Lecture 16, Homemade generator

8/6/2019 Lecture 16, Homemade generator

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Slide 1 of 10

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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Slide 2 of 10

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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Slide 3 of 10

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


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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


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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Slide 9 of 10

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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Slide 10 of 10

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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Lecture 16, Homemade generator