lecture 16, homemade generator
TRANSCRIPT
8/6/2019 Lecture 16, Homemade generator
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Taday’s lecture
† Thrust distribution
† Heavy jet mass distribution
† Three jet resolution scale y 23 distribution
Literature:
S. Catani, L. Trentadue, G. Turnock, B. R. Webber, Nucl. Phys., 1993, B407, 3 (Thrust,
HJM)
S. Catani, Yu. Dokshitzer, M. Olsson , G. Turnock, B. Webber, Phys.Lett. 269 (1991)
432 Hk T -clustering algorithm)
A.Heister et al., Eur.Phys.J. C35 (2004) 457 (ALEPH results)
Adeva et al., Z. Phys C55 (1992) 39 (L3 results)
Event shapes for toy generator
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Analytic result
F HwL = L f 1HlL + f 2HlL,
R Thrust HtL =expH2 F L
GH1 - 2 g HlLL , R HJMHtL =expH2 F L
GH1 - g HlLL2 ,
LL NLL
L = Ln1t, l = b0
as
4 pL where
g HlL = f 1HlL + l f 1 ' HlL
t =
1-
1-
2 IP
L
2+ P
R
2
M ëQ 2 +
IP
L
2- P
2
2
M2
ëQ 4
º IP L 2
+ P R 2M ëQ 2
r2
º MaxIP L 2, P R
2M ëQ 2
f 1 = -2A1
b0 lIH1 - 2 lL Log@1 - 2 lD - 2 H1 - lL Log@1 - lDM;
f 2 = -8A2
b02 I2Log@1 - lD - Log@1 - 2 lDM +
2B 1
b0Log@1 - lD -
4A1 g E
b0ILog@1 - lD - Log@1 - 2 lDM
- 2A1 b1 b0
3 Log@1 - 2 lD - 2Log@1 - lD + 12
Log@1 - 2 lD2 - Log@1 - lD2 ;
f 1 ' =A1
2 p b0 l2 ILog@1 - 2 lD - 2Log@1 - lDM;
Cumulative distribution
A1 = C F
A2
=1
2C
F K
B 1 = -32
C F
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DGLAP kernels and MC scheme
P qq =as
2 p
C F 1 + z 2
1 - z
+as
2 p
2C F K
2
1 - z
,
P gg =as
2 p2C A
1 z H1 - z L - 2 + z H1 - z L +
as
2 p
22C A K
1 z H1 - z L ,
as
2 p+
as
2 p
2K Ø
as
2 p MC
K = C A67
18
-p2
6
-5
9
N f where
LMC = LMS expK
b0or alternalively
S .Catani, B .R .Webber, G . Marchesini, QCDcoherent branchingand semiinclusive processes at large x ,
Nucl.Phys. B349 H1991L635
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Slide 4 of 10
Heavy jet mass
0.0 0.2 0.4 0.6 0.8
0
1
2
3
4
r
d s ê d r
MC scheme
Leading DGLAP
pure perturbative region
artificial zeroas
4 p b0 Ln 1
r2 =
12
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Slide 5 of 10
Thrust
0.0 0.2 0.4 0.6 0.8
0
1
2
3
4
t1ê2
2 t 1
2 d s ê d t
MC scheme
Leading DGLAP
artificial zeroas
4 p b0 Ln 1
t=
12
pure perturbative region
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Slide 6 of 10
Thrust
0.0 0.1 0.2 0.3 0.4 0.5 0
5
10
15
20
t
d s ê d t
MC
pure perturbative region
power corections are needed
ALEPH data
ood agreement in the logarithmically big region
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Slide 7 of 10
Y 23 distribution. Analytic result
pdf I y M =1
1 - ADq IQ 2 t0ME2d
dyADq IQ 2 y Q 2ME2 probability density function
-Ln Dq IQ 2 m2M = C F ‡
m2
Q 2 d m '2
m '2as I m '2M
2 pLn
Q 2
m '2-
32
=2C F
b0F HL , lL
can be calculated in explicit form
F HL , lL = L f 1HlL - b1
b02 f 2HlL +
32
f 3HlL + b1
b0
as
4 pf 4HlL
LL NLL NNLL piece (not really worth to keep)
L = LnQ 2
m '2, l = b0
as
4 pL
f 1 = -LogH1 - lL
l- 1,
f 2 =12
LogH1 - lL2 + LogH1 - lL +l
1 - lILogH1 - lL + 1M,
f 3 = LogH1 - lL,f 4 =
11 - l
ILogH1 - lL + lM.
where
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Slide 8 of 10
Y 23 distribution.
See although
...
G. Dissertori and M. Schmelling, An improved theoretical prediction for the two jet rate
in e+e-annihilation, Phys. Lett. B 361 (1995) 167.
A. Banfi, G. P. Salam, G. Zanderighi, Semi-numerical resummation of event shapes
JHEP 0201 (2002) 018
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Y 23 distribution. Comparison with L3
0.00 0.05 0.10 0.15 0.20 0.25 0.300.001
0.01
0.1
1
10
100
y 23
d s ê d y 2 3
MC scheme
Leading DGLAP
large y region should be improvedby CKKW or MLM
the agreement is not bad
in the small y region
NLL result is not valid here
log(R)-matching is needed
Banfi, Salam, Zanderighi
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Y 23 distribution. Comparison with ALEPH
2 4 6 8 10-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
-lnH y 23L
y 2 3
d s ê d y 2 3
MC scheme
Leading DGLAP
Banfi, Salam, Zanderighi
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