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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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
Answer :Yes
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。
Increase ofhas been shown to be at most
by Froissart (1961) using Analyticity and Unitarity.
Soft Pomeron fit : DonnachieLandshoff
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
with
at high energies.
M : proton mass
ν, k : incident proton energy, momentum in the laboratory system
6
7
(as example)
8
8
and the fitting is done by three parameters:
giving the least .
These predict at higher energies including LHC energies.
9
9
LHC
LHC
ISR(=2100GeV)
(a) All region
Predictions for and
The fit is done for data up to ISR
LHC
As shown by arrow.
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10
(b)
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11
ー
ｐｐ
Universal for all hadronic scatterings ?
COMPETE collab. (adopted in Particle Data Group)
Ferreiro,Iancu,Itakura(KEK),McLerran(Head of TH group,RIKENBNL)’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
for
through search for simultaneous best fit toexperimental.
14
14
energy. So, will be determined with good accuracy.
with reasonable accuracy.
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
√
●
NonRegge comp.(parabola)
1 10 102 103 104 105 106 log ν(GeV)
Tot. cross sec.= NonReggeon comp. + Reggeon(P’) comp.
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
NonRegge comp(parabola)
●
1 10 102 103logν(GeV)
Fig.2 πp
17

, pp Scattering
pp
σtot
ー
For pp scatterings
We have data in TeV.
σtot = Bｐｐ(log s/s0)2 + Z (+ ρ trajectory)
in highenergies.
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
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18
Estimated Bπｐ , BＫｐ have large uncertainties.
No Data
No Data
Ｋｐ
Ｋ+ｐ
πｐ
π+ｐ
19
19
ー
ｐｐ
: Ecm = 0.9TeV SPS; 1.8TeV Tevatron
πｐ ： 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
ＦＥＳＲ(1): a kind of P’ sum rule
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20
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 πｐ(ν)= fπ+ｐ(ν)* , fＫｐ(ν) = fＫ+ｐ(ν)*
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21
average of πｐ, π+ｐ； Ｋｐ, 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)
Im F()asymp(ν) = βV/m (ν/m)αV(0) ρtrajecctory:αV(0) ~0.5
βＰ’ , βV is Negligible to σtot(= 4π/k Im F(ν) ) in high energies.
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22
has open(meson) ch. below ,and div. above th.
No such effects in .
RHS is calculable from
The lowenergy ext. of Im Fasymp.
LHS is estimated from
Lowenergy exp.data.
23
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 highenergy from lowenergy (FESR1）
Moment sum rule において、n=1 とおくと P’ sum rule に reduce.
24
in lowenergy regions should coincide with
the lowenergy extension of the asymptotic
formula
highenergy parameters:
Very Important Point
25
in πｐ & π+ｐ
the more accurate
c2 (and Bπｐ)obtained.
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
27
27
No FESR
FESR used
c2=(164±29)・105 c2=(121±13)・105
Bπｐ＝0.411±0.073mb Bπｐ＝0.304±0.034mb
FESR integral
Fitted region
Fitted region
πｐ
π+ｐ
much improved
28
28
No FESR
FESR used
Fitted region
FESR integral
Fitted region
c2=(266±95)・104 c2=(176±49)・104
BＫｐ＝0.535±0.190mb BＫｐ＝0.354±0.099mb
large uncertainty much improved
29
29
ー
No FESR
FESR used
FESR integral
Fitted region
large
Fitted region
large
c2=(491±34)・104 c2=(504±26)・104
Bｐｐ＝0.273±0.019mb Bｐｐ＝0.280±0.015mb
Improvement is not remarkable in this case.
30
30
FESR used
No FESR
Bπｐ≠? Bｐｐ =? BＫｐ
No definite conclusion in this case.
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31
we have analyzed π±ｐ;Ｋ±ｐ; ,ｐｐ independently.
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32
Ｋｐ
πｐ
ｐｐ
Universality of B
suggested.
Use of FESR is essential
to lead tothis conclusion.
gluon scatt. gives dominant cont. at very high energies( flav. ind. ).
approx. satisfy ratio predicted by quark model.
2:2:3
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33
Our results
predicts at 7TeV
at 14TeV
at 335TeV
Our Conclusions at 7TeV, 14TeV
will be tested by LHC TOTEM.
34
ref.
IshidaIgi (this work)
IgiIshida (2005)
BlockHalzen (2005)
COMPETE (2002)
Landshoff (2007)
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35
IshidaIgi’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 ultrahigh energies including GZK
Fitted energy region
From Resonances
Cosmic rays
GZK
ν=6×1010GeV
Tevatron
SPS
LHC
Ecm=7, 14TeV
NonRegge
comp.
(parabola)
Define
We obtain