Stefan E. Müller Institut für Kernphysik

Universität Mainz

New ISR measurements with

KLOE

Institutsseminar Kernphysik

Mainz, 20.07.2009

ISR: Initial state radiation

1

Particle factories (DANE, PEP-II, KEK-B) can measure hadronic cross sections as a function of the hadronic c.m. energy using initial state radiation (radiative return to energies below the collider energy √s).

hadrons

hard photon radiated in initial state

incoming e+ and e-

with M2ee= s

virtual photon with M2

< s

The emission of a hard in the bremsstrahlung process in the initial state reduces the energy available to produce the hadronic system in the e+e-

collision.

ISR: Initial state radiation

2

= σ(e+ e → hadrons, Μ2

hadr ) s

dσ(e+ e → hadrons + γ ) dΜ2

hadr H(s, Μ2

hadr )

= x

Neglecting final state radiation (FSR) terms, on can relate the measured differential cross section dhadr+ /dM2

hadr to the hadronic cross section hadr using the radiation function H(s, M2

hadr):

Theoretical input: •  precise calculation of the radiation function H(s, M2

hadr) EVA + PHOKHARA MC Generator

Binner, Kühn, Melnikov; Phys. Lett. B 459, 1999 H. Czyż, A. Grzelińska, J.H. Kühn, G. Rodrigo, Eur. Phys. J. C 27, 2003 (exact next-to-leading order QED calculation of the radiator function)

ISR vs. energy scan:

3

Energy scan (CMD2, SND):

Radiative return (KLOE, BaBar, BELLE):

•  energy of colliding beams is changed to the desired value •  “direct” measurement of cross sections •  needs dedicated accelerator/physics program •  needs to measure luminosity and beam energy for every data point

•  runs at fixed-energy machines (meson factories) •  use initial state radiation process to access lower lying energies or resonances •  data come as by-product of standard physics program •  requires precise theoretical calculation of the radiator function •  luminosity and beam energy enter only once for all energy points •  needs larger integrated luminosity

{ (gµ-2) :

4

etc. etc.

Hadrons

etc.

aµQED aµ

weak aµhad + +

but…

aµ=(gµ-2)/2 = 0 (Dirac!)

€

µ = g

e2mc

s = gµB s Magn. moment:

muons (s=1/2):

€

s = spinm = lepton mass

(gµ-2) :

5

aµQED:

aµEW:

Calculated up to 5 loops [mostly T. Kinoshita et al.], using the latest value of ae to obtain -1=137.035 999 084 (51) [D. Hanneke et al., Phys.Rev.Lett.100 (2008) 120801] gives

aµQED= (116 584 718.10 ± 0.14 ± 0.04± 0.03± 0.02)·10-11

O(5)

Calculated up to 2 loops, [Jegerlehner/Nyffeler arXiv: 0902.3360]:

aµEW= (153.2 ± 1.8)·10-11

Error from hadronic loops and dependence on Higgs mass. (3-loop effect negligible)

num. error

mass ratios

aµhad:

Three contributions:

aµhad,lo:

aµhad,ho:

aµhad,lbl:

Dominant term, calculated via dispersion integral from hadr. cross sections:

€

aµhad,lo =

14π 3

dsσ had s( )K4mπ2

∞

∫ s( )

Calculated via a dispersion integral from hadr. cross sections, less impact due to higher order

Different approaches used, relies heavily on (effective field) theories and models

6

Dispersion integral for aµhad,lo :

aµhad,lo can be expressed in terms of

(e+e hadrons) by the use of a dispersion integral:

€

aµhad,lo =

14π 3

dsσhad,exp s( )K4mπ2

ECut2

∫ s( ) + dsσhad,pQCD s( )KECut

2

∞

∫ s( )

•  Ecut is the threshold energy above which pQCD is applicable •  s is the c.o.m.-energy squared of the hadronic system (M2

hadr) •  K(s) is a smooth function that goes with 1/s, enhancing low energy contributions of hadr(s)

7

Dispersion integral: Contributions of different energy regions to the dispersion integral and the error on aµ

had

F. Jegerlehner, Talk at PHIPSI08

Experimental errors on had translate into theoretical uncertainty of aµhad!

Needs precision measurements, especially below 2 GeV!

8

2 EBeam, MeV

Cross section data:

S. Eidelman, Talk at TAU08

9

Below 1 GeV, the process e+e→, → + dominates the data. It contributes ~70% to aµ

had,lo, and ~30% to (Δaµhad,lo)2

e.g. from CMD2 experiment in Novosibirsk:

aµhad,lo, aµ

had,ho and aµhad,lbl: }

aµhad,ho:

aµhad,lbl:

Procedure is similar to the one for the leading-order contribution (using experimental data and a dispersion integral with a suitable Kernel function), one obtains [Jegerlehner/Nyffeler arXiv: 0902.3360]:

aµhad,ho= (-100. ± 1.)·10-11

Different approaches lead to different values and errors:

Year Author aµhad,lbl [10-10]

1996(2002) J. Bijnens, J. Prades, E. Pallante 8.3±3.2

1998(2002) M. Hayakawa & T. Kinoshita 9.0±1.5

2003 K. Melnikov & A. Vainshtein 13.6±2.5

2004 M. Davier & W.Marciano 12.0±3.5

2006 J. Bijnens & J. Prades 11.0±4.0

2009 A. Nyffeler 11.6±4.0

aµhad,lbl= (116. ± 40.)·10-11 I chose (arbitrarily) the last one

in this presentation:

10

aµhad,lo:

aµhad,lo ≅ (7000. ± 50.)·10-11

Evaluating the dispersion integral typically gives: (more details later!)

First summary: 11

•  Precise measurements of hadronic cross sections, especially at energies below 1-2 GeV, enter the theoretical evaluation of aµ

had,lo and contribute the largest part to the uncertainty of aµ

theo+

•  In the energy region below 1 GeV, the process e+e→, → ++dominates, its contribution to aµ

had,lo is ~70%

•  At meson factories operating at fixed √s one can use the radiative return (ISR method) to measure hadronic cross sections from the production threshold up to √s

The KLOE multi-purpose detector at the DANE -factory in Frascati is ideally suited for the measurement of below 1 GeV

DANE: A -Factory 12

LINAC

Damping Ring

KLOE

SIDDHARTA

FINUDA DEAR

e+

e+510MeV

510MeV

LNF Frascati / Rome

DEAR,

, SIDDHARTA

e+e - collider with =m1.0195 GeV s

DANE: A -Factory

Integrated Luminosity

Peak Luminosity Lpeak= 1.4 • 1032cm-2s-1

Total KLOE int. Luminosity: ∫L dt ~ 2.1 fb-1 (2001 - 05)

2006: •  Energy scan with 4 points around m-peak •  250 pb-1 at = 1 GeV s

13

KLOE Detector Driftchamber

p/p = 0.4% (for 900 tracks) xy 150 µm, z 2 mm

Excellent momentum resolution

14

Full stereo geometry, 4m diameter, 52.140 wires 90% Helium, 10% iC4H10

KLOE Detector 15

Electromagnetic Calorimeter

E/E = 5.7% / E(GeV) T = 54 ps / E(GeV) 100 ps (Bunch length contribution subtracted from constant term)

Excellent timing resolution

Pb / scintillating fibres (4880 PMT) Endcap - Barrel - Modules

measurement: small angle

€

p γ = p miss = −(

p + + p − )

  high statistics for ISR events   low relative FSR contribution   suppression of +0 background

2 pion tracks at large angles 50o< θ <130o

Photons at small angles θγ < 15o or θγ > 165o

photon momentum from kinematics:

statistics: 242pb-1

3.1 Mill. Events

16

Event selection

To further clean the samples from radiative Bhabha events, a particle ID estimator for each charged track based on Calorimeter Information and Time-of-Flight is used.

•  Experimental challenge: Fight background from

–  φ→ π+π-π0

–  e+e- → e+e- γ –  e+e- → µ+µ- γ,

separated by means of kinematical cuts in trackmass MTrk (defined by 4-momentum conservation under the hypothesis of 2 tracks with equal mass and a γ)

€

s − p12 + Mtrk

2 − p22 + Mtrk

2( )2− ( p1 + p2)

2 = 0

€

dσππγ

dsπ =

Nobs −Nbkg

Δsπ ⋅ 1εsel

⋅ 1 L

17

KLOE measures L with Bhabha scattering

55° < θ < 125° acollinearity < 9°

p ≥ 400 MeV

e-

e+

γ

F. Ambrosino et al. (KLOE Coll.) Eur.Phys.J.C47:589-596,2006

newer version (BABAYAGA@NLO) gives 0.7% decrease in cross section,

and better accuracy: 0.1%

Systematics on Luminosity Theory 0.1 %

Experiment 0.3 %

TOTAL 0.1 % th ⊕ 0.3% exp = 0.3%

Now:

Luminosity: 18

s+

Radiative corrections

-  ISR-Process calculated at NLO-level PHOKHARA generator (H.Czyż, A.Grzelińska, J.H.Kühn, G.Rodrigo, EPJC27,2003)

Precision: 0.5%

Radiator-Function H(s,s) (ISR):

Radiative Corrections: i) Bare Cross Section divide by Vacuum Polarisation (s)=((s)/(0))2 from F. Jegerlehner

ii) FSR Cross section must be incl. for FSR

for use in the dispersion integral of aµ

FSR corrections have to be taken into account in the efficiency eval. (Acceptance, MTrk) and in

the passage sπ → sγ*

FSR contr. (sQED):

Net effect of FSR is ca. 0.8%

€

s ⋅dσππγ

dsπ=σππ (sπ ) × H(s,sπ)

s > s+

Vac. Pol. corr:

Radiator:

(H.Czyż, A.Grzelińska, J.H.Kühn, G.Rodrigo, EPJC33,2004)

s+

19

New KLOE result:

KLOE 2008

€

σππ (sπ ) =πα 2βπ

3

3sFπ (sπ )

2

s [GeV2]

Reconstruction Filter negligible Background subtr. 0.3% Trackmass cut 0.2% /e particle ID negligible Tracking 0.3%

Trigger 0.1% Acceptance (ππ) 0.2% Acceptance () negligible Unfolding negligible

Software Trigger 0.1% √s dep. of H 0.2% Luminosity(0.1th ⊕ 0.3exp)% 0.3%

FSR resummation 0.3% Radiator H 0.5% Vacuum polarization 0.1%

Systematic errors on aµ:

experimental fractional error on aµ = 0.6 %

theoretical fractional error on aµ = 0.6 %

aµ(0.35-0.95GeV2) = (387.2 ± 0.5stat±2.4sys ±2.3theo) · 10-10 Disp. Integral:

Phys. Lett. B 670 (2009) 285

€

aµhad =

14π 3 σ had s( )K

x1

x2

∫ s( )d s

20

|F|2 for different exp.:

aµhadC,S- aµ

hadK

€

aµhad =

14π 3 σ had s( )K

x1

x2

∫ s( )d sabs. contr. to per bin:

Improved agreement with spectra from energy scan experiments – no compensation of different regions in the dispersion integral!

Phys. Lett. B 670 (2009) 285

[10-9]

21

aµ for different exp.:

22

Good agreement in aµ for different experiments

The threshold region: Kinematics do not allow events with M2

ππ< 0.35 GeV2 in the small angle selection cuts - a high-energy ISR photon (≅ small M2

ππ) emitted at a small angle forces the pions also to be at low angles:

p+

p- pγ

MC

, L=8

00pb

-1

M2ππ

50o < θγ < 130o

θγ < 15o or θγ > 165o

Monte Carlo (PHOKHARA):

23

The threshold region:

Monte Carlo (PHOKHARA):

If the high-energy photon is emitted at a large angle, also the pions will be emitted at large angles; and thus the event will be selected.

pγ

p+

p-

24

MC

, L=8

00pb

-1

M2ππ

50o < θγ < 130o

θγ < 15o or θγ > 165o

Kinematics do not allow events with M2ππ< 0.35 GeV2 in the small angle selection

cuts - a high-energy ISR photon (≅ small M2ππ) emitted at a small angle forces

the pions also to be at low angles:

measurement: large angle 2 pion tracks at large angles

50o< θ <130o

Photons at large angles 50° < θγ < 130o

  independent complementary analysis   threshold region (2mπ)2 accessible   γISR photon detected (4-momentum constraints)

  lower signal statistics   larger contribution from FSR events   larger φ → π+π-π0 background contamination   irreducible background from φ decays (φ → f0 γ → π+π-γ)

2002 Data L = 240 pb-1

Error on LA dominated by syst. uncertainty on f0 contr.

LA stat.+syst. error

& &

FSR f0 ρπ

Threshold region non-trivial due to irreducible FSR-effects, which have to be estimated from MC using phenomenological models

25

measurement: large angle 2 pion tracks at large angles

50o< θ <130o

Photons at large angles 50° < θγ < 130o

  independent complementary analysis   threshold region (2mπ)2 accessible   γISR photon detected (4-momentum constraints)

  lower signal statistics   larger contribution from FSR events   larger φ → π+π-π0 background contamination   irreducible background from φ decays (φ → f0 γ → ππ γ)

nevt

s/0.

01 G

eV2

statistics: 233pb-1

650 000 Events

Use data sample taken at √s≅1000 MeV, 20 MeV below the peak

26

measurement: large angle 27

events from MC events from MC

Detection of the radiated photon allows to exploit the kinematic closure of the event Cut on angle Ω btw. ISR-photon and missing momentum

π+

π-

missp

ãp

Ω

γ

Cut out remaining background events from +0 while retaining a high efficiency for signal events. +

Prel. Result:

statistical errors only

  Selection cuts established   Efficiencies evaluated   Systematics almost completed   still doing several cross checks

Very good agreement between the spectrum of the preliminary new result and the KLOE 08 published analysis

This analysis is very close to a final result!

28

Forward-backward asymmetry:

In the case of a non-vanishing FSR contribution, the interference term between ISR and FSR is odd under exchange π+ ↔ π- .This gives rise to a non-vanishing asymmetry: Binner, Kühn, Melnikov, Phys. Lett. B 459, 1999

€

A =N(θ+ > 90o) − N(θ+ < 90o)N(θ+ > 90o) + N(θ+ < 90o)

θπ [ο] Pion polar angle

N- (θ) N+ (θ)

90o

Forward-backward asymmetry:

Ideal tool to test the validity of models used in Monte Carlo to describe the pionic final state radiation (point-like pion assumption, RT, etc.)

29

Forward-backward asymmetry: In a similar way like FSR, radiative decays of the φ into scalar mesons decaying to π+π - also contribute to the asymmetry. Czyz, Grzelinska, Kühn, hep-ph/0412239

MC (ISR+FSR only) Data 2006

Data 2006 √s = 1.0 GeV

Data 2002 √s = 1.02 GeV

Effect of φ decay greatly reduced for data taken 20 MeV below the mass of the φ meson.

30

Future measurement: /µ+An alternative way to obtain |F|2 is the bin-by-bin ratio of pion over muon yields (instead of using absolute normalization with Bhabhas).

€

Fπ s'( )2≈4 1+ 2mµ

2 s'( )βµ

βπ3

dσππγ /d ′ s dσ µµγ /d ′ s

meas. quantities

kinematical factor (µµ

Born / Born)

Many radiative corrections drop out: •  radiator function •  int. luminosity from Bhabhas •  Vacuum polarization

Data ππγ, µµγ ππγ+µµγ

ππγ µµγ

MTrk[MeV]

Separation between pions and muons done experimentally using kinematical cuts: •  muons: MTrk < 115 MeV •  pions : MTrk > 130 MeV

31

aµhad,lo from different evaluations:

Year Author aµhad,lo [10-10]

1995 S. Eidelman, F. Jegerlehner 702 ± 15.3

2003 M. Davier et al. (e+e- data) 696.3 ± 7.2

2003 M. Davier et al. ( data) 711.0 ± 5.8

2006 M. Davier et al. 690.8 ± 4.4

2008 K. Hagiwara et al. 689.4 ± 4.6

2008 F. Jegerlehner 692.3 ± 6.0

2009 F. Jegerlehner/A. Nyffeler 690.3 ± 5.3

2009 M. Davier et al. (e+e- data) 689.1 ± 4.4

2009 M. Davier et al. ( data) 705.4 ± 4.4

Full evaluations of the dispersion integral depend on many factors: •  Combination of data from different experiments •  Choice of data •  Threshold energy above which pQCD is used •  …

32

incl. KLOE08

33

{ Hadr. cross sections from data: } #

e+ e

*

u u d d

W

d u u u + +0+ + +

- 0+ e+e + +

τππ

=

ππ→≤

πα=σ −−+−+ Ms,v

s4

0

21Iee

Isospin invariance assumed, one can relate the isovector cross sections (e+e-+) to the spectral function : 0v

ππ−

Isospin symmetry breaking effects have to be taken into account! Recent update regarding data: [Davier et al. arXiv: 0906.5443]

CVC

{ (gµ-2) experiment at BNL: }

34

Longitudinally polarized muons in uniform magnetic field B: →

•  muons perform relativistic cyclotron motion with angular frequency

•  muon spin precesses with angular frequency

•  measurement of a= (S C) and B allows to determine aµ

•  the direction of electrons from the rel. decay µ → e e µ (or c.c.) is strongly correlated with the muon spin direction a from time-dependent electron rate impinging on calorimeters on inside of storage ring

€

ωC =eBγmµ

€

ωS =eBγmµ

+ aµ

eBmµ

→

-

aµEXP= (116 592 080. ± 63.)·10-11 [0.54 ppm]

[Phys. Rev. D73 (2006) 072003]

Average value of aµ+ and aµ (assuming CPT symmetry):

35

Status on (gµ-2) :

aµexp

(gµ-2)/2 = (11 659 2080. ± 63.) × 10-11 E821, Phys. Rev. D73 (2006) 072003

The current status of aµ from experiment and (SM-) theory:

based on τ decays

based on e+e- data

aµexp - aµ

theo,SM = 1.8 – 3.2 σ difference

aµQED = ( 11 658 4718.1 ± 0.1) × 10-11

aµEW = ( 153.2 ± 1.8) × 10-11

= ( 7060. ± 57.) × 10-11

= ( 6919. ± 66.) × 10-11

(gµ-2)/2 = aµQED + aµ

EW + aµhad

aµtheo,SM

aµhad

JN arXiv: 0902.3360

JN arXiv: 0902.3360

JN arXiv: 0902.3360

D et al. arXiv:0906.5443

Status on (gµ-2) : Compilation of theory: Jegerlehner-Nyffeler arXiv:0902.3360 (only aµ

had,lo differs in the several theoretical values) E821: Phys. Rev. D73 (2006) 072003

incl. KLOE08

36

Summary: 37

•  The radiative return has proven to be an important tool, used now routinely at the KLOE, BaBar and Belle experiments to measure precise hadronic cross sections and do hadron spectroscopy

•  One still needs to push the precision of hadronic cross sections at low energies in order to resolve the g-2 “puzzle”

•  The KLOE experiment has used the radiative return to obtain in the range 0.35 < M

2<0.95 GeV2 and an analysis extending this towards the 2 pion threshold using data taken below the resonance is close to completion

•  An analysis using a bin-by-bin nomalization with muon events is in progress, allowing to cross check most of the theoretical input

•  The forward-backward asymmetry allows to test the models used for the process with pionic final state radiation, and gives a further handle to determine the model parameters of scalar mesons