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高エネルギーでのハドロン全断面積の 普遍的増加とＬＨＣでのｐｐ全断面積の予言

高エネルギーでのハドロン全断面積の 普遍的増加とＬＨＣでのｐｐ全断面積の予言. 　　　 理研仁科センター　　　　　　　猪木慶治 　 ２０１１年３月９日　京都大学　基研研究会 　　　　　　素粒子物理学の進展２０１１ Phys.Lett.B670(2009)395 Phys.Rev.D79(2009)096003 +α In collaboration with Muneyuki Ishida. Outline of this talk. Prediction of σ(pp) at 7TeV, 14TeV (LHC)

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高エネルギーでのハドロン全断面積の 普遍的増加とＬＨＣでのｐｐ全断面積の予言

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  1. 高エネルギーでのハドロン全断面積の普遍的増加とＬＨＣでのｐｐ全断面積の予言高エネルギーでのハドロン全断面積の普遍的増加とＬＨＣでのｐｐ全断面積の予言 　　　 理研仁科センター　　　　　　　猪木慶治 　 ２０１１年３月９日　京都大学　基研研究会 　　　　　　素粒子物理学の進展２０１１ Phys.Lett.B670(2009)395 Phys.Rev.D79(2009)096003 +α In collaboration with Muneyuki Ishida

  2. Outline of this talk • Prediction of σ(pp) at 7TeV, 14TeV (LHC) • Test of Universality (Blog2s ) Is B universal between 2 body had. scatt.? Answer :Yes • σ（＋）：parabola as function of logν • 高エネルギーのデータを使って　B　を決めるのが普通、parabola左側の共鳴領域のデータをも使うことができ、Ｂ の決定の精度大。 Universality

  3. 5. それをつかって、ＬＨＣにおいて、7TeV, 14TeV での予言。さらに、他のグループではできないπｐ、Ｋｐの予言。 6. 最後にＧＺＫエネルギー（Ｅ＝３３５ＴｅＶ）を含む超高エネルギーでの予言 Auger 観測所との比較が楽しみ。

  4. Test of Universality Increase ofhas been shown to be at most by Froissart (1961) using Analyticity and Unitarity. Soft Pomeron fit : Donnachie-Landshoff σtot ~ s0.08 but violates unitarity COMPETE collab.(PDG) further assumed for all hadronic scattering to reduce the number of adjustable parameters based on the arguments of CGC(Color Glass Condensate) of QCD. 4 4

  5. Particle Data Group (by COMPETE collab.) The upper side：σ σ The lower side：ρ－ratio B (Coeff. of Assumed to be universal Theory:Colour Glass Condensate of QCD sug. ρ Not rigorously proved from QCD Test of univ. of B:necessary even empirically. 5 5

  6. Ｉncreasing tot.c.s. • Consider the crossing-even f.s.a. with • We assume at high energies. M : proton mass ν, k : incident proton energy, momentum in the laboratory system 6

  7. The ratio • The ratio = the ratio of the real to imaginary part of 7

  8. How to predict σ and ρ for ppat LHC based on FESR duality? (as example) • We searched for simultaneous best fit of σ and ρ up to some energy(e.g.,ISR) in terms of high-energy parameters constrained by FESR. • We then predicted and in the LHC regions. 8 8

  9. Both and data are fitted through two formulas simultaneously with FESR as a constraint. • FESR is used as constraint of and the fitting is done by three parameters: giving the least . • Therefore, we can determine all the parameters These predict at higher energies including LHC energies. 9 9

  10. LHC LHC ISR(=2100GeV) (a) All region • : High energy region Predictions for and The fit is done for data up to ISR LHC As shown by arrow. 10 10 (b)

  11. Summary of Pred. for and at LHC • Predicted values of agree with pp exptl. data at cosmic-ray regions within errors. • It is very important to notice that energy range of predicted is several orders of magnitude larger than energy region of the input. • Now let us test the universality of B. 11 11

  12. ー ｐｐ Main Topic:Universal Rise of σtot ? • B (coeff. of (log s/s0)2) : Universal for all hadronic scatterings ? • Phenomenologically B is taken to be universal in the fit to πｐ,Ｋｐ,,ｐｐ,∑ｐ,γｐ, γγforward scatt. COMPETE collab. (adopted in Particle Data Group) • Theoretically Colour Glass Condensate of QCD suggests the B universality. Ferreiro,Iancu,Itakura(KEK),McLerran(Head of TH group,RIKEN-BNL)’02 Not rigourously proved yet only from QCD.  Test of Universality of B is Necessary even empirically. 12 12

  13. Particle Data Group (by COMPETE collab.) The upper side：σ The lower side：ρ－ratio B (Coeff. of Assumed to be universal Theory:Colour Glass Condensate of QCD sug. Not rigorouslyproved from QCD Test of univ. of B:necessary even empirically. 13 13

  14. We attempt to obtain for through search for simultaneous best fit toexperimental. 14 14

  15. New Attempt for • In near future, will be measured at LHC energy. So, will be determined with good accuracy. • On the other hand, have been measured only up to k=610 GeV. So, one might doubt to obtain for (as well as ), with reasonable accuracy. • We attack this problem in a new light. 15

  16. σtot(mb) - 100 50 40 - Fig.1 pp, pp Fig.1 pp, pp s = 60 GeV ISR √ √ Tevatron s= 1.8 TeV ● ● ● ● ● SPS s = 0.9 TeV √ ● Non-Regge  comp.(parabola) 1 10 102 103 104 105 106 log ν(GeV) Practical Approachfor search ofB Tot. cross sec.= Non-Reggeon comp. + Reggeon(P’) comp. • Non-Reg. comp. shows shape of parabola as a fn. of logν with a min. • Inf. of low-energy res. gives inf. on P’ term. Subtracting this P’ term from σtot(+), we can obtain the dash-dotted line(parabola). • We have good data for large values of log ν compared with LHS, so (ISR, SPS, Tevatron)-data is most important for det. of c2(pp)(or Bpp) with good accuracy. 16

  17. σtot (mb) Fig.2 πp 50 40 30 Resonances ↓ √ s = 26.4 GeV kL = 610 GeV - √ s = 26.4 GeV (cf. with pp, pp). highest energy Non-Regge  comp(parabola) ● 1 10 102 103logν(GeV) Fig.2 πp • σtot measured only up to • So, estimated Bπp • may have large uncertainty. • The πp has many res. at low energies, however. • So, inf. on LHS of parabola obtained by subtracting P’ term from σtot(+) is very helpful to obtain accurate value of B(πp). • (res. with k < 10GeV). • ( Kp : similar to πp ) . 17

  18. Fitting high-energy data - , pp Scattering pp σtot ー For pp scatterings We have data in TeV. σtot = Bｐｐ(log s/s0)2 + Z (+ ρ trajectory) in high-energies. parabola of log s Tevatron Ecm=1.8TeV SPS Ecm<0.9TeV ー ｐｐ ISR Ecm<63GeV CDF D0 Bｐｐ= 0.273(19) mb estimated accurately. Depends the data with the highest energy. (CDF D0) 　ｐｐ Fitted energy region 18 18

  19. πｐ , Ｋｐ Scatterings • No Data in TeV  Estimated Bπｐ , BＫｐ have large uncertainties. No Data No Data Ｋ-ｐ Ｋ+ｐ πｐ π+ｐ 19 19

  20. ー ｐｐ Test of Universality of B • Highest energy of Experimetnal data: : Ecm = 0.9TeV SPS; 1.8TeV Tevatron π-ｐ ： Ecm < 26.4GeV Ｋｐ ： Ecm < 24.1GeV No data in TeV B : large errors. Bｐｐ = 0.273(19) mb Bπｐ= 0.411(73) mb  Bｐｐ =? Bπｐ=? BＫｐ　? BＫｐ = 0.535(190) mb No definite conclusion • It is impossible to test of Universality of B only by using data in high-energy regions. • We attack this problem using duality constraint from 　 ＦＥＳＲ(1): a kind of P’ sum rule 20 20

  21. Kinematics ν :Laboratory energy of the incident particle s =Ecm2= 2Mν+M2+m2~ 2Mν M : proton mass of the target. Crossing transf. νー ν m : mass of the incident particle m=mπ , mＫ , M for πｐ； Ｋｐ；ｐｐ; k = (ν2 –m2)1/2 : Laboratory momentum~ν Forward scattering amplitudes fap(ν): a = ｐ,π+,Ｋ+ Im fap (ν) = (k / 4 π)σtotap : optical theorem Crossing relation for forward amplitudes: f π-ｐ(-ν)= fπ+ｐ(ν)* , fＫ-ｐ(-ν) = fＫ+ｐ(ν)* 21 21

  22. Kinematics • Crossing-even amplitudes : F(+)(ーν)=F(+)(ν)* average of π-ｐ, π+ｐ； Ｋ-ｐ, Ｋ+ｐ；ｐｐ, Im F(+)asymp(ν) = βＰ’/m (ν/m)α’(0) +(ν/m2)[c0+c1log ν/m +c2(log ν/m)2] βＰ’ term : P’trajecctory (f2(1275)): αＰ’(0) ~ 0.5 : Regge Theory c0,c1,c2terms: corresponds to Z + B (log s/s0)2 c2 is directly related with B . (s～2Mν) • Crossing-odd amplitudes : F(-)(ーν)= ーF(-)(ν)* Im F(-)asymp(ν) = βV/m (ν/m)αV(0) ρ-trajecctory:αV(0) ~0.5 βＰ’ , βV is Negligible to σtot(= 4π/k Im F(ν) ) in high energies. 22 22

  23. ＦＥＳＲ(1)　Ｄｕａｌｉｔｙ • Remind that the P’ sum rule in the introd.. • Take two N’s(FESR1) • Taking their difference, we obtain has open(meson) ch. below ,and div. above th. • If we choose to be fairly larger than we have no difficulty. ( : similar) No such effects in . RHS is calculable from The low-energy ext. of Im Fasymp. LHS is estimated from Low-energy exp.data. 23

  24. FESR(1) corresponds to n = -1K.IGI.,PRL,9(1962)76 The following sum rule has to hold under the assumption that there is no sing.with vac.q.n. except for Pomeron(P). Evid.that this sum rule not hold  pred. of the traj. with and the f meson was discovered on the 0.0015 -0.012 2.22 VIP: The first paper which predicts high-energy from low-energy (FESR1） Moment sum rule において、n=-1 とおくと P’ sum rule に reduce. 24

  25. Average of in low-energy regions should coincide with the low-energy extension of the asymptotic formula • This relation is used as a constraint between high-energy parameters: Very Important Point 25

  26. Choice of N1 for πｐ Scattering • Many resonances Various values of N1 in π-ｐ & π+ｐ • The smaller N1 is taken, the more accurate c2 (and Bπｐ)obtained. • We take various N1 corresponding to peak and dip positions of resonances. (except for k=N1=0.475GeV) For each N1, FESR is derived. Fitting is performed. The results checked. Δ(1232) N(1520) N(1650,75,80) - Δ(1905,10,20) Δ(1700) 26 26

  27. N1 dependence of the result • # of Data points : 162. • best-fitted c2 : very stable. • We choose N1=0.818GeV • as a representative. • Compared with the fit by • 6 param fit with • No use of FESR(No SR) 27 27

  28. Result of the fit to σtotπｐ No FESR FESR used c2=(164±29)・10-5 c2=(121±13)・10-5 Bπｐ＝0.411±0.073mb Bπｐ＝0.304±0.034mb FESR integral Fitted region Fitted region π-ｐ π+ｐ much improved 28 28

  29. Result of the fit to σtotＫｐ No FESR FESR used Fitted region FESR integral Fitted region c2=(266±95)・10-4 c2=(176±49)・10-4 BＫｐ＝0.535±0.190mb BＫｐ＝0.354±0.099mb large uncertainty much improved 29 29

  30. ー Result of the fit to σtotｐｐ,ｐｐ No FESR FESR used FESR integral Fitted region large Fitted region large c2=(491±34)・10-4 c2=(504±26)・10-4 Bｐｐ＝0.273±0.019mb Bｐｐ＝0.280±0.015mb Improvement is not remarkable in this case. 30 30

  31. Test of the Universal Rise • σtot= B (log s/s0)2 + Z FESR used No FESR • Bπｐ= Bｐｐ= BＫｐ within 1σ • Universality suggested. Bπｐ≠? Bｐｐ =? BＫｐ No definite conclusion in this case. 31 31

  32. Concluding Remarks • In order to test the universal rise of σtot , we have analyzed π±ｐ;Ｋ±ｐ; ,ｐｐ independently. • Rich information of low-energy scattering data constrain,through FESR(1), the high-energy parameters B to fit experimental σtot and ρratios. • The values of B are estimated individually for three processes. 32 32

  33. Ｋｐ πｐ ｐｐ • We obtain Bπｐ= Bｐｐ= BＫｐ. Universality of B suggested. Use of FESR is essential to lead tothis conclusion. • Universality of B suggests gluon scatt. gives dominant cont. at very high energies( flav. ind. ). • It is also interesting to note that Z for approx. satisfy ratio predicted by quark model. 2:2:3 33 33

  34. Our results predicts at 7TeV at 14TeV at 335TeV Our Conclusions at 7TeV, 14TeV will be tested by LHC TOTEM. • Our Conclusions will be tested by LHC TOTEM. 34

  35. Finally, let us compare our pred. at 14TeV with other pred. ref. Ishida-Igi (this work) Igi-Ishida (2005) Block-Halzen (2005) COMPETE (2002) Landshoff (2007) • Pred. in various models have a wide range. • The LHC(TOTEM) will select correct one. 35 35

  36. Very Important Point Ishida-Igi’approach gives predictions not only for pp but also for πp, Kp scatterings, although experiments are not so easy in the very near future.

  37. Predictions for up to ultra-high energies including GZK Fitted energy region From Resonances Cosmic rays GZK ν=6×1010GeV Tevatron SPS LHC Ecm=7, 14TeV Non-Regge comp. (parabola)

  38. Concluding Remarks の続き • この図からわかるように、入射陽子が宇宙背景輻射の光子と衝突してエネルギーを失うＧＺＫエネルギー（335TeV)でも、我々の予言の誤差は驚くほど小さくなっている。 • Bの値は最高エネルギーのデータポイントの値に比較的強く依存する。 の値の予言のためにも、 LHCでの測定は大変重要。 • また、LHCの測定で、CDF,D0のどちらが正しいかも決まる。

  39. Appendices:FESR(1) Define We obtain

  40. FESR(2) • Dolen-Horn-Schmid : (nth)-moment sum rule において、 • n=1とおくと、FESR(2) • n= -1とおくと、FESR(1)=P’ sum rule(1962)

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