eﬀectof&quark&interac0ons&on&& … fileranges of masses for lkps. however, the...

Effect of quark interac0ons on dark ma4er kine0c decoupling and the smallest dark halos

Kenji Kadota Physics Dept, Nagoya University, Japan

Based on the work with Paolo Gondolo (Utah) and Junji Hisano (Nagoya)

1205.1914[hep-‐ph]

(c.f. Alma Gonzalez’s talk for more astronomy aspects)

Outline

•  What is kine0c decoupling? •  Smallest dark ma4er halo •  Results: Ø  Model independent approach: Effec0ve Field Theory Ø  Model specific approach: MSSM

•  Chemical decoupling: Annihila0on < Hubble expansion, T~ mχ/20 •  Kine0c decoupling: Elas0c sca4ering < Hubble expansion, T~mχ/2000

(Kolb&Turner)

Chemical decoupling and kine0c decoupling

Outline


Why bother with DM kine0c decoupling?

•  Probe on the nature of dark ma4er (DM) An applica0on: The size of smallest dark ma4er halo (protohalo or smallest gravita0onally bound objects) •  Analogous to: Physics of baryon decoupling probing the nature of Universe via BAO and CMB

1e-13

1e-12

1e-11

1e-10

1e-09

1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01 0.1 1 10

Mha

lo /MSu

n

Tkd (GeV)

HorizonFree Streaming (m =10 GeV)

Free Streaming (m =100 GeV)Free Streaming (m =1 TeV)

Mkd ~ (! kd )3 ~ (Tkd )!3

M fs ~ Tkd /m" ! kd( )3

P. Gondolo, J. Hisano, KK (2012)

Comparison with previous works •  DM & lepton-‐photon fluids (e.g. Schmid, Shwarz,Widerin,Fayet,Chen,Kamionkowski,ZhangKasahara,Hoffman,Green,Profumo ,Ullio,

,Sigurdson, Berezinsky,Dokuchaev,Eroshenko, Boehm, Loeb,Zaldarriaga,Bertchinger,Bringmann.Cornell,…) 3

Z

l l

!(1) !(1)

(a)

l(1)R,L

l B(1)

B(1) l

(b.1)

l(1)R,L

l

B(1)B(1)

l

(b.2)

FIG. 2: Feynman diagrams contributing to the scattering of!

(1) (a) and B(1) (b.1 and b.2) o! leptons.

ments [11], the LKP relic abundance [12], and direct-detection experiments [13] strongly constrain the viableranges of masses for LKPs. However, the allowed rangeof masses for the LKP sensitively depends upon the de-tails of the spectrum of the first and second KK ex-citations, which can include significant coannihilationand resonant-annihilation e!ects. We compute here thescattering cross section of !(1) and of B(1) o! leptons,for which the relevant Feynman diagrams are shown inFig. 2. In the case of the B(1), we expect large scatter-ing cross sections, since the intrinsically degenerate na-ture of the KK spectrum, where mB(1) ! mL(1) , clearlyenforces a resonant enhancement. We find, to leadingorder in El/mX , and in the relativistic limit for l andnon-relativistic limit for the LKP particle, that

"!(1)l !|g

!(1)!(1)Z|2

4#m4Z

!g2

L + g2R

"E2

l , (3)

"B(1)l !E2

l

2#

#

R,L

(g1YR,L)4$

m2B(1) " m2

l(1)R,L

%2 , (4)

where gR,L stand for the L and R couplings of the leptonl to the Z0 gauge boson, YR,L for the hypercharge quan-tum number, and g

!(1)!(1)Z= e/(sin 2$W ). The "Xl # E2

lscaling found in the case of neutralino dark matter isvalid for this alternative class of WIMPs as well. Inthe case of the KK neutrino, further, "!(1)l does notdepend on the LKP mass. We stress that consistencywith direct-detection experiments requires m!(1) ! 50TeV [13]. While this latter range is in conflict with es-timates of the thermal relic abundance of !(1) [12], theparticle properties of the latter, assuming the couplingg!(1)!(1)Z with the Z0, to be a free parameter instead ofbeing fixed by the standard gauge interactions, apply toother dark-matter candidates including the Dirac right-handed neutrino of 5D warped grand unification [14].

Di!erent WIMP models give rise to di!erent Tkd,and therefore to di!erent Mc. We apply our elastic-scattering cross section for WIMPs from light leptonsto the MSSM parameter space, following the scan pro-cedure of Ref. [15], requiring that the neutralino density

0 500 1000 1500 2000mX (GeV)

10-4

10-3

10-2

10-1

100

101

T kd (GeV)

MSSMmSUGRAUED !(1)

UED B(1)("R=20)

A

B

C

DB(1) (2<"R<200)

FIG. 3: The kinetic-decoupling temperature Tkd as a functionof the WIMP mass for supersymmetric models (red emptydots are for the general MSSM while light-blue filled dots arefor mSUGRA) giving a neutralino thermal relic abundanceconsistent with cosmology, and for UED models featuring aB

(1) and a !(1) LKP. The four benchmark models A-D dis-

cussed in the text are also shown.

0 500 1000 1500 2000mX (GeV)

MSSMmSUGRAUED !(1)

UED B(1)("R=20)0.1

1

10

100

k c (pc-1 )

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

M c / MA

B

C

D

B(1) (2<"R<200)

FIG. 4: The WIMP protohalo characteristic comovingwavenumber kc (left axis) and mass Mc (right axis) as a func-tion of the WIMP mass, for the same models as in Fig. 3.

Profumo, Sigurdson,Kamionkowski (2006) l Our work (P. Gondolo, J. Hisano, KK (1205.1914[hep-‐ph]))

Quark-‐DM interac/ons LHC, DM direct detec0on experiments

!

!

qq

Outline


Os = !qmq

"3 !!qq

OA = !q1"2 (!"

µ" 5! )(q"µ"5q)

DM-‐quark interac0ons: Effec0ve operators

!

!

q

q

10

100

1000

1 10 100 1000 10000

(GeV)

m (GeV)

Tkd=1GeVTkd=0.5GeVTkd=0.1GeV

Direct DetectionCollider

10

100

1000

10000

1 10 100 1000 10000

(GeV)

m (GeV)

Tkd=1GeVTkd=0.5GeVTkd=0.1GeV

Direct DetectionCollider


Outline


0.01

0.1

1

10

10 100 1000 10000

T kd (

GeV

)

m (GeV)

Quarks includedNo quarks

TQCD


Conclusion

•  Bo4om-‐up effec0ve operator approach: Kine0c decoupling temp > 100 MeV

•  MSSM: DM-‐quark interac0ons increase the halo mass by more than 100%

Dark Ma4er-‐Quark interac0on is important !

•  Momentum transfer per collision ~ T •  Required number of collisions ~ m/T •  Kine0c decoupling:

e.g. ! ~ T 6 /m5 !H

! ~ m /T !"elastic #H

Order of magnitude es0mate for momentum transfer rate

3

where Tc(Nf ) is the critical temperature for the theorywith Nf light fermion flavours. Besides this, there ap-pears to be only negligible Nf -dependence within thecurrent numerical accuracy. We are therefore motivatedto neglect quark mass e!ects, take the Nf = 0 latticedata (in the continuum limit) and the Nf = 0 DR for-mula of Kajantie et al. [5], and scale the temperaturedependence by Tc(3)/Tc(0). The correction factors arematched at 1.2 GeV using the undetermined O(g6) pa-rameter, which we take to be 0.6755, close to the value0.7 used in Ref. [5]. At higher temperatures one crossesthe c and b mass thresholds. However, for Nf > 3 theO(g6) fitting parameter is unknown, and the appropriatecritical temperatures are also unknown. Hence we be-lieve that scaling the Nf = 0 result is the best we can doat present. We will discuss later how improvements canbe made.

In the confined phase we label our model equations ofstate (EOS) A,B and C. EOS A ignores hadrons com-pletely, as the lattice shows that f(T ) very rapidly ap-proaches zero below Tc. EOS B and C model hadronsas a gas of free mesons and baryons. It was noted inRef. [6] that such a gas, including all resonances, givesa pressure which fits remarkably well to the Nf = 2 + 1lattice results although, as the authors themselves pointout, this result should be treated with caution as thesimulations are not at the continuum limit. We includeall resonances listed in the Particle Data Group’s tablemass width 02.mc [20].

We make a sharp switch to the hadronic gas at a tem-perature THG. For our EOS B we take THG = Tc = 154MeV, and for EOS C we take THG = 200 MeV andTc = 185.5 MeV, values chosen to give as smooth a curvefor he! as possible. The e!ects of these equations of stateon the relic densities turn out to di!er by less than 0.3%in the relevant temperature interval, so in the followingwe concentrate on EOS B.

Before presenting our results we note that "ch2 is di-rectly proportional to the entropy density today s0 =(2!2/45)he!(T!)T 3

! , and that this must be determinedas accurately as possible. The photon temperature T! =2.725 ± 0.001 is very accurately measured [21], but thecontribution from neutrinos requires a separate freeze-outcalculation. Recent work [22] gives he!(T!) = 3.9172.We find that taking freeze-out temperatures to be 3.5MeV for "µ and "" and 2 MeV for "e, as recommended inRef. [7], gives he!(T!) = 3.9138, which is accurate enoughfor our purposes. DarkSUSY uses he!(T!) = 3.9139.

In Figs. 1 we plot for our EOS B the e!ective num-

bers of degrees of freedom he!(T ) and g1/2! (T ) defined

in Eqs. (3) and (5), compared with those used in Dark-

SUSY [2] and MicrOMEGAs [3]. The spike in our g1/2! (T )

is an artefact of the matching of the scaled lattice dataand the hadronic equation of state (i.e. the first deriva-tive jumps). Since for physical QCD the transition is a

10−4 10−2 100 102 1040

2

4

6

8

10

12

14

16

T/GeV

g1/2 *

10−4 10−2 100 102 1040

20

40

60

80

100

120

T/GeV

h eff

FIG. 1: Degrees of freedom factors g1/2! (T ) and he!(T ), de-

fined in Eqs. 3 and 5, for our equation of state B (solid)compared with those currently used in DarkSUSY and Mi-crOMEGAs (dashed). The spike in the upper panel is a nu-merical artefact without physical impact, see text.

smooth crossover, this spike is unphysical. However, ithas no noticeable influence on the freeze-out of WIMPsat higher temperatures.

In Table I we exhibit the e!ect of the new equationof state on the density of relic neutralinos #, for themSUGRA models used to test DarkSUSY in the standarddistribution [23]. We find changes of about 1.5–3.5%. Inorder to quantify the e!ect of uncertainty in the latticedata, we introduce two new models B2 and B3, whichare constructed by scaling the lattice curve by 0.9 and1.1 respectively, and then adjusting the O(g6) parame-ter in the DR pressure curve so that it meets the scaledlattice curve at T = 4.43Tc. Thus a 10% uncertaintyin the lattice pressure curve translates to an uncertaintyin the relic density in the range 0.5 – 1%. Note thatthe lowest freeze-out temperature in the table is about4 GeV. This corresponds to more than 20Tc, where the

2

of massless quarks applicable down to a few times Tc.By fitting for the non-perturbative and as yet unknownO(g6) coe!cient, the authors of Ref. [5] were able tomatch their calculated pressure reasonably well to pure-glue lattice data near the critical temperature.

Around the transition, there now exist lattice calcula-tions for the pressure and energy density for Nf = 0, 2, 3degenerate quark flavours, as well as first data for Nf =2 + 1, i.e. two light and one heavier flavour. The pseudo-critical temperatures Tc(Nf ) (defined as the peak of asusceptibility) are currently given as Tc(0) = 271 ± 2MeV, Tc(2) = 173 ± 8 MeV and Tc(3) = 154 ± 8 MeV[18]. It has to be stressed, however, that only the pureglue case has been extrapolated to the continuum. Basedon experience with that theory, the dynamical fermion re-sults are estimated to display a systematic error of about15% at the currently available lattice spacing. Correc-tions due to quark masses deviating from the physicalones appear to be negligible in comparison [18].

Finally, below the phase transition the hadronic res-onance gas model, which treats the plasma as an idealgas of mesons, baryons and their excited states, matchesreasonably well to lattice data [6].

We now review relic density calculations. Considera particle of mass m and number density n, undergo-ing annihilations XX ! . . . with total cross-section !,assumed to be a typical weak interaction cross-section,proportional to G2

F . Then [19]

n + 3Hn = "#!vMøl$ (n2 " n2eq), (1)

where neq is the equilibrium number density, H = a/ais the Hubble parameter, and vMøl is the Møller veloc-ity which is a relativistic generalisation of the relativevelocity of the annihilating particles [19].

In order to solve the equation it is convenient to con-vert the time variable to x = m/T , and to measure therelic abundance in terms of Y = n/s, where s is the en-tropy density. If the total entropy S = sa3 is conserved,then we can write

dY

dx=

1

3H

ds

dx#!vMøl$ (Y 2 " Y 2

eq). (2)

This adiabaticity assumption is violated if the QCD tran-sition is first order, but it is most likely to be a cross-overtransition at the low chemical potentials which are rele-vant for the early Universe [16, 17].

Using the Friedmann equation H2 = 8"G#/3, anddefining e"ective numbers of degrees of freedom for theenergy and entropy densities, s = (# + p)/T , through

# ="2

30ge!(T )T 4, s =

2"2

45he!(T )T 3, (3)

one finds an approximate solution

Y0 %

!

45

"

"1

2 1

mMP #!vMøl$Tf

xf

g1

2

! (Tf ), (4)

where Tf is the freeze-out temperature, defined to be thetemperature at which the relic abundance is a certainfactor (taken to be 2.5) above the equilibrium abundance.We see that the relic density depends on the parameter

g1/2! (T ) =

he!

g1/2e!

!

1 +T

3

d lnhe!

dT

"

. (5)

It is through this parameter that the QCD equation ofstate influences the relic density.

In an ideal gas at temperature T , a particle of massmi = xiT contributes to ge! , he! the amounts

gi,e! &#i

#0=

15

"4

# "

xi

(u2 " x2i )

1

2

eu ± 1u2du, (6)

hi,e! &si

s0=

45

12"4

# "

xi

(u2 " x2i )

1

2

eu ± 1(4u2 " x2

i )du, (7)

where #0 and s0 are the energy and entropy densities fora free massless boson.

Interactions correct the ideal gas result, and ge! , he!

have to be extracted from calculations of the energy andentropy, Eqs. (3). Note that in the relevant temperaturerange 40 to 0.4 GeV, 16 out the 18 bosonic degrees of free-dom are coloured, with the coloured fermionic degreesof freedom dropping from 60/78 to 36/50. The domi-nant corrections are therefore expected to come from thecoloured sector of the Standard Model, weak correctionsare moreover suppressed by the boson masses and negli-gible.

The relic density codes DarkSUSY and MicrOMEGAsuse identical equations of state, developed in Refs.[7, 8, 9]. Below Tc the hadronic degrees of freedom aremodelled by an interacting gas of hadrons and their res-onances, while above Tc the quarks and gluons are takento interact with a linear potential VQ(r) = Kr, with aphenomenologically motivated value K = 0.18GeV2, de-rived from the slope of Regge trajectories. In this model,the pressure is already very close to ideal at temperaturesabove 1.6 GeV. All other Standard Model particles arefree.

In this work we also take the ideal gas contributionsfor the particles of the Standard Model, with massesgiven by the Particle Data Group central values [20].In the confined phase quarks and gluons are replacedby hadronic models described below. In the deconfinedphase, the contribution to the pressure of the coloureddegrees of freedom is scaled by a function f(T ), definedto be the ratio between the true QCD pressure p(T ) andthe Stefan-Boltzmann result pSB for the same theory,f(T ) = p(T )/pSB(T ). This correction factor is derivedfrom lattice [18] and perturbative [5] calculations forNf = 0, and uses an approximate universality in the pres-sure curves for di"erent Nf observed by Karsch et al. [18].Near the transition, the lattice-derived curves for f(T )have the approximate form f(T, Nf) = fQCD(T/Tc(Nf )),

2

of massless quarks applicable down to a few times Tc.By fitting for the non-perturbative and as yet unknownO(g6) coe!cient, the authors of Ref. [5] were able tomatch their calculated pressure reasonably well to pure-glue lattice data near the critical temperature.

Around the transition, there now exist lattice calcula-tions for the pressure and energy density for Nf = 0, 2, 3degenerate quark flavours, as well as first data for Nf =2 + 1, i.e. two light and one heavier flavour. The pseudo-critical temperatures Tc(Nf ) (defined as the peak of asusceptibility) are currently given as Tc(0) = 271 ± 2MeV, Tc(2) = 173 ± 8 MeV and Tc(3) = 154 ± 8 MeV[18]. It has to be stressed, however, that only the pureglue case has been extrapolated to the continuum. Basedon experience with that theory, the dynamical fermion re-sults are estimated to display a systematic error of about15% at the currently available lattice spacing. Correc-tions due to quark masses deviating from the physicalones appear to be negligible in comparison [18].

Finally, below the phase transition the hadronic res-onance gas model, which treats the plasma as an idealgas of mesons, baryons and their excited states, matchesreasonably well to lattice data [6].

We now review relic density calculations. Considera particle of mass m and number density n, undergo-ing annihilations XX ! . . . with total cross-section !,assumed to be a typical weak interaction cross-section,proportional to G2

F . Then [19]

n + 3Hn = "#!vMøl$ (n2 " n2eq), (1)

where neq is the equilibrium number density, H = a/ais the Hubble parameter, and vMøl is the Møller veloc-ity which is a relativistic generalisation of the relativevelocity of the annihilating particles [19].

In order to solve the equation it is convenient to con-vert the time variable to x = m/T , and to measure therelic abundance in terms of Y = n/s, where s is the en-tropy density. If the total entropy S = sa3 is conserved,then we can write

dY

dx=

1

3H

ds

dx#!vMøl$ (Y 2 " Y 2

eq). (2)

This adiabaticity assumption is violated if the QCD tran-sition is first order, but it is most likely to be a cross-overtransition at the low chemical potentials which are rele-vant for the early Universe [16, 17].

Using the Friedmann equation H2 = 8"G#/3, anddefining e"ective numbers of degrees of freedom for theenergy and entropy densities, s = (# + p)/T , through

# ="2

30ge!(T )T 4, s =

2"2

45he!(T )T 3, (3)

one finds an approximate solution

Y0 %

!

45

"

"1

2 1

mMP #!vMøl$Tf

xf

g1

2

! (Tf ), (4)

where Tf is the freeze-out temperature, defined to be thetemperature at which the relic abundance is a certainfactor (taken to be 2.5) above the equilibrium abundance.We see that the relic density depends on the parameter

g1/2! (T ) =

he!

g1/2e!

!

1 +T

3

d lnhe!

dT

"

. (5)

It is through this parameter that the QCD equation ofstate influences the relic density.

In an ideal gas at temperature T , a particle of massmi = xiT contributes to ge! , he! the amounts

gi,e! &#i

#0=

15

"4

# "

xi

(u2 " x2i )

1

2

eu ± 1u2du, (6)

hi,e! &si

s0=

45

12"4

# "

xi

(u2 " x2i )

1

2

eu ± 1(4u2 " x2

i )du, (7)

where #0 and s0 are the energy and entropy densities fora free massless boson.

Interactions correct the ideal gas result, and ge! , he!

have to be extracted from calculations of the energy andentropy, Eqs. (3). Note that in the relevant temperaturerange 40 to 0.4 GeV, 16 out the 18 bosonic degrees of free-dom are coloured, with the coloured fermionic degreesof freedom dropping from 60/78 to 36/50. The domi-nant corrections are therefore expected to come from thecoloured sector of the Standard Model, weak correctionsare moreover suppressed by the boson masses and negli-gible.

The relic density codes DarkSUSY and MicrOMEGAsuse identical equations of state, developed in Refs.[7, 8, 9]. Below Tc the hadronic degrees of freedom aremodelled by an interacting gas of hadrons and their res-onances, while above Tc the quarks and gluons are takento interact with a linear potential VQ(r) = Kr, with aphenomenologically motivated value K = 0.18GeV2, de-rived from the slope of Regge trajectories. In this model,the pressure is already very close to ideal at temperaturesabove 1.6 GeV. All other Standard Model particles arefree.

In this work we also take the ideal gas contributionsfor the particles of the Standard Model, with massesgiven by the Particle Data Group central values [20].In the confined phase quarks and gluons are replacedby hadronic models described below. In the deconfinedphase, the contribution to the pressure of the coloureddegrees of freedom is scaled by a function f(T ), definedto be the ratio between the true QCD pressure p(T ) andthe Stefan-Boltzmann result pSB for the same theory,f(T ) = p(T )/pSB(T ). This correction factor is derivedfrom lattice [18] and perturbative [5] calculations forNf = 0, and uses an approximate universality in the pres-sure curves for di"erent Nf observed by Karsch et al. [18].Near the transition, the lattice-derived curves for f(T )have the approximate form f(T, Nf) = fQCD(T/Tc(Nf )),

Hindmarsh and Philipsen (2005)

3

greater than 2.20 bar were excluded, reducing the Stage2 exposure to 6.71 kgd; correlation with the signalrecord yielded 1 recoil event consistent with the esti-mated 2.2±0.3 background neutrons. The Stage 1 eventswere similarly pressure-correlated, reducing the expo-sure to 13.47 kgd; reanalysis of the recoil signals via aHilbert transform-based demodulation identified 4 withexponential decay characteristic of nonuniform impulsesobserved in acoustic background studies associated withSDDs in vibrational contact with their support and airbubbles from water inflow, reducing the recoil events to10, slightly below the estimated 13±0.6 background neu-trons.The first Stage 1 results resulted in part from a the-

oretical bubble nucleation e!ciency given by !(E)=1-Ethr/Edep [8]. This ! however represents only a firstapproximation to the statistical nature of the energy de-position and its conversion into heat [9]: a detailed re-analysis of previous monochromatic (54 and 149 keV)neutron irradiation data [10], at 1 and 2 bar as a functionof temperature, yielded a refined e!ciency of !’=1-exp[-"(E/Ethr-1))] with "=4.2± 0.3, independent of pressure.We show in Fig. 3 the impacts of the Stage 2 and

reanalyzed Stage 1 results on SD WIMP-proton scatter-ing, together with the competitive results of other direct[11–13] and indirect [14, 15] experiments. The contoursare calculated using the previous [1] Feldman-Cousins ap-proach [16] based on observing n events against a back-ground one systematic uncertainty below the estimatedneutron-generated recoil background, !’ with "=3.6, thestandard isothermal halo and a WIMP scattering rate[18] with zero momentum transfer, spin-dependent crosssection "SD

p for elastic scattering. The form factors of[18] have been used for all odd-A nuclei, with the spinvalues of [19] used for 19F; for 35Cl and 37Cl, the spinvalues are from [20], while for 13C they were estimatedusing the odd group approximation. The Stage 2 resultis seen to nearly equal the revised Stage 1 result with itsrevised minimum of "p = 9.2 ! 10!3 pb at 35 GeV/c2,despite half the exposure.The above representation neglects the non-negligible

spin contribution of the neutron sector in 19F, whichis captured in a model-independent SD formulation [20]with "SD " [ap <Sp >+an <Sn >]2, where ap,n are theWIMP-proton,neutron coupling strengths, and <Sp,n >

are the expectation values of the proton (neutron) groupspins. In this representation, experiments define a band(single nuclei targets) or an ellipse (multi-nuclei target),with the allowed area defined by the intersect of the mostsensitive results in ap, an. At MW = 50 GeV/c2, com-bined with neutron-sensitive XENON10 [21], the allowedarea reduction is better than 2/3 compared with Ref. [1];masses above or below this choice yield slightly increasedlimits for most all experiments. More relevant wouldhowever be the model-independent results for MW " 10GeV/c2, unavailable for the majority of experiments.The impact of the results in the SI sector is shown

in Fig. 4 in comparison with results from other leading

FIG. 3: various spin-dependent WIMP-proton exclusion con-tours for Phase II, together with the leading direct [11–13]and indirect SuperK [14], IceCube [15] search results; shownare the Stage 2 result, the reanalyzed Stage 1 result, and amerging of the two. The region outlined in grey is favored bycMSSM [17].

search e#orts [12, 13, 21–31], again calculated with thestandard isothermal halo and WIMP elastic scatteringrate of Ref. [18] using Feldman-Cousins, a Helm nuclearform factor, and !’. Again, the Stage 2 contour is nearlyequal to the revised Stage 1 contour with its contour min-imum of 7.6!10!6 pb at 35 GeV/c2. Owing to the lowrecoil energy threshold, both results enter the possiblelight mass WIMP region recently suggested by CoGeNT[31] and CRESST-II [29].A straightforward combination of the two results us-

ing the Feldman-Cousins approach, based on 11 candi-dates with an assumed background 1 "(syst) below theexpected total background, yields the ”merged” contoursindicated in each of Figs. 3 and 4; in the SI case, thecontour minimum drops to 4.7!10!6 pb and the resultis in tension with the recent reports of CoGeNT [31],DAMA/LIBRA [30] and CRESST [29] regarding lightmass WIMPS, using a significantly di#erent techniquewith di#erent systematics than the XENON [32] andCDMS [33] experiments. For the case of SD interac-tions, the contour minimum drops to 5.7!10!3 pb, con-stituting the most restrictive direct search limit on SDWIMP-proton scattering for MW # 60 GeV/c2 to date,and beginning to complement the more sensitive resultsobtained by indirect detection measurements.The improved restrictions of the revised Stage 1 con-

tour are a direct result of the more detailed signal analy-sis, improved radio-assays of the shielding materials, andthe revised nucleation e!ciency in the analysis: Stage2, with the additional benefit of its improved neutronshielding, provides an almost identical sensitivity withhalf the Stage 1 exposure. While the merging may bequestioned, the results are su!cient motivation for a

5

for moderate variations in the definition of any of the dataquality cuts. These events were observed on January 23,February 12, and June 3, at 30.2 keVnr, 34.6 keVnr, and12.1 keVnr, respectively. The event distribution in theTPC is shown in Fig. 4. Given the background expecta-tion of (1.8±0.6) events, the observation of 3 events doesnot constitute evidence for dark matter, as the chanceprobability of the corresponding Poisson process to re-sult in 3 or more events is 28%.

]2WIMP Mass [GeV/c6 7 8 910 20 30 40 50 100 200 300 400 1000

]2W

IMP

-Nuc

leon

Cro

ss S

ecti

on [

cm

-4510

-4410

-4310

-4210

-4110

-4010

-3910

]2WIMP Mass [GeV/c6 7 8 910 20 30 40 50 100 200 300 400 1000

]2W

IMP

-Nuc

leon

Cro

ss S

ecti

on [

cm

-4510

-4410

-4310

-4210

-4110

-4010

-3910

]2WIMP Mass [GeV/c6 7 8 910 20 30 40 50 100 200 300 400 1000

]2W

IMP

-Nuc

leon

Cro

ss S

ecti

on [

cm

-4510

-4410

-4310

-4210

-4110

-4010

-3910

DAMA/I

DAMA/Na

CoGeNT

CDMS (2010)

CDMS (2011)

EDELWEISS (2011)

XENON10 (S2 only, 2011)

XENON100 (2010)

XENON100 (2011)observed limit (90% CL)

Expected limit of this run:

expected! 2 ± expected! 1 ±

Buchmueller et al.

Trotta et al.

FIG. 5: Spin-independent elastic WIMP-nucleon cross-sectionσ as function of WIMP mass mχ. The new XENON100 limitat 90% CL, as derived with the Profile Likelihood method tak-ing into account all relevant systematic uncertainties, is shownas the thick (blue) line together with the expected sensitivityof this run (yellow/green band). The limits from XENON100(2010) [7], EDELWEISS (2011) [6], CDMS (2009) [5] (re-calculated with vesc = 544 km/s, v0 = 220 km/s), CDMS(2011) [19] and XENON10 (2011) [20] are also shown. Ex-pectations from CMSSM are indicated at 68% and 95% CL(shaded gray [21], gray contour [22]), as well as the 90% CL ar-eas favored by CoGeNT [23] and DAMA (no channeling) [24].

The statistical analysis using the Profile Likelihoodmethod [17] does not yield a significant signal excess ei-ther, the p-value of the background-only hypothesis is31%. A limit on the spin-independent WIMP-nucleonelastic scattering cross-section σ is calculated whereWIMPs are assumed to be distributed in an isothermalhalo with v0 = 220 km/s, Galactic escape velocity vesc =(544+64

−46) km/s, and a density of ρχ = 0.3GeV/cm3. TheS1 energy resolution, governed by Poisson fluctuations ofthe PE generation in the PMTs, is taken into account.Uncertainties in the energy scale as indicated in Fig. 1,in the background expectation and in vesc are profiledout and incorporated into the limit. The resulting 90%confidence level (CL) limit is shown in Fig. 5 and hasa minimum σ = 7.0 × 10−45 cm2 at a WIMP mass ofmχ = 50GeV/c2. The impact of Leff data below 3 keVnr

is negligible at mχ = 10GeV/c2. The sensitivity is theexpected limit in absence of a signal above backgroundand is also shown in Fig. 5. Due to the presence oftwo events around 30 keVnr, the limit at higher mχ is

weaker than expected. Within the systematic differencesof the methods, this limit is consistent with the one fromthe optimum interval analysis, which calculates the limitbased only on events in the WIMP search region. Itsacceptance-corrected exposure, weighted with the spec-trum of a mχ = 100GeV/c2 WIMP, is 1471 kg × days.This result excludes a large fraction of previously unex-plored WIMP parameter space, and cuts into the regionwhere supersymmetric WIMP dark matter is accessibleby the LHC [21]. Moreover, the new result challengesthe interpretation of the DAMA [24] and CoGeNT [23]results as being due to light mass WIMPs.We gratefully acknowledge support from NSF, DOE,

SNF, Volkswagen Foundation, FCT, Region des Pays dela Loire, STCSM, DFG, and the Weizmann Institute ofScience. We are grateful to LNGS for hosting and sup-porting XENON.

∗ Electronic address: [email protected]† Electronic address: [email protected]

[1] G. Steigman and M. S. Turner, Nucl. Phys. B253, 375(1985); G. Jungman, M. Kamionkowski, and K. Griest,Phys. Rept. 267, 195 (1996).

[2] N. Jarosik et al., Astrophys. J. Suppl. 192, 14 (2011);K. Nakamura et al. (Particle Data Group), J. Phys. G37,075021 (2010).

[3] M. W. Goodman and E. Witten, Phys. Rev. D31, 3059(1985).

[4] J. D. Lewin and P. F. Smith, Astropart. Phys. 6, 87(1996).

[5] Z. Ahmed et al. (CDMS), Science 327, 1619 (2010).[6] E. Armengaud et al. (EDELWEISS) (2011),

arXiv:1103.4070.[7] E. Aprile et al. (XENON100), Phys. Rev. Lett. 105,

131302 (2010).[8] E. Aprile et al. (XENON100) (2011), arXiv:1103.5831.[9] E. Aprile et al., Phys. Rev. C79, 045807 (2009).

[10] E. Aprile et al. (XENON100) Phys. Rev. D83, 082001(2011).

[11] E. Aprile and T. Doke, Rev. Mod. Phys. 82, 2053 (2010).[12] G. Plante et al. (2011), arXiv:1104.2587.[13] F. Arneodo et al., Nucl. Instrum. Meth. A449, 147

(2000); D. Akimov et al., Phys. Lett. B524, 245 (2002);R. Bernabei et al., Eur. Phys. J. direct C3, 11 (2001).E. Aprile et al., Phys. Rev. D72, 072006 (2005). V. Che-pel et al., Astropart. Phys. 26, 58 (2006). A. Manzuret al., Phys. Rev. C81, 025808 (2010).

[14] F. Bezrukov et al., (2010), arXiv:1011.3990.[15] E. Aprile et al., Phys. Rev. Lett. 97, 081302 (2006).[16] G. Alimonti et al., Astropart. Phys. 16, 205 (2002).[17] E. Aprile et al. (XENON100) (2011), arXiv:1103.0303.[18] S. Yellin, Phys. Rev. D66, 032005 (2002).[19] Z. Ahmed et al. (CDMS), Phys. Rev. Lett. 106, 131302

(2011).[20] J. Angle et al. (XENON10) (2011), arXiv:1104.3088.[21] O. Buchmueller et al. (2011), arXiv:1102.4585.[22] R. Trotta et al. J. High Energy Phys. 12, 024 (2008).[23] C. E. Aalseth et al. (CoGeNT), Phys. Rev. Lett. 106,

131301 (2011).[24] C. Savage et al., JCAP 0904, 010 (2009).

eﬀectof&quark&interac0ons&on&& … fileranges of masses for lkps. however, the...

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