The single-spin asymmetry in pp and
pA-collisions
V.V. Abramov, IHEP, Protvino
(NRC “Kurchatov Institute” SSC RF IHEP)
The 21st International Symposium on
Spin Physics (Spin2014)
October 20-24, 2014, Beijing, China
Talk content
1. Introduction to the Chromo-magnetic polarization of quarks
(CPQ) model
2. Comparison of single-spin asymmetry data and CPQ model
predictions for pp and pA-collisions
3. Calculation of AN(√s,pT,xF) in the framework of CPQ model in
unexplored yet kinematical regions
4. Conclusions
2
Studies performed over the past 35 years have shown that there are
significant spin effects in the inclusive processes at energies from a
few GeV up to hundreds of GeV in the c.m.s.
Object of the study - single-spin processes:
A↑ +B → C + X (single-spin asymmetry AN(√s,pT,xF) (1)
The presence of large (> 10%) spin effects can not be explained within
the framework of QCD perturbation theory:
AN ~ PN ~ αsmq/pT ≈ 0,1%.
(2)
Further experimental studies and a global analysis of all available
information on single-spin processes are needed. This studies will
reveal regularities in the behavior of the polarization data, including
the dependence on the type of hadrons participating in the reaction.
3
Chromo-magnetic polarization of quarks (CPQ) model
1) After initial color charge-exchange longitudinal chromoelectric
field Ea and circular transverse chromomagnetic field Ba are generated.
2) Single-spin asymmetry is due to the Stern-Gerlach force acting on a
quark in inhomogeneous transverse circular chromomagnetic field.
3) Quark spin precession in the color fields leads to the oscillation of
AN (xF) and PN (xF) in case of strong field, and to their approximate
linear dependence on xF in the case of weak field.
4) Quark flow diagrams and quark counting rules (QCR) describe the
contributions of quarks and antiquarks to the effective color field.
Contributions of quarks and antiquarks are linear functions of their
numbers with weights determined by the color factors CF(qq) and
CF(qq̃).
[1] V.V. Abramov, Phys. At. Nucl. 72 (2009) 1872.
4
Circular transverse chromomagnetic field
There are longitudinal chromoelectric field Ea and circular transverse
chromomagnetic field and Ba.
A.B.Migdal, S.B.Khohlachev, JETP Lett. 41 (1985) 194.
M.G. Ryskin, Sov. J. Nucl. Phys. 48 (1988) 708.
μaQ = sgags/2MQ – chromomagnetic moment of the constituent quark.
Ryskin’s model describes AN for π0,π± in π-p↑ and p↑p,
(3)
PN for pA→Λ↑ X.
Model of chromomagnetic quark polarization
(microscopic Stern-Gerlach apparatus):
5
Quark spin precession in the color field
dξ/dt ≈ a[ξ Ba]
(F-T-BMT-equation)
a = gs(gaQ – 2 + 2MQ/EQ)/2MQ
Quark masses MU ≈ MD ≈ 0.3 GeV, EQ – quark energy.
(4)
(5)
ΔμaQ =(gaQ-2)/2 (quark anomalous chromomagnetic moment).
 Due to the spontaneous breaking of chiral symmetry appear the
ΔMQ(q) ≈ 0.3 GeV and ΔμaQ(q) of the constituent quarks.
ΔμaQ (0) ≈ –0.4
(N. Kochelev);
ΔμaQ (0) ≈ –1.6
(D. Diakonov).
 Model-dependent estimate of ΔμaQ for u,d,s,c,b-quarks are obtained
from the global data analysis of polarization data:
 ΔμaQ (u,c) = -0,471±0,007,
q=+2/3;
 ΔμaQ (d,s,b) ≈ √(2/3) ΔμaQ(u,c),
q=-1/3.
In the instanton model:
6
Equations for AN, PN and (ρ00-1/3)
AN ≈ C(√s) F(pT, A)[G(φA) – σG(φB) ],
(6)
G(A) = [1 – cos A]/A + εφA, spin precession and S-G force (7)
C (√s) = v0/[(1 - ER/√s )2+δR2]1/2,
spin precession vs EQ
(8)
F(pT,A) ={1 - exp[-(pT/p0T)2.5 ]}(1 -αA lnA), color form factor (9)
v0 = -Dr gaQ ξ0y /2(gaQ –2 ),
φA = ω0AyA,
φB = ω0ByB ,
magnitude of AN and PN
(10)
integral precession angles (11)
yA = xA – (E0/√s + f0 )[1 + cosθcm ] + a0[1 – cosθcm ],
(12)
yB = xB – (E0/√s + f0 )[1 – cosθcm ] + a0[1 + cosθcm ],
(13)
xA = (xR+xF)/2, xB= (xR-xF)/2.
scaling variables (14)
ω0A(B) = gsαsνA(B) S0(gaQ – 2)/(MQ cρ2), ε = -0.00476 ± 0.00011. (15)
νA(B) - effective contributions of the spectator quarks to the field Ba. 7
Quark counting rules for νA (A + B → C + X)
SPECTATORS
∫Ea ~ ∫Ba ~ νA= [3λ - 3τ λ] <0;
∫Ea ~ ∫Ba ~ νA=[2 + 2λ - 3τ λ] >0
AN ~ PUνA(gaU - 2)/2MU > 0;
PN ~ νA(gaS -2)/2MS < 0.
qq, q̃q̃ -SU(3)c antitriplet, weight ν = λ;
CF = 2/3 – color factor
weight ν = 1.
CF = 4/3 – color factor
qq̃, q̃q -SU(3)c singlet,
 S.P. Baranov, Phys. Rev. D54, 3228 (1996).
 λ = −|ψqq(0)|2 /|ψq q̃(0)|2  1-e1/8  -0.1332
 λ = −0.1338±0.0014, τ = 0.0265±0.0009
|ψ|2 ~ (CFαS)3. (16)
color factor (17)
for 80 reactions.
8
Comparison of data and the CPQ model calculations
+
-
Fig. 1. AN(xF) in reaction p↑ + p(A)
→ π++X at √s = 200 (1a, 1b), 64.2 (2),
19.4 (3) and 8.77 (4) GeV.
Рис. 2. AN(xF) in reaction p↑ + p(A)
→ π-+X at √s = 200 (1a, 1b), 64.2 (2),
19.4 (3) and 8.77 (4) GeV.
The data are from BRAHMS(RHIC) (1a,1b, 2), E704(FNAL) (3) and FODS(IHEP) (4).
9
Predictions of the CPQ model for p↑ + p → π++X
+
Fig. 3. AN(xF) in the
reaction p↑ + p → π++X.
pT=3 GeV/c for √s>60 GeV
and 2 GeV/c for √s≤60 GeV.
+
Fig. 4. AN(xF) in the
reaction p↑ + p → π-+X.
xF=0.45.
√s = 500 (1), 200 (2), 130 (3), 64.2 (4), 19.4 (5) and 8.77 (6) GeV.
An approximate scaling of AN(xF) is seen for √s ≤ 70 GeV.
10
Predictions of the CPQ model for p↑ + p(A) → π-+X
-
Fig. 5. AN(xF) in the
reaction p↑ + p → π-+X.
pT=3 GeV/c for √s>60 GeV
and 2 GeV/c for √s≤60 GeV.
Fig. 6. AN(xF) in the
reaction p↑ + p → π-+X.
xF=0.45.
√s = 500 (1), 200 (2), 130 (3), 64.2 (4), 19.4 (5) and 8.77 (6) GeV.
Scaling of AN(xF) is violated for √s > 70 GeV due to qq̃ –pair production.
11
Comparison of data and the CPQ model calculations
Fig. 7. AN(xF) in the reaction
p↑ + p → π0+X at √s = 19.4 (1),
9.78 (2), and 200 (3) GeV.
Рис. 8. AN(xF) in reaction
p↑ + p → π0+X at xF=0.2 (1), 0.28 (2),
and 0.36 (3). STAR,√s = 500 GeV.
The data are from STAR(RHIC) (3), E704(FNAL) (1) and FODS(IHEP) (2).
12
Predictions of the CPQ model for p↑ + p → π0+X
Fig. 9. AN(xF) in the
reaction p↑ + p → π0+X.
pT=3 GeV/c for √s>60 GeV
and 2 GeV/c for √s≤60 GeV.
Fig. 10. AN(xF) in the
reaction p↑ + p → π0+X.
xF=0.45.
√s = 500 (1), 200 (2), 130 (3), 64.2 (4), and 8.77 (5) GeV.
13
Comparison of data and the CPQ model calculations
K+
Fig. 11. AN(xF) in the reaction
p↑ + p(A) → K++X at √s = 200
(1), 64.2 (2), and 8.77 (3) GeV.
K-
Рис. 12. AN(xF) in the reaction
p↑ + p(A) → K-+X at √s = 200 (1),
64.2 (2), 8.77 (3) and 4.89 (4) GeV.
The data are from BRAHMS(RHIC) (1, 2), FODS(IHEP) (3) and ANL (4).
14
Predictions of the CPQ model for p↑ + p → K++X
K+
Fig. 13. AN(xF) in the
reaction p↑ + p → K++X.
pT=3 GeV/c for √s>60 GeV
and 2 GeV/c for √s≤60 GeV.
K+
Fig. 14. AN(xF) in the
reaction p↑ + p → K++X.
xF=0.45.
√s = 500 (1), 200 (2), 130 (3), 64.2 (4), 19.4 (5) and 8.77 (6) GeV.
15
Predictions of the CPQ model for p↑ + p → K-+X
K-
K-
Fig. 13. AN(xF) in the
reaction p↑ + p → K-+X.
pT=3 GeV/c for √s>60 GeV
and 2 GeV/c for √s≤60 GeV.
Fig. 14. AN(xF) in the
reaction p↑ + p → K-+X.
xF=0.45.
√s = 500 (1), 200 (2), 130 (3), 64.2 (4), 19.4 (5) and 8.77 (6) GeV.
16
Comparison of data and the CPQ model calculations
p
p̃
Fig. 15. AN(xF) in the reaction
p↑ + p(A) → p +X at √s = 200 (1),
64.2 (2), 8.77 (3) and 6.51 (4) GeV.
Рис. 16. AN(xF) in the reaction
p↑ + p(A) → p̃ +X at √s = 200 (1),
8.77 (2) GeV.
The data are from BRAHMS(RHIC) (1, 2), FODS(IHEP) (2,3) and ANL (4).
17
Predictions of the CPQ model for p↑ + p → p +X
p
Fig. 17. AN(xF) in the
reaction p↑ + p → p +X.
pT=3 GeV/c for √s>60 GeV
and 2 GeV/c for √s≤60 GeV.
p
Fig. 18. AN(xF) in the
reaction p↑ + p → p +X.
xF=0.45.
√s = 500 (1), 200 (2), 130 (3), 64.2 (4), 19.4 (5) and 8.77 (6) GeV.
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Predictions of the CPQ model for p↑ + p → p̃ +X
p̃
Fig. 19. AN(xF) in the
reaction p↑ + p → p̃ +X.
pT=3 GeV/c for √s>60 GeV
and 2 GeV/c for √s≤60 GeV.
p̃
Fig. 20. AN(xF) in the
reaction p↑ + p → p̃ +X.
xF=0.45.
√s = 500 (1), 200 (2), 130 (3), 64.2 (4), 19.4 (5) and 8.77 (6) GeV.
19
References to the Chromo-magnetic polarization of quarks model
[1] V.V. Abramov, Phys. At. Nucl. 72 (2009) 1872.
[2] V.V. Abramov, Phys. Part. Nucl. 45 (2014) 62.
[3] V.V. Abramov, J. Phys. Conf. Ser. 295 012086 (2011).
[4] V.V.Abramov, Proc. of the XIV Advanced Research Workshop on High Energy
Spin Physics (DSPIN-11), edited by A.V. Efremov and S.V. Goloskokov (Dubna,
2012) p. 21-26.
[5] V.V.Abramov, Proc. of the XIII Advanced Research Workshop on High Energy
Spin Physics (DSPIN-09), edited by A.V. Efremov and S.V. Goloskokov (Dubna,
2010) p. 25-28. e-Print: arXiv:0910.1216 [hep-ph].
[6] V.V. Abramov, Proc. of the XII Advanced Research Workshop on High Energy
Spin Physics (DSPIN-07), edited by A.V. Efremov and S.V. Goloskokov (Dubna,
2008) p. 13-16. e-Print: arXiv:0711.0323 [hep-ph].
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References to the single-spin data
BRAHMS Coll., √s=62.4 and 200 GeV, AN for π+, π-, K+ , K-, p and p̃.
[1] I.Arsene et al., Phys.Rev.Lett. 101(2008)042001.
FODS Coll., √s=8.77 GeV, AN for π+, π-, K+ , K-, p and p̃.
[2] V.V.Abramov et al., Phys.Atom.Nucl. 70 (2007) 1515-1526.
E704 Coll., √s=19.4 GeV, AN for π+, π- and π0.
[3] D.L. Adams et al., PL 264B(1991)462. (π+, π-).
[4] D.L. Adams Phys.Rev. D53 (1996)4747-4755. (π0).
STAR Coll., √s=200 and 500 GeV, AN for π0.
[5] L.Adamczyk et al., Phys.Rev. D86 (2012) 051101.
[6] B.I.Abelev et al., Phys.Rev.Lett. 101 (2008) 222001.
[7] Y.Pan, Phys.Part.Nucl. 45 (2014) 105-107 (500 GeV).
[8] S.Heppelmann, PoS DIS2013 (2013) 240 (500 GeV).
PROZA Coll., √s=9.78 GeV, AN for π0.
[9] V.V.Abramov et al., Phys.Atom.Nucl. 77 (2014) 595-601.
PROZA Coll., √s=9.78 GeV, AN for π0.
[10] V.V.Abramov et al., Phys.Atom.Nucl. 77 (2014) 595-601.
[11] K.Krueger,C.Allgower et al., Phys.Lett.B459(1999)412 (p+, √s=6.51 GeV)
[12] W.H.Dragoset et al., Phys.Rev. D18 (1978) 3939-3954 (K-, √s=4.89 GeV).
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Conclusions
1) AN(xF) shows an approximate scaling for π+, π-, π0 and K+
production at √s < 70 GeV. Polarized valence quarks go to the
observed hadrons for these reactions.
2) Generation of new qq̃ pairs at √s > 70 GeV violates this AN(xF)
scaling for π+, π-, π0, K+ production.
3) AN(xF)>0 at large xF > 0.5 and √s < 70 GeV for K- and p̃ are similar
to AN(xF) for π+ due to the dominance of u-quark fragmentation.
4) Large oscillating AN(xF) is expected for proton production due to
valence quark spin precession in the effective color field.
5) Predictions are made for single-spin asymmetry in p↑p-collisions in
a wide range of kinematical variables.
22