Transcript Strange Quarks Polarisation from Gluon Anomaly IWHSS

тяжелая странность
Multiscale Nucleon and Heavy
Strangeness
Сессия-конференция Секции Ядерной
физики Отделения Физических наук РАН
Протвино , ИФВЭ, 24 декабря 2008 г.
О.В. Теряев
ЛТФ ОИЯИ
Heavy strange quark?!
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With respect to WHAT?
Light with respect to hadron mass
BUT
Heavy with respect to higher twists
parameters
Multiscale nucleon
Possible origin – small correlations of gluon
(and quark) fields
Outline
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Axial (and trace) anomaly for massless and massive
fermions: decoupling
Axial anomaly and heavy quarks polarization in
nucleon
When strange quarks can be heavy: multiscale
hadrons
Support: small higher twist with IR safe QCD coupling
Strangeness sign and transversity
(Heavy) unpolarized strangeness momentum
Charm/strange universality?
Conclusions
Symmetries and conserved
operators
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(Global) Symmetry -> conserved
current (   J   0 )
Exact:
U(1) symmetry – charge conservation electromagnetic (vector) current
Translational symmetry – energy
momentum tensor T  0
Massless fermions (quarks) –
approximate symmetries
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Chiral symmetry (mass flips the helicity)
  J 5  0
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Dilatational invariance (mass introduce
dimensional scale – c.f. energymomentum tensor of electromagnetic
radiation )
T  0
Quantum theory
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Currents -> operators
Not all the classical symmetries can be
preserved -> anomalies
Enter in pairs (triples?…)
Vector current conservation <-> chiral
invariance
Translational invariance <-> dilatational
invariance
Calculation of anomalies
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Many various ways
All lead to the same operator equation
UV vs IR languagesunderstood in physical
picture (Gribov, Feynman,
Nielsen and Ninomiya)
of Landau levels flow (E||H)
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Counting the Chirality
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Degeneracy rate of Landau levels
“Transverse”
HS/(1/e)
(Flux/flux quantum)
“Longitudinal” Ldp= eE dt L
(dp=eEdt)
Anomaly – coefficient in front of
4-dimensional volume - e2 EH
Massive quarks
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One way of calculation – finite limit of
regulator fermion contribution (to TRIANGLE
diagram) in the infinite mass limit
The same (up to a sign) as contribution of
REAL quarks
For HEAVY quarks – cancellation!
Anomaly – violates classical symmetry for
massless quarks but restores it for heavy
quarks
Dilatational anomaly
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Classical and anomalous terms
Beta function – describes the appearance of
scale dependence due to renormalization
For heavy quarks – cancellation of classical
and quantum violation -> decoupling
Decoupling
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Happens if the symmetry is broken both
explicitly and anomalously
Selects the symmetry in the pair of anomalies
which should be broken (the one which is
broken at the classical level)
For “non-standard” choice of anomalous
breakings (translational anomaly) there is no
decoupling
Defines the Higgs coupling, neutralino
scattering…
Heavy quarks matrix elements
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QCD at LO
From anomaly cancellations (27=33-6)
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“Light” terms
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Dominated by s-of the order of cancellation
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Heavy quarks polarisation
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Non-complete cancellation of mass and anomaly terms
(97)
Gluons correlation with nucleon spin – twist 4 operator NOT directly
related to twist 2 gluons helicity BUT related by QCD EOM to singlet
twist 4 correction (colour polarisability) f2 to g1
“Anomaly mediated” polarisation of heavy quarks
Numerics
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Small (intrinsic) charm polarisation
Consider STRANGE as heavy! – CURRENT
strange mass squared is ~100 times smaller –
-5% - reasonable compatibility to the data!
(But problem with DIS and SIDIS)
Current data on f2 – appr 50% larger
Can s REALLY be heavy?!
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Strange quark mass close to matching scale
of heavy and light quarks – relation between
quark and gluon vacuum condensates (similar
cancellation of classical and quantum
symmetry violation – now for trace anomaly).
BUT - common belief that strange quark
cannot be considered heavy,
In nucleon (no valence “heavy” quarks)
rather than in vacuum - may be considered
heavy in comparison to small genuine higher
twist – multiscale nucleon picture
Are higher twists small?
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More theoretically clear – non singlet
case – pQCd part well known (Bjorken
sum rule)
Low Q region – Landau pole – IR stable
coupling required (Analytic,freezing…)
Allows to use very accurate JLAB data
to extract HT
Advantage of “denominator”
form of QCD coupling
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“PDG” expansion
“Denominator” form – no artificial
singularities
Higher twists from Bjorken
Sum Rule
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Accurate data + IR stable coupling -> low Q
region
HT – small indeed
Down to Lambda
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pQCD+ HT
Comparison : Gluon Anomaly for
massless and massive quarks
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Mass independent
Massless – naturally (but NOT uniquely) interpreted
as (on-shell) gluon circular polarization
Small gluon polarization – no anomaly?!
Massive quarks – acquire “anomaly polarization”
May be interpreted as a kind of circular polarization
of OFF-SHELL (CS projection -> GI) gluons
Very small numerically
Small strange mass – partially compensates this
smallness and leads to % effect
Sign of polarisation
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Anomaly – constant and OPPOSITE to
mass term
Partial cancellation – OPPOSITE to mass
term
Naturally requires all “heavy” quarks
average polarisation to be negative IF
heavy quark in (perturbative) heavy
hadron is polarised positively
Heavy Strangeness
transversity
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Heavy strange quarks – neglect higher twist:
0=
Strange transversity - of the same sign as
helicity and enhanced by M/m
But: only genuine HT may be be small –
relation to twist 3 part of g2
Unpolarized strangeness – can
it be considered as heavy?
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Heavy quark momentum – defined by
<p|GGG|p> matrix element
(Franz,Polyakov,Goeke)
IF no numerical suppression of this matrix
element – charm momentum of order 0.1%
IF strangeness can be also treated as heavy –
too large momentum of order 10%
Heavy unpolarized
Strangeness: possible escape
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Conjecture: <p|GGG|p> is suppressed
by an order of magnitude with respect
to naïve estimate
Tests in models/lattice QCD?
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Charm momentum of order 0.01%
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Strangeness momentum of order of 1%
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Charm/Strangeness
universality
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Universal behaviour of\heavy quarks
distributions
c(x)/s(x) = (ms /mc)2 ~ 0.01
Delta c(x)/Delta s(x)= (ms /mc)2 ~ 0.01
Delta c(x)/Delta s(x)= c(x)/s(x)
Experimental tests – comparison of
strange/charmed hadrons asymmetries
Higher corrections
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Universality may be violated by higher mass
corrections
Reasonable numerical accuracy for strangeness – not
large for s –> negligible for c
If so, each new correction brings numerically small
mass scale like the first one
Possible origin – semiclassical gluon field
If not, and only scale of first correction is small,
reasonable validity for s may be because of HT
resummation
Conclusions
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Heavy quarks – cancellation of anomalous
and explicit symmetry breaking
Allows to determine some useful hadronic
matrix elements
Multiscale picture of nucleon - Strange quarks
may be considered are heavy sometimes
Possible universality of strange and charmed
quarks distributions – similarity of spin
asymetries of strange and charmed hadrons
Other case of LT-HT relations – naively
leading twists TMD functions –>infinite
sums of twists.
Case study: Sivers function - Single Spin
Asymmetries
Main properties:
– Parity: transverse polarization
– Imaginary phase – can be seen T-invariance
or technically - from the imaginary i in the
(quark) density matrix
Various mechanisms – various sources of
phases
Phases in QCD
QCD factorization – soft and hard parts Phases form soft, hard and overlap
 Assume (generalized) optical theorem –
phase due to on-shell intermediate states –
positive kinematic variable (= their invariant
mass)
 Hard: Perturbative (a la QED: Barut, Fronsdal
(1960):
Kane, Pumplin, Repko (78) Efremov (78)
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Perturbative PHASES IN QCD
Short+ large overlap–
twist 3
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Quarks – only from hadrons
Various options for factorization – shift of SH
separation
New option for SSA: Instead of 1-loop twist 2
– Born twist 3: Efremov, OT (85, Ferminonc
poles); Qiu, Sterman (91, GLUONIC poles)
Twist 3 correlators
Twist 3 vs Sivers function(correlation
of quark pT and hadron spin)
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Twist 3 – Final State Interaction -qualitatively
similar to Brodsky-Hwang-Schmidt model
Path order exponentials (talk of N. Stefanis)
– Sivers function (Collins; Belitsky, Ji, Yuan)
Non-suppressed by 1/Q-leading twist? How it
can be related to twist 3?
Really – infinite sum of twists – twist 3
selected by the lowest transverse moment
Non-suppression by 1/Q – due to gluonic pole
= quarks correlations with SOFT gluons
Sivers and gluonic poles at large
PT
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Sivers factorized (general!) expression
M – in denominator formally leading
twist (but all twists in reality)
Expand in kT = twist 3 part of Sivers
From Sivers to twist 3 - II
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Angular average :
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As a result
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M in numerator - sign of twist 3. Higher moments –
higher twists. KT dependent function – resummation
of higher twist.
Difference with BFKL IF – subtracted UV; Taylor
expansion in coordinate soace – similar to vacuum
non-local condensates
From Sivers to gluonic poles III
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Final step – kinematical identity
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Two terms are combined to one
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Key observation – exactly the form of Master
Formula for gluonic poles (Koike et al, 2007)
Effective Sivers function
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Expressed in terms of twist 3
x
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f
(1)
S
( x )   Ci
1
T j ( x, x ),
2M
Up to Colour Factors !
Defined by colour correlation between
partons in hadron participating in (I)FSI
SIDIS = +1; DY= -1: Collins sign rule
Generally more complicated
Factorization in terms of twist 3 but NOT SF
Colour correlations
SIDIS at large pT : -1/6 for mesons from quark, 3/2 from gluon
fragmentation (kaons?)
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DY at large pT: 1/6 in quark antiquark annihilation, - 3/2 in
gluon Compton subprocess – Collins sign rule more elaborate –
involve crossing of distributions and fragmentations - special
role of PION DY (COMPASS).
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Direct inclusive photons in pp = – 3/2
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Hadronic pion production – more complicated – studied for Pexponentials by Amsterdam group + VW
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IF cancellation – small EFFECTIVE SF (cf talk of F. Murgia)
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Vary for different diagrams – modification of hard part
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FSI for pions from quark fragmentation
-1/6 x (non-Abelian Compton) +1/8 x (Abelian Compton)
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Colour flow
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Quark at large PT:-1/6
Gluon at large PT : 3/2
Low PT – combination of quark and gluon:
4/3 (absorbed to definition of Sivers
function)
Similarity to colour transparency
phenomenon
Twist 3 factorization (Bukhvostov,
Kuraev, Lipatov;Efremov, OT;
Ratcliffe;Qiu,Sterman;Balitsky,Braun)
• Convolution of soft
(S) and hard (T) parts
• Vector and axial
correlators: define
hard process for both
double (g ) and single
asymmetries
2
Twist 3 factorization -II
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Non-local operators for quark-gluon
correlators
Symmetry properties (from Tinvariance)
Twist-3 factorization -III
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Singularities
Very different: for axial – Wandzura-Wilczek
term due to intrinsic transverse momentum
For vector-GLUONIC POLE (Qiu, Sterman ’91)
– large distance background
Sum rules
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EOM + n-independence (GI+rotational
invariance) –relation to (genuine twist
3) DIS structure functions
Sum rules -II
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To simplify – low moments
Especially simple – if only gluonic pole
kept:
Gluonic poles and Sivers
function
• Gluonic poles – effective
Sivers functions-Hard and
Soft parts talk, but
SOFTLY
• Implies the sum rule for
effective Sivers function x
(soft=gluonic pole
dominance assumed in the
whole allowed x’s region 1
of quark-gluon correlator) 
0
f
T
( x) 
2
dxx
_
1
1
T ( x, x )   ( x )
2M
4 v
1
4
g 2 ( x) 
dxx

3 0
f
T
( x)(2  x)
Compatibility of SSA and DIS
• Extractions of and modeling of Sivers function: –
“mirror” u and d
• Second moment at % level
• Twist -3 g - similar for neutron and proton and of the
same sign – no mirror picture seen –but supported by
colour ordering!
• Scale of Sivers function reasonable, but flavor
dependence differs qualitatively.
• Inclusion of pp data, global analysis including gluonic
(=Sivers) and fermionic poles
• HERMES, RHIC, E704 –like phonons and rotons in
liquid helium; small moment and large E704 SSA
imply oscillations
• JLAB –measure SF and g2 in the same run
2
CONCLUSIONS
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(At least) 2 reasons for relations between
various twists:
exact operator equations
naively leading twist object contains in reality
an infinite tower
Strange quark (treated as heavy) polarization
– due to (twist 4, anomaly mediated) gluon
polarization
Sivers function is related to twist 4 gluonic
poles – relations of SSA’s to DIS
2nd Spin structure - TOTAL Angular
Momenta - Gravitational Formfactors
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Conservation laws - zero Anomalous
Gravitomagnetic Moment :
(g=2)
May be extracted from high-energy
experiments/NPQCD calculations
Describe the partition of angular momentum between
quarks and gluons
Describe interaction with both classical and TeV
gravity
Electromagnetism vs Gravity
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Interaction – field vs metric deviation
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Static limit
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Mass as charge – equivalence principle
Equivalence principle
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Newtonian – “Falling elevator” – well known and
checked
Post-Newtonian – gravity action on SPIN – known
since 1962 (Kobzarev and Okun’) – not checked on
purpose but in fact checked in atomic spins
experiments at % level
Anomalous gravitomagnetic moment iz ZERO or
Classical and QUANTUM rotators behave in the SAME
way
Gravitomagnetism
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Gravitomagnetic field – action on spin – ½
from
spin dragging twice
smaller than EM
Lorentz force – similar to EM case: factor ½
cancelled with 2 from
Larmor frequency same as EM
Orbital and Spin momenta dragging – the
same - Equivalence principle
Equivalence principle for
moving particles
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Compare gravity and acceleration:
gravity provides EXTRA space
components of metrics
Matrix elements DIFFER
Ratio of accelerations:
confirmed by explicit solution of Dirac
equation (Silenko,OT)
Generalization of Equivalence
principle
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Various arguments: AGM  0 separately
for quarks and gluons – most clear from
the lattice (LHPC/SESAM)
Extended Equivalence
Principle=Exact EquiPartition
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In pQCD – violated
Reason – in the case of EEP - no smooth
transition for zero fermion mass limit (Milton,
73)
Conjecture (O.T., 2001 – prior to lattice data)
– valid in NP QCD – zero quark mass limit is
safe due to chiral symmetry breaking
Supported by smallness of E (isoscalar AMM)
Polyakov Vanderhaeghen: dual model with
E=0
Vector mesons and EEP
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J=1/2 -> J=1. QCD SR calculation of Rho’s
AMM gives g close to 2.
Maybe because of similarity of moments
g-2=<E(x)>; B=<xE(x)>
Directly for charged Rho (combinations like
p+n for nucleons unnecessary!). Not reduced
to non-extended EP: Gluons momentum
fraction sizable. Direct calculation of AGM are
in progress.
EEP and AdS/QCD
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Recent development – calculation of
Rho formfactors in Holographic QCD
(Grigoryan, Radyushkin)
Provides g=2 identically!
Experimental test at time –like region
possible
Another relation of Gravitational FF
and NP QCD (first reported at 1992:
hep-ph/9303228 )
BELINFANTE (relocalization) invariance :
decreasing in coordinate –
smoothness in momentum space
 Leads to absence of massless
pole in singlet channel – U_A(1)
 Delicate effect of NP QCD
 Equipartition – deeply
related to
relocalization
invariance by QCD evolution
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Conclusions
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2 spin structures of nucleon – related to
fundamental properties of NPQCD
Axial anomaly – may reside not only in gluon,
but in strangeness polarization (connection of
laeding and higher twists)
Multiscale (“fluctonic”) nucleon:
M>>m(strange)>>HT
Total angular momenta – connection to
(extended) equivalence principle and
AdS/QCD
Relation of 2 spin structures?!
Sum rules -II
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To simplify – low moments
Especially simple – if only gluonic pole
kept:
Compatibility of SSA and DIS
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Extractions of Sivers function: – “mirror” u and d
First moment of EGMMS = 0.0072 (0.0042 –
0.014)
Twist -3g - similar for neutron and proton (0.005)
2
and of the
same sign – nothing like mirror
picture seen –but supported by colour ordering!
Current status: Scale of Sivers function – seems
to be reasonable, but flavor dependence differs
qualitatively.
Inclusion of pp data, global analysis including
gluonic (=Sivers) and fermionic poles
Relation of Sivers function to
GPDs
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Qualitatively similar to Anomalous Magnetic
Moment (Brodsky et al)
Quantification : weighted TM moment of
Sivers PROPORTIONAL to GPD E
x f T ( x ) : xE ( x )
(hep-ph/0612205 ):
Burkardt SR for Sivers functions is now
related to Ji SR for E and, in turn, to
Equivalence Principle
  dxx f
q ,G
T
( x)  
q ,G
 dxxE ( x )  0
Sivers function and Extended
Equivalence principle
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Second moment of E – zero SEPARATELY for quarks
and gluons –only in QCD beyond PT (OT, 2001) supported by lattice simulations etc.. ->
Gluon Sivers function is small! (COMPASS, STAR,
Brodsky&Gardner)
BUT: gluon orbital momentum is NOT small: total –
about 1/2, if small spin – large (longitudinal) orbital
momentum
Gluon Sivers function should result from twist 3
correlator of 3 gluons: remains to be proved!