Production of triply heavy baryons and six free heavy quarks at

Transcription

1 Production of triply heavy baryons and six free heavy quarks at LHC October 25, 2012

2 OUTLINE. Triply heavy baryons production.overview of the triply heavy baryons..the production of the triply heavy baryons.. Six free heavy quarks production

3 1.1 Overview of the triply heavy baryons.the color configuration: 1 6 ε ijk Q 1i Q 2j Q 3k.Three energy scales: m >> mv >> mv 2.Size: 1/ mv.spin structure: Ω ccc : 3 2, Ω ccb :3 2, Ω ccb: 1 2.The nonrelativistic triply heavy baryon in the ground state is: Ω Q1Q 2Q 3,S,S Z, P d 3 V 1 d 3 V 2 = 0 = εξ1ξ2ξ3 (2π) 3 (2π) 3 S,S Z η 1,η 2,η 3 ξ 6 i,η i 2M 1 ψ( V 1, V 2 ) Q 1,ξ 1,η 1, p 1 = V 1 2E1 2E 2 2E 3 d! Q 2,ξ 2,η 2, p 2 = V 2 Q 3,ξ 3,η 3, p 3 = V 1 V 2.

4 1.2 The process of pp Ω Q1 Q 2 Q 3 Q1 Q2 Q3 +X The production mechanism: g g fusion, q q annihilation (u, d, s). Ω. Energy scales: m >> mv. the short-distance coefficient. the long-distance matrix element

5 .For g-g fusion process: All diagrams shrink to seven basic diagrams: Q 1 Q 2 Q 3 Q 1 Q 3 Q 2 Q 2 Q 3 Q 1 Q 2 Q 1 Q 3 Q 1 Q 2 Q3 Q 1 Q 3 Q2 Q 2 Q 3 Q1 Q 2 Q 1 Q3 Q 3 Q 1 Q 2 Q 3 Q 2 Q 1 Q 1 Q 3 Q 1 Q 2 Q2 Q3 Q 3 Q 1 Q2 Q 3 Q 2 Q1 Figure: The seven inequivalent topological constructions of three heavy quark pairs assuming three heavy quarks with different heavy flavors.

6 .Feynman diagram generation Feynman diagrams containing a quartic-gluon vertex: =34 Feynman diagrams without quartic-gluon vertex: (6+3) 11 7=693 The number of the Feynman diagrams: =727 Distinct amplitudes: =795

7 . For process gg ccb c c b. two permutations: (c 1 c 1 c 2 c 2 b b), (c 1 c 2 c 2 c 1 b b), Feynman diagrams: 727 2!=1454 Distinct amplitudes: 795 2!=1590. For process gg ccc c c c:.six permutations: (c 1 c 1 c 2 c 2 c 3 c 3 ), (c 1 c 1 c 2 c 3 c 3 c 2 ), (c 1 c 2 c 2 c 3 c 3 c 1 ), (c 1 c 2 c 2 c 1 c 3 c 3 ), (c 1 c 3 c 2 c 1 c 3 c 2 ), (c 1 c 3 c 2 c 2 c 3 c 1 ). Feynman diagrams: 727 3!=4362 Distinct amplitudes: 795 3!=4770

8 .Simplification Color factor antisymmetry. Spin wave function symmetry. Non-relativistic approximation.

9 . Generating basic Feynman diagrams automatically three integers: i denoting the position of the first gluon j denoting the position of the second gluon k denoting the topological construction of three heavy quark pairs.amplitudes of the Feynman diagrams: gauge invariance: ward identity (12 independent color factors)

10 Twelve independent color factors. C 1 = εξ 1ξ 2 ξ 3 6 (λ a λ b ) ξ1 χ 2 δ ξ2 χ 1 δ ξ3 χ 3,C 2 = εξ 1ξ 2 ξ 3 6 (λ b λ a ) ξ1 χ 2 δ ξ2 χ 1 δ ξ3 χ 3, C 3 = εξ 1ξ 2 ξ 3 6 (λ a λ b ) ξ1 χ 1 δ ξ2 χ 2 δ ξ3 χ 3,C 4 = εξ 1ξ 2 ξ 3 6 (λ b λ a ) ξ1 χ 1 δ ξ2 χ 2 δ ξ3 χ 3, C 5 = εξ 1ξ 2 ξ 3 6 (λ a λ b ) ξ1 χ 3 δ ξ2 χ 1 δ ξ3 χ 2,C 6 = εξ 1ξ 2 ξ 3 6 (λ b λ a ) ξ1 χ 3 δ ξ2 χ 1 δ ξ3 χ 2, C 7 = εξ 1ξ 2 ξ 3 6 (λ a ) ξ1 χ 1 (λ b ) ξ2 χ 2 δ ξ3 χ 3,C 8 = εξ 1ξ 2 ξ 3 6 (λ a ) ξ1 χ 2 (λ b ) ξ2 χ 1 δ ξ3 χ 3, C 9 = εξ 1ξ 2 ξ 3 6 (λ a ) ξ1 χ 2 (λ b ) ξ2 χ 3 δ ξ3 χ 1,C 10 = εξ 1ξ 2 ξ 3 6 (λ a ) ξ1 χ 3 (λ b ) ξ2 χ 2 δ ξ3 χ 1, C 11 = εξ 1ξ 2 ξ 3 6 (λ a ) ξ1 χ 3 (λ b ) ξ2 χ 1 δ ξ3 χ 2,C 12 = εξ 1ξ 2 ξ 3 6 (λ a ) ξ1 χ 1 (λ b ) ξ2 χ 3 δ ξ3 χ 2.

11 . In leading order (expansion in v), the differential cross section of g g fusion is: dˆσ = S Z (2π) 4 2ŝ δ4 (k 1 +k 2 P q 1 q 2 q 3 ) d 3 P (2π) 3 2E 1 A 2 64 d 3 q 1 (2π) 3 2E 1 d 3 q 2 (2π) 3 2E 2 d 3 q 3 M Ψ(0,0) 4m 1 m 2 m 3 (2π) 3 2E 3 d! 2. (2) The differential cross section of pp Ω S Q 1 Q 2 Q 3 Q1 Q2 Q3 +X is: dσ = 1 dp T d! dx 1 dx 2 f g1 (x 1,Q)f g2 (x 2,Q) dˆσ dp T (3)

12 1.3 Numerical results and conclusions for the triply heavy baryons production. The parameters: mass: m c =1.5 GeV, m b =4.9 GeV, and M=m 1 +m 2 +m 3, wave function at the origin: Ψ(0,0) 2 = GeV 6 for Ω ccc, Ψ(0,0) 2 = GeV 6 for Ω ccb and Ω ccb. energy scales: Q=µ R /2, µ R, where µ 2 R =P2 T +M2.

13 Table: Hadronic Production Cross sections (in unit nb) of the triply heavy baryons at LHC with s = 7.0 TeV. Some typical P T cuts are adopted. As for the pseudo-rapidity cut, we take η < 2.5 for CMS and ATLAS, and 1.9 < η < 4.9 for LHCb. - - LHC (CMS, ATLAS) LHCb η cut - η < < η < 4.9 P Tcut Q - µ R µ R/2 µ R µ R/2 Ω ccc 0GeV (6) 0.132(1) (3) (7) - 5GeV (8) (3) (3) (6) - 10GeV 2.6(1)E-4 6.3(2)E-4 4.8(1)E (2)E-4 Ω ccb 0GeV (1) (2) 7.24(6)E (2) - 5GeV 6.49(5)E (1) 1.89(1)E (4)E-4-10GeV 9.62(7)E (2)E (2)E (5)E-5 Ω ccb 0GeV 4.89(3)E (1) 2.15(1)E (4)E-4-5GeV 2.43(2)E (4)E (5)E (1)E-4-10GeV 4.49(4)E (1)E (9)E (2)E-5

14 Table: Hadronic Production Cross sections (in unit nb) of the triply heavy baryons at LHC with s = 14.0 TeV. There typical P T cuts are adopted. For the pseudo-rapidity cut, we take η < 2.5 for CMS and ATLAS, and 1.9 < η < 4.9 for LHCb. - - LHC (CMS, ATLAS) LHCb η cut - η < < η < 4.9 P Tcut Q - µ R µ R/2 µ R µ R/2 Ω ccc 0GeV 0.113(1) 0.216(3) (6) 0.135(2) - 5GeV (2) (5) (8) (9) - 10GeV (9) (2) (5) (6) Ω ccb 0GeV (2) (5) (2) (3) - 5GeV (1) (3) (4) (1) - 10GeV 2.34(2)E (5)E (7)E (2)E-4 Ω ccb 0GeV (1) (2) (3) (1) - 5GeV (5) (1) (1) (3) - 10GeV (1) (2) 0.289(4)E (8)E-4

15 (nb) 1 d /dp T pp ccc Q= R Q= R (nb) 1E-3 d /dp T 1E-4 pp * ccb Q= R /2 Q= R 1E-3 1E-4 1E-5 1E-5 1E-6 1E P T (GeV) P T (GeV) d /dp T (nb) 1E-4 1E-5 pp ccb Q= R /2 Q= R 1E-6 1E P T (GeV) Figure: The P T -distributions of the production cross sections of the baryons with three heavy quarks in CMS and ATLAS at s=7 TeV.

16 (nb) 0.1 d /dp T E-3 pp ccc Q= R /2 Q= R (nb) 1E-3 d /dp T 1E-4 pp * ccb Q= R /2 Q= R 1E-4 1E-5 1E-5 1E-6 1E-6 1E-7 P T (GeV) E P T (GeV) (nb) 1E-4 d /dp T 1E-5 pp ccb Q= R /2 Q= R 1E-6 1E P T (GeV) Figure: The P T -distributions of the production cross sections of the baryons with three heavy quarks in LHCb at s=7 TeV.

17 d /dy(nb) E-3 1E-4 1E-5 1E-6 1E-7 pp ccc Q= R /2 Q= R y 6 (nb) 1E-3 * Q= R /2 d /dy pp ccb Q= 1E-4 R 1E-5 1E-6 1E-7 1E-8 1E y (nb) 1E-3 Q= R /2 d /dy pp ccb Q= 1E-4 R 1E-5 1E-6 1E-7 1E-8 1E-9 1E y Figure: The y-distributions of the production cross sections of the baryons with three heavy quarks at LHC, with s=7 TeV.

18 Table: The events with a luminosity of L cm 2 s 1 and P T > 5 GeV in unit (year 1 ). s(tev) baryon CMS, ATLAS LHCb - Q = µ R Q = µ R /2 Q = µ R Q = µ R /2 Ω ccc Ω ccb Ω ccb

19 Table: The events with a luminosity of L cm 2 s 1, and with P T > 5 GeV in LHCb and P T > 10 GeV in in ATLAS and CMS. (year 1 ) s(tev) baryon CMS, ATLAS LHCb - Q = µ R Q = µ R /2 Q = µ R Q = µ R /2 Ω ccc Ω ccb Ω ccb

20 2.1 Production of six free heavy quarks.feynman diagrams 727: three pairs quarks with different flavors: gg c cb bt t 1454: two of the final three quarks with the same flavor, eg. gg c cc cb b 4362: three quarks with the same flavor, eg. gg c cc cc c

21 .there are 72 independent color factors.a more integer, L, is asked to produce and describe the Feynman diagrams.the integral dimensions of phase space are much more running time: pp c cc cc c+x: event: 12800, time: 4 s, computer: 128-core (Madgraph: pp l + l jjjj, 10000, MG4: 7:16 h, MG5: 2:45 h) (In MG: p,j = g/u/ū/d/ d/s/ s/c/ c)

22 Table: Hadronic Production Cross sections (in unit nb) of three pairs of free quarks at LHC with s = 7.0 TeV. Some typical P T cuts are adopted. As for the pseudo-rapidity cut, we take η < 2.5 P Tcut 0 GeV 5 GeV 10 GeV final states c cc cb b 15.9(1) 1.23(2) 0.121(3) c cb bb b 2.56(3) 0.488(9) 0.066(1) c cc cc c 40.4(4) 1.02(3) 0.071(2) b bb bb b 0.154(1) (7) (2)

23 Table: Hadronic Production Cross sections (in unit nb) of three pairs of free quarks at LHC with s = 14.0 TeV. Some typical P T cuts are adopted. As for the pseudo-rapidity cut, we take η < 2.5 P Tcut 0 GeV 5 GeV 10 GeV final states c cc cb b 32.0(2) 3.27(7) 0.41(2) c cb bb b 5.87(8) 1.33(4) 0.228(6) c cc cc c 69.28) 2.60(8) 0.225(8) b bb bb b 0.401(3) 0.183(3) (7)

24 d dm (nb/gev) E-3 ~145GeV 3c 2cb c2b 3b 1E-4 1E M (GeV) Figure: The differential cross sections, with M being the invariant mass of the final states and s=14 TeV.

25 100 (nb) 10 n=1 n=2 n=3 (nb) 0.1 n=1 n=2 n=3 n= n=6 n=5 n= n=6 n= P Tmin (GeV) P Tmin (GeV) 20 Figure: 1:gg c cc cc c and 2:gg b bb bb b, with n being the number of final particles who has P T > P Tmin, and with s=14 TeV.

26 10 20 (nb) 10 n=1 n=2 1(nb) n=1 n=2 n=3 1 n=3 n=4 n= P Tmin (GeV) 10 P Tmin (GeV) 20 Figure: gg c cc cb b,with n being the number of four c( c) quarks who has P T > P Tmin and no cut for two b quarks in first fig and both b quarks P T > 10 GeV in the second fig, and with s=14 TeV. 1(nb) n=3 n=1 n=2 1 (nb) n=3 n=2 n=1 n=4 0.1 n= P Tmin (GeV) P Tmin (GeV) 20 Figure: gg c cb bb b,with n being the number of four b( b) quarks who has P T > P Tmin and no cut for two c quarks in first fig and both c quarks P T > 10 GeV in the second fig, and with s=14 TeV.

27 Thanks!