On the precision of scattering from chiral dispersive calculations José R. Peláez Departamento de Física Teórica II. Universidad Complutense de Madrid.

On the precisionof

scatteringfrom

chiral dispersive calculations

José R. Peláez

Departamento de Física Teórica II. Universidad Complutense de Madrid

J. R. Peláez and F.J. Ynduráin. PRD68:074005,2003F.J. Ynduráin. ‘QCD@Work’, hep-ph/0310206

J. R. Peláez and F.J. Ynduráin. hep-ph/0312187. To appear in Phys. Rev. D.

Motivation: Why a precise determination of scattering ?

Pions Goldstone Bosons of the spontaneous chiral symmetry breaking

In massless QCD, pions also massless2

0

),,(f

sutsA

Massless GB non interacting at low energies!!

Quark massesmassive pseudo-GB.

...AMMBM qq 20

2 42

Mq = quark mass

If B0 large: 20

2

),,(f

MsutsA

NO free parameters!!

20

0

00

f

qqB

But

How the QCD vacuum behaves(ferromagnet or antiferromagnet or what)?

A precise determination of scattering checks how big is B0, and tells us...

DIRAC has been a CERN experiment to measure the scattering lengths

Roy Equations: results

Recent Revival :

Using “data” from N + ”Regge” + old Kl4: 10

0 06.024.0 maFig.14. Ananthanarayan, Colangelo,Gasser & Leutwyler (2001)

Adding ChPT+ Other, non ChPT, inputs (Fs...):

100 005.0220.0 ma

120 0010.00444.0 ma

Colangelo,Gasser & Leutwyler (2001)

TINY ERRORS CENTRAL VALUE LOWERED AGAINNO NEW DATA

CGL

Set of coupled integral equations relating all channels used to analyse scattering data.

70’s: Using data from N+Regge+ old Kl4:10

0 05.026.0 ma

Basdevant, Froggat, Petersen (74-77)

We have recently questioned this high precisionJ. R. Peláez and F.J. Ynduráin. PRD68:074005,2003

They also give tiny errors for phase shifts and the mass and width

QUESTIONS ON THE CGL CALCULATION

Inconsistent with other sum rules, high energy data, and Regge Theory

Ignores systematic errors in data

Input from scalar factor model dependent and challenged

Inconsistent with other sum rules, high energy data, and Regge Theory

1) Inconsistency with High energy data and Regge:When using correct Regge behavior (as from QCD) in the Olsson and Froissart-Gribov sum rules there is a 2.5 to 4 sigma mismatch (even more now).

J. R. Peláez and F.J. Ynduráin. PRD68:074005,2003

Consistency checks

Amplitudenedded only

at t=0 or t=4M2

Olsson sum rule:

24 2

120

00

)4(

)0,(Im52

M

I

Mss

sFaa

t

Froissart-Gribov:

24 2

2

21

2'cos )4,(Im)1(

)4(

)4,(Im4'

M lll s

MsFl

Mss

MsFCb

24 1

2 )4,(Im

M ll s

MsFCa

Unsubtracted, OF COURSE, to have an independent check from Roy eqs.

We do not extract the low energy from here. We use the low energy from CGL and check the consistency with standard Regge.

Example: D-wave scattering length a+0 from Froissart-Gribov Sum

0)4,(Im)4,(Im

04 3

2221

2

as

MsFMsFC

M

IsIs

S2 and P waves up to 820 MeV -a0+ from Roy-CGL = (-2.10 ±0.01)10-4

Other waves up to 1420S2 and P waves from 820 to 1420 MeVfrom CERN-Munich data & CGL.

= (1.84±0.05)10-4

4 sigma mismatch.Also 4 sigma for a00, b1 and 2.5 sigma for Olsson Sum Rules

Low energy

Pomeron >1420 MeV = (0.68 ±0.07)10-4

We used a standard Pomeron residue P=3.0 ±0.3 generous error!!

We will see...

I=2 Regge >1420 MeV = (-0.06 ±0.02)10-4

0=(0.36±0.09)10-4

High energy

Suggested our Regge behavior was incorrectdue to crossing symmetry sum rules violations

noticed in the 70’s (Pennington.)

when used with CERN-Munich data.

They claimed that FACTORIZATION didnot apply to scattering

Caprini, Colangelo, Gasser & Leutwyler...

Regge Analysis of , N and NN J. R. Peláez and F.J. Ynduráin. hep-ph/0312187

At high energy, the amplitudes are governed by the exchange of Regge polesrelated to resonances that couple in the t channel.

)()ˆ/()()(),(Im tRB

RABABA

RsstftftsF

Regge Pole

In QCD the f’s only depend on t and the initial hadrons(like structure functions) factorize (Gell-Mann, Gribov, DGLAP), that is

GeVs

sstftftsF

sstftftsF

sstftftsF

tRR

tRN

RNN

tRN

RNNNNN

R

R

R

1ˆ

)ˆ/()()(),(Im

)ˆ/()()(),(Im

)ˆ/()()(),(Im

)(

)(

)(

So that we get the pole and fNR(t)/ fR(t) from N and NN scattering.

Regge parameters of N and NN J. R. Peláez and F.J. Ynduráin. hep-ph/0312187

Fit to 270 data points of N , KN and NN total cross sectionsfor kinetic energy between 1 and 16.5 GeV

2.5 3 4 5 6 7 8 9 10 15 20sGeV

20

30

40

50

60

latoT

NN,0

dnaNbm pp pp2

KpK p2 p

p

)(')(2

21

),,(

42 22

2ˆ sPsPP

PN

pp

pppp

f

f

mms

)())(')((

61

),,(

422

2

ssPsPP

PN

pf

f

mmsN

2 4 6 8 10sGeV

10

20

30

40

50

latoT

bm

Data : Robertson et al.

Biswas et al.

Hanlon et al.PY

Regge: PY

Hyams et al.

2 4 6 8 10sGeV

10

20

30

40

50

latoT

bm

+- (mb)

s(GeV)

1.5 2 2.5 3 3.5 4sGeV

10

20

30

40

50

latoT

0bm Regge: PY

Data: Biswas etal.

PY

1.5 2 2.5 3 3.5 4sGeV

10

20

30

40

50

latoT

0bm

Regge description of ,N, NN cross sections

1.5 2 5 10 15sGeV

10

20

30

40

50

latoT

bm

Regge: PY

Data: Robertson etal.Biswas etal.Abramowicz etal.

PYHooglandetal.

1.5 2 5 10 15sGeV

10

20

30

40

50

latoT

bm

-- (mb) 0- (mb)

Excelent fitabove 2 GeV

J. R. Peláez and F.J. Ynduráin. hep-ph/0312187

Results between total data and CERN- Munich for 1.4< s<2GeV

Matches CERN- Munich at 1.4 GeV.

4 EXPERIMENTS, ‘67, ’73, ’76,’80: IGNORED by Colangelo,Gasser & Leutwyler

Pomeranchuk theorem: Same 13.2±0.3 mb. CGL use 5±3 mb

Regge description of ,N, NN cross sections

Best Values

fNP/fP 1.406±0.007

0.366±0.010

0.94 ±0.10 ±0.10

P 2.56 ±0.03

P’ 1.05 ±0.05

Veneziano model ~0.95Rho dominance model ~0.84

: Excellent fit above 2 GeVHas to be used above >1.42 GeV

Quark-model value =3/2

Respects QCD factorization

Remarkable description of KWithin 20% of SU(3) limit= 0.82

fNP/fK

P 0.67±0.01

J. R. Peláez and F.J. Ynduráin. hep-ph/0312187

Impressive description of N, NN OUR DESCRIPTION

Drammatic improvement in Pomeron

1.5 2 5 10 15

sGeV10

20

30

40

50

latoT

bm

Regge: PY

Data: Robertson etal.Biswas etal.Abramowicz etal.

PYHooglandetal.

1.5 2 5 10 15sGeV

10

20

30

40

50

latoT

bm

2 4 6 8 10sGeV

10

20

30

40

50

latoT

bm

Data : Robertson et al.

Biswas et al.

Hanlon et al.PY

Regge: PY

Hyams et al.

2 4 6 8 10sGeV

10

20

30

40

50

latoT

bm

“non standard Regge” used in recent dispersive calculations.

1.5 2 2.5 3 3.5 4sGeV

10

20

30

40

50

latoT

0

bm Regge: PY

Data: Biswas etal.

PY

1.5 2 2.5 3 3.5 4sGeV

10

20

30

40

50

latoT

0

bm

+- (mb)

2 4 6 8 10sGeV

10

20

30

40

50

latoT

bm

Data : Robertson et al.

Biswas et al.

Hanlon et al.PY

Regge: PY

Hyams et al.

ACGL

2 4 6 8 10sGeV

10

20

30

40

50

latoT

bm

1.5 2 5 10 15sGeV

10

20

30

40

50

latoT

bm

ACGLRegge: PY

Data: Robertson etal.Biswas etal.Abramowicz etal.

PYHooglandetal.

1.5 2 5 10 15sGeV

10

20

30

40

50

latoT

bm

1.5 2 2.5 3 3.5 4sGeV

10

20

30

40

50

latoT

0

bm ACGLRegge: PY

Data: Biswas etal.

PY

1.5 2 2.5 3 3.5 4sGeV

10

20

30

40

50

latoT

0

bm

The “non standard Regge” of CGL lies systematically BELOW the DATA (despite the large compensates a bit the too small Pomeron)

s(GeV)

0- (mb)-- (mb)

Regge description of ,N, NN cross sections J. R. Peláez and F.J. Ynduráin. hep-ph/0312187

For us, a description up to ~15 GeV is enough, but at higher energies hadroniccross sections RAISE. We improve: )

)(loglog

~(

22/7

1

2

sss

sAPP

The <15 GeVdescription is unaffected

2 4 6 8 10sGeV

10

20

30

40

50

latoT

bm

Data : Robertson et al.

Biswas et al.

Hanlon et al.PY

Regge: PY

Hyams et al.

ACGL

2 4 6 8 10sGeV

10

20

30

40

50

latoT

bm

s

3 5 10 20 50 100 200 500 1000 2000 5000 10000 20000sGeV

40

60

80

100

120 pp pp2

s

Crossing sum rules to improve the rho residue

The crossing sum rule 02 222

122

2

121

)4(

)0,(Im)2(8)0,(Im)4,(Im

m mss

sFmsm

s

sFmsF ItItIt

ds

At low energy, the S wave cancels and the well known P wave dominates.At high energy is purely Regge rho exchange.

= 0.94 ±0.10(Stat.) ±0.10(Syst.)

J. R. Peláez and F.J. Ynduráin. hep-ph/0312187

Crossing sum rules satisfied if Regge is used

down to ~1.42 MeV

ConclusionThe Regge used by CGL does NOT describe the data.

The updated analysis confirms the mismatch in their analysis

QUESTIONS ON THE CGL CALCULATION

Inconsistent with other sum rules, high energy data, and Regge Theory

Ignores systematic errors in data

Input from scalar factor model dependent and challenged

Ignores systematic errors in data

One of their main sources of error is the matching phase at 800 MeV.CGL consider 11- 00 “in the hope” that some errors would cancel in that combination. NOWHERE the experimentalistsclaim that such cancellation occurs at 800 MeV. Experimentalists NEVER give such a difference.

ChPT + Roy Equations. Uncertainties on the matching point.

Combined with 11=108.9 ±2o they arrive at:

23.4 ±4o CERN-Munich Analysis B24.8 ±3.8o Estabrooks & Martin, “s-channel” 30.3 ±3.4 Estabrooks & Martin, “t-channel” 26.5 ±4.2 Protopopescu VI

26.6±3.7o11- 00 =26.6±2.8o

00=82.3 ±3.4o

Still, ACGL choose at 800 MeV:

Estabrooks & Martin: “ ...systematic changes in 00 of the order of 10o”

The CERN-Munich experiment has 5 analysis with 10o systematic errorBUT

ChPT + Roy Equations. Uncertainties on the matching point.

One of the largest sources of uncertainty is the matching phase at s = 800 MeV

The five CERN Munich analysis yield ~ 4o statistical errors in 00, but disagree

between themselves and the Berkeley data by ~ 10o systematic errors throughout the whole low energy region.

The differences at 800 are not oscillations of statistical nature that can be averaged but systematic errors of the different procedures to extract the phases

ChPT + Roy Equations. Uncertainties on the matching point.

Ananthanarayan, Colangelo Gasser & Leutwyler consider 11- 00 “in the hope”that some errors would cancel in that combination. NOWHERE the experimentalistsclaim that such cancellation occurs at 800 MeV. They NEVER give such a difference.

Combined with 11=108.9 ±2o they arrive at:

23.4 ±4o CERN-Munich Analysis B24.8 ±3.8o Estabrooks & Martin, “s-channel” 30.3 ±3.4 Estabrooks & Martin, “t-channel” 26.5 ±4.2 Protopopescu VI

26.6±3.7o11- 00 =26.6±2.8o

00=82.3 ±3.4o

Still, ACGL choose at 800 MeV:

Estabrooks & Martin: “ ...systematic changes in 00 of the order of 10o”

The CERN-Munich experiment has 5 analysis with 10o systematic error

Protopopescu also gives 11- 00=19 ±4 again 10o of systematic error

One of their largest sources of error is subestimated by a factor of 3

BUT

CONCLUSIONS

2) Neglects systematic errors in data from N: Most relevant input, phases at matching point (800MeV), assumed error 3.4o,

is too small by a factor up to 3 F.J. Ynduráin. ‘QCD@Work’, hep-ph/0310206

3) Other non-ChPT input: Pion scalar radius needed for l3. <r2>S=0.61+-0.04 fm2

Dispersive estimate model dependent. S. Descotes et al. EJPC24,469(2002)

Estimate with recent data <r2>S= 0.75+-0.06 fm2

Bound: <r2>S>=0.70+-0.06 fm2 F.J. Yndurain, Phys.Lett.B578:99-108,2004

Donoghue, Gasser, Leutwyler.NPB343,341(1990)

1) Inconsistent with High energy data and Regge:When using correct Regge behavior (as from QCD) in the Olsson and Froissart-Gribov sum rules there was a 2 to 4 sigma mismatch (even more now).

J. R. Peláez and F.J. Ynduráin. PRD68:074005,2003

The recent chiral dispersive scattering calculations by Colangelo Gasser & Leutwyler

With our most recent description of DATA, the mismatch persists.Several sum-rules OFF by 2.5 to 4 sigmas.

Factorization & crossing can be accomodated simultaneously in a Regge description of scattering data

J. R. Peláez and F.J. Ynduráin. PRD in press.

Using “data” from N +”Regge” +new Kl4 (E865 (01)) 10

0 012.0228.0 ma

120 0038.00382.0 ma

Descotes et al. Kaminski et al.

100 013.0224.0 ma

120 0036.00343.0 ma

Larger central valuesLarger errors

Despite using incorrect Regge, other recent Roy analysis safer due tolarger central values and errors

All numbers from Colangelo, Gasser and Leutwyler: scattering lengths, scattering phases, and the mass and width of the (f0(600))

should be taken cautiously, since the uncertainties are largely underestimated