeV; k B min = 50 GeV R kj GeV R kj GeV kj GeV kj GeV kj GeV kj GeV s = 13 TeV; k B min = 35 GeV s = 13 TeV; k B min = 50 GeV R kj GeV R kj GeV kj GeV kj GeV kj GeV kj GeV [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (2016)]

18 David Gordo Gómez Probing high energy effects in multijet production 18 / 27 Three-jet at hadronic level. NLLA Three-jet at hadronic level. NLLA corrections We introduce higher order corrections to the GGF to check the stability of the perturbative expansion. BLM optimization procedure. [ S.J. Brodsky, G.P. Lepage, P.B. Mackenzie (1983)] [F. Caporale, D.u. Ivanov, B. Murdaca, A. Papa (2015)] [B. Ducloué, L. Szymanowski, S. Wallon (2014)] It allows us to estimate the theoretical uncertainty. Also checked for different PDF s sets. Impact factors at NLO are missing! Much more time-consuming but needed to compare with experiment (when data is available). 35 GeV k A 60 GeV; 50 GeV k B 60 GeV; asymmetric cuts = A B fixed; Also integrating 3 A,B 4.7 y J = ( A + B )/2.Integrated over a rapidity bin of 1. Also displaced from the center. s = 7, 13 TeV

19 David Gordo Gómez Probing high energy effects in multijet production 19 / 27 Three-jet at hadronic level. NLLA R k min A vs at 13 TeV - NLLA = 35 GeV, k min B = 50 GeV, k max A = k max B = 60 GeV (asymmetric) s 13 TeV; k min 50 GeV; k bin 1, bin 2, bin R LLA NLA MOM BLM [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (2017)] is the rapidity difference between the most forward/backward jet; y J = A + B 2.

20 Introduction Multi-jet production Conclusions & Outlook Three-jet at hadronic level. NLLA 12 R33 vs at 13 and 7 TeV - NLLA 2 LLA k J Î æ bin-1, æ bin-2, æ bin-3 LLA 0 12 R33 NLA MOM BLM NLA MOM BLM kbmin = 50 GeV; R33 6 s = 7 TeV; k J Î æ bin-1, æ bin-2, æ bin kbmin = 50 GeV; s = 13 TeV; We have entered in an asymptotic regime! [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (2017)] David Gordo Go mez Probing high energy effects in multijet production 20 / 27

21 David Gordo Gómez Probing high energy effects in multijet production 21 / 27 Three-jet at hadronic level. NLLA R vs y i at 13 TeV - NLLA k min A = 35 GeV, k min B = 50 GeV, k max A = k max B = 60 GeV (asymmetric) [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (2017)] A, B, y J integrated over bins. y i is the center of the central jet bin.

22 David Gordo Gómez Probing high energy effects in multijet production 22 / 27 Ongoing project Ongoing project: Veto Introduced by Lipatov and [B. Andersson, G. Gustafson, J. Samuelsson (1996)]. [Carl R. Schmidt (1999)] [J.R. Forshaw, D.A. Ross, A. Sabio Vera (1999)] Gluon rapidities in the ladder constrained by y i+1 y i b. It puts a cutoff in how close the emissions can be. Another way of controlling the higher order corrections (NLLA corrections are very large). Originally considered in the >> 1, >> b limit. Is it relevant for phenomenology? Different implementations depending on the choice of NNLO terms. Test it in an observable which experimentalists point out could be between BFKL and DGLAP regimes: Mueller Navelet jets at 7 TeV. Data is already available.

23 David Gordo Gómez Probing high energy effects in multijet production 23 / 27 Ongoing project NLLA NLO and exp at =4.75 k min A = k min B = 35 GeV, k max A = k max B = 60 GeV (symmetric) R 2 3 =4.75, NLL_NLOVeto_Ser, cutk=2, cut ν=20 R 0 2 =4.75, NLL_NLOVeto_Ser, cutk=2, cut ν= b b [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (in progress)]

24 David Gordo Gómez Probing high energy effects in multijet production 24 / 27 Conclusions Study of processes with three and four tagged jets to propose and predict new, more exclusive, BFKL observables: generalized azimuthal correlation with dependence on the transverse momenta of extra jets. Ratios of correlation functions used to minimize the influence of higher order corrections. Very stable observables under NLLA corrections to the GGF. Comparison with other approaches such as fixed order calculations and Monte Carlo simulations are needed to determine if the observable is a genuine BFKL signal. Comparison with experimental data suggested and needed to know the window of applicability of the BFKL framework at LHC.

25 David Gordo Gómez Probing high energy effects in multijet production 25 / 27 Outlook Three- and four-jets at full NLO accuracy (NLLA GGF+NLO IF) : improved kernel(s), scale optimization [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (in progress)] Exploring the meaning and application of the veto. [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (in progress)] Comparison with analyses where the four-jet predictions stem from two independent gluon ladders (double parton scattering) [R. Maciula, A. Szczurek (2014, 2015)] [K. Kutak, R. Maciula, M. Serino, A. Szczurek, A. van Hameren (2016, 2016)] Suggestion from experimentalists are welcome!

26 Thanks for your attention!!

27 BACKUP slides

28 David Gordo Gómez Probing high energy effects in multijet production November 16th, 2017 Motivation BACKUP slides So far, search for BFKL effects had these general drawbacks: too low s or rapidity intervals among tagged particels in the final state too inclusive observables, other approaches can fit them Advent of LHC: higher energies larger rapidity gaps unique opportunity to test pqcd in the high-energy limit disentangle applicability region of energy-log resummation (BFKL approach) [V.S. Fadin, E.A. Kuraev, L.N. Lipatov (1975, 1976, 1977)] [.. Balitskii, L.N. Lipatov (1978)] Last years: hadroproduction of two jets featuring high transverse momenta and well separed in rapidity, so called Mueller Navelet jets......possibility to define infrared-safe observables......and constrain the PDFs......theory vs experiment [B. Ducloué, L. Szymanowski, S. Wallon (2014)] [F. Caporale, D.u. Ivanov, B. Murdaca, A. Papa (2014)]

29 David Gordo Gómez Probing high energy effects in multijet production November 16th, 2017 BACKUP slides Partonic prediction of R for k J = 30, 45, 70 GeV k A = 40, k B = 50, A = 10, B = 0 k J = R y J [F. Caporale, G. Chachamis, B. Murdaca, A. Sabio Vera (2015)] A B is fixed to 10; y J varies beetwen 0.5 and 9.5.

30 David Gordo Gómez Probing high energy effects in multijet production November 16th, 2017 BACKUP slides R33 12 vs at 7 TeV - NLLA preliminary results k min A = 35 GeV, k min B = 50 GeV, k max A = k max B s 7 TeV; k min 50 GeV; k bin 1, bin 2, bin 3 = 60 GeV (asymmetric) R LLA NLA MOM BLM [F. Caporale, F.G. Celiberto, G. Chachamis, D. G.G., A. Sabio Vera (in progress)] is the rapidity difference between the most forward/backward jet; y J = A+ B 2.

31 BACKUP slides 22 R23 vs at 13 and 7 TeV - NLLA preliminary results kbmin = 50 GeV; s = 13 TeV; k J Î æ bin-1, æ bin-2, æ bin s = 13 TeV; 0.0 kbmin = 50 GeV; kj Î æ bin-1, æ bin-2, æ bin R LLA x H%L NLA MOM BLM s = 7 TeV; k J Î æ bin-1, æ bin-2, æ bin-3 7 kbmin = 50 GeV; s = 7 TeV; kbmin = 50 GeV; kj Î æ bin-1, æ bin-2, æ bin R LLA x H%L NLA MOM BLM [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (in progress)] David Gordo Go mez Probing high energy effects in multijet production November 16th, 2017

32 BACKUP slides Four-jets: generalized azimuthal coefficients - partonic level David Gordo Gómez Probing high energy effects in multijet production November 16th, 2017 with 2π 2π 2π 2π C MNL = dϑ A dϑ B dϑ 1 dϑ 2 cos (M (ϑ A ϑ 1 π)) ( ) d 6 σ 4 jet ka, kb, A B cos (N (ϑ 1 ϑ 2 π)) cos (L (ϑ 2 ϑ B π)) dk 1 dy 1 dϑ 1 dk 2 dϑ 2 dy 2 = 2π2 ᾱ s (µ R ) 2 k 1 k 2 ( 1) M+N+L ( Ω M,N,L + Ω M,N, L + Ω M, N,L + Ω M, N, L + Ω M,N,L + Ω M,N, L + Ω M, N,L + Ω M, N, L ) + + 2π 2π Ω m,n,l = dp A p A dp B p B dφ A dφ B ) n ) n e imφ A e ilφ B (p A e iφ A + k 1 (p B e iφ B k 2 (p 2 A + k p ) n (p Ak 1 cos φ 2 A B + k2 2 2p ) n B k 2 cos φ B ϕ m ( ka, p A, A y 1 ) ϕ l ( p B, kb, y 2 B ) ) ϕ n ( pa 2 + k p Ak 1 cos φ A, pb 2 + k2 2 2p B k 2 cos φ B, y 1 y 2

33 BACKUP slides Four-jets: generalized azimuthal coefficients - partonic level David Gordo Gómez Probing high energy effects in multijet production November 16th, π 2π 2π 2π C MNL = dϑ A dϑ B dϑ 1 dϑ 2 cos (M (ϑ A ϑ 1 π)) ( ) d 6 σ 4 jet ka, kb, A B cos (N (ϑ 1 ϑ 2 π)) cos (L (ϑ 2 ϑ B π)) dk 1 dy 1 dϑ 1 dk 2 dϑ 2 dy 2 Main observables: generalized azimuthal correlations R MNL PQR = C MNL = cos(m(ϑ A ϑ 1 π)) cos(n(ϑ 1 ϑ 2 π)) cos(l(ϑ 2 ϑ B π)) C PRQ cos(p(ϑ A ϑ 1 π)) cos(q(ϑ 1 ϑ 2 π)) cos(r(ϑ 2 ϑ B π))

34 David Gordo Gómez Probing high energy effects in multijet production November 16th, 2017 BACKUP slides R and R vs = A B and s for two k 1 bins s = 7 TeV; k A min = 35 GeV; k B min = 45 GeV; k 2 min = 60 GeV; k 2 max = 90 GeV s = 13 TeV; k A min = 35 GeV; k B min = 45 GeV; k 2 min = 60 GeV; k 2 max = 90 GeV k1 GeV k1 GeV k1 GeV k1 GeV R R s = 7 TeV; k A min = 35 GeV; k B min = 45 GeV; k 2 min = 60 GeV; k 2 max = 90 GeV s = 13 TeV; k A min = 35 GeV; k B min = 45 GeV; k 2 min = 60 GeV; k 2 max = 90 GeV k1 GeV k1 GeV k1 GeV k1 GeV R R [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (in progress)]

35 David Gordo Gómez Probing high energy effects in multijet production November 16th, 2017 BACKUP slides R and R vs = A B and s for two k 1 bins s = 7 TeV; k A min = 35 GeV; k B min = 45 GeV; k 2 min = 60 GeV; k 2 max = 90 GeV s = 13 TeV; k A min = 35 GeV; k B min = 45 GeV; k 2 min = 60 GeV; k 2 max = 90 GeV k1 GeV k1 GeV k1 GeV k1 GeV R R s = 7 TeV; k A min = 35 GeV; k B min = 45 GeV; k 2 min = 60 GeV; k 2 max = 90 GeV s = 13 TeV; k A min = 35 GeV; k B min = 45 GeV; k 2 min = 60 GeV; k 2 max = 90 GeV R R k1 GeV k1 GeV k1 GeV k1 GeV [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (in progress)]

36 BACKUP slides NLLA NLO and exp at =4.75 David Gordo Gómez Probing high energy effects in multijet production November 16th, 2017 k min A = k min B = 35 GeV, k max A = k max B = 60 GeV (symmetric) R 1 2 =4.75, NLL_NLOVeto_Ser, cutk=2, cut ν=20 R 0 1 =4.75, NLL_NLOVeto_Ser, cutk=2, cut ν= b b [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (in progress)]

37 David Gordo Gómez Probing high energy effects in multijet production November 16th, 2017 R 2 1 BACKUP slides vs at 7 TeV - NLLA NLO k min A = k min B = 35 GeV, k max A = k max B = 60 GeV (symmetric) 0.8 R Experiment b=0 b=0.2 b=0.4 b=0.6 b= [F. Caporale, F.G. Celiberto, G. Chachamis, D.G.G., A. Sabio Vera (in progress)]