the dispersion relations and analysis of the new lhc data€¦ · o.v. selyugin bltph, jinr “the...
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O.V. Selyugin
BLTPh, JINR
“The dispersion relations and analysis
of the new LHC data ”
Acireale (Italy)
September, 02-08
International workshop Diffraction in High Energy Physics
(“DIFFRACTION-2016")
in collaboration with J.-R. CUDELL
FAGO, Univ. Liege
Contents
* Introduction
* Elastic hadron scattering – new data LHC
* Comparing the data with High Energy Generalized structure model (HEGS)
* Results and Summery
* The real part of the scattering amplitude from the data
* Phenomenological analysis of the new data
* Total cross sections
the new LHC data (elastic scattering)
at 7 and 8 TeV
7 TeV (TOTEM) - t [0.00515 – 0.371] 17.08.2012
7 TeV (ATLAS) - t [0.0062 – 0.3636] 25.08.2014
8 TeV (TOTEM) - t [0.028500 – 0.1947] 12.09.2015
8 TeV (ATLAS) - t [0.01050 – 0.3635] 25.06.2016
8 TeV (TOTEM) - t [0.000741 – 0.201] 11.12.2015
Total cross sections
(98.3 2.8) ;
(98.6 2.2) ;
(99.1 4.3) ;
(98.0 2.5) ;
tot mb
mb
mb
mb
96.07( 1.34)tot mb
TOTEM ATLAS
98.5( 2.9)tot mb
102.9( 2.3)tot mb
95.35( 2.0)tot mb
7000 ;s GeV
8000 ;s GeV
3.1 ;5 mb
7 ;6. mb
1 1 ˆln( )
1 2ˆ( , ) ( ) ( ) ;t sB
emF s t h G t s e 1 1 ˆ/4 ln( )2
3 3ˆ( , ) ( ) ( ) ;t sB
AF s t h G t s e
2 1 3 2ˆ ˆ ˆ ˆ ˆ( , ) ( , ) (
( ,
1 / ) ] ( , ) (1 /
;
) ]
)
B B B
B
odd
F s t F s t R s F s t R
F s
s
t
/
0
2
0
2ˆ
s 4 .
/ ;i
p
s s s
m
e
Extending of model (HEGS1) – O.V. S. Phys.Rev. D 91, (2015) 113003
1 1 ˆ/4 ln( )
2
2 ˆ(( , ) ( )) ;1
B
Odd Odd
t s
A
o
G t st
F s t hr t
e
0
1 0
ˆ ˆ( ) ( ) ln .k st ln
k qB et s
2
9 000 ;
3416; 0.00037
8
980 15| | ;
Gs
n
e
Gt
V
eV
High Energy General Structure (HEGS) model O.V.S. - Eur. Phys. J. C (2012) 72:2073
6
( , )
00
1( , ) ( ) [1 ]
2
h s bF s t b J bq e db
00
( , ) 2 ( ) ( , )h
Bs b q J bq F s q dq
2 21
( , ) [ ]2
s b dzV z bk
UNITARIZATION eikonal representation
1 10.11; 0 ;.24 ;fixed
2
9 000 ; 3416;8
. 8/ N 1 2
GeV Ns
1 2 0
2( 0.14 ;0.82; 0.31; 0.163 ;.8);Odd oh rh h k
1 253.7; 4.45; 0.05.sfR R h
High energy parameters
Low energy parameters
7 TeV (TOTEM) - t [0.00515 – 0.371]
n = 0.94
7 TeV (ATLAS) - t [0.0062 – 0.3636]
n=1.0
8 TeV (TOTEM) - t [0.0285 – 0.1947]
n=0.9
8 TeV (TOTEM) - t [0.000741 – 0.201]
n=0.9
8 TeV (ATLAS) - t [0.01050 – 0.3635]
n=1.0
4 . . .0.24 0.04 ( )UA Coll M Bozzo et al
4 / 2 ., . .0.135 0.015 ( )UA Coll C Augier et al
Problems540CERN pp pp s GeV
. . , . . )55, 8411992 0.24 0.0. 03 (19 OV Selyugin Yad Fiz
Comment
. . , . . 198, 5831995 0.135 0.. 2 )0 0 (17 OV Selyugin Phys Lett B
. , . , . , : 0905.1955( )
2009 0.009
(
0.172
A Kendi E Ferreira T Kodama arXiv hep ph
1800FNAL pp pp s GeV
(71.42 1.55) .tot mb SCINT Coll
(80.03 2.24) .tot mb CDF Coll
Problems
Comment
Very likely that this difference reflects the true errors of
the fitting procedure of the experimental data obtained
by the luminosity independent method.
ch I f
Ch II
Non-exponential behavior (origins)
1. Non-linear Regge trajectory (L. Jenkovsky et al.)
(Pion loops ) Anselm, Gribov, G. Coken-Tannoudji et.al.; Khoze, Martin;
3. Unitarization
2. Different slopes of the other contributions
(real part, odderon, spin-flip amplitude)
Dependence of the slope B(s,t) from the size of
the examined interval t for UA4/2 experiment
triangles – exponential form of F
Circles - + additional term in the slope - sqrt(-t) k
O.V.S. Phys.Lett (1994)
Ch II
2 2 2 2
1( ) 1 ( / 32 ) ( );P Pq C q h q
2 2 2 22 3/2
1 2 2
2
2
2
22
( / 4 )
( / 4
1 14( ) [ (1 ) ( ) ( )
1
8;
1 )]
qq mh q Ln L
qn
q q
2 2 2 22 3/2
1 2 2
2
2
2
22
(1 14( ) [ (1 ) ( ) (
4 / )
()
4
8
/];
1 1)
qq mh q L
qqn
qLn
A.A. Anselm, V.N. Gribov, Phys.Lett. 40B, (1972).
V.A. Khoze, A.D. Martin and M.G. Ryskin, J.Phys.G (2014)
2 2
2 2
2
4 ;
8[ ( ) ];
3
q
q mLn
( )( )( , ) ;Ln sb tF s t es
/
0
2
0
2ˆ
s 4 .
/ ;i
p
s s s
m
e
( )( )( , ) ;b n tL sF s t i es
( )( , ) ;( ) b tLn ssF s t e
Regge representation
COMPETE Collaboration Local DDR
( )( )( ) ( ) [ ].
( ) ( )m
EEC EE E dE P
P P E E E E E E
Integral dispersion relations s
2
0
0
Re ( , ) ( ) [ Im ( , ) / Im ( , 0)]Im ( , 0), , (ln( / ) .ln( / )
dF s t F s t F s t F s t as s t s s
s s d
S.M. Roy (2016)
Re ( ,0) ( ) tan[ ( 1 )]Im ( ,0) /( )2p p
E d EF E E F E
m dE m
Im ( , ) ; ( , ) ( , 0)(1. ).BtF s t he s t s t Bt
27
( , )
00
1( , ) ( ) [1 ]
2
h s bF s t b J bq e db
00
( , ) 2 ( ) ( , )h
Bs b q J bq F s q dq
2 21( , ) [ ]
2s b dzV z b
k
UNITARIZATION eikonal representation
( );( , ) ( )Born btLn sF s t s e
Pi-meson cloud
J.Pumplin, G.L. Kane, 1975, Phys.Rev. D11; pi-mezon scattering
O.V.S., S. Goloskokov, 1980, Yad.Fiz. 31, pp-scattering
2 22 2
2 2 3/21
( )( , ) (1 ) );
( 1)! ( ))
bn
n
n thT s t is b n t e
n n t
S.V. Goloskokov, O.V.S., Mod.Phys.Lett. A9 (1994)
Table rho, B 541 and 1800
Seminar in the TOTEM O.V.S. (2009) ; and
J.-R. Cudell, O.V.S. - Phys.Rev.Lett. (2009)
ch II f
/2( , ) ( )4 0.38938
h BttotF s t i e
2/2( , ) ( )4 0.38938
h Bt CttotF s t i e
2( 4 2 )] 2
.( , ) ( ) ( ) ;4 0.38938
D th totemF s t i e f t
/2 ( )( , )4 0.38938
h Bt i ttotF s t h e
2/2 ( 4 2 )]( , ) ( )
4 0.38938
Bt D th totF s t i e
ch III
20.005 | | 0.31 ; 86 .t GeV N
O.V.S., Nucl.Phys. A922 (2014) 180
TOTEM 7TeV
TOTEM 7 TeV
O.S. – J. Nucl.Phys. (Yad.Phys.) v.55 (1992)
2 2
exp.[ |( ) (Im ( ) Im ([Re ( ) Re ( ) )] / ( )] Ch С h
R td
k F t F t kd
F tt
F t
O.S. - New methods for calculating parameters of the diffraction
scattering amplitude, "VI Intern. Conf. On Diffraction...", Blois, France,(1995).
O.S. “Additional ways to determination of structure of high energy elastic scattering
amplitude” arxiv.org:[hep-ph/0104295]
P. Gauron, B. Nicolescu, O.S. “A New Method for the Determination of the Real Part of the
Hadron Elastic Scattering Amplitude at Small Angles and High Energies”
Phys.Lett. B629 (2005) 83-92
n=1. n=0.95
.
TOTEM – arXiv:1503
TOTEM – 12 (2015) CERN preprint
Ch III f
Like TOTEM analysis (N=223, 5 row)
7 8
2
7 8 8 (7) (8)
1
5 1. 1. 1. 1. 1. 0. 96.3 99.2 48212
5 0.93 0.9 0.9 0.045 95.3 98.2 2870.98 1.
1.18 1.2 106.1 1
2
5 1.14 1.1 1.1 0. 09.3025 1508
N
par T T a T b totA A
fix
tot ikn k k
b
kk
Born case:
2 31 2 32 ( /2 ) ( )
( , ) ( ) ( )B t B t B t Ln sh
totF s t h i Ln s e
2 22
1
( ( 4 2 )2 ] ) ( )(( , ) ( )
4 0.38938)
D t Ln sh t CtotF s t i Ln s f t e
2
7 8 8 (7) (8)7 8
3 1. 1. 1. 1. 1. 0.18 96.1 99.0 4774
3 0. 0.93 0.9 0.901 0.198 1 95.7 98.68 1320 7. 2
N
par T T a T b tA ot toA t in k k kk k
2 2( ( 4 2 )] ) ( )1. 24
1( , ) ( ) ( )4 0.38938
D t Ct Ln sh totF s t i Ln s f t e
1.0 1.03 0.95 0.9 0.903 0. 97.1 99.12 12 1311
; ; 22 ˆ( )2
1
( 4 2 )ˆ) (, )(Lnt th
B tot
sF s t h ets f
7 8
8 8
2
7 87(0)
0.09 0.075 1454 97 0.94 1 0.8 6.3 97 0.88.0 7.1 .0 81
par T T a T b tot totA An k k kk k
EIKONAL
2 31 2 3( /2 ) ( )
( , ) ( ) ( )B t B t B t Ln sh
B totF s t h i s e
7 8
2 7 8
7 8 8(0)
0.06 0.076 1797 0.966 1 0.9 0.91 1 96.7 98.5.01 .026 5
par T T a T b tot tA A otn k k kk k
2 determineddoes notC t
; ; 22 ˆ([ (4 2 ) )2
1
]( , ) [ (( 1 )] ;)
Ln
B
sh
t
tt
toF s t h i k t es f t
7 8
7 88 87
2
0
(0)
0.15 332 1.076 11.0.0 .14 1.127 3 95.1.02 37 9 97.fi
T T a T b totA toA
x
tk kk k k
1.0.08 97.10.14 341 1.05 1.11 1.1 0.0 9899 .8fixfix
; ; 22 ˆ( )2
1
( 4 2 )ˆ) (, )(Lnt th
B tot
sF s t h ets f
2 7 8
7 87 88(0)
0.11 3820.087 1.04 0.99 0.7 1.1 1.097 97.7 99.4599
T T a T b toA A t totk kk k k
EIKONALIZATION
2 320.47/2 8.8/2 20/2( , ) (0.9927 0.11915)h t t tF s t a i e
8 102.9tot mb TOTEM 8 TeV
2( ) [Re ( ) Re ( ;)]th h С
R t F t F t 2
exp.[ | * (Im( ) ( ) Im ( )] / ( )Ex
R
Cp hdn k F t F t k
dtt
Empty circles: n=1 Closed circles: n=0.9
dq3b1227
2 22
1
( ( 4 2 )2 ] ) ( )(( , ) ( )
4 0.38938)
D t Ln sh t CtotF s t i Ln s f t e
Final results (or) the beginning new story
* The new data bounded the different models essentially.
LHC
The problems of the determination of
• The thin structure of the slope - B(s,t), (non-exponential, oscillations)
• The term ct^2 mimic the unitarization procedure –> it is better use the
eikonal representation
• The term (or like it) play important value;
• It is need taking into account the form factors of hadrons
• The slope of Re F(s,t) exceeded the slope of Im F(s,t);
• The new LHC data show the problem with the normalization.
Wait the high precision new data at small t and 13 TeV
The new High Energy Generalized Structure model (HEGS) gives the
quantitatively description of the elastic nucleon scattering at high energy
with only 6 fitting high energy parameters. Is is shown the discrepancy
in the normalization of the TOTEM and ATLAS data.
Phenomenological analysis
It is need obtain the data in CNI region.
( ) ( , )tot s and s t
2( 4 )2D t
THANKS For your attention