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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 PowerPoint PPT Presentation


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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.     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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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

In collaboration with Muneyuki Ishida


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


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。


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


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


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


The ratio

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

7


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


  • 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


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)


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


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


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


  • We attempt to obtain

    for

    through search for simultaneous best fit toexperimental.

14

14


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


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


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


Fitting high-energy data

-

, pp Scattering

pp

σtot

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

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


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


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


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


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


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


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


  • 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


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


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


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


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


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


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


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


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


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


  • 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


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.


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)


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。


Appendices:FESR(1)

Define

We obtain


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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