Hadron Mass Effects on Kaon production on deuteron Juan Guerrero - - PowerPoint PPT Presentation
Hadron Mass Effects on Kaon production on deuteron Juan Guerrero Hampton University & Jefferson Lab Hadronic Physics with Lepton and Hadron Beams September 6, 2017 Based on: J. G., J. Ethier, A. Accardi, S. Casper ,W.
Juan Guerrero Hampton University & Jefferson Lab Hadronic Physics with Lepton and Hadron Beams September 6, 2017
Based on:
J.G & Alberto Accardi, work in progress…
juanvg@jlab.org Jefferson Lab, Sep 6 2017 2
Interested in the s-quark.
3 “valence quarks” p = (u u d) Gluons sea quarks: strange, charm, bottom.
Parton (momentum) Distributions Function (PDFs):
Well determined for the “valence quarks”and gluons. Not the case for the sea quarks.
Partons:
juanvg@jlab.org Jefferson Lab, Sep 6 2017 3
For example: Semi inclusive Deep inelastic scattering (SIDIS): e− + p → e− + h + X
h = K
How can we access the s-quark PDF? “Tagging” Kaon in Hard Scattering reactions
Kaon contains an s-quark in their valence structure. Detect a Kaon: good proxy for a strange quark BUT: Not necessarily negligible at HERMES and COMPASS experiments
mK ' 0.5 GeV
X
¯ s
u
s
¯ u
¯ s
K+
Kaon FF:DK
q
s-PDF
juanvg@jlab.org Jefferson Lab, Sep 6 2017 4
Theoretically LO, neglect masses: Comparing these two expressions Extract the s-quark PDF. Experimentally HERMES, COMPASS: Use “integrated Kaon Multiplicities”
M K
exp =
R
exp dQ2 R 0.8 0.2 dzh dN K dxBdQ2dzh
R
exp dQ2 dN e dxBdQ2
M K = P
q e2 q q(xB)
R 0.8
0.2 dzhDh q (zh)
P
q e2 q q(xB)
= s(xB) Z dzhDK
s (zh)
+light quarks
juanvg@jlab.org Jefferson Lab, Sep 6 2017 5
Where does this discrepancy come from?
HERMES: Claim very different s-quark shape compared to CTEQ6L. Measurements from ATLAS/CMS at LHC also show different s-PDF. Strange PDF may not be what we think! But COMPASS: Different xB dependence COMPASS overall value higher.
2 −
10
1 −
10 1 0.1 0.15 0.2
x
COMPASS HERMES
ℳK + + ℳK −
Is it real or apparent?
juanvg@jlab.org Jefferson Lab, Sep 6 2017 6
Maybe masses are not so negligible!
Usually in pQCD, the masses of the Proton and the Kaon (detected hadron) are neglected.
¯ u
s
u
d
u
Q2C & Q2H ' 1 10 GeV2 mp ' 1 GeV mK ' 0.5 GeV
juanvg@jlab.org Jefferson Lab, Sep 6 2017 7
Jefferson Lab experiments: Usually low Q2. 1/Q2 corrections have to be controlled. O(m2/Q2 ) = Hadron Mass Corrections (HMCs)
Pions at JLab (Exp. # E00-108)
Q2 ∼ 2.5 GeV2
Accardi et al JHEP 0911, 084 (2009)
mπ ∼ 0.14 GeV Let’s consider an example for Pion Mass effects at JLab.
m = MP , mπ
juanvg@jlab.org Jefferson Lab, Sep 6 2017 8
Back to Kaons:
2 −
10
1 −
10 1 0.1 0.15 0.2
x
COMPASS HERMES
ℳK + + ℳK −
HERMES & COMPASS: relatively low Q2, m2
K ∼ 12m2 π
juanvg@jlab.org Jefferson Lab, Sep 6 2017 9
s
Proton or neutron detected hadron lepton Undetected particles
DIS invariants
SIDIS invariants
h = p2 h
juanvg@jlab.org Jefferson Lab, Sep 6 2017 10
a+ a− aµ P0 P3
a− = a0 − a3 √ 2 a+ = a0 + a3 √ 2
Scaling Variables
Q2 → ∞ ξ → xB Bjorken limit: Nachtmann:
BM 2/Q2
Fragmentation: Q2 → ∞ ζh → zh Bjorken limit:
ζh ≡ p−
h
q− = zh 2 ξ xB 1 + s 1 − 4x2
BM 2m2 h
z2
h Q4
!
juanvg@jlab.org Jefferson Lab, Sep 6 2017 11
(p,q) frame: p and q are collinear and have zero transverse momentum
need to match partonic & hadronic kinematics
e k02 =?
Fragmentation into a massive hadron Approx.: On-shell parton collinear to proton:
e k2 = 0 e k = (xp+, 0, 0T)
Fragmenting parton collinear to hadron
e k0 = e k02 + (ph⊥/z)2 2p
h /z
, p
h
z , ph⊥ z !
Y X
H
k ≈ e k k0 ≈ e k0
juanvg@jlab.org Jefferson Lab, Sep 6 2017 12
Hard scattering: 4-momentum conservation at LO Fragmenting blob: momentum conservation in + direction
Bjorken limit:
x = xB z = zh
H
z = ζh x = ξ ✓ 1 + e k02 Q2 ◆
Albino et al. Nucl. Phys. B803 (2008) 42-104
Standard choice:
e k02 = 0 e k02 ≥ m2
h
z = m2
h
ζh
LO
e k0+ = p+
h + Y + ≥ p+ h
Y
respects gauge invariance
HLO(k, k0) ≈ HLO(e k, e k0) ∝ δ(4)(q + e k − e k0)
juanvg@jlab.org Jefferson Lab, Sep 6 2017 13
Parton model definition
M h(0)(xB) = R
q e2 q q(xB, Q2)
R 0.8(0.85)
0.2
Dh
q (zh, Q2)dzh
R
q e2 q q(xB, Q2)
✓M 2 Q2 , m2
h
Q2 ◆ → 0
Bjorken limit:
ξh ≡ ξ ⇣ 1 + m2
h
ζhQ2 ⌘
M h(xB) = R
0.2
Jh(ξ, ζh, Q2) P
q e2 q q(ξh, Q2) Dh q (ζh, Q2)dzh
R
q e2 q q(ξ, Q2)
Scale dependent Jacobian Finite Q2 scaling variables
With Hadron Masses:
Note: Theory integrated over z, Q2 experimental bins for each xB.
juanvg@jlab.org Jefferson Lab, Sep 6 2017
Massless HMCs
14
D/T ratio allows to compare experiments at different Q2 Normalization of Kaon FFs poorly known
After HMCs: Size discrepancy reduced Slope more flat COMPASS well described (except normalization) Residual tension with HERMES slope
COMPASS vs. HERMES:
juanvg@jlab.org Jefferson Lab, Sep 6 2017 15
“Theoretical correction ratios”
Produce approximate “massless” parton model multiplicities Make data directly comparable Largely insensitive to DK normalization
COMPASS: HERMES:
M h(0)
exp ≡ M h exp × Rh HMC × RH→C evo
M h(0)
exp ≡ M h exp × Rh HMC
HMC ratio Evolution ratio (HERMES to COMPASS)
Rh
HMC = M h(0)
M h RH→C
evo
= M h(0)(xB)
M h(0)(xB)
juanvg@jlab.org Jefferson Lab, Sep 6 2017 16
Hadron mass effects dominant over evolution effects At COMPASS smaller HMCs than at HERMES.
RHERMES
HMC
RCOMPASS
HMC
RH→C
evo
Theoretical correction ratios
juanvg@jlab.org Jefferson Lab, Sep 6 2017 17
Removing HMCs reduce the discrepancy in size. Corrections rather stable with respect to FF choice.
K = K+ + K−
Experimental Data “Massless data” at same Q2
juanvg@jlab.org Jefferson Lab, Sep 6 2017 18
Ratio reduces experimental systematics.
Size discrepancy persists Slopes are now compatible Except last two HERMES points?.
2 −
10
1 −
10 1 1 1.5 2 2.5
x
COMPASS HERMES
ℳK +/ℳK −
K+/K−
juanvg@jlab.org Jefferson Lab, Sep 6 2017 19
D/T ratio allows to compare experiments at different Q2
Massless HMCs
K+/K− K+/K−
After HMCs:
HERMES overall agreement with COMPASS
except last bins? Strange quark in current PDF fits too soft?
juanvg@jlab.org Jefferson Lab, Sep 6 2017 20
Experimental Data
K+/K− K+/K−
HERMES & COMPASS fully compatible. large x bins at HERMES still suspicious. “Massless data” at same Q2
juanvg@jlab.org Jefferson Lab, Sep 6 2017 21
Can we extract s-quark from SIDIS Kaon multiplicities? Yes, but: Make sure you control the FFs
Include mass corrections Non negligible even at small-x (because Q2 is small) Our proposed scheme with with seems able to reconcile HERMES & COMPASS Kaon multiplicities.
e k02 = m2
h/ζh
juanvg@jlab.org Jefferson Lab, Sep 6 2017 22
Evaluating HMCs for polarized asymmetries. Prove factorization at NLO with Use the multiplicity data in new fits of FFs with HMC corrected theory k02 6= 0. HMCs at LO are captured by new scaling variables ξh and ζh K+ + K- multiplicities: HERMES vs. COMPASS size discrepancy reduced Difference in slopes still needs to be solved. K+/ K- ratio: No slope problem systematics in HERMES K+ + K- ?
juanvg@jlab.org Jefferson Lab, Sep 6 2017 23
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Data (dots) vs. Theory (lines)
K = K+ + K−
Kaon FFs poorly known in absolute value Large FFs systematics HMCs are large
juanvg@jlab.org Jefferson Lab, Sep 6 2017 26
COMPASS: theory dependence similar to experimental values HERMES: less steep than theory and at large-x Some PDF systematics, due very likely to s PDF (slopes) need to refit the s quark PDF
Data (dots) vs. HMC Theory (lines)
juanvg@jlab.org Jefferson Lab, Sep 6 2017 27
HMC ratios: HERMES (blue line), COMPASS (red line) Evolution ratio (green line) Systematic theoretical uncertainties: (FFs, PDFs)
HMCs much smaller than for Kaons. Comparable to evolution effects.
juanvg@jlab.org Jefferson Lab, Sep 6 2017 28
Slopes still incompatible also for pions. “Hockey stick” shape as for Kaons, likely due to nuclear effects.
Parton level multiplicities Experimental Data
juanvg@jlab.org Jefferson Lab, Sep 6 2017 29
Fragmentation Functions Systematics
Large variations of the multiplicities with the choice of FFs, why?
Parton model: M K(xB, Q2) = Q(xB, Q2)R DK
Q (z, Q2)dz + S(xB, Q2)R DK S (z, Q2)dz
5Q(xB, Q2) + 2S(xB, Q2)
Q(x) ≡ u(x) + ¯ u(x) + d(x) + ¯ d(x) S(x) ≡ s(x) + ¯ s(x)
DK
S (z) ≡ 2DK s (z)
DK
Q (z) ≡ 4DK u (z) + DK d (z) 30
Fragmentation Functions Systematics
Large variations of the multiplicities with the choice of FFs, why?
Parton model: M K(xB, Q2) = Q(xB, Q2)R DK
Q (z, Q2)dz + S(xB, Q2)R DK S (z, Q2)dz
5Q(xB, Q2) + 2S(xB, Q2)
Q(x) ≡ u(x) + ¯ u(x) + d(x) + ¯ d(x) S(x) ≡ s(x) + ¯ s(x)
DK
S (z) ≡ 2DK s (z)
DK
Q (z) ≡ 4DK u (z) + DK d (z) 31
Large uncertainty with the choice of FFs because
DHKNS
Q
> DDSS
Q
Q > S
< zh >∼ 0.38
z
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
)
2z D(z,Q
10
10
10
10 1 10
http://lapth.cnrs.fr/generators
2= 5 GeV
2Q DSS LO
s K HKNS LO
s K DSS LO
s K HKNS LO
s K
http://lapth.cnrs.fr/generators z
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
)
2z D(z,Q
10
10
10
10 1 10
http://lapth.cnrs.fr/generators
2= 5 GeV
2Q DSS LO
d K HKNS LO
d K DSS LO
d K HKNS LO
d K
http://lapth.cnrs.fr/generators z
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
)
2z D(z,Q
10
10
10
10 1 10
http://lapth.cnrs.fr/generators
2= 5 GeV
2Q DSS LO
u K HKNS LO
u K DSS LO
u K HKNS LO
u K
http://lapth.cnrs.fr/generators
u, d, s FFs
K = K+ + K−