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34. Monte Carlo numbering scheme 1

34. MONTE CARLO PARTICLE NUMBERING SCHEME

Revised June 2006 by L. Garren (), I.G. Knowles (Edin- f. The sixth digit nr is used to label radially excited burgh U.), S. Navas (U. Granada), P. Richardson (Durham U.), above the . T. Sj¨ostrand (Lund U.), and T. Trippe (LBNL). g. Numbers have been assigned for complete nr =0S-and The Monte Carlo particle numbering scheme presented here is P -wave , even where states remain to be identified. intended to facilitate interfacing between event generators, detector h. In some instances assignments within the qq¯ model simulators, and analysis packages used in particle . The are only tentative; here best guess assignments are made. numbering scheme was introduced in 1988 [1] and a revised i. Many states appearing in the Meson Listings are not yet version [2,3] was adopted in 1998 in order to allow systematic inclusion assigned within the qq¯ model. Here nq2−3 and nJ are of model states which are as yet undiscovered and hypothetical assigned according to the state’s likely flavors and ; all such as SUSY particles. The numbering scheme is used in such unassigned isoscalar states are given the flavor several event generators, e.g. HERWIG and PYTHIA/JETSET, and code 22. Within these groups nL =0, 1, 2,... is used to in the /HEPEVT/ [4] standard interface. distinguish states of increasing . These states are flagged The general form is a 7–digit number: using n = 9. It is to be expected that these numbers will evolve as the of the states are elucidated. Codes are assigned to all mesons which are listed in the one-page table ±nn n n n n n . L q1 q2 q3 J at the end of the Meson Summary Table as long as they have a prefered or established spin. Additional heavy meson states This encodes information about the particle’s spin, flavor content, and expected from heavy quark spectroscopy are also assigned internal numbers. The details are as follows: codes. 1. Particles are given positive numbers, negative 6. The numbering of is again guided by the nonrelativistic + numbers. The PDG convention for mesons is used, so that K , see Table 14.6. and B+ are particles. a. The numbers specifying a ’s quark content are such 2. and are numbered consecutively starting from 1 that in general n ≥ n ≥ n . and 11 respectively; to do this they are first ordered by family q1 q2 q3 b. Two states exist for J =1/2 baryons containing 3 different and within families by weak . types of quarks. In the lighter baryon (Λ,Ξ,Ω,...)thelight 3. In composite quark systems (diquarks, mesons, and baryons) quarks are in an antisymmetric (J = 0) state while for n are quark numbers used to specify the quark content, while 0 q1−3 the heavier baryon (Σ ,Ξ ,Ω ,...)theyareinasymmetric the rightmost digit n =2J + 1 gives the system’s spin (except J (J = 1) state. In this situation n and n are reversed for for the K0 and K0 ). The scheme does not cover particles of spin q2 q3 S L the lighter state, so that the smaller number corresponds to J>4. the lighter baryon. 4. Diquarks have 4-digit numbers with n ≥ n and n =0. q1 q2 q3 c. At present most Monte Carlos do not include excited baryons 5. The numbering of mesons is guided by the nonrelativistic (L–S and no systematic scheme has been developed to denote decoupled) quark model, as listed in Tables 14.2 and 14.3. them, though one is foreseen. In the meantime, use of the a. The numbers specifying the meson’s quark content conform PDG 96 [5] numbers for excited baryons is recommended. ≥ to the convention nq1 =0andnq2 nq3 . The special case d. For states n =9,nrnLnq1 nq2 gives the four 0 ≥ ≥ ≥ KL is the sole exception to this rule. quark numbers in order nr nL nq1 nq2 , nq3 gives the b. The quark numbers of flavorless, light (u, d, s)mesonsare: antiquark number, and n =2J + 1, with the assumption 0 0 J 11 for the member of the isotriplet (π ,ρ ,...), 22 for the that J =1/2 for the states currently reported. lighter isosinglet (η,ω,...), and 33 for the heavier isosinglet 7. The , when considered as a gauge , has official number (η ,φ,...). Since isosinglet mesons are often large mixtures 21. In codes for , however, 9 is used to allow a notation of uu + dd and ss states, 22 and 33 are assigned by mass and in close analogy with that of . do not necessarily specify the dominant quark composition. 0 8. The and odderon trajectories and a generic reggeon c. The special numbers 310 and 130 are given to the KS and 0 trajectory of states in QCD are assigned codes 990, 9990, and 110 KL respectively. respectively, where the final 0 indicates the indeterminate nature d. The fifth digit nL is reserved to distinguish mesons of the of the spin, and the other digits reflect the expected “valence” same total (J) but different spin (S) and orbital (L) angular flavor content. We do not attempt a complete classification of all quantum numbers. For J>0thenumbersare: reggeon trajectories, since there is currently no need to distinguish − (L, S)=(J 1, 1) nL =0, (J, 0) nL =1, (J, 1) nL =2 a specific such trajectory fromitslowest-lyingmember. and (J +1, 1) nL = 3. For the exceptional case J =0the 9. Two-digit numbers in the range 21–30 are provided for the numbers are (0, 0) nL =0and(1, 1) nL =1(i.e. nL = L). gauge and Higgs. See Table 34.1. 10. Codes 81–100 are reserved for -specific pseudoparticles and concepts. 11. The search for physics beyond the Standard Model is an active Table 34.1: Meson numbering logic. Here qq stands for area, so these codes are also standardized as far as possible. n 2 n 3. q q a. A standard fourth generation of is included by analogy with the first three. − L = J 1, S =1 L = J, S =0 L = J, S =1 L = J +1,S =1 b. The and the boson content of a two-Higgs-doublet J code JPC L code JPC L code JPC L code JPC L scenario and of additional SU(2)×U(1) groups are found in −+ ++ the range 31–40. 0 ———00qq10 0 ———10qq10 1 c. “One-of-a-kind” exotic particles are assigned numbers in the 1 00qq31−− 0 10qq31+− 1 20qq31++ 1 30qq31−− 2 range 41–80. 2 00qq52++ 1 10qq52−+ 2 20qq52−− 2 30qq52++ 3 d. Fundamental supersymmetric particles are identified by 3 00qq73−− 2 10qq73+− 3 20qq73++ 3 30qq73−− 4 adding a nonzero n to the . The ++ −+ −− ++ of a boson or a left-handed has n = 1 while the 4 00qq94 3 10qq94 4 20qq94 4 30qq94 5 superpartner of a right-handed fermion has n =2.When mixing occurs, such as between the winos and charged to give , or between left and right e. If a set of physical mesons correspond to a (non-negligible) , the lighter physical state is given the smaller basis mixture of basis states, differing in their internal number. numbers, then the lightest physical state gets the smallest e. states have n = 3, with technifermions treated basis state number. For example the K1(1270) is numbered like ordinary fermions. States which are ordinary color 1 10313 (1 P1 K1B)andtheK1(1400) is numbered 20313 singlets have nr = 0. Color octets have nr =1.Ifastate 3 (1 P1 K1A). has non-trivial quantum numbers under the groups 2 34. Monte Carlo particle numbering scheme

SU(3)1 × SU(3)2, the quantum numbers are specified by QUARKS DIQUARKS tech,ij,wherei and j are 1 or 2. nL is then 2i + j.The d 1 (dd)1 1103 coloron, V8, is a heavy gluon color octet and thus is 3100021. f. Excited (composite) quarks and leptons are identified by u 2 (ud)0 2101 s 3 setting n =4. (ud)1 2103 c 4 g. Within several scenarios of new physics, it is possible to (uu)1 2203 have colored particles sufficiently long-lived for color-singlet b 5 t 6 (sd)0 3101 hadronic states to form around them. In the context of supersymmetric scenarios, these states are called R-hadrons, b 7 (sd)1 3103 t 8 since they carry odd R-. R- codes, defined here, (su)0 3201 should be viewed as templates for corresponding codes also LEPTONS (su)1 3203 in other scenarios, for any long-lived particle that is either e− 11 an unflavored color octet or a flavored color triplet. The (ss)1 3303 ν 12 R-hadron code is obtained by combining the SUSY particle e (cd)0 4101 µ− 13 code with a code for the light degrees of freedom, with as (cd)1 4103 ν 14 many intermediate zeros removed from the former as required µ (cu)0 4201 to make place for the latter at the end. (To exemplify, a τ − 15 (cu)1 4203 sparticle n00000n˜q combined with quarks q1 and q2 obtains ντ 16 − (cs)0 4301 code n00n˜qnq1 nq2 nJ .) Specifically, the new-particle spin τ 17 decouples in the limit of large , so that the final nJ (cs)1 4303 ντ 18 digit is defined by the spin state of the light-quark system (cc)1 4403 alone. An appropriate number of nq digits is used to define EXCITED (bd)0 5101 the ordinary-quark content. As usual, 9 rather than 21 is PARTICLES used to denote a gluon/ in composite states. The sign ∗ (bd)1 5103 d 4000001 of the hadron agrees with that of the constituent new particle ∗ u 4000002 (bu)0 5201 (a color triplet) where there is a distinct new , ∗ e 4000011 (bu)1 5203 and else is defined as for normal hadrons. Particle names are ∗ ν 4000012 R with the flavor content as lower index. A non-exhaustive e (bs)0 5301 list of R-hadron codes is given below. (bs)1 5303 GAUGE AND 12. Occasionally program authors add their own states. To avoid HIGGS BOSONS (bc)0 5401 confusion, these should be flagged by setting nnr = 99. g (9) 21 (bc)1 5403 13. Concerning the non-99 numbers, it may be noted that only γ 22 (bb)1 5503 quarks, excited quarks, squarks, and diquarks have n =0;only q3 Z0 23 diquarks, baryons (including ), and the odderon have TECHNICOLOR W + 24 nq1 = 0; and only mesons, the reggeon, and the pomeron have 0 0 PARTICLES n =0andn = 0. Concerning mesons (not antimesons), if n h / 25 0 q1 q2 q1 0 πtech 3000111 is odd then it labels a quark and an antiquark if even. Z /Z2 32 + 14. Nuclear codes are given as 10-digit numbers ±10LZZZAAAI. 0 πtech 3000211 Z /Z3 33 0 For a (hyper)nucleus consisting of n , n and + π 3000221 p n W /W 34 tech n Λ’s, A = n + n + n gives the total , Z = n 2 0 Λ p n Λ p 0 0 ηtech 3100221 the total and L = nΛ the total number of strange quarks. H /H2 35 0 I gives the isomer level, with I = 0 corresponding to the ground 0 0 ρtech 3000113 A /H3 36 + state and I>0toexcitations,see[9], where states denoted + ρ 3000213 H 37 tech m, n, p, q translate to I =1− 4. As examples, the deuteron 0 ωtech 3000223 is 1000010020 and 235U is 1000922350. To avoid ambiguities, nuclear codes should not be applied to a single hadron, like p, n V8 3100021 0 1 or Λ , where quark-contents-based codes already exist. πtech,22 3060111 8 πtech,22 3160111 This text and lists of particle numbers can be found on the ρtech,11 3130113 WWW [6]. The StdHep Monte Carlo standardization project [7] ρtech,12 3140113 maintains the list of PDG particle numbers, as well as numbering ρtech 21 3150113 schemes from most event generators and software to convert between , the different schemes. ρtech,22 3160113 References: 1. G.P. Yost et al., Particle Data , Phys. Lett. B204, 1 (1988). 2. I. G. Knowles et al.,in“Physics at LEP2”, CERN 96-01, vol. 2, p. 103. 3. C. Caso et al., , Eur. Phys. J. C3, 1 (1998). 4. T. Sj¨ostrand et al.,in“Z physics at LEP1”, CERN 89-08, vol. 3, p. 327. 5. R.M. Barnett et al.,PDG,Phys.Rev.D54, 1 (1996). 6. pdg.lbl.gov/2006/mcdata/mc particle id contents.html. 7. L. Garren, StdHep, Monte Carlo Standardization at FNAL, Fermilab PM0091 and StdHep WWW site: http://cepa.fnal.gov/psm/stdhep/. 8. S. Eidelman et al.,PDG,Phys.Lett.B592, 1 (2004). 9. G. Audi et al.,Nucl.Phys.A729, 3 (2003) See also http://www.nndc.bnl.gov/amdc/web/nubase en.html. 34. Monte Carlo particle numbering scheme 3

R-HADRONS SUSY LIGHT I =1MESONS LIGHT I =0MESONS 0 0 R 1000993 PARTICLES π 111 (uu, dd,andss Admixtures) gg  + 0 dL 1000001 π 211 R 1009113 0 η 221 gd d a0(980) 9000111 uL 1000002 + + η (958) 331 R 1009213  a0(980) 9000211 gu d sL 1000003 f0(600) 9000221 0  π(1300)0 100111 R 1009223 cL 1000004 guu + f0(980) 9010221 0  a π(1300) 100211 R 1009313 b1 1000005 η(1295) 100221 gd s  a 0 + t1 1000006 a0(1450) 10111 R 1009323 − + f0(1370) 10221 gu s e 1000011 a0(1450) 10211 L η(1405) 9020221 R0 1009333 0 gs s νeL 1000012 π(1800) 9010111 − − η(1475) 100331 R 1091114 µ 1000013 π(1800)+ 9010211 gddd L f0(1500) 9030221 0  ρ(770)0 113 R 1092114 νµL 1000014 gudd + f0(1710) 10331 + − a τ1 1000015 ρ(770) 213 η(1760) 9040221∗ Rguud 1092214 0 b1(1235) 10113 ∗ ++ ντL 1000016 9050221 R 1092224 + f0(2020) guuu  b1(1235) 10213 ∗ dR 2000001 9060221 − 0 f0(2100) R 1093114 1 ∗ gsdd uR 2000002 a (1260) 20113 9070221 0 + f0(2200) Rgsud 1093214 sR 2000003 a1(1260) 20213 η(2225) 9080221∗ 0 +  π1(1400) 9000113 R 1093224 cR 2000004 gsuu + ω(782) 223 −  a π1(1400) 9000213 R 1093314 b2 2000005 φ(1020) 333 gssd  a 0 0 t2 2000006 ρ(1450) 100113 − h1(1170) 10223 Rgssu 1093324  + eR 2000011 ρ(1450) 100213 − − 0 f1(1285) 20223 Rgsss 1093334 µ 2000013 π1(1600) 9010113 R h1(1380) 10333 + − a + R 1000612 τ2 2000015 π1(1600) 9010213 t1d 0 ∗ f1(1420) 20333 0 g 1000021 a1(1640) 9020113 R 1000622 ω(1420) 100223 t1u 0 b a (1640)+ 9020213∗ + χ1 1000022 1 R 1000632 0 f1(1510) 9000223 t1s 0 b ρ(1700) 30113 ∗ χ2 1000023 h1(1595) 9010223 0 + R 1000642 + b ρ(1700) 30213 t1c χ1 1000024 0 ∗ ω(1650) 30223 + 0 b ρ(1900) 9030113 R 1000652 χ3 1000025 φ(1680) 100333 t1b + ∗ 0 b ρ(1900) 9030213 0 χ4 1000035 f2(1270) 225 R 1006113 0 ∗ t1dd1 + b ρ(2150) 9040113 + χ2 1000037 + ∗ f2(1430) 9000225 R 1006211 ρ 9040213 t1ud0  (2150) G 1000039 0 f2(1525) 335 + a2(1320) 115 R 1006213 f2(1565) 9010225 t1ud1 SPECIAL + ++ a2(1320) 215 R 1006223 PARTICLES 0 f2(1640) 9020225 t1uu1 π2(1670) 10115 η2(1645) 10225 R0 1006311 G (graviton) 39 + t1sd0 0 π2(1670) 10215 R 41 0 ∗ f2(1810) 9030225 0 a2(1700) 9000115 R 1006313 c t1sd1 LQ 42 + ∗ η2(1870) 10335 + a2(1700) 9000215 R 1006321 reggeon 110 f2(1910) 9040225 t1su0 0 9010115∗ pomeron 990 π2(2100) + + ∗ f2(1950) 9050225 R 1006323 π2(2100) 9010215 t1su1 odderon 9990 f2(2010) 9060225 0 0 R 1006333 ρ3(1690) 117 t1ss1 + f2(2150) 9070225 ρ3(1690) 217 0 f2(2300) 9080225 ρ3(1990) 9000117 for MC internal + f2(2340) 9090225 use 81–100 ρ3(1990) 9000217 0 ω3(1670) 227 ρ3(2250) 9010117 + φ3(1850) 337 ρ3(2250) 9010217 0 f4(2050) 229 a4(2040) 119 + fJ (2220) 9000229 a4(2040) 219 f4(2300) 9010229 4 34. Monte Carlo particle numbering scheme

STRANGE CHARMED LIGHT BOTTOM MESONS MESONS cc MESONS BARYONS BARYONS 0 + 0 KL 130 D 411 ηc(1S) 441 p 2212 Λb 5122 0 D0 421 − K 310 χc0(1P ) 10441 n 2112 Σ 5112 S D∗(2400)+ ++ b 0 0 10411 ∆ 2224 0 K 311 ηc(2S) 100441 Σ 5212 D∗(2400)0 + b + 0 10421 ∆ 2214 + K 321 J/ψ(1S) 443 0 Σ 5222 K∗(800)0 9000311∗ ∗ + ∆ 2114 b 0 D (2010) 413 h (1P ) 10443 − ∗− ∗ 0 c ∆ 1114 Σ 5114 K∗(800)+ 9000321∗ D (2007) 423 b 0 χ 1(1P ) 20443 ∗0 + c Σ 5214 ∗ 0 D1(2420) 10413 STRANGE b K0 (1430) 10311 ψ(2S) 100443 ∗+ ∗ + 0 BARYONS Σ 5224 K0 (1430) 10321 D1(2420) 10423 ψ(3770) 30443 b + Λ 3122 − 0 D1(H) 20413 Ξ 5132 K(1460) 100311 ψ(4040) 9000443 Σ+ 3222 b + D (2430)0 0 Ξ0 5232 K(1460) 100321 1 20423 ψ(4160) 9010443 Σ 3212 b 0 ∗ ∗ + − − K(1830) 9010311 D2(2460) 415 Σ 3112 Ξb 5312 ψ(4415) 9020443 ∗+ d + ∗ ∗ 0 Σ 3224 0 K(1830) 9010321 D2(2460) 425 Ξ 5322 χc2(1P ) 445 ∗0 d b + Σ 3214 ∗− ∗ 0 9020311∗ D 431 ∗ ∗− K0 (1950) s χc2(2P ) 100445 Σ 3114d Ξb 5314 ∗ + ∗ ∗ + 0 ∗0 K0 (1950) 9020321 Ds0(2317) 10431 Ξ 3322 Ξ 5324 − b ∗ 0 ∗+ − Ds 433 bb MESONS Ξ 3312 K (892) 313 ∗0 d Ωb 5332 ∗ + + η (1S) 551 Ξ 3324 ∗− K (892) 323 Ds1(2536) 10433 b ∗− d Ω 5334 + Ξ 3314 b 0 D 1(2460) 20433 χb0(1P ) 10551 − 0 K1(1270) 10313 s Ω 3334 Ξ 5142 + ∗ + η (2S) 100551 bc K1(1270) 10323 Ds2(2573) 435 b + CHARMED Ξbc 5242 0 χb0(2P ) 110551 K1(1400) 20313 BARYONS Ξ0 5412 + BOTTOM η (3S) 200551 bc K1(1400) 20323 b + + MESONS Λc 4122 Ξ 5422 ∗ 0 0 χb0(3P ) 210551 bc K (1410) 100313 ++ ∗0 B 511 Σc 4222 ∗ + + Υ (1S) 553 Ξbc 5414 K (1410) 100323 B 521 Σ+ 4212 ∗+ 0 ∗ ∗0 h (1P ) 10553 c Ξ 5424 K1(1650) 9000313 B0 10511 b 0 bc ∗+ Σc 4112 0 + ∗ χ 1(1P ) 20553 Ω 5342 K1(1650) 9000323 B0 10521 b ∗++ bc Σ 4224 0 ∗ 0 ∗0 Υ1(1D) 30553 c K (1680) 30313 B 513 ∗+ Ωbc 5432 ∗+ Σ 4214 ∗ + B 523 Υ (2S) 100553 c Ω∗0 5434 K (1680) 30323 0 ∗0 bc B1(L) 10513 Σc 4114 + ∗ 0 hb(2P ) 110553 K2 (1430) 315 + + Ωbcc 5442 B1(L) 10523 Ξc 4232 ∗ + χb1(2P ) 120553 ∗+ K (1430) 325 0 0 Ω 5444 2 Ξc 4132 bcc 0 B1(H) 20513 Υ1(2D) 130553 − K2(1580) 9000315 + + Ξ 5512 Ξc 4322 bb + B1(H) 20523 Υ (3S) 200553 0 K2(1580) 9000325 ∗0 0 Ξ 5522 B 515 Ξc 4312 bb 0 2 hb(3P ) 210553 ∗− K2(1770) 10315 ∗+ ∗+ Ξc 4324 Ξbb 5514 + B2 525 χb1(3P ) 220553 K2(1770) 10325 ∗0 ∗0 0 Ξc 4314 Ξ 5524 0 Bs 531 Υ (4S) 300553 bb K2(1820) 20315 0 − ∗0 Ωc 4332 Ω 5532 + Bs0 10531 Υ (10860) 9000553 bb K2(1820) 20325 ∗0 ∗− ∗0 Ωc 4334 Ω 5534 ∗ 0 ∗ Bs 533 Υ (11020) 9010553 + bb K2(1980) 9010315 0 Ξ 4412 0 B 1(L) 10533 cc Ω 5542 K∗(1980)+ 9010325∗ s χb2(1P ) 555 ++ bbc 2 0 Ξcc 4422 ∗0 B 1(H) 20533 η 2(1D) 10555 Ω 5544 0 9020315∗ s b ∗+ bbc K2(2250) ∗0 Ξcc 4414 − B 535 Υ2(1D) 20555 Ω 5554 + 9020325∗ s2 ∗++ bbb K2(2250) + Ξcc 4424 ∗ 0 Bc 541 χb2(2P ) 100555 + K3 (1780) 317 ∗+ Ωcc 4432 ∗ + Bc0 10541 ηb2(2D) 110555 ∗+ K3 (1780) 327 ∗+ Ωcc 4434 0 Bc 543 Υ2(2D) 120555 ++ K3(2320) 9010317 + Ωccc 4444 + Bc1(L) 10543 χb2(3P ) 200555 K3(2320) 9010327 + ∗ 0 Bc1(H) 20543 Υ3(1D) 557 PENTAQUARKS K4 (2045) 319 ∗+ + ∗ + Bc2 545 Υ3(2D) 100557 Θ 9221132 K4 (2045) 329 −− 0 Φ 9331122 K4(2500) 9000319 + K4(2500) 9000329

Footnotes to the Tables: ∗) Numbers or names in bold face are new or have changed since the 2004 Review [8]. a) Particulary in the third generation, the left and right states may mix, as shown. The lighter mixed state is given the smaller number. 0 +  0  0  + b) The physical χ states are admixtures of the pure γ, Z , W , H1 , H2 ,andH states. c) In this draft we have only provided one generic code. More general classifications according to spin, and flavor content would lead to a host of states, that could be added as the need arises. d) Σ∗ and Ξ∗ are alternate names for Σ(1385) and Ξ(1530).