Angular Correlations in Associated Production of Single Top and Higgs with and without anomalous $Wtb$ Couplings

0.14 MB·English

by  S. F. Taghavi

Angular Correlations in Associated Production of Single Top
and Higgs with and without anomalous Wtb Couplings
3
1
0
2

n S. F.Taghaviand M. Mohammadi Najafabadi
a
J School ofParticlesand Accelerators, InstituteforResearch inFundamentalSciences (IPM),

4 P.O. Box 19395-5531,Tehran, Iran
1

]
h
p
-
p
e
h Abstract
[

1 We study the angular correlation and the amount of top quark polarization in the production
v
of a higgs boson in association with a single top quark in the t channel at the LHC. We also
3
−
7 study the effect of anomalousWtb couplings on the angular correlation and on the production
0
cross section of the process. The cross section and angular correlation is almost insensitive to
3
. the variation of the Higgs boson mass within 3 GeV. The robustness of the angular correlation
1
0 against the center-of-mass energy of the proton-proton collision, the variation of parton distri-
3 bution functions, and the change of factorization scale is investigated. The sensitivity of this
1
process totheanomalouscouplingsisexamined.
:
v
i
X
r
a PACS number(s): 14.65.Ha,14.80.Bn,12.60.-i
1 Introduction
The Higgs boson discovery has been one of the most challenging goals of present high-energy
experiments, in particular at the LHC experiments. From another side, the study of top quark
interactions provide a window to new physics beyond the Standard Model (SM). Because of
the large mass of the top quark, it is maximally coupled to the Higgs boson. Therefore, its
interactions seem to be more sensitive to the mechanism of electroweak symmetry breaking
than other Standard Model particles [1],[2],[3],[4],[5],[6]. Recently, LHC experiments have
observedanexcessabovetheexpectedbackground,atamassnear125GeV,whichisthesignal
for production of a new particle. The measured significance for a SM Higgs boson with this
massis 5.8standard deviations[7].
In thetopquark sector, oneshouldnotethatthetopquarkcouplingsstillneed to bemea-
sured more precisely because it can provide a place to observe any deviations from the SM
predictions. In this work, by adopting an effective Lagrangian approach, the new physics ef-
fectsareparameterizedintermsofhigherdimensionaloperatorsconstructedfromtheStandard
Modelfields [8],[9]:
L L (cid:229) ciOi
= + +... (1)
eff SM L 2
i
where in the above relation c’s are dimensionless coefficients pointing to the strength of the
i
anomalous couplings, O are dimension 6 gauge invariant operators containing the Standard
i
Model fields and L is the new physics scale. It is notable that due to the excellent agreement
between the SM expectations and the present experimental data, any deviations from the SM
areexpectedtobesmall. Accordingly,theneweffectivetermsmustbeverysmallandtheinter-
ference term between SM and new effective terms could be big enough to be measured. With
on-shell top, bottom quark and W boson, the most general form of theWtb vertex originating
from thedimensionsixoperatorscan bewritten asfollows[11],[12],[10]:
L = g b¯[g (V P +V P )+is µn qn (g P +g P )]tWµ+h.c., (2)
eff µ L L R R L L R R
−√2 mW
1 g
whereqisthemomentumoftheinvolvedW boson,PR,L= ±2 5,gistheweakcoupling. Within
theStandardModel,onlythefirsttermwithV =V 1ispresentandtheremainingtermsare
L tb
≃
anomalous terms which vanish at tree level and can be generated by radiativecorrections. The
assumptionofCP conservationleads thatV ,g tobereal.
L,R L,R
There are indirect and direct constraints on the anomalous couplings. The indirect con-
straints have been extracted from the measured branching ratio of b sg . In particular, the
→
bounds onV and g are tight. These bounds are stronger than what can be possibly obtained
R L
from studying the top quark production and decay at the LHC. This is because of the fact that
the decay amplitude of B-meson is enhanced by a factor m /m . The bounds are presented
t b
below[13]:
0.0007<V <0.0025, 0.0013<g <0.0004, 0.15<g <0.57 (3)
R L R
− − −
The recent direct constraints on the anomalous couplings have been obtained using pp¯
collision data corresponding to an integrated luminosity of 5.4 fb 1 collected by the D0 de-
−
tector. The analysis is based on the t-channel and s-channel single top quark production cross
1
q q’ q q’
W W H
H
b t b t
Figure 1: Feynman diagrams contributing to the t-channel single top plus Higgs production at
hadron colliders.
sections. The result represents the most stringent direct limits on anomalous Wtb couplings
which can befoundin thefollowing(assumingV 1)[14]:
tb
≃
V <0.96, g <0.36, g <0.24 (4)
R L R
| | | | | |
As it can be seen, the indirect constraints are much stronger than the direct ones except
for the upper constraint on g . In spite of the direct constraints, the indirect bounds are not
R
symmetric. Inthiswork,becauseofthestronglimitonV andforsimplicitywedonotconsider
R
it. There are several studieson theanomalousWtbcouplingswhich forexamplesomeof them
can befound in[15], [16],[17],[18],[19], [20], [21],[22],[23],[24],[25].
At the LHC, the production of Higgs and single top quark are through three channels:
t-channel (qb qtH), s-channel (qq¯ b¯tH), andW-associated (gb tW H) [26]. Sincet-
′ ′ −
→ → →
channelhasthelargestcrosssectionamongthesechannels,weonlyfocusonthet-channel. The
possibilityofdetectionasignalforthet-channelprocess(whichhasthelargestcrosssection)at
the LHC, viathe Higgs decay intobb¯ has been discussedin [26]. Figure 1 showstheFeynman
diagramsforthet-channelprocess.
In single top production in the t-channel mode (qb qt), the top quarks are produced
′
→
highly polarized along the direction of the light-quark in the final state [27],[28]. The top
quark spin is maximally correlated with the light-quark momentum in the final state and this
correlation can beobservedintheangulardistributionofthetopdecay products.
Inthispaper,firstwestudythespincorrelationeffectfortheproductionofaHiggsboson
plus a single top in the t-channel at the LHC (qb qtH) in the Standard Model. We investi-
′
→
gate the robustness of the spin correlation against variation of the parton distributionfunctions
(PDFs), variationofthefactorizationscale, andchangeof thecenter-of-massenergy ofproton-
proton collision. Then we investigate the effect of anomalousWtb couplings as introduced in
Eq.2onthespincorrelationandtheproductioncrosssectionoftheqb qtH process. Wealso
′
→
study the change of cross section with the anomalouscouplings and its sensitivityto the Higgs
boson mass. The angular correlation distribution of the charged lepton is used to examine the
sensitivityofthisprocesstotheanomalouscouplingsg andg . Allresultsarepresentedatthe
L R
LHCwiththecenter-of-mass energy of8 TeV.
The paper is organized as follows. In section 2, the spin correlation in the process of
qb qtH is investigated. In section 3, we investigate the dependency of the cross section of
′
→
2
the t-channel process to the anomalous couplings for different Higgs boson masses as well as
the spin correlation distribution. We also present the dependence of the rapidity distribution
of the light quark to the anomalous couplings. In section 3, using the charged lepton angular
distribution,thesensitivityoftheprocessto theanomalouscouplingsisexamined. Section 4is
dedicated toconclusions.
2 Spin Correlation in qb q tH
′
→
Itiswell-knownthatforthedecayofatopquarkintoachargedlepton,ab-quarkandaneutrino
theangulardistributionsinthetopquark rest frameisgivenby:
1 dG 1
= (1+a cosq ) (5)
G dcosq 2 i i
i
where q is the angle between the top spin and the three-momentum of the ith product. The
i
constants a are called spin correlation coefficients or spin analyzing power of the ith product
i
which variesfrom -1to 1. In theSM at treelevel, a l+ =1,a n l =−0.319 anda b =−0.406.
In the t-channel single top production (qb qt), top quarks are produced highly polar-
′
→
ized alongthelight-quarkdirectioninthefinal state. Thecorrespondingangulardistributionof
thecharged leptonin thetop quarkdecay isgivenby:
1 dG 1
= (1+Pa cosq ) (6)
G dcosq 2 l l
l
where the angle q is the angle between the charged lepton momentum and the top spin quan-
l
P
tization axis in the top quark rest frame. is the spin asymmetry and it is dependent on the
P
basis. In a basis where top quarks are 100% polarized, =1. Choosing the momentumof the
light-quark (q ) in the final state (“spectator basis”) as the spin quantization axis leads to high
′
P
degree polarization forthe top quark ( =97%). There is anotherbasis which is called “beam
line”basiswherethepolarizationdegreeislessthan thespectatorbasis[27], [29],[30],[31].
Now,weinvestigatethespincorrelationintheprocessof qb qtH andtrytoobtainthe
′
→
thedegreeofpolarizationinthespectatorbasisforthisprocess. Thishas beencalculated using
tree-levelmatrixelementsgeneratedbyCompHEP[33]convolutedwiththepartondistribution
function set CTEQ6L [34]. We used m =173.1 GeV and G =1.4 GeV. We consider the top
t t
quark decays into a W-boson and a b-quark and then W-boson decays into a charged lepton
andaneutrino. Figure2depictstheangularcorrelationdistributionofthecharged leptoninthe
spectatorbasisforthreevaluesoftheHiggsbosonmass.
AsitcanbeseeninFigure2,similartotheprocessqb tq,alinearbehaviorisobserved.
′
→
Thus,wefitalinearfunctionofaz+b,wherez=cosq ,totheangulardistributiontoextractthe
parameters a and b. Comparingwith Eq. 6, a=Pa . If we assumea =1 then a=P. Forthe
l l
P
Higgs boson mass m =125 GeV, we obtained to be 76.4%. Variation of the Higgs boson
H
mass within 5 GeV leads to a negligible change of 3% in the spin asymmetry. It is interesting
to notethatwith respect to thesingletopt-channel process qb qt,in thespectatorbasis,the
′
→
spinasymmetryinthisprocess isdegraded around22%.
Now, we check the sensitivity of the polarization degree to the change of proton parton
distributionfunctionsand thevariationof thefactorization scale. In orderto examinetheinflu-
P
ence of the choice of PDF on the polarization degree , we compare the angular distributions
3
hhssmm112200
0.022
m = 120 GeV
H
0.02
m = 125 GeV
H
0.018
m = 130 GeV
H
0.016
S = 8 TeV, CTEQ6L1, Q = m
qos t
c0.014
d
/
sd0.012

s1/ 0.01
0.008
0.006
0.004
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
cosq
Figure 2: Angular correlation in single top and anti-top for various Higgs boson mass in the
spectatorbasis.
hhcctteeqq55 hhqq00
0.022 0.022 Q = m/2
0.02 CTEQ5L 0.02 Q = mt
0.018 CTEQ6L1 0.018 Q = 2mt
MSTW2008 NLO t
q/dcos00..001146 S = 8 TeV, mH = 125 GeV q/dcos00..001146 S = 8 TeV, mH = 125 GeV, CTEQ6L1
s d0.012 s d0.012
s1/ 0.01 s1/ 0.01
0.008 0.008
0.006 0.006
0.004 0.004
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
cosq cosq
Figure 3: Angular distribution using three PDF sets (left) and for three values of factorization
scalewithagivenPDFset (right).
obtainedwith CTEQ6L1,CTEQ5L, and MSTW2008nlo. Figure3 (left plot)showstheresults.
Asitcanbeseen,noconsiderabledifferencesisobservedwhenweusedifferentsetofPDFs. In
P
the spectatorbasis, the maximumdifferences in between using three PDF sets is 1.5%. Fig-
ure 3 (right plot) shows the angular distribution for a given PDF set (CTEQ6L1) with various
factorization scales µ =m /2,m ,2m . According to figure, the polarization does not receive
F t t t
any substantial changes when different factorization scales are used in the calculations. The
differenceis at thelevelof1%.
The Large Hadron Collider has started its operation with the center-of-mass energy of 7
TeV and around 5 fb 1 of data collected by the experiments. Large amount of data (around 20
−
fb 1) has been collected at 8 TeV center-of-mass energy in 2012. The plan is to increase the
−
energytolargervalueintheupgradeofthemachine. Thus,it isusefultocheckthedependency
of the polarization to different center-of-mass energies at the LHC. Figure 4 shows the angular
distribution for three center-of-mass energies of the proton-proton collisions in the spectator
4
S = 7 TeV hh77tteevv
0.022
S = 7 TeV
0.02 S = 8 TeV
0.018 S = 14 TeV
0.016 CTEQ6L1, m = 125 GeV, Q = m
qos H t
c0.014
d
/
sd0.012

s1/ 0.01
0.008
0.006
0.004
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
cosq
Figure 4: Angular distribution for various center-of-mass energies in the spectator basis at the
LHC.
basis. Thedegreeofpolarizationisstableagainstvariationofthecenter-of-massenergies. Note
that thecenter-of-mass energies are chosenlarge enoughabovethethresholdofproduction.
3 Associated Production of a Single Top and a Higgs Boson
with Anomalous Wtb interactions
In this section we focus on the effect of the anomalous Wtb interactions on the t-channel
(qb qtH) single top quark production in association with a Higgs boson. This has been
′
→
calculated using tree-level matrix elements generated by CompHEP [33] convoluted with the
partondistributionfunctionsetCTEQ6L1[34]. Thetopquarkmasshasbeentakenm =173.1
t
GeV and itswidthis1.4 GeV.
With the general effective Lagrangian for the Wtb coupling, the cross section of the t-
channel can beparameterized as thefollowing:
s =s (V2+A g2+A g2 +A V g +A V g +A g g ) (7)
SM tb 1 L 2 R 3 tb L 4 tb R 5 L R
× × × × ×
wherewehavetakenV =V 1. A coefficientsdeterminethedependenceofthecrosssection
L tb i
≃
to theanomalouscouplings. These coefficients are dependent on theproton parton distribution
functions (PDF’s) as well as the Q-scale and other parameters such as masses of the top and
bottom quarks. It should be noted that A factors are different for top quark and anti-top quark
i
productioncrosssections.
InTable1,theA coefficientsarelistedforthreedifferentmassesoftheHiggsboson. The
i
cross section of the single top (anti-top) process within the SM (s ) is 10.627 (4.634) fb for
SM
m =125 GeV/c2.
H
As it can be seen inTable 1, thecoefficients of g2 and g2 terms are greaterthan theother
L R
terms. Thishasbeenexpectedfromqn factorintheinteractionwhichhasanenhancementeffect
on the cross section. Similar situation occurs in the SM single top production with anomalous
5
Table 1: The coefficients of anomalous terms appear in the cross section of thet-channel pro-
cessforthreevaluesoftheHiggsbosonmassforsingletopandsingleanti-topquarkseparately.
m [GeV/c2] At At At At At¯ At¯ At¯ At¯
H 1 2 3 4 1 2 3 4
124 14.178 7.603 -2.645 -0.0626 8.669 15.553 -1.250 -0.0264
125 14.041 7.500 -2.623 -0.0644 8.634 15.507 -1.237 -0.0277
127 13.963 7.422 -2.605 -0.0464 8.488 15.312 -1.221 -0.0271
000.2..235 single topsingle anti-top Total (single t + single t) 00..681 single top Total (single t + single t )
ss/SM0.15 ss/SM 0.4 single anti-top
D 0.1 D
0.2
0.05
0
0
-0.2
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
g g
R L
Figure 5: The relative correction coming from the anomalous interactions to the cross section
for production of Higgs plus single top in the t-channel at the LHC (pp, √s = 8 TeV). The
dependenceofthechangeofcross sectionon g (left)and ong (right)for m =125 GeV.
R L H
couplings[39]. AccordingtoTable1,thecoefficientoftheinterferencetermV g isoforderof
tb L
unityandcouldnotbeneglected. WhilethecoefficientsoftermsV g andg g areverysmall,
tb R L R
at the order of 10 2 and 10 3, respectively. Therefore, it might not be a precise assumption to
− −
takeonlyonenon-zero anomalouscouplingat atime.
In comparison between the coefficients of single top and single anti-top quarks in Table
1,itisnotablethatthecoefficientofg2 terminsingletopislargerthansingleanti-topwhilethe
L
situationis viceversaforthe g2 term. Therefore, theratioofthetopto anti-topcross sectionis
R
moresensitiveto g .
L
From Table 1, it can be seen that the coefficients are sensitive to the Higgs boson mass.
However, the sensitivity is not significant. The coefficients change by less than 2% when the
Higgsbosonmassvaries within3 GeV.
Fig. 5 depicts the relative change of the cross section for production of a Higgs boson
plus a singletop in thet-channel at the LHC with the center-of-mass energy of √s=8 TeV in
thepresenceoftheanomalousWtbinteractions. Thedependenceofthechangeofcrosssection
on g (left)and on g (right)isfor m =125GeV.
R L H
By comparing both plots in Fig. 5, one can observe that the cross section is more sensi-
tive to g (left-handed with tensor structure) than g (right-handed with tensor structure). For
L R
example, the contribution that the cross section can receive from g =0.05 reaches up to 20%
L
whilefromg =0.05is6%. AccordingtoFig. 5theanomaloustermof g couldbedestructive
R L
andreducesthecrosssectionfromitsStandardModelvalueuptoaround20%whileg always
R
increases thecross section.
6
]
u.
a.
[ 12
nt V = 0, g = g = 0.5
ve R R L
e 10
8
6
4
V = g = g = 0.0 (SM)
R R L
2
-6 -4 -2 0 2 4 6
y
Figure6: Rapiditydistributionforthelightquarkin thefinal-statein thet-channel at theLHC.
One of the interesting aspect of the t-channel process is that the light-quark in the final
state tend to fly in the forward/backward region of the detector. The presence of a light-jet
in the forward or backward region is related to the cross section behavior as a function of the
momentum of the virtualW-boson exchanged in thet-channel. Similar to the t-channel single
topproduction(withoutHiggsbosonin thefinal state),theregion q2 m2 dominates[35].
W
− ≤
In Fig. 6 we present the rapidity distribution of the light-quark in the final-state of the
t-channel in the SM framework and in the presence of anomalous couplings with for example
g = g = 0.5. As it can be seen in Fig. 6, the light quark tends to reside at large rapidities,
L R
peaking at around the value of 3 in the SM framework which is corresponding to an angle
of around 5.7 . The interesting point is that the presence of anomalous couplings leads the
◦
light quark to be more central. For example, when g = g = 0.5 the light quark rapidity
L R
distribution is peaking at around 2 (corresponding to an angle of 15.4 ), one unit below the
◦
SM case. Therefore, in the presence of the anomalous couplings the spectator quark tends
to fly more central and it affects the spin correlation and angular distribution which have been
discussedintheprevioussection. Inthenextsection,weusetheangulardistributiontoexamine
thesensitivityoftheprocessto theanomalouscouplings.
4 Sensitivity to Anomalous Couplings
As we showed in section 2, there is a correlation between the spin of the top quark and the
three-momentum of the light-quark in the top quark rest frame. The polarization degree in
qb qtH process in the spectator basis is around 76% for m = 125 GeV. The presence of
′ H
→
anomalous couplings in the vertex of Wtb changes this polarization degree. In Table 2, the
degreeofpolarizationisshownforvariousvaluesof g andg inthespectatorbasis. Thereare
L R
interestingobservations:
When we change g in the range of 0.0 to 0.1, an increase of around 4% is seen with
R
•
respect to the SM expectation and when we move in the negative direction from 0.0 to
7
Table 2: The coefficients of anomalous terms appear in the cross section of thet-channel pro-
cessforthreevaluesoftheHiggsbosonmassforsingletopandsingleanti-topquarkseparately.
g g DegreeofPolarization
L R
0.1 0.0 0.7938
0.0 0.1 0.7963
0.1 0.1 0.8091
-0.1 -0.1 0.5392
0.2 0.2 0.6030
-0.2 -0.2 0.3416
-0.1 0.0 0.5536
0.0 -0.1 0.7497
-0.1, we face with a decrease of 3 4%. Therefore, the polarization degree is weakly
−
sensitivetog .
R
Forthecasethat g variesfrom 0.0to0.1, thereisan increaseof3 4%inthepolariza-
L
• −
tion degree while variation from of g from 0.0 to -0.1 leads to a significant deviation of
L
27%. Thepolarizationdegreeisstronglysensitiveto g wheng <0.0.
L L
In summary,the angularcorrelation of the charged lepton is moresensitiveto g than g
L R
and in particular to negative values of g . We use the charged lepton angular distribution to
L
examinethesensitivityofthisprocessto theanomalouscouplings.
To obtain a realistic estimation of the sensitivity of the single top in association with the
Higgs boson in t-channel, one has to consider all backgrounds, selection cuts, and detector
effects. However, a comprehensive analysis taking into account all backgrounds and detector
effects isbeyondthescopeofthispaperand mustbeperformed bytheexperimentalcollabora-
tions.
In this study, we use c 2 criterion from the charged lepton angular distribution to estimate the
sensitivityto theanomalouscouplings:
c 2(g ,g )= (cid:229) (Ninew(gL,gR)−NiSM)2 (8)
L R D
i=bins i
where Nnew is the number of expected events in ith bin of the charged lepton distribution in
i
the presence of anomalous couplings. The same as [26], we considerthe leptonic decay of the
W-boson form the top quark and the decay of the Higgs boson to bb¯. Since for a Higgs boson
lighterthan130 GeV/c2, thedominantdecay modeis bb¯, we willhavemorestatisticswith this
choice. Therefore,ourfinalstateconsistsofl +MissingTransverseEnergy(MET)+3bjet+one
±
light forward jet. As discussed in [26] and in a more recent paper [32], the main backgrounds
are tt¯, tt¯j, tZj with Z bb¯, and tbb¯j. Following the set of cuts proposed in [32] leads to
→
significant suppressionof the backgrounds. In [32], the acceptance cuts has been taken similar
to the ATLAS analysis of tt¯H [36]. The transverse momenta of the charged lepton and the
bjet are required to be greater than 25 GeV with h <2.5. The light jet must have p >30
l,b T
| |
8
hh1111 Signal (g = g = 0.0) hhbbgg
L R
Signal (g = g = 0.0)
0.06 L R
Backgrounds
0.05
sdqcos0.04
d
1
s 0.03
0.02
0.01
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
cosq
Figure 7: Thecosq distributionsofthecharged lepton intop decay forsignaland backgrounds
afterthecuts.
and h <5.0. It is also required that D R >0.4. Where D R = (h h )2+(f f )2, this
ij ij i j i j
requ|ire|mentisappliedonallobjects. NocutonMETisapplied. Ipnthe−c 2 definition,−D denotes
i
theuncertaintiesineachbinoftheangulardistributionandisdefinedas: D =NSM d 2 +d 2 .
i i q stat sys
After imposing the kinematic cuts, the charged lepton angular distributions are distorted. A
significant drop intheregion ofcosq 1 appears which is mainlyoriginatingfrom the p and
T
D R cuts. This behaviorhas been alrea∼dy observed in the SM singletop production qb tq. It
′
→
is important to note that the main characteristic feature of signal in the charged lepton angular
distribution,whichisadistinctslope,remains. Thebackgroundhasaflatdistributionevenafter
the cuts are imposed. In the SM single top production qb tq, this feature remains after full
′
→
detectorsimulationandhas been observedin real datatoo[37].
To get a rough estimate of the limits on the anomalous couplings, we consider an inte-
gratedluminosityof25fb 1 ofdata. The68%C.L.intervalforg andg are[ 0.32,0.65]and
− L R
−
[ 0.74,0.74],respectively. Indeed,theseareroughestimationsandintherealisticcasedetector
−
effects,allbackgroundsmustbetakenintoaccount. Becauseofsmallerstatistics,thelimitsthat
obtainedfromsingletopproductioninassociationwiththeHiggsbosonprocessarelooserthan
the ones that can be obtained from for example t-channel single top [39]. However, the same
as[39]whereallsingletopchannelshavebeencombined,thecombinationofthischannelwith
othersensitivechannels can improvetheconstraintson the anomalousterms[38],[39],[40].
5 Conclusions
In this paper, we studied the single top quark production in association with a Higgs boson at
the LHC, namely qb tqH. In particular, we concentrated on the spin correlation effects in
′
→
this process within the SM framework and in presence of the anomalous Wtb couplings. We
have found that in the SM, in the process of qb tqH, thetop quarks are 76% polarized in
′
→ ∼
thedirectionofthelight-quarkq inthefinalstate. Itwasshownthepolarizationdegreedeviates
′
negligiblybychangingthePDFsetandthecenter-of-massenergyofthecollision(7,8,14TeV).
Thedependenceofthespincorrelationon thefactorization scalehas been foundtobe1%.
9