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Study of Multiplicity and Event Shapes using ZEUS detector at HERA
Michele Rosin
University of Wisconsin, Madison on behalf of the ZEUS Collaboration QFTHEP 2004 June 17th

Multiplicity and Event Shapes, Michele Rosin U. Wisconsin

QFTHEP 2004, June 17th 2004

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HERA DIS

description & kinematics
DESY Hamburg, Germany

·920 GeV p+ (820 GeV before 1998) ·27.5 GeV e- or e+ ·318 GeV cms (300 GeV) ·Equivalent to a 50 TeV Fixed Target ·DIS Kinematics:
e(k)
e'(k')
remnant

H1

Q 2 = - q 2 = -(k - k

)2

ZEUS

(q)

p(P) q'

Q2 = -q2 =-(k -k) Virtuality of photon
2

p q y= p k

Inelasticity 0 y 1

Q2 x= 2q p

Fraction of p momentum carried by struck parton
QFTHEP 2004, June 17th 2004 2

Multiplicity and Event Shapes, Michele Rosin U. Wisconsin


+ e+e-- & ep : Breit Frame DIS event
Breit Frame Breit Frame Lab Frame
e e

·

Breit Frame definition:

2xP + q = 0
· "Brick wall frame" incoming quark scatters off photon and returns along same axis. ·Current region of Breit Frame is analogous to e+e-.

q
q e

e

PT
-Q/2 Q/2

PL

Current

Target
QFTHEP 2004, June 17th 2004 3

Multiplicity and Event Shapes, Michele Rosin U. Wisconsin


Hard and soft processes

·

Hard processes: perturbative QCD

· Soft processes: (hadronization) non-perturbative QCD
Multiplicity and Event Shapes, Michele Rosin U. Wisconsin QFTHEP 2004, June 17th 2004 4


+ Mean multiplicity: e+e-- and pp

s

e+e

-

=

(

pe - + p

e

+

)

2

s

pp

=

(

pp + p

p

)

2

(q )

had 2 tot

=

[(q

inc 1

-q

leading 1

) + (q

inc 2

-q

leading 2

)]

2

Multiplicity vs. invariant mass of system is universal for pp & e+eQFTHEP 2004, June 17th 2004 5

Multiplicity and Event Shapes, Michele Rosin U. Wisconsin


Motivation for the use of Meff as eff energy scale
· Analogous to the pp study: want to measure the dependence of of on the invariant mass of the system ·Boost in proton direction => proton remnant & fraction of string escape down the beam pipe Lab Frame Meff ·Can measure only a fraction of string: assume vs. invariant mass is universal, can compare to pp data ·Use Meff as a scale

M = ( E ) - ( p ) - ( p ) - ( p )
2 eff i 2 ie ie i x 2 ie i y 2 ie i z
Multiplicity and Event Shapes, Michele Rosin U. Wisconsin

2

Meff: HFS measured in the detector where the tracking efficiency is maximized
QFTHEP 2004, June 17th 2004 6


Comparison of multiplicity + for ep, with e+e-- & pp


18

16

ZEUS 95 Prelim., inclusive ZEUS 94-97, current region

· mean charged multiplicity, , for different energy scales: e+e(s), pp (q2) and ep (Meff) ·Excess in observed for ep data ·Possible explanations: Different contributions from gluons (HERA can reach smaller x than pp)

14

(multiplied by a factor of 2)

12

10

8

6 e e TASSO 4 e+e- PLUTO e+e- JADE 2 e e MARK I pp ISR 0 10 Meff 10 (GeV)
7
2
++-

Multiplicity and Event Shapes, Michele Rosin U. Wisconsin

QFTHEP 2004, June 17th 2004


Compare to LEP data
·LEP data at higher energy: should have contribution from gluons ·Can't conclude from this plot, it seems both ep and pp data could meet LEP points · vs. Q for ep in current region of Breit frame agrees with e+e- and pp data, for high Q ·Working on improving this measurement using more statistics, and spitting data into x and Q2 bins, in current and target region aiming for new results for ICHEP 2004.
Multiplicity and Event Shapes, Michele Rosin U. Wisconsin



ZEUS
30

ZEUS 95 Prelim. ZEUS 94-97 Breit (x2)

25

20

15

10

pp ISR LEP I LEP II e e TASSO
++-

5

e e PLUTO e+e- JADE e+e- MARK I

0 10

s

e+e-,

(q )

2

10

2

had,

Q, or M

eff

(GeV)
8

QFTHEP 2004, June 17th 2004


Study using

Hadronization Event Shapes

· Event shape variables measure aspects of the topology of the hadronic final state · Event shapes in DIS should allow investigation of QCD over a wide range of energy scales, though hadronization corrections are large for these variables · Power Correction: analytical calculation suggested by Dokshitzer & Webber to describe the effect of hadronization for these variables · Event shape analysis is done in current region of the Breit frame

Multiplicity and Event Shapes, Michele Rosin U. Wisconsin

QFTHEP 2004, June 17th 2004

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Power corrections: an analytical approach
·Power correction is used to calculate hadronization corrections for any infrared safe event shape variable, F ·Mean event shape variables are sum of perturbative and nonperturbative (power correction) parts ·The power correction depends on two parameters, 0 and
s

Used to determine the hadronization corrections

F=F
F
pow

perturbati ve

+F

power correction

16 µ I P Q QK = aF ln · 0 ( µ I ) - s (Q ) - 0 (ln + + 1) s2 (Q 3 Q 2 µI µI 0

)

0 =

"non-perturbative parameter"
-(Dokshitzer, Webber Phys. Lett. B 352(1995)451)
QFTHEP 2004, June 17th 2004 10

Multiplicity and Event Shapes, Michele Rosin U. Wisconsin


Event Shape Variables
Thrust
n for TT axis Photon axis n : T

Tk =

max
^ n
k

r ^ i pi r nk i pi

rr i p â n B= r i p

M2 =

( p ) (2 E )
i i

µ2
2

· Thrust: longitudinal momentum sum · Broadening: transverse momentum sum

· Measured with n set to the thrust axis, and photon axis · Sum over all momenta in current region of Breit frame.
Multiplicity and Event Shapes, Michele Rosin U. Wisconsin

rr 3ij pi p j sin 2 ( C= rr 2ij pi p j

ij

)

· Jet Mass and C parameter: correlations of pairs of particles

QFTHEP 2004, June 17th 2004

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Mean event shape variables
·NLO + Power correction fits to means measured in bins of X and Q2 ·High x points (open circles) not fitted


ZEUS
<1-T T>
0.2 0.25 0.2 0.15 0.1 0.1 0.05 0.05 0 0.6
DISASTER++ & PC DISASTER++

0.15

ZEUS (prel.) 98-00 Unfitted data

·All variables fitted with a good 2 ·Photon axis variables (1-T) show large x-dependence


2

0 0.1

0.4 0.05 0.2

·1-T correction very small and negative ·Model describes data well

<1-T >

0 0.4

0 0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

10
Multiplicity and Event Shapes, Michele Rosin U. Wisconsin

10

10

10

2

(GeV)

(GeV)
QFTHEP 2004, June 17th 2004 12


Extraction of 0 0 NLO + PC fits
0.5 BT M 0.45 C 0.4 B

and s from s to means
·

ZEUS
1-T
2 T

0



1 s.d. errors 95% confidence region (stat. + exp. sys. errors) ZEUS (prel.) 98-00

Not all variables give same s and o.

· 1 ­ T fit poorly defined -large systematic errors · Extracted parameters: o 0.45, s0.12
1-T


0.35

0.3

0.25 0.11

0.115

0.12

0.125

0.13

0.135

s (M Z )

0.14

0.145

Multiplicity and Event Shapes, Michele Rosin U. Wisconsin

QFTHEP 2004, June 17th 2004

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Differential distributions
NLO+PC Fits to Differential Distributions
ZEUS


ZEUS


1/N dn/dT

10

6

= 21 GeV = 29 GeV = 42 GeV

= 60 GeV = 82 GeV = 113 GeV

1/N dn/dB

}

ZEUS (prel.) 98-00

10

7

ZEUS (prel.) 98-00

{

= 21 GeV = 29 GeV = 42 GeV

= 60 GeV = 82 GeV = 113 GeV

NLO + PC (fitted) NLO + PC (unfitted)

NLO + PC (fitted) NLO + PC (unfitted)

10

4

10

5

10

2

10

3

1

10

10

-2

0

0.2

0.4

0.6

0.8

1

10

-1

0

0.1

0.2

0.3

0.4

0.5

· Try to improve our understanding using differential distributions


T

B



·Power correction is interpreted as a `shift' in the NLO distribution
Multiplicity and Event Shapes, Michele Rosin U. Wisconsin

1 dn (F ) = 1 dnNLO (F - F N dF N dF
QFTHEP 2004, June 17th 2004

pow

)

14


Extraction of 0 0 fits to differential
ZEUS
0
0.7 M T 0.6
T 2

and s from s distributions
·Photon axis variables fit with high s, but other variables consistent with each other in and o ·Fits o somewhat high compared to that from means

1 s.d. errors 95% confidence region (stat. + exp. sys. errors) ZEUS (prel.) 98-00



s

C

0.5

T



· Extracted parameters: o 0.65, s 0.12
B

0.4

0.3

·Method a little unstable, try adding NNLO effectsresummations
0.13

0.11

0.115

0.12

0.125

s (M Z )

Multiplicity and Event Shapes, Michele Rosin U. Wisconsin

QFTHEP 2004, June 17th 2004

15


Differential distributions: with resummation
NNLO+NLO+PC Fits to Differential Distributions
ZEUS


ZEUS


1/N dn/dT

10

6

= 21 GeV = 29 GeV = 42 GeV

= 60 GeV = 82 GeV = 113 GeV

1/N dn/dB

}

ZEUS (prel.) 98-00

10

7

ZEUS (prel.) 98-00

{

= 21 GeV = 29 GeV = 42 GeV

= 60 GeV = 82 GeV = 113 GeV

NLO + NLL + PC (fitted) NLO + NLL + PC (unfitted)

NLO + NLL + PC (fitted) NLO + NLL + PC (unfitted)

10

4

10

5

10

2

10

3

1

10

10

-2

0

0.2

0.4

0.6

0.8

1

10

-1

0

0.1

0.2

0.3

0.4

0.5

T



B



Calculation describes data better; able to enlarge range of fit
Multiplicity and Event Shapes, Michele Rosin U. Wisconsin QFTHEP 2004, June 17th 2004 16


Extraction of 0 0 fits to differential
0.55

and s from s distributions
·C is consistent in s but low in o. C result very sensitive to fitted range: under investigation · 0 consistent with results from fit to means. Extracted parameters: o 0.118, s 0.5
ZEUS
1/N dn/dC
10
7

ZEUS
T


0

1 s.d. errors 95% confidence region (stat. + exp. sys. errors) ZEUS (prel.) 98-00


0.5 T
T

M 0.45

2

B

ZEUS (prel.) 98-00

{

= 21 GeV = 29 GeV = 42 GeV

= 60 GeV = 82 GeV = 113 GeV

0.4

NLO + NLL + PC (fitted) NLO + NLL + PC (unfitted)

10

5

C 0.35
10
3

10

0.3 0.11

0.115

0.12

0.125

s (M Z )

0.13
10
-1

0

0.2

0.4

0.6

0.8

1

C

Multiplicity and Event Shapes, Michele Rosin U. Wisconsin

QFTHEP 2004, June 17th 2004

17


Summary
Showed results for two methods of investigating hadronization: ·Multiplicity: · Mean charged multiplicity vs. effective mass was measured for ep and compared to e+e- and pp. Multiplicity shows excess in data for ep. · Current study aiming for higher precision using new data ·Event Shapes: ·NLO + power correction has been fitted to the mean event shape data, s 0.12, 0 0.45. Consistent with published results. Photon axis variables poorly determined ·NNLO Resummed calculations give better results than NLO + power correction only, with s 0. 118, 00.5. Resummation gives consistent s,o for all event shape variables, but C fit dependant on range ·Current investigation of new event shape variables & new methods. (Kout for events with 2 or more jets, 2 jets can fix the NLO predictions better)
Multiplicity and Event Shapes, Michele Rosin U. Wisconsin QFTHEP 2004, June 17th 2004 18