10/6/2006 e. de la cruz burelo, spin 2006, kyoto japan 1 hyperon polarization in a quark-quark...

10/6/200610/6/2006E. De La Cruz Burelo, SPIN 2006, KyE. De La Cruz Burelo, SPIN 2006, Kyoto Japan oto Japan

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Hyperon polarization in a Hyperon polarization in a quark-quark scattering modelquark-quark scattering model

Eduard De La Cruz BureloEduard De La Cruz Burelo

Homer A. NealHomer A. Neal

10/6/200610/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 22

OutlineOutline Hyperon polarization remains a major Hyperon polarization remains a major

open question even at energies of open question even at energies of hundreds of GeVhundreds of GeV

Extraordinary behavior of hyperon Extraordinary behavior of hyperon polarization has no simple explanationpolarization has no simple explanation

Polarization in Polarization in pppp pp pp and and pppp H H + X+ X : : could both be the result of simple quark-could both be the result of simple quark-quark scattering?quark scattering?

A proposed model based on quark-quark A proposed model based on quark-quark scattering.scattering.

The qualitative explanation of the hyperon The qualitative explanation of the hyperon polarization for a variety of processespolarization for a variety of processes


Hyperon polarizationHyperon polarization

An unresolved question: An unresolved question: What causes the large polarization in What causes the large polarization in

inclusive hyperon production in p-p inclusive hyperon production in p-p collisions?collisions?

Vanishingly small polarizations are Vanishingly small polarizations are predicted in QCD. predicted in QCD.

No model is now able to explain all No model is now able to explain all features of Hyperon polarization at features of Hyperon polarization at the same time.the same time.


ParticleParticle Quark content* PolarizationPolarization

pN pN H+X H+XΛΛ00 (ud)0 s Negative

ΣΣ00 (ud)1 s Positive

ΣΣ++ (uu)1 s Positive

ΣΣ-- (dd)1 s Positive

ΞΞ-- (ss)1 d Negative

ΞΞ00 (ss)1 u Negative

ΩΩ-- s s s ~Zero

ΛΛ00 (u d)0 s Zero

ΞΞ++ (s s)1 d Negative

ΣΣ-- (ūū)1 s Positive

ΛΛbb(ud)0 b ?

Hyperon polarization Hyperon polarization characteristicscharacteristics

ParticleParticle Quark content* PolarizationPolarization

pN pN H+X H+XΛΛ00 (ud)0 s Negative

ΣΣ00 (ud)1 s Positive

ΣΣ++ (uu)1 s Positive

ΣΣ-- (dd)1 s Positive

ΞΞ-- (ss)1 d Negative

ΞΞ00 (ss)1 u Negative

ΩΩ-- s s s ~Zero

ΛΛ00 (u d)0 s Zero

ΞΞ++ (s s)1 d Negative

ΣΣ-- (ūū)1 s Positive

* (Diquark)J state

J=0 : Negative

J = 1 + s quark:

Positive

2 s-quarks: Negative

Plans to measure it (LHC)


ΛΛ00: Lowest mass hyperon … : Lowest mass hyperon … more intriguingmore intriguing

Very little dependence on the initial proton energy and in the target material.

Grows negative linearly with pT until a plateau is reached around 1 GeV/c.

For constant xF (=pL/pmax) value, the plateau extends from 1 GeV/c to the highest measured pT.


Intriguing questions:Intriguing questions:

Why do the Λ0 and Ξ polarizations look similar?

Why is the Σ polarization positive?

Why is the Ω polarization almost ~zero?

Why is there a plateau in the Λ0 polarization?


Features we would like to Features we would like to explain:explain:

The shape and magnitude of the The shape and magnitude of the ΛΛ0 0

polarizationpolarization The different signs in the The different signs in the ΛΛ0 0 and and ΣΣ

polarizationpolarization The similarity of the polarization for The similarity of the polarization for

the the ΛΛ0 0 and and ΞΞ The small value of the The small value of the ΩΩ polarization polarization


q-q scattering: relating pp q-q scattering: relating pp pp pp to pp to pp ΛΛ + X process + X process

Is there any connection between the Is there any connection between the observed polarization in these two observed polarization in these two processes? processes? – They could come from the same source: quark-They could come from the same source: quark-

quark scattering.quark scattering.

udu u

d

s

Λ0pro

tonu

dup

roto

n

u

du p

roto

n udu u

d

s

pro

tonu

dup

roto

n udu p

roto

n

u

ssss ssΛ0


pppppp in a quark-quark pp in a quark-quark scattering modelscattering model

Neal et al. proposed a q-q scattering model to explain the polarization in elastic p-p scattering:

First region is due to q-q scattering

Second region is due to 2q-2q or q-2q

Subsequent data is consistent with 3q-3q scattering*.

Can we apply the same idea to Can we apply the same idea to

pppp ΛΛ + X process? + X process?

Neal et al. proposed a q-q scattering model to explain the polarization in elastic p-p scattering:

First region is due to q-q scattering

Second region is due to 2q-2q or q-2q

Subsequent data is consistent with 3q-3q scattering*.

Can we apply the same idea to Can we apply the same idea to

pppp ΛΛ + X process? + X process?

H.A. Neal et al.

Phys. Lett. B 51 (1974) 79*) H.A. Neal et al.

Phys. Lett. B 439 (1998) 407


pppp ΛΛ + X in a quark-quark + X in a quark-quark scattering modelscattering model

From a preexisting pair in the incoming From a preexisting pair in the incoming proton, the s quark scatters, get highly proton, the s quark scatters, get highly polarized, and end up in the hyperon.polarized, and end up in the hyperon.

Hyperon polarization: PHyperon polarization: PHH=P=Pqq(x,p(x,pTT). ). PPqq(x(xFF,p,pTT) : quark polarization effect due to a ) : quark polarization effect due to a q-q scattering process.q-q scattering process.

ss


ΛΛ00 polarization from polarization polarization from polarization in in pppppp (1)pp (1)

Model: Model: PPHH=P=Pqq(x,p(x,pTT))

– In a multiple quark scattering* P In a multiple quark scattering* P ~ mqPq(pT)

*) J. Szwed, Phys. Lett. B 105 (1981) 403.

2

1~

)(

)(0

s

u

m

m

XppP

ppppP

Assuming ms~2mu

)()(2 0 XppPppppP


ΛΛ00 polarization from polarization polarization from polarization in in pppppp (2)pp (2)

What pWhat pTT((ΛΛ00)) vs. p vs. pTT(p) should we compare?(p) should we compare?– For a elastic p-p scattering in a q-q region (Neal et al.):

– For pp Λ + X in q-q region:

We should compare at:We should compare at:

)()( qppp TT

)(2

3)()()( 00 TTTT psppsp

Assuming s-quark account for half of the Λ0 mass.

)()(3

2 0 TT ppp


Comparison of proton and Comparison of proton and ΛΛ00 polarizationpolarization

Proton polarization multiplied by 2

Proton pT multiplied by 2/3

If we let proton data to tell us what values prefer to match Λ0 data, selected values are around to 2 and 2/3.


What about the plateau?What about the plateau?

The plateau in the Λ0 polarization can be understood as the saturation of the s quark polarization (P=100%).

Po

lari

zati

on

Po

lari

zati

on


Explaining the other featuresExplaining the other features

Why the similar polarization for the Why the similar polarization for the ΛΛ0 0 and and ΞΞ??

If the polarization of both hyperons is due to one s quark becoming highly polarized from the scattering process, then we expect the polarization of both hyperons to be similar.


Why the different sign in the Why the different sign in the ΛΛ0 0

and and ΣΣ polarization? polarization?

u d

s

u d

s

Beam quarks does not Beam quarks does not contributed to the contributed to the ΛΛ00 polarizationpolarization

s quark is responsible for the s quark is responsible for the large polarization of the large polarization of the ΛΛ00..

s quark polarization is negative.s quark polarization is negative.

s quark polarization is negative which force the polarization of the u and d quarks to be positive, so overall polarization is positive.

If we assume the s quark being responsible of the polarization, it can be showed that the sign of the Σ polarization is opposite to that of the Λ polarization.


Why Why ΩΩ polarization is ~0?polarization is ~0?

One of 3 s quarks get polarized in the scattering, One of 3 s quarks get polarized in the scattering, setting a maximum of 33% to the polarization of setting a maximum of 33% to the polarization of the the ΩΩ..

Should be similar to the Should be similar to the ΛΛ00 polarization in the one polarization in the one quark scattering region.quark scattering region.

Λ0 polarization compared to the Ω polarization. Statistics too low to make strong conclusions.


Future tests/ImplicationsFuture tests/Implications

ΛΛb b polarization is planned to be measured polarization is planned to be measured

in LHC (ATLAS & LHCb)in LHC (ATLAS & LHCb) Polarization could be huge if the q-q Polarization could be huge if the q-q

contribution to production is important and contribution to production is important and the Szwed mass scaling holds.the Szwed mass scaling holds.

Simple relation should exist between Simple relation should exist between ΛΛ and and ΛΛbb polarization is our q-q idea is polarization is our q-q idea is

correct.correct.


Conclusions:Conclusions:

A model based in a simple q-q scattering A model based in a simple q-q scattering process is proposed:process is proposed:

Polarization due the scattering process PPolarization due the scattering process Pqq(p(pTT) is the ) is the same for all quark species.same for all quark species.

s quark scatters from the incoming proton is the s quark scatters from the incoming proton is the responsible for the large hyperon polarization.responsible for the large hyperon polarization.

ΛΛ and proton polarization seems to have a and proton polarization seems to have a common source.common source.

The model is able to qualitatively address The model is able to qualitatively address all of the main observed features of all of the main observed features of hyperon polarization.hyperon polarization.

10/6/2006 e. de la cruz burelo, spin 2006, kyoto japan 1 hyperon polarization in a quark-quark...

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