高エネルギーでのハドロン全断面積の
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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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4319122

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

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


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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

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

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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


Ncreasing tot c s

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 = the ratio of the real to imaginary part of

7


How to predict and for pp at lhc based on fesr duality

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.

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  • 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.

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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

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


Main topic universal rise of tot

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.

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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.

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  • We attempt to obtain

    for

    through search for simultaneous best fit toexperimental.

14

14


New attempt for

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


Practical approach for search of b

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.

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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

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


Scatterings

πp , Kp Scatterings

  • No Data in TeV

     Estimated Bπp , BKp have large uncertainties.

No Data

No Data

K-p

K+p

πp

π+p

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19


Test of universality of b

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

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)*

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Kinematics1

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.

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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 1 k igi prl 9 1962 76

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.

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  • 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 n 1 for scattering

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)

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26


N 1 dependence of the result

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)

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27


Result of the fit to tot

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

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28


Result of the fit to tot1

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

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Result of the fit to tot2

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.

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30


Test of the universal rise

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.

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Concluding remarks

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.

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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

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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.

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  • 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.

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Very important point

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

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 remarks1

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

Appendices:FESR(1)

Define

We obtain


Fesr 2

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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