Some new aspects of double parton scattering effects in the reactions with at least single charm pair production

Transcription

1 Some new aspets of double parton sattering effets in the reations with at least single harm pair prodution Antoni Szzurek Institute of Nulear Physis (PAN), Kraków, Poland Rzeszów University, Rzeszów San Cristobal, Mexio, November 7th - Deember th, 6

2 Outline Introdution Prodution of Prodution of in DPS SPS prodution in k t -fatorization 5 Perturbative parton splitting 6 Gluon fragmentation to D mesons and onsequenes 7 First exploration of j 8 Fist exploration of jj 9 Conlusions

3 Introdution Eearly extration of σ eff gave 5 mb Reently some onfusion from reent analyses σ eff =.8±.5±.5 mb from J/ψJ/ψ at D σ eff =.±.7±.9 mb from J/ψΥ at D σ eff = 6 mb from MSSS6 analysis of D D Naive geometry with smeared gluons: σ eff mb Gaunt, Maiuła, Szzurek, Phys. Rev. D9 () 57. Parton splitting effetively modifies σ eff (down) σ eff = σ eff ( y) Nonperturbative parton splitting (Blok, Strikman) More involved analyses regarding SPS and DPS ontributions needed Here we onsider two new proesses: pp j (SPS, ollinear- and k t -fatorization) helpfull in understanding prodution pp jj (DPS and SPS, ollinear fatorization) ompetition of DPS and SPS

4 -step proess QCD pqcd fragmentation deyas pp Quarks Hadrons eletrons Heavy quarks Q Q pairs prodution experimental observable m =.5 GeV, m b =.75 GeV perturbative QCD Heavy quarks hadronization (fragmentation) Semileptoni deays of D and B mesons dσ e dyd p = dσq dyd p D Q H f H e ν X e π + D D + D + D + D D X e + ν π

5 Dominant mehanisms of Q Q prodution Leading order proesses ontributing to Q Q prodution: gluon-gluon fusion dominant at high energies q q anihilation important only near the threshold some of next-to-leading order diagrams: NLO ontributions K-fator

6 k t -fatorization (semihard) approah p X harm and bottom quarks prodution at high energies gluon-gluon fusion p k,t k,t Q Q X QCD ollinear approah only inlusive one partile distributions, total ross setions LO k t -fatorization approah κ,t, κ,t Q Q orrelations multi-differential ross setion dσ d κ,t = dy dy d p,t d p,t π i,j d κ,t π 6π (x x s) M ij Q Q δ ( κ,t + κ,t p,t p,t )F i (x, κ,t )F j(x, κ,t ) off-shell M gg Q Q Catani, Ciafaloni, Hautmann (rather long formula) major part of NLO orretions automatially inluded F i (x, κ,t ),F j(x, κ,t ) - unintegrated parton distributions x = m,t s exp(y ) + m,t s exp(y ), x = m,t s exp( y ) + m,t s exp( y ), where m i,t = p i,t + m Q.

7 Fragmentation funtions tehnique X p p k,t k,t Q Q hadronization M M fragmentation funtions extrated from e + e data often used: Braaten et al., Kartvelishvili et al., Peterson et al. resalling transverse momentum at a onstant rapidity (angle) X from heavy quarks to heavy mesons: dσ(y, p M t ) DQ M (z) dσ(y, pq t ) dz dyd pt M z dyd p Q t where: p Q t = pm t and z (, ) z approximation: rapidity unhanged in the fragmentation proess y Q y M Prodution of D mesons in this framework: Maiula, Szzurek, Phys. Rev. D87 () 9.

8 Prodution of p p p p Łuszzak, Maiuła, Szzurek, Phys. Rev. D85 () 95.

9 Formalism Consider reation: pp X Modeling double-parton sattering Fatorized form: σ DPS (pp X) = σ eff σ SPS (pp X ) σ SPS (pp X ). In general σ eff an depend on kinematis he simple formula above an be generalized to inlude differential distributions dσ dy dy d p t dy dy d p t = σ eff dσ dy dy d p t dσ dy dy d p t. σ eff is a model parameter (5 mb). Found e.g. from experimental analysis of four s (see also Siódmok et al.) In priniple does not need to be universal.

10 Energy dependene of prodution SPS p p X vs. DPS p p X ) (mb) s ( GRV9 LO GJR8 LO MSW8 LO CEQ6 LO σ tot (Donnahie - Landshoff) σ tot - - SPS DPS s (GeV) y 8. σ eff = 5 mb µ = µ = M R F LO: g g Luszzak,Maiula,Szzurek, Phys. Rev. C86 () 95 spetaular result: Already at the LHC prodution of two pairs as probable as prodution of one pair.

11 DPS in k t -fatorization eah step: p X k,t k,t Q Q hadronization M M p X

12 DPS in k t -fatorization Generalize the LO ollinear approah to k t -fatorization approah. More ompliated (more kinematial variables) as momenta of outgoing partons are less orrelated We need information about eah quark and antiquark σ eff dσ dy dy d p,t d p,t dy dy d p,t d p,t = dσ dy dy d p,t d p,t dσ dy dy d p,t d p,t ()

13 DPS in k t -fatorization Eah individual sattering in the k t -fatorization approah dσ = dy dy d p,t d p,t 6π ŝ M off δ ( k t + k t p t p t )F(x, k t, µ )F (x, k t, µ ) d k t π d k t π dσ = dy dy d p,t d p,t 6π ŝ M off δ ( k t + k t p t p t )F(x, k t, µ )F (x, k t, µ ) d k t d k t π π Effetively 6 dimensions, Monte Carlo method Maiula-Szzurek, hep-ph-.69, Phys. Rev.D87 () 79.

14 Single parton sattering proess? ) (mb) σ tot s ( - - p p X vs. p p X g g g g - - s (GeV) y 8. CEQ6 LO Only about % at high energies Muh smaller than DPS prodution of

15 inlude gluon transverse momenta A. van Hameren, R. Maiula and A. Szzurek, arxiv:5.69, Phys. Lett. B78 (5) 77. SPS in k t -fatorization approah p A x k t x k t p p p p p B

16 Results for k t -fatorization approah (nb/gev) D dσ/dm D - p p (D < p < GeV. < y D <. D ) X M D D (GeV) s = 7 ev LHCb DPS + SPS DPS SPS Peterson FF ε =. dσ/d ϕ (nb) π p p (D D ) X < p < GeV. < y <. D LHCb ϕ /π s = 7 ev DPS + SPS DPS SPS Figure: Distributions in D D invariant mass (left) and in azimuthal angle between both D s (right) within the LHCb aeptane. he DPS ontribution (dashed line) and the SPS ontribution within the k t -fatorization approah (dashed-dotted line). he ollinear SPS result from our previous studies (dotted line).

17 Parton splitting mehanism here are perturbative mehanisms not inluded in onventional DPS. p x x p x x x p x x p x Gaunt, Maiuła, Szzurek, Phys. Rev. D9 () 57.

18 A bit of formalism for parton splitting Conventional DPS: σ(v) = σ eff,v dy dy d p t dy dy d p t 6πŝ M(gg ) x x x x () D gg (x, x, µ, µ ) Dgg (x, x, µ, µ ) Parton splitting DPS σ(v) = σ eff,v dy dy d p t dy dy d p t 6πŝ M(gg ) x x x x (ˆDgg (x, x, µ, µ )Dgg (x, x, µ, µ ) + Dgg (x, x, µ, µ )ˆDgg (x, x, µ here are two different normalization parameters. hey are related in a geometrial piture. Presene of the two omponents leads to a dependene of effetive parameter on different kinematial variables.

19 Parton splitting vs onventional DPS dσ/dy (mb/gev) DPS: p p X p GeV t s = 7 ev v MSW8 PDFs v GS9 dpdfs - m =.5 GeV µ = m µ = m t t y Asymmetri v and v ontributions

20 Parton splitting vs onventional DPS.9.8 DPS: p p X p GeV t s = 7 ev dσ/dy(v) dσ/dy(v) R = µ = M, µ = m t µ = M, µ = m t.. m =.5 GeV y Rapidity and fatorization sale dependene here ould be also transverse momentum dependene.

21 Parton splitting vs onventional DPS µ = M, µ = M, DPS: p p X σ(v) σ(v).6.5. = m µ t µ = m t. y 8.. p GeV t. σ eff,v = σ eff,v / 5 s (GeV)

22 Parton splitting vs onventional DPS s) (mb) σ eff ( DPS: p p X p GeV t y 8. µ = m µ = m t t µ = M, µ = M, s (GeV) σ eff,v = σ eff,v / σ eff is no longer a onstant

23 Gluon fragmentation to D mesons Kniehl and Kramer disussed several fragmentation of a parton (gluon,u, d, s, ū, d, s,, ) to D mesons Important ontribution to inlusive prodution of D mesons in p p ollisions omes from g D(Kniehl, Kramer, Shienbein, Spiesberger) Similar alulation in k t -fatorization by Karpishkov, Nefedov, Saleev, Shipilova, 5. Good desription of D meson transverse momentum distributions at the LHC (similar to Maiula, Szzurek). What are onsequenes of the "new" mehanism for double D meson prodution? (with Maiula, Saleev and Shipilova - work in preparation).

24 DGLAP evolution of fragmentation funtions Fragmentation funtions fulfill the DGLAP equation: d dlnµ f D a (x, µ f ) = α s(µ) dy π x y P a b (y, α s(mu))d b where a = g, u, ū, d, d, s, s,, Initial onditions: b D (z, µ ) = N z( z) (( z) + ϸ) D g (z, µ ) =. ( ) x y, µ f In our ase we will take: µ = m t Fragmentation funtions fitted (with massless DGLAP evolution) to e + e data (with mass effets in the ross setion) A onsequene of the evolution is a muh smaller ontribution of gg Dmehanism at intermediate and large p t and appearene of new terms..

25 Single D meson prodution (µb/gev) p p (D + D ) X LHCb data s = 7 ev. < y D <.5 Peterson FF: ε =.5 D (µb/gev) LHCb data p p (D + D ) X s = 7 ev.5 < y D <. Peterson FF: ε =.5 D dσ/dp KKKS8 FF: + g D dσ/dp KKKS8 FF: + g D g D g D D KMR MMHlo D KMR MMHlo p (GeV) p (GeV) Figure: Left and right panels orrespond to two different rapidity intervals. he Peterson DFF (solid lines) are ompared to the seond senario alulations with the KKKS8 FF (long-dashed lines) with D (dotted) and g D (short-dashed) omponents that undergo DGLAP evolution equation. Both methods desribe the existing data

26 Figure: A diagrammati illustration of the onsidered mehanisms. New mehanisms R R R R R R g g R R g R R g R R g R R

27 DPS parton prodution mehanisms DPS prodution of or gg system, assuming fatorization of the DPS model: dσ DPS (pp X) dy dy d p,t d p,t = dσ DPS (pp ggx) dy dy d p,t d p,t = dσ DPS (pp gx) dy dy d p,t d p,t = σ eff dσsps (pp X ) dσsps (pp X ) dy d p,t dy d, p,t σ eff dσsps (pp gx ) dσsps (pp gx ) dy d p,t dy d. p,t σ eff dσsps (pp gx ) dy d p,t dσsps (pp X ) dy d p,t.

28 SPS parton prodution mehanisms In the k t -fatorization approah, the ross setion for relevant SPS ross setions: dσ SPS (pp X) d k t d k t = dy dy d p,t d p,t 6π (x x S) π π M RR δ ( k t + k t p t p t )F(x, k t, µ )F (x, k t, µ ), dσ SPS (pp ggx) dy dy d p,t d p,t = 6π (x x S) d k t π d k t π M RR gg δ ( k t + k t p t p t )F(x, k t, µ )F (x, k t, µ ), dσ SPS (pp gx) dyd p t = π (x x S) d k t π d k t π M RR g δ ( k t + k t p t )F(x, k t, µ )F (x, k t, µ ).

29 Fragmentation In order to alulate orrelation observables for two mesons we follow the fragmentation funtion tehnique for hadronization proess: dσ DPS(pp DDX) D D (z ) = D D(z ) dσdps (pp X) dy dy d p D t d p D z t z dy dy d p t d p dz dz, t Dg D (z ) + Dg D(z ) dσdps (pp ggx) z z dy dy d p g t d p g dz dz t + Dg D (z ) z D D(z ) z dσdps (pp gx) dy dy d p g t d p dz dz, t where: p g, t = pd,t, p g, z,t = pd t and meson longitudinal frations z z, z (, ). For SPS DD-prodution via digluon fragmentation: dσ SPS gg (pp DDX) dy dy d p D t d p D t Dg D (z ) z Dg D(z ) z dσsps (pp ggx) dy dy d p g t d p g dz dz, t where: p g t = pd,t z, p g,t = pd t z and meson longitudinal frations z, z (, ).

30 First results in the new approah (µb/gev) p p (D + D ) X LHCb data s = 7 ev. < y D <.5 Peterson FF: ε =.5 D (µb/gev) LHCb data p p (D + D ) X s = 7 ev.5 < y D <. Peterson FF: ε =.5 D dσ/dp KKKS8 FF: + g D g D D KMR MMHlo dσ/dp KKKS8 FF: + g D g D D KMR MMHlo p (GeV) p (GeV)

31 Larger σ eff (nb/gev) dσ/dp p p (D D ) X. < y <. D LHCb p (GeV) s = 7 ev σ eff = 5 mb σ eff = mb σ eff = 6 mb KKKS8 FF with DGLAP evolution σ eff = 6 mb desribes the data

32 Larger σ eff (nb/gev) D dσ/dm D LHCb. < y <. D < p < GeV p p (D D ) X s = 7 ev σ eff = 5 mb σ eff = mb σ eff = 6 mb KKKS8 FF with DGLAP evolution M D D (GeV) σ eff = 6 mb desribes the data

33 Larger σ eff 5 p p (D < p < GeV D ) X. < y <. D s = 7 ev dσ/d ϕ (nb) π 5 = 5 mb σ eff = mb σ eff = 6 mb σ eff 5 LHCb KKKS8 FF with DGLAP evolution ϕ /π σ eff = 6 mb desribes the data

34 First exploration of j g g g q( q) q( q) g Only SPS mehanisms full phase spae

35 Prodution of j in ollinear fatorization dσ(pp + ) = dx dx [g(x, µ F )g(x, µ F ) dˆσ gg g + Σ f q f (x, µ F )g(x, µ F ) dˆσ qg q + g(x, µ F )Σ f q f (x, µ F ) dˆσ gq q + Σ f q f (x, µ F )g(x, µ F ) dˆσ qg q + g(x, µ F )Σ f q f (x, µ F ) dˆσ g q q], () where g(x,, µ F ), q f(x,, µ F ) and q f(x,, µ F ) are the standard ollinear parton distribution funtions (PDFs) for gluons, quarks and antiquarks, respetively, arrying x, momentum frations of the proton and evaluated at the fatorization sale µ F. Here, dˆσ are the elementary partoni ross setions for a given subproes

36 Prodution of j in k t -fatorization dσ(pp + ) = d k t dx π dx d k t π [F g (x, k t, µ F )F g(x, k t, µ F ) dˆσ + F q (x, k t, µ F )F g(x, k t, µ F ) dˆσ q g q +F g (x, k t, µ F )F q(x, k t, µ F ) d + F q (x, k t, µ F )F g(x, k t, µ F ) dˆσ q g q +F g (x, k t, µ F )F q(x, k t, µ F ) d Here, k,t are transverse momenta of inident partons (new degrees of freedom) andf (x, kt, µ F ) s are transverse momentum dependent, so-alled, unintegrated parton distribution funtions (updfs)

37 Results, ollinear fatorization (nb/gev) dσ/dp 5 p p + g g g (dashed) q g q (dotted) 6 8 -quark p s = ev (GeV) p > GeV, y < 8. MMHnlo (nb/gev) dσ/dp 5 p p + g g g (dashed) q g q (dotted) p (GeV) s = ev, y < 8. MMHnlo Figure: ransverse momentum distribution of -quark (let panel) and assoiated (right panel) in the ollinear approah.

38 Results, ollinear fatorization 5 p p + s = ev p > GeV y < 8. 5 p p + s = ev p > GeV y < 8. dσ/dy (nb) dσ/dy (nb) g g g (dashed) q g q (dotted) MMHnlo g g g (dashed) q g q (dotted) MMHnlo quark y y Figure: Rapidity distribution of -quark (left panel) and assoiated (right panel) in the ollinear appraoh.

39 Results, ollinear fatorization 6 p p + s = ev 6 p p + s = ev (nb/rad) 5 p > GeV, y < 8. MMHnlo (nb/rad) 5 p > GeV, y < 8. dσ/dϕ - dσ/dϕ g g g (dashed) q g q (dotted) MMHnlo g g g (dashed) q g q (dotted) ϕ - (deg) ϕ (deg) Figure: Distribution in azimuthal angle between -quark and (left panel) and between -quark and -antiquark (right panel) in the ollinear approah.

40 Results, k t -fatorization (nb/gev) 5 p p + only g* g* g s = ev p > GeV, y < 8. JH set Jung seta (nb/gev) 5 p p + only g* g* g s = ev, y < 8. JH set Jung seta dσ/dp KMR KMR k < GeV ollinear 6 8 -quark p (GeV) dσ/dp KMR KMR k < GeV ollinear p (GeV) Figure: ransverse momentum distribution of -quark (let panel) and assoiated (right panel) in the k -fatorization approah with different ugdfs.

41 Results, k t -fatorization 5 p p + s = ev p > GeV y < 8. 5 p p + s = ev p > GeV y < 8. dσ/dy (nb) only g* g* g JH set Jung seta KMR KMR k < GeV ollinear dσ/dy (nb) only g* g* g JH set Jung seta KMR KMR k < GeV ollinear quark y y Figure: Rapidity distribution of -quark (left panel) and assoiated (right panel) in the k -fatorization appraoh with different ugdfs.

42 Results, k t -fatorization (nb/rad) 6 5 p p + only g* g* g p > GeV, y < 8. s = ev (nb/rad) 6 5 p p + only g* g* g s = ev p > GeV, y < 8. dσ/dϕ - KMR KMR k < GeV ollinear JH set Jung seta dσ/dϕ JH set Jung seta KMR KMR k < GeV ollinear ϕ - (deg) ϕ (deg) Figure: Distribution in azimuthal angle between -quark and (left panel) and between -quark and -antiquark (right panel) in the k -fatorization approah with different ugdfs.

43 Results, omparison of both methods 5 p p + s = ev 5 p p + s = ev (nb/gev) p > GeV, y < 8. (nb/gev), y < 8. dσ/dp k -fat.: KMR k < GeV (solid) ollinear: MMHnlo (dotted) 6 8 dσ/dp k -fat.: KMR k < GeV (solid) ollinear: MMHnlo (dotted) quark p (GeV) p (GeV) Figure: Comparison of transverse momentum distributions of -quark (let panel) and assoiated (right panel) for ollinear approah (dotted) and the k -fatorization approah with the KMR ugdf and extra ut on initial gluon transverse momenta (solid).

44 Results, omparison of both methods 5 p p + s = ev p > GeV y < 8. 5 p p + s = ev p > GeV y < 8. dσ/dy (nb) dσ/dy (nb) k -fat.: KMR k < GeV (solid) ollinear: MMHnlo (dotted) k -fat.: KMR k < GeV (solid) ollinear: MMHnlo (dotted) quark y y Figure: Comparison of rapidity distribution of -quark (left panel) and assoiated (right panel) in the ollinear approah (dotted) and the k -fatorization appraoh with the KMR ugdf and extra ut on initial gluon transverse momenta (solid).

45 Results, omparison of both methods 6 p p + s = ev 6 p p + s = ev (nb/rad) 5 p > GeV, y < 8. (nb/rad) 5 p > GeV, y < 8. dσ/dϕ - k -fat.: KMR k < GeV (solid) ollinear: MMHnlo (dotted) dσ/dϕ k -fat.: KMR k < GeV (solid) ollinear: MMHnlo (dotted) ϕ - (deg) ϕ (deg) Figure: Comparison of distribution in azimuthal angle between -quark and (left panel) and between -quark and -antiquark (right panel) in the ollinear approah (dotted) and in the k -fatorization approah with the KMR ugdf and extra ut on initial gluon transverse momenta (solid).

46 Preditions for D + prodution at the LHC (nb/rad) 6 5 p p ALAS D y <.5 p D D + >.5 GeV s = ev p > GeV y <.9 - D dσ/dϕ k -fat. KMR < GeV k -fat. KMR k ollinear k -fat. Jung seta ϕ D - Figure: Azimuthal angle orrelation between D meson and for ollinear and k -fatorization approahes. he uts are speified in the figure aption. (rad)

47 Preditions for D + prodution at the LHC able: he alulated ross setions in mirobarns for inlusive D + prodution in pp-sattering at s = ev Here, the D meson is required to have y D <.5 and p D >.5 GeV and the rapidity of the assoiated is y <.9, that orresponds to the ALAS detetor aeptane. Cuts ollinear MMHnlo KMR KMR k < p > GeV p > 5 GeV p > 5 GeV...9

48 First exploration of pp jj p p x x x x x x p p Both DPS and SPS mehanisms full phase spae

49 Proesses inluded in SPS 9 types: gg gg gg q q gq/ q gq/ q q/ qg gq/ q q q q q q q gg qq qq qq qq

50 Jet transverse momentum distribution (nb/gev) 5 p p + s DPS SPS s only s = ev, y < 8. dσ/dp LO ollinear-fat. MMH p (GeV) he ross setion for dis only slightly bigger than that for dis assoiated with harm

51 Charm transverse momentum distribution (nb/gev) 6 5 p p + s DPS SPS s = ev p > GeV, y < 8. dσ/dp LO ollinear-fat. MMH quark p (GeV) DPS dominates at low transverse momenta

52 Rapidity distributions dσ/dy (nb) 5 p p + s p > GeV y < 8. SPS s = ev DPS dσ/dy (nb) 6 5 p p + s p > GeV y < 8. s = ev SPS DPS LO ollinear-fat. MMH y LO ollinear-fat. MMH quark y he harm DPS distribution broader than harm SPS distribution

53 Other distributions (nb) dσ/d Y p p + s DPS SPS LO ollinear-fat. MMH 6 8 Y - s = ev p > GeV, y < 8. (nb/rad) dσ/dϕ p p + s DPS SPS LO ollinear-fat. MMH ϕ - (rad) s = ev, y < 8. p > GeV he DPS distribution in η j is broader than its SPS ounterpart he distribution in φ j should be very flat.

54 Comparison of j and jj (nb/gev) dσ/dp 5 p p + s s = ev, y < 8. DPS SPS + LO ollinear-fat. MMH p (GeV) jj muh bigger than j

55 Comparison of j and jj (nb/gev) dσ/dp 6 5 p p + s DPS SPS s = ev p > GeV, y < 8. + LO ollinear-fat. MMH quark p (GeV) Summary: > jj(dps) jj > jj(sps) j

56 Conlusions k t -fatorization provides good desription of harm prodution at RHIC and LHC. Surprisingly large ross setions for inlusive due to DPS. Relatively small ross setions for SPS. Multiple pairs an be produed in p p ollisions at the LHC and FCC. Look at orrelations between same flavour harmed mesons suh as D D. Look at orrelations between e + µ + or e µ from semileptoni deays (ALICE, CMS). Enhanement of the number of pairs in AA ollisions important for reombination/oalesene further enhanement of hidden-harm meson prodution (J/ψ, ψ ) at higher energies.

57 Conlusion, ontinued Gluon fragmentation hanges the piture. Several new ontributions (both DPS and SPS) dσ/dφ DD onst Diffiult to get it from DPS mehanisms (Ehevarria, Kasemets, Mulders, Pisano) as spin orrelations. oo big D D ross setion with anonial value σ eff = 5 mb. Possible solutions: larger σ eff (good reasons) (larger rapidity) wrong small-x UGDF, saturation? (strong effet) wrong large-x UGDF? problems with massless evolution of FF? We an desribe the LHCb data with strongly redued σ eff and strongly modified low-x glue. Are the strong low-x modifiations onsistent with other proesses?

58 Conlusion, ontinued First theoretial study related to assoiated prodution of harm and single prodution. We have limited to ( ) quark level and full phase spae. he results, one dimesional and two-dimensional distributions, with the KMR ugdf and a pratial orretion to exlude prodution of more than one are very similar as those obtained within the ollinear approah. We have performed first feasibility studies for ALAS (and/or CMS) uts. We have obtained rather large ross setion. We have presented first alulations for jj within ollinear fatorization approah DPS ontribution muh larger than SPS ontribution SPS jj of the same order as SPS j σ(jj) σ(jj ) - searh for assoiated prodution of harm outside of the s to identify DPS.